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84 Pages

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Course: PX 407, Fall 2009
School: East Los Angeles College
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Word Count: 44167

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2 %div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 %d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx %setmatrix } def /Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx % DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) % setmatrix } def setmatrix pop } def % DG/SR modification end /CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth def } def /CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth def } def /CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub 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repeat closepath pop pop } ifelse } def /SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def /ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def /SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def /FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix rotate matrix concatmatrix exch findfont exch makefont setfont } def /Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto x1 y1 lineto closepath } def /OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse /b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } ifelse } def /Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add /y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse } def /BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def /OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } ifelse } def /ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { 6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def /BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } def /Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def } def /Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if /dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} {z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i w add def } repeat grestore gsave n 0 gt % DG/SR modification begin - Nov. 7, 1997 - Patch 1 %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } % DG/SR modification end { 2 setlinecap } ifelse /i y1 def /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g exch t L stroke /i i h add def } repeat grestore } def /ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c mul neg d } def /Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def /Rot { CP CP translate 3 -1 roll neg rotate NET } def /RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle dup a add ] cvx def } def /RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def /PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def /PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def /PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def /Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { h1 abs h sub dup s mul abs } ifelse } def /UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q { x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add exch } def /BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible /IfVisible true def } if } { IfVisible { Invisible /IfVisible false def } if } ifelse } def /InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def /Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def /IfVisible true def } def end % END pstricks.pro %%EndProcSet %%BeginProcSet: pst-dots.pro %!PS-Adobe-2.0 %%Title: Dot Font for PSTricks %%Creator: <a href="/keyword/timothy-van-zandt/" >timothy van zandt</a> <tvz@Princeton.EDU> %%Creation Date: May 7, 1993 %% Version 97 patch 1, 99/12/16 %% Modified by Etienne Riga <etienne.riga@skynet.be> - Dec. 16, 1999 %% to add /Diamond, /SolidDiamond and /BoldDiamond 10 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for % % % % % % Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put dup (P) 0 get /BoldPentagon put DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga dup (l) 0 get /SolidDiamond put dup (d) 0 get /Diamond put (D) 0 get /BoldDiamond put DG/SR modification end /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga /SolidDiamond 1008 def /Diamond 1008 def /BoldDiamond 1008 def DG/SR modification end /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga /Diamond { -428.5 -742.5 428.5 742.5 } def /BoldDiamond /Diamond load def /SolidDiamond /Diamond load def DG/SR modification end /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def % DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath } def /SolidDiamond { DiamondPath fill } def /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def % DG/SR modification end /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind def end /PSTricksDotFont exch definefont pop %END pst-dots.pro %%EndProcSet %%BeginProcSet: pst-grad.pro %! % PostScript prologue for pst-grad.tex. % Version 97, 93/05/12 % For distribution, see pstricks.tex. % % For the PSTricks gradient fillstyle. % % Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee). % % Syntax: % R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill /tx@GradientDict 40 dict def tx@GradientDict begin /GradientFill { rotate /MidPoint ED /NumLines ED /LastBlue ED /LastGreen ED /LastRed ED /FirstBlue ED /FirstGreen ED /FirstRed ED % This avoids gaps due to rounding errors: clip pathbbox %leave llx,lly,urx,ury on stack /y ED /x ED 2 copy translate y sub neg /y ED x sub neg /x ED % This avoids gaps due to rounding errors: LastRed FirstRed add 2 div LastGreen FirstGreen add 2 div LastBlue FirstBlue add 2 div setrgbcolor fill /YSizePerLine y NumLines div def /CurrentY 0 def /MidLine NumLines 1 MidPoint sub mul abs cvi def MidLine NumLines 2 sub gt { /MidLine NumLines def } { MidLine 2 lt { /MidLine 0 def } if } ifelse MidLine 0 gt { /Red FirstRed def /Green FirstGreen def /Blue FirstBlue def /RedIncrement LastRed FirstRed sub MidLine 1 sub div def /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def MidLine { GradientLoop } repeat } if MidLine NumLines lt /Red LastRed def /Green LastGreen def /Blue LastBlue def /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def NumLines MidLine sub { GradientLoop } repeat } if } def /GradientLoop { 0 CurrentY moveto x 0 rlineto 0 YSizePerLine rlineto x neg 0 rlineto closepath Red Green Blue setrgbcolor fill /CurrentY CurrentY YSizePerLine add def /Blue Blue BlueIncrement add def /Green Green GreenIncrement add def /Red Red RedIncrement add def } def end % END pst-grad.pro %%EndProcSet %%BeginProcSet: pst-node.pro %! % PostScript prologue for pst-node.tex. % Version 97 patch 1, 97/05/09. % For distribution, see pstricks.tex. % /tx@NodeDict 400 dict def tx@NodeDict begin tx@Dict begin /T /translate load def end /NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end grestore } def /InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def } def /InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch Sin mul } def } def /GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse } def /InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED /NodePos { GetRnodePos } def } def /DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup Cos mul exch Sin mul } def /TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul } ifelse } def /InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan sin def /NodePos { TriNodePos } def } def /OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul } def { /GetCenter { begin X Y NodeMtrx transform CM itransform end } def /XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } { 0 Dist Sin mul } ifelse } ifelse Do } def /GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse } def /AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse } def /GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA AddOffset yA add /yA1 ED xA add /xA1 ED } def /GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB AddOffset yB add /yB1 ED xB add /xB1 ED } def /GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED } ifelse } def /GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED } ifelse } def /InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED /NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def /LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def /LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop } repeat LPutLine cleartomark } def /BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def /HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def } def /HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def /NAngle yyB yyA sub xxB xxA sub Atan def } def /HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def /HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def } ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def /VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def } def /VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def /NAngle yyB yyA sub xxB xxA sub Atan def } def /VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def /VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def } ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark VPosEnd } def /HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx def grestore exec /LPutVar /SaveLPutVar load def } def /NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { LPutVar VPutLine } def LPutVar } def /NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop end } def /NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan /AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } ifelse } def /NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines } HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def /NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def % DG/SR modification begin - May 9, 1997 - Patch 1 %/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r %r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add %exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 %mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED /NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED % DG/SR modification end } def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r Div def /y ED /x ED } def /NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB 180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def /LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos { xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar tx@Dict begin false Polygon end } def /NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def /x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } { x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def 0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos { LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } { t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { LPutPos } def } def /Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos { LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } { pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin /ArrowA { moveto } def /ArrowB { } def false Line closepath end } def /LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg exch X sub neg exch moveto setmatrix CP grestore } def /LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse LPutCoor 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distributed as long as the %% original source files, as listed above, are part of the %% same distribution. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark {restore}if %%EndFont %%BeginFont: HFBR8 %!PS-AdobeFont-1.0: HFBR8 0.6 %%Title: HFBR8 %%CreationDate: Fri Nov 22 09:12:21 2002 %%Creator: Harald Harders %%DocumentSuppliedResources: font HFBR8 % Part of the hfbright font family by Harald Harders, h.harders@tu-bs.de % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/HFBR8 known{/HFBR8 findfont dup/UniqueID known{dup /UniqueID get 4214376 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /HFBR8 def /FontBBox [-81 -223 1112 753 ]readonly def /UniqueID 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dup 120 /x put dup 121 /y put readonly def currentdict end currentfile eexec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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark {restore}if %%EndFont %%BeginFont: HFBRBX10 %!PS-AdobeFont-1.0: HFBRBX10 0.6 %%Title: HFBRBX10 %%CreationDate: Fri Nov 22 09:17:31 2002 %%Creator: Harald Harders %%DocumentSuppliedResources: font HFBRBX10 % Part of the hfbright font family by Harald Harders, h.harders@tu-bs.de % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/HFBRBX10 known{/HFBRBX10 findfont dup/UniqueID known{dup /UniqueID get 4214384 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /HFBRBX10 def /FontBBox [-71 -223 1099 756 ]readonly 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark {restore}if %%EndFont %%BeginFont: HFBR10 %!PS-AdobeFont-1.0: HFBR10 0.6 %%Title: HFBR10 %%CreationDate: Fri Nov 22 09:13:31 2002 %%Creator: Harald Harders %%DocumentSuppliedResources: font HFBR10 % Part of the hfbright font family by Harald Harders, h.harders@tu-bs.de % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/HFBR10 known{/HFBR10 findfont dup/UniqueID known{dup /UniqueID get 4214378 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /HFBR10 def /FontBBox [-77 -223 1049 751 ]readonly def /UniqueID 4214378 def /PaintType 0 def /FontInfo 9 dict dup begin /version 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Fo(c)58059 58788 y Fn(\260)p Fm(M)886 b(P)g(Allen)h(2003)p 0.000 0.000 0.000 TeXcolorrgb eop end PStoPSsaved restore userdict/PStoPSsaved save put PStoPSmatrix setmatrix 560.740852 14.173228 translate 90 rotate 0.664750 dup scale userdict/PStoPSmatrix matrix currentmatrix put userdict/PStoPSclip{0 0 moveto 612.000000 0 rlineto 0 792.000000 rlineto -612.000000 0 rlineto closepath}put initclip PStoPSxform concat TeXDict begin @landscape 2 1 bop 0.000 0.000 0.000 TeXcolorrgb Black -8000 59998 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0. true 0.0 0.0 383.30276 296.18846 .5 Frame gsave 1.000 1.000 0.878 setrgbcolor fill grestore end @endspecial 0.098 0.098 0.439 TeXcolorrgb -6740 -4468 a Ft(Lecture)765 b(15:)1018 b(Molecules)764 b(to)g(Metals)p Black 0.098 0.098 0.439 TeXcolorrgb 49100 w(15-2)p Black 0.098 0.098 0.439 TeXcolorrgb -6740 -3544 85479 98 v -6740 -3119 V Black -5102 -1323 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end -5102 -1323 a 0.000 0.000 0.000 TeXcolorrgb 9423 2305 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0. true 3.8 neg 6.67998 neg 231.32463 15.8 .5 Frame gsave 0.098 0.098 0.439 setrgbcolor fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 1.000 0.843 0.000 TeXcolorrgb Fs(Tight-Binding)1402 b(App)-123 b(ro)g(ximation)p 0.000 0.000 0.000 TeXcolorrgb -5102 7534 a Fr(A)915 b(H)-11 b(\304)-1435 b(uck)-80 b(el-lik)g(e)915 b(app)-80 b(roach)916 b(can)g(be)g(used)g (to)g(describe)g(the)f(bonding)k(in)d(a)-5102 11462 y(one-dimensional)h (metal)d(o)-80 b(r)916 b(quantum)h(w)-80 b(ell)914 b(structure:)p 0.000 0.000 0.000 TeXcolorrgb 0.690 0.188 0.376 TeXcolorrgb -3868 16691 a Fq(\344)p 0.000 0.000 0.000 TeXcolorrgb 0.000 0.000 0.000 TeXcolorrgb 1447 w Fr(again)h(w)-80 b(e)915 b(consider)h(the)g(case)f(of)1788 b @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0.804 0.729 0.588 setrgbcolor 0. true 3.8 neg 5.8 neg 120.46892 12.13333 .5 Frame gsave 1.000 0.906 0.729 setrgbcolor fill grestore gsave 0.8 SLW 0.804 0.729 0.588 setrgbcolor 0 setlinecap stroke grestore end @endspecial(one)917 b(electron)e(per)h(atom,)p 0.000 0.000 0.000 TeXcolorrgb 0.690 0.188 0.376 TeXcolorrgb -3868 21258 a Fq(\344)p 0.000 0.000 0.000 TeXcolorrgb 0.000 0.000 0.000 TeXcolorrgb 1447 w Fr(but)g(this)g(time)f(the)h (atomic)f(w)-80 b(avefunctions)914 b(a)-80 b(re)1787 b @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0.804 0.729 0.588 setrgbcolor 0. true 3.8 neg 3.8 neg 53.09955 12.13333 .5 Frame gsave 1.000 0.906 0.729 setrgbcolor fill grestore gsave 0.8 SLW 0.804 0.729 0.588 setrgbcolor 0 setlinecap stroke grestore end @endspecial(s)916 b(o)-80 b(rbitals.)-5102 26666 y(This)916 b(is)g(called)f(the)1788 b @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0.804 0.729 0.588 setrgbcolor 0. true 3.8 neg 5.8 neg 143.97878 12.13333 .5 Frame gsave 1.000 0.906 0.729 setrgbcolor fill grestore gsave 0.8 SLW 0.804 0.729 0.588 setrgbcolor 0 setlinecap stroke grestore end @endspecial(tight)916 b(binding)i(app)-80 b(ro)g(ximation)871 b(.)9168 42843 y @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0. true 5.8 neg 5.8 neg 237.41191 62.70549 .5 Frame gsave 3.0 -45 PtoC Shadow 0.545 0.545 0.478 setrgbcolor gsave fill grestore stroke grestore gsave 1.000 1.000 1.000 setrgbcolor gsave fill grestore stroke grestore gsave 1.000 1.000 1.000 setrgbcolor fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 1.0 SLW 0 setgray 28.45274 28.45274 14.22636 .5 CLW mul sub 0 360 arc closepath gsave 0 1 setgray currentrgbcolor 1 0.545 0.000 0.000 setrgbcolor currentrgbcolor 2 grestore 100 0.3 0.7 0 tx@PstSlopeDict begin CcSlopesFill end end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 1.0 SLW 0 setgray 28.45274 28.45274 2.84544 .5 CLW mul sub 0 360 arc closepath gsave .5 setgray fill grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 1.0 SLW 0 setgray 85.35823 28.45274 14.22636 .5 CLW mul sub 0 360 arc closepath gsave 0 1 setgray currentrgbcolor 1 0.545 0.000 0.000 setrgbcolor currentrgbcolor 2 grestore 100 0.3 0.7 0 tx@PstSlopeDict begin CcSlopesFill end end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 1.0 SLW 0 setgray 85.35823 28.45274 2.84544 .5 CLW mul sub 0 360 arc closepath gsave .5 setgray fill grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 1.0 SLW 0 setgray 142.26372 28.45274 14.22636 .5 CLW mul sub 0 360 arc closepath gsave 0 1 setgray currentrgbcolor 1 0.545 0.000 0.000 setrgbcolor currentrgbcolor 2 grestore 100 0.3 0.7 0 tx@PstSlopeDict begin CcSlopesFill end end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 1.0 SLW 0 setgray 142.26372 28.45274 2.84544 .5 CLW mul sub 0 360 arc closepath gsave .5 setgray fill grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 1.0 SLW 0 setgray 199.1692 28.45274 14.22636 .5 CLW mul sub 0 360 arc closepath gsave 0 1 setgray currentrgbcolor 1 0.545 0.000 0.000 setrgbcolor currentrgbcolor 2 grestore 100 0.3 0.7 0 tx@PstSlopeDict begin CcSlopesFill end end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 1.0 SLW 0 setgray 199.1692 28.45274 2.84544 .5 CLW mul sub 0 360 arc closepath gsave .5 setgray fill grestore end @endspecial -5102 47024 a(Applying)916 b(periodic)g (bounda)-80 b(ry)917 b(conditions,)g(this)e(p)-80 b(roblem)916 b(is)g(the)g(same)f(as)-5102 50952 y(that)g(of)h(a)g(cyclic)e (conjugated)j(system,)d(such)i(as)g(benzene.)p 0.098 0.098 0.439 TeXcolorrgb -6740 56276 85479 98 v 0.000 0.000 0.000 TeXcolorrgb 0.098 0.098 0.439 TeXcolorrgb -6740 58788 a Fp(PX407)874 b(Quantum)g(Physics)i(I)77 b(I$Annotated$)p 0.000 0.000 0.000 TeXcolorrgb 0.098 0.098 0.439 TeXcolorrgb 58773 58712 a Fo(c)58059 58788 y Fn(\260)p Fm(M)886 b(P)g(Allen)h(2003) p 0.000 0.000 0.000 TeXcolorrgb eop end PStoPSsaved restore %%Page: (2,3) 2 userdict/PStoPSsaved save put PStoPSmatrix setmatrix 560.740852 421.000000 translate 90 rotate 0.664750 dup scale userdict/PStoPSmatrix matrix currentmatrix put userdict/PStoPSclip{0 0 moveto 612.000000 0 rlineto 0 792.000000 rlineto -612.000000 0 rlineto closepath}put initclip /showpage{}def/copypage{}def/erasepage{}def PStoPSxform concat TeXDict begin @landscape 3 2 bop 0.000 0.000 0.000 TeXcolorrgb Black -8000 59998 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0. true 0.0 0.0 383.30276 296.18846 .5 Frame gsave 1.000 1.000 0.878 setrgbcolor fill grestore end @endspecial 0.098 0.098 0.439 TeXcolorrgb -6740 -4468 a Ft(Lecture)765 b(15:)1018 b(Molecules)764 b(to)g(Metals)p Black 0.098 0.098 0.439 TeXcolorrgb 49100 w(15-3)p Black 0.098 0.098 0.439 TeXcolorrgb -6740 -3544 85479 98 v -6740 -3119 V Black -5102 -1323 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end -5102 -1323 a 0.000 0.000 0.000 TeXcolorrgb 9423 2305 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0. true 3.8 neg 6.67998 neg 231.32463 15.8 .5 Frame gsave 0.098 0.098 0.439 setrgbcolor fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 1.000 0.843 0.000 TeXcolorrgb Fs(Tight-Binding)1402 b(App)-123 b(ro)g(ximation)p 0.000 0.000 0.000 TeXcolorrgb -5102 7534 a Fr(Consider)916 b(a)g(periodic)g(1D)g(lattice) e(of)i Fl(N)1101 b Fr(atoms.)1220 b(Eigenvalues)915 b(a)-80 b(re:)764 13739 y @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0.804 0.729 0.588 setrgbcolor 0. true 3.8 neg 5.3 neg 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y Fk(n)42940 19300 y Fj(=)1685 b @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0.804 0.729 0.588 setrgbcolor 0. true 3.8 neg 6.46666 neg 110.28639 12.8 .5 Frame gsave 1.000 0.906 0.729 setrgbcolor fill grestore gsave 0.8 SLW 0.804 0.729 0.588 setrgbcolor 0 setlinecap stroke grestore end @endspecial Fl(\256)651 b Fj(+)f(2)p Fl(\257)621 b Fj(cos)q($2)p Fl(\274)92 b(n)67 b(=)-170 b(N)185 b Fj($)-5102 25505 y Fr(Allo)-80 b(wing)915 b Fl(N)998 b Fi(!)813 b(1)917 b Fr(gives)e(a)h(simple)f(model)i(of)f(a)g(one-dimensional)g(solid.) -5102 30929 y(There)984 b(will)g(be)g(an)g(in\257nite)h(number)g(of) -5102 34857 y(closely-spaced)856 b(states,)867 b(occup)-80 b(ying)858 b(an)-5102 38785 y(energy)915 b Fh(band)1180 b Fr(of)916 b(\257nite)g(width:)3558 44990 y @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0.804 0.729 0.588 setrgbcolor 0. true 3.8 neg 5.79999 neg 107.38379 12.13333 .5 Frame gsave 1.000 0.906 0.729 setrgbcolor fill grestore gsave 0.8 SLW 0.804 0.729 0.588 setrgbcolor 0 setlinecap stroke grestore end @endspecial Fl(E)5555 45334 y Fg(max)9748 44990 y Fi(\241)650 b Fl(E)14672 45334 y Fg(min)18623 44990 y Fj(=)813 b Fi(\241)p Fj(4)p Fl(\257)-5102 51195 y Fr(remember)915 b Fl(\257)1048 b Fr(is)916 b(negative.)40223 53825 y @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0. true 5.8 neg 5.8 neg 148.49706 112.49776 .5 Frame gsave 3.0 -45 PtoC Shadow 0.545 0.545 0.478 setrgbcolor gsave fill grestore stroke grestore gsave 1.000 1.000 1.000 setrgbcolor gsave fill grestore stroke grestore gsave 1.000 1.000 1.000 setrgbcolor fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 59820 41577 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 0.0 42.67911 .5 CLW mul sub 0 360 arc closepath gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0.545 0.000 0.000 setrgbcolor /ArrowA { moveto } def /ArrowB { } def [ 42.67911 90. PtoC 42.67911 90. PtoC /Lineto /lineto load def false Line gsave 0.8 SLW 0.545 0.000 0.000 setrgbcolor 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray SD end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 SD end 42.67911 90. PtoC 2.13408 setgray 42.67911 90. PtoC 2.13408 @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0.545 0.000 0.000 setrgbcolor /ArrowA { moveto } def /ArrowB { } def [ 42.67911 85. PtoC 42.67911 95. PtoC /Lineto /lineto load def false Line gsave 0.8 SLW 0.545 0.000 0.000 setrgbcolor 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray SD end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 SD end 42.67911 95. PtoC 2.13408 setgray 42.67911 85. PtoC 2.13408 @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0.545 0.000 0.000 setrgbcolor /ArrowA { moveto } def /ArrowB { } def [ 42.67911 80. PtoC 42.67911 100. PtoC /Lineto /lineto load def false Line gsave 0.8 SLW 0.545 0.0...

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