62 Pages

hw5

Course: CS 15781, Fall 2009
School: Carnegie Mellon
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Word Count: 24192

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%%Creator: %!PS-Adobe-2.0 dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: hw5.dvi %%CreationDate: Mon Nov 03 17:00:20 2003 %%Pages: 4 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: Times-Bold Times-Roman Courier CMMI12 CMR12 CMSY10 CMR8 %%+ CMMI8 CMSY8 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips hw5.dvi -o hw5.ps -tletter %DVIPSParameters: dpi=600,...

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Coursehero >> Pennsylvania >> Carnegie Mellon >> CS 15781

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%%Creator: %!PS-Adobe-2.0 dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: hw5.dvi %%CreationDate: Mon Nov 03 17:00:20 2003 %%Pages: 4 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: Times-Bold Times-Roman Courier CMMI12 CMR12 CMSY10 CMR8 %%+ CMMI8 CMSY8 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips hw5.dvi -o hw5.ps -tletter %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.11.03:1700 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round 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closepath mtrx setmatrix } def % DG modification begin - Jan. 15, 1997 %/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { %pop } { 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 } 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 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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: Timothy Van Zandt <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-coil.pro %! % PostScript prologue for pst-coil.tex. % Version 97 patch 1, 98/06/02 % For distribution, see pstricks.tex. % /tx@CoilDict 40 dict def tx@CoilDict begin /CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def /Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP % DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) % TotalLength 0 ArrowB lineto } def TotalLength 0 ArrowB lineto pop pop pop pop } def % DG/SR modification end /AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def /ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat TotalLength ArmA sub 0 TotalLength 0 } def end % END pst-coil.pro %%EndProcSet %%BeginProcSet: pst-text.pro %! % PostScript header file pst-text.pro % Version 97, 94/04/20 % For distribution, see pstricks.tex. /tx@TextPathDict 40 dict def tx@TextPathDict begin % Syntax: <dist> PathPosition % Function: Searches for position of currentpath distance <dist> from % beginning. Sets (X,Y)=position, and Angle=tangent. /PathPosition { /targetdist exch def /pathdist 0 def /continue true def /X { newx } def /Y { newy } def /Angle 0 def gsave flattenpath { movetoproc } { linetoproc } { } { firstx firsty linetoproc } /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if grestore } def /movetoproc { continue { @movetoproc } { pop pop } ifelse } def /@movetoproc { /newy exch def /newx exch def /firstx newx def /firsty newy def } def /linetoproc { continue { @linetoproc } { pop pop } ifelse } def /@linetoproc { /oldx newx def /oldy newy def /newy exch def /newx exch def /dx newx oldx sub def /dy newy oldy sub def /dist dx dup mul dy dup mul add sqrt def /pathdist pathdist dist add def pathdist targetdist ge { pathdist targetdist sub dist div dup dy mul neg newy add /Y exch def dx mul neg newx add /X exch def /Angle dy dx atan def /continue false def } if } def /TextPathShow { /String exch def /CharCount 0 def String length { String CharCount 1 getinterval ShowChar /CharCount CharCount 1 add def } repeat } def % Syntax: <pathlength> <position> InitTextPath /InitTextPath { gsave currentpoint /Y exch def /X exch def exch X Hoffset sub sub mul Voffset Hoffset sub add neg X add /Hoffset exch def /Voffset Y def grestore } def /Transform { PathPosition dup Angle cos mul Y add exch Angle sin mul neg X add exch translate Angle rotate } def /ShowChar { /Char exch def gsave Char end stringwidth tx@TextPathDict begin 2 div /Sy exch def 2 div /Sx exch def currentpoint Voffset sub Sy add exch Hoffset sub Sx add Transform Sx neg Sy neg moveto Char end tx@TextPathSavedShow tx@TextPathDict begin grestore Sx 2 mul Sy 2 mul rmoveto } def end % END pst-text.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 } def /HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } def /VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } def end % END pst-node.pro %%EndProcSet %%BeginProcSet: 8r.enc % @@psencodingfile@{ % author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry", % version = "0.6", % date = "1 July 1998", % filename = "8r.enc", % email = "tex-fonts@@tug.org", % docstring = "Encoding for TrueType or Type 1 fonts % to be used with TeX." % @} % % Idea is to have all the characters normally included in Type 1 fonts % available for typesetting. This is effectively the characters in Adobe % Standard Encoding + ISO Latin 1 + extra characters from Lucida. % % Character code assignments were made as follows: % % (1) the Windows ANSI characters are almost all in their Windows ANSI % positions, because some Windows users cannot easily reencode the % fonts, and it makes no difference on other systems. The only Windows % ANSI characters not available are those that make no sense for % typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen % (173). quotesingle and grave are moved just because it's such an % irritation not having them in TeX positions. % % (2) Remaining characters are assigned arbitrarily to the lower part % of the range, avoiding 0, 10 and 13 in case we meet dumb software. % % (3) Y&Y Lucida Bright includes some extra text characters; in the % hopes that other PostScript fonts, perhaps created for public % consumption, will include them, they are included starting at 0x12. % % (4) Remaining positions left undefined are for use in (hopefully) % upward-compatible revisions, if someday more characters are generally % available. % % (5) hyphen appears twice for compatibility with both % ASCII and Windows. % /TeXBase1Encoding [ % 0x00 (encoded characters from Adobe Standard not in Windows 3.1) /.notdef /dotaccent /fi /fl /fraction /hungarumlaut /Lslash /lslash /ogonek /ring /.notdef /breve /minus /.notdef % These are the only two remaining unencoded characters, so may as % well include them. /Zcaron /zcaron % 0x10 /caron /dotlessi % (unusual TeX characters available in, e.g., Lucida Bright) /dotlessj /ff /ffi /ffl /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef % very contentious; it's so painful not having quoteleft and quoteright % at 96 and 145 that we move the things normally found there to here. /grave /quotesingle % 0x20 (ASCII begins) /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash % 0x30 /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question % 0x40 /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O % 0x50 /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore % 0x60 /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o % 0x70 /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /.notdef % rubout; ASCII ends % 0x80 /.notdef /.notdef /quotesinglbase /florin /quotedblbase /ellipsis /dagger /daggerdbl /circumflex /perthousand /Scaron /guilsinglleft /OE /.notdef /.notdef /.notdef % 0x90 /.notdef /.notdef /.notdef /quotedblleft /quotedblright /bullet /endash /emdash /tilde /trademark /scaron /guilsinglright /oe /.notdef /.notdef /Ydieresis % 0xA0 /.notdef % nobreakspace /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen % Y&Y (also at 45); Windows' softhyphen /registered /macron % 0xD0 /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown % 0xC0 /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis % 0xD0 /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls % 0xE0 /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis % 0xF0 /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def %%EndProcSet %%BeginProcSet: texps.pro %! TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} def end %%EndProcSet %%BeginProcSet: special.pro %! 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TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll }repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def /TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{ setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{ /currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC /Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC /Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0 setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0 setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61 0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC /Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0 setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87 0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{ 0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{ 0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC /Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0 setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0 setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90 0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC /Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0 setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0 0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{ 0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{ 0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC /BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0 setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC /CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0 0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1 0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11 0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0 setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0 0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC /Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0 setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0 0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0 1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC /PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0 setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{ 0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor} DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70 setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0 setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1 setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end %%EndProcSet %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 33 /arrowright put dup 49 /infinity put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueXX 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a18bfd18d2ff279844b29842a5e4038099fec03d6bd8b54b8032bfa4 a254b5088017073ff3524df950e3f9ff878a0be788cb39580aef5db4fbe9e1f0 e940aeaac02269677cf9c144feb668ba2e2f15cb6388f4bc0e7d96ccd9f0bbce 95e547270fd5bef6d0e1219973b50e22a0414beddf0d16dd65005c2c221afbb1 d122f54150dc895421ee85c7c33dbc94d9cf8d77a615581335b8c4b2d8d7a571 4ef32d9690385945562f5197f51864990aed522b52c162a16249fc735486a902 18b805adf5c5db98e9612950e89e6067fdd1eea11a2af1b5fa3ec251e450f075 006cbd5297e5583501b5d135960a046148774186261ee2faafc46a4c08db2886 6045b68b1045e045ed95d9c7d1aeaee66da330745ff157ca8aabc883fc89c736 170db4aaac386b8578f0ad051449119435360f3597dfc64fadfa00fb78214aa0 6cb3a4acfd16c5402899e3f9a2fbedd699061105fb9462d03108415721ba5ef4 bbb0ff73bcb88418872b3e1ab555376d9fbd1ec25f4031a8b9565967e054e64a 1c6de8833c328bf7c055e810d6f7945901bc6d9bb81d871697d4daf1193ee673 ce2b07c78dfd1c23a4dd13ab0b7d65db3f46c64872ca3951197e1b7423ff727e 44aea76c2d27e7eecca6f7cc93b30519f1f96b52fd8e41eab28d97439511af07 630a1d80a1cf6a7c7d70c9f607c6143af7861712ed1e66f6b290961316d24a5b 5c0ffd6ddb17bd89a8c2e1c486cf2620bc42f17b9fbd527cd22d07e920c078f4 118b44a708d53c6bb9937898 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 110 /n put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueXX 5087383 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a196cf14c95a4e02f9cd2da8c db2546c6df52e524745992e18d9ff87aa25e4e1800bbe4ebb357c6ef55ed6d03 6d3a00c1ee8073266c21d2f0ac85d656abf61d7e5a4fa87da8ec3b5329e434d0 d2adab706b42a2e5331be5295399d803ccac03f631f01f39a022fcdf63486b68 7d15ef284a77def7fde4898543e7b5f7ec267756103e477f547cfb8d2311c4b0 09deff56085f5d419697af1846c8b88c1bbbae149f0f19ca3c8dafe19cec48fe 6b38357246d8b5cef80b53bab4cbbbe8bc8318cc462a4158258f456e697f6058 86010493f252073ee4e4c9531f23485415ad6bc901bbaea659ef701f825f4b6d 5c9bed0dce7b63810f906b33ea4955531ca1ed1fc120cc56dc1e277a33222cc6 c3a97552607b865783faf0895cbeccd0df54f57bd162a88494768435eda71a39 69718c0c5912d3167bb0971546d733e735aa9bcd89f5aa154656031ab3f6fe41 94ec225ad03ab8b67a9da43ab365c4df17c23e79f685c3b6fd5b654e4a6f2603 6cec3a8641b0b57f93eb95f9e238832aeac2061f3153e0f375513c974f1c38f7 b59edcc94716f2862cf71c9a2be8430985da1cd813b1e1c1b9310564a2eb1aff 52c190f50fc981dccb64bb2c1f7a62c216f211c162c2ed1c554ef49fbaf12b31 aa3b2a80fee259dc0a2a4242869ddec7c29e2941792b28bba7f2c6f77ef69638 12b07d6843f33b51e01c8626b26edc34e1e0fffadede5fb468e8cd5de7e5a64c 366967578f415484d122834de4a647541d66989f7d8b25d1712d8d16729bd9a6 472df1ef13518758e7ab8ce8429d80f39ebd0dd390e2838a0d71801f323745b6 c3c6f4c0c3c2201d3a533e99d44497cf6cf3d73d535f2072146edcd815789bcb 63606e6679adca313dc61f8cc8b909f64ea5d51eb005ac2ed66194b83b2bfdeb f2cb9f43f00552ee170f0d058b18eb8e3b98ef281dc3ca15d674e47b9b8893c2 204b037995ee1a1fb7211ee55edb7f197dbd82179b70f34a8e5aa94b1b9fcc23 503d7db21a5c2f78f8a5cd9b3be02101b6f5334ccc81ab47ae955a423319d4cc 8a49be4e4361772ea39664d587592054d08d0b508fb8360fb8c0e8b89951669b 972f0cf1f8a213f418edb618bb4c3461e870e16951a90809ed5a8037b88294b1 68b92655aaad5e0f795e09146c1d586f7b891d1b0fbcb856225e171489a703c1 01c783de3e223ba48630888f0506b1c52127fb75a1d56d70b4d9ae989e5d4c22 78769d93781994bda6d44ceeab0bf7fd46d9c18382df5ac075aa25553e90cf74 7ca7df70efc23d19257716e62c299183416175ed70058183180a315c9f2524a3 3e144680df1e37199946 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 58 /period put dup 59 /comma put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 71 /G put dup 74 /J put dup 80 /P put dup 113 /q put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueXX 5087386 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put dup 50 /two put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 b1ccad69742a8c9b0ad943482bf2a4ad0aed40baeb69a0233bad36b4ca2d2da7 322956c70375d152653500b2f22d2ab6990cadde2da14b4917f7515e64bc3d96 bf775258fc7dae4e42a4c9b6da8eddec4a800c8aadc8d75e48cae52137e05c03 677f5d6a82fa46d9f2fc7f56d62e5c605a1b7898b8d1401c2cac1a0122a2c8a7 aae09607f2c5f29293a09b9959399283be89051452898238b777db9830ff4318 a298b221c4a820c700ca964fc99e6b1d9eb0bafc39be9aa9dffa2fa326b2a466 1e67261bb3dbc85844e76f9313ab533ee16bcb478166de5502b68e6ec1ea6110 f53206cf1cfea419571b0243244b32ea38b828a01e62b03bcf476a32c2341cec b8a0fa2a3f3f339315d5f3aa7704408f6617d026ffee4925aa48537a4b2e556d 225be09392546ad561cd46cf766f0ba14c6854c5af1a528c3842b0c5aeefefcf 19f19cbce5d967153c4f88e51c776cfbe10d39328466f7a3b83d85601ef4d1ce 0cc136610fa6a74d9676e4e99291d565cad27b9eb2337b0eba4148efd0eb2866 ebf0a4209ba135ad1376cf9cc2d4110f36121055caa3f2e01780740eece6c18a 13a2dd210687a04dfffff58cb60076d0c846beca648599d315a17a383f314b42 d52fd3d82d662c6abb4441906670f5f666543b0b36c5642d3ae46d9eca26e8c1 fd8d72ec0ce1c52e40c7b959291bbedd6512a2e039fc64fd70bbb364a704dfd2 e31a495c7aad7d6f5600c80905607855702cddadbae5b0946bf4b456cee0376f c1e4528557b109f203ffa3f9b4a678922e77e262910476aac8edf750512f46ec ebdaef9983568c755ae765e35faaaf933b8234be3cf48ef69a964fa45701bb16 93a02706fdd27a318f49e472e64a54341dde2db1882a8e71d919c37e4974d0c7 feb795afa50d8091d8de8da0ad5c0bb2cf9d8c37b6b09c66146094c7323b43e6 b64bf0a12b6205300939f64c46b1aea8e7db3d1cedb307819d55fb922042f602 51c5c2e2b11d14081a32a27ee3de85e5161e6a337a60a00f5a61e8809934c678 4067fd2df0653575ab1d8898ee032cdc35d6e7f4c894bfb46820037ef9fee8d4 373a95d0d6a1430e6cb9cdb6e4c4297ba7d059b9201b8c81a16d2dc183e5fe56 02b86d6be0dd998b31303a558be89bb1161827ea36eea49d15e7be9dbaf865a1 d411e41f7ae1a011bae0e6a744354e58b7187152d26dfdbdf75c255e10086f1a 2c188d7639afddd92968639b37a0820b7e39b4713660a0efef1dce627223455e b4cc71433f2ad0e4800674cb858434a0187aab2847247c86a67466164e8d4884 1dde6574758567246efa5902c4a2d5fde6b4190ad0b84f836db28929b2e4c595 f12f6d7f6cf983f4a577336a62174990fb5fdd8e926ec0cd78150bfa466cb101 79 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueXX 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c43079a611075699b4d5902c9a10bde669900444dd85445b886cdcb2afbd7 ee349676ca95b6f65f4338242389ad9bb6d4ab073d3ee7644b72736ff867e44e fb5edcaf82f7eabb080d8d178bf45302a5417d9c0fc8956d34d58fc66dff8668 ac38258aee6d10f0b9f2edc5cd7750b56d33a4e3508629588c0e82dfeef11ccd 6b1cdbbf47df3f8723a3893d8b9886c53aa2cbb87128191d32e5e72bb1f59b14 7c5c735cce861085777fe7d14a1006d5490ac02354fb10ae3d36d29dbb8b6798 a9dde3b3095e1aa4926532ad9cd43c866fa378a5bbb825c8d42ec2843863068e f892e1e1919743d07e27ea764bb477ead0da59aa190df2c93cf95e6abd6d52da c08a571ef517d494f1f6aca35a6f5b7130686cb0520c6ff94f39b28fb04f26b6 6f67b6f7669d5fa7c9342435d93eebbca8cc89dae9721fb7b9699f8effb7826f 777eedd73e2bb1f61ee3cb482e685dfd3861cb49b6d939afd5984305d0b58a6d 8021af9bf32cd23d935b745d45738661327f740222f3dbd97ed9f23fdfaaf5cc 9ed5f28f29767ae4413d46b0c44b43fedca9772ee393467614dd3f7fb21dc7cc 65cd151c1906acb702757db1b14a7efc1c90de5cfee3456f7dfdf11337e86186 4a90f69816149f71addb2259d28dea4cff64abe8c90acf70bc07ba583f283a42 7115ebca0251c4ec9cffe1b44a511fad7d0769b06ae9f5ddf08590d5d019c20e 943cfb4116a623544f19bb68353138d3babb2461c08d53749e51828f07fb7799 4164f81615aff1d65d0b78d3d0b55e401a318cd1d63a4a32c1cf7ce9a879e2fd 7c52f0da1dc9ae3c9f7e041ae200b4ad838b4a710b 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 61 /equal put dup 105 /i put dup 108 /l put dup 109 /m put dup 126 /tilde put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueXX 5000794 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204a520640fd7c4d05e35ea5486f a43d0e970787203855daccb1ed0b16325828b13b7c767a1a58c87902f0546ea5 404440fa6526975783c2d7a9572b8e5d5176bac598b8960609f49016aebf3763 89c1adfe6a1ffc0c53b3acd9d168ec3a278fd4f1d9b085dc2df701346c9d0887 3d230a161692b42a45bb5da343b4edd839dd60685a59aaa49fc65cd8e2ad2a9c 5cab953495172a1a9f40d5f38e922443a519dd96f667201a408bd1d89e35f4ab 98e2f68c3366efc14b5afe1018d9c845d808d4f8e07ea8168518a171ab4d6e21 70eeac099eb7ef46eb9781384da1fac3b3133bb718bc80082eaea88759745188 f266b31d0c7e791d633f16ed94e05517a32163e74cbd96dc5db066f2a5313d6d 7f09465608cb404613e0f058073af000e5bdfafbbf9da0c0d5c02a3447f2cdc1 f56481901e34265c26d331ac3f85bdcbc7c51ef9eddf2b9c189c5253f8e74282 d6f053d7d183ae17ea175e5ebc401e67d21a9fea139cbbf3bb1358c713a75843 b39a69aa2b1a7b975f53ff22d1dc3bdf7acd17afa1da21568310c68241b31d3d 03bf404bd30baf9cc19c75b958bce7155f03cb0cfe2cae0327aad4b603284a51 7c26de75b8c6f6aaa9debe4aec08ca4b646d787a9dfac85b2c01760e9c6c6162 fbbc67dbd0796831e00c477d8e23c375ffab46d289be9d2328aec2b7534ae4cd d782ec2453e7787f6e6b4537b46c01545cba6f90b8e9a1bccac1937bceeaa5e7 8e9f368ce067a0a31da98bfbb545be555a7270f0031fadd4f9b186629e5d2c5f d264f8f24cd5a1c0f68399ff4b29fd77c4a54d8296523419f2c915170877e1cb 9a5a755add1aed12badabf376d0b082734be6a4bbfb101378bf9dd43d7c49c99 07215a235d7675adf34c00dc687516c529e98c9b92e19c37b456aa6d3bef191f c6fb8bbd9ad025a739618f5f0f41e997c8e18457f6fcb0d6752085769ae3c3b8 e5caae4b36d647bc48860f359a2a64c80207b0b68b4ca2bb5b54307989605205 f457e9a33f90db9c6f6c675a2b88065c5465f3e05f084877148c4099f00c878c 6ae791bd90910bfd5343bdccbb7cccd897933135f4162eaace92df01c1f0b4c1 efaa198add4638c657f50f4ef7e4e2f8cad94e5afbd635758ebc1240f8ba6348 60016ca82daa7d0bc02dd7bf50e89c486b57db8b500cf0b38b38731354e356c3 e8ad0a5a9f029dfa54531718947371628da2256e0133ed4748bbd28b37d2efec f7f325671c17ef36f141ce59606007adaeeba943878529abb2ca15ffe29ea756 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b(No)o(v)25 b(4,)f(2003)1568 b(Due:)50 b(start)26 b(of)e(class)h(No)o(v)f(11,)g(2003)170 812 y Fl(If)h(you)g(ha)n(v)o(e)f(questions,)f(please)i(contact)g(Jiayong)f (Zhang)g Fk(<zhangjy@cs.cmu.edu>)p Fl(.)p 24 897 3838 4 v Black 144 1108 a(1.)p Black 49 w(\()p Fm(40pts)p Fl(,)k(Ev)n(aluation\))e(F)o(or)i(\(a\)-\(e\),)h(compute)e(the)h(follo) n(wing)d(probabilities)h(from)i(the)f(gi)n(v)o(en)f(Bayes)268 1229 y(nets.)34 b(These)26 b(e)o(xamples)f(ha)n(v)o(e)h(been)h (designed)e(so)h(that)g(none)g(of)g(the)g(calculations)f(should)g(tak)o (e)h(you)268 1349 y(longer)h(than)g(a)h(fe)n(w)g(minutes.)38 b(If)28 b(you)f(\002nd)h(youself)f(doing)g(dozens)g(of)h(calculations)f (on)g(a)h(question)268 1469 y(sit)c(back)h(and)f(look)h(for)g (shortcuts.)268 1517 y tx@Dict begin { 113.81096 -22.76219 } PutCoor PutBegin end 268 1517 a 268 1612 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@A 11 {InitCnode } NewNode end end 268 1612 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 1612 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 1612 a 333 1645 a Fl(A)369 1612 y tx@Dict begin PutEnd end 369 1612 a 268 1517 a tx@Dict begin PutEnd end 268 1517 a 268 1517 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 1517 a 268 1517 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 1517 a 23 x Fj(P\(A\)=0.2)268 1517 y tx@Dict begin PutEnd end 268 1517 a 268 1517 a tx@Dict begin PutEnd end 268 1517 a 268 1517 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 1517 a 268 1517 a tx@Dict begin { 45.52438 -45.52438 } PutCoor PutBegin end 268 1517 a 268 1612 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@C 11 {InitCnode } NewNode end end 268 1612 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 0 setlinecap stroke grestore end setgray @endspecial 369 1612 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 1612 a 336 1645 a Fl(C)369 1612 y tx@Dict begin PutEnd end 369 1612 a 268 1517 a tx@Dict begin PutEnd end 268 1517 a 268 1517 a tx@Dict begin PutEnd end 268 1517 a 268 1517 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@C known { /N@C load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 1517 a 268 1517 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 1517 a 317 1483 a Fj(P\(C|A\)=0.3)317 1596 y(P\(C|\230A\)=0.6)268 1517 y tx@Dict begin PutEnd end 268 1517 a 268 1517 a tx@Dict begin PutEnd end 268 1517 a 268 1517 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@A /N@C InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 1517 a 915 x Fl(\(a\))g Fi(P)14 b Fh(\()p Fi(A)p Fg(j)p Fi(C)7 b Fh(\))27 b(=)268 2504 y tx@Dict begin { 113.81096 -22.76219 } PutCoor PutBegin end 268 2504 a 268 2598 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@A 11 {InitCnode } NewNode end end 268 2598 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 2598 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 2598 a 333 2631 a Fl(A)369 2598 y tx@Dict begin PutEnd end 369 2598 a 268 2504 a tx@Dict begin PutEnd end 268 2504 a 268 2504 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 2504 a 268 2504 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end y 268 2504 a 22 x Fj(P\(A\)=0.2)268 2504 tx@Dict begin PutEnd end 268 2504 a 268 2504 a tx@Dict begin PutEnd end 268 2504 a 268 2504 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 2504 a 268 2504 a tx@Dict begin { 91.04877 0.0 } PutCoor PutBegin end 268 2504 a 268 2598 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@B 11 {InitCnode } NewNode end end 268 2598 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 2598 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 2598 a 336 2631 a Fl(B)369 2598 y tx@Dict begin PutEnd end 369 2598 a 268 2504 a tx@Dict begin PutEnd end 268 2504 a 268 2504 a tx@Dict begin PutEnd end 268 2504 a 268 2504 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@B known { /N@B load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 2504 a 268 2504 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 2504 a 22 x Fj(P\(B\)=0.4)268 2504 y tx@Dict begin PutEnd end 268 2504 a 268 2504 a tx@Dict begin PutEnd end 268 2504 a 268 2504 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 2504 a 268 2504 a tx@Dict begin { 45.52438 -45.52438 } PutCoor PutBegin end 268 2504 a 268 2598 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@C 11 {InitCnode } NewNode end end 268 2598 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 2598 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 2598 a 336 2631 a Fl(C)369 2598 y tx@Dict begin PutEnd end 369 2598 a 268 2504 a tx@Dict begin PutEnd end 268 2504 a 268 2504 a tx@Dict begin PutEnd end 268 2504 a 268 2504 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@C known { /N@C load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 2504 a 268 2504 a tx@Dict begin { 18.20981 -10. PtoC } PutCoor PutBegin end 268 2504 a 317 2357 a Fj(P\(C|A,B\)=0.3) 317 2470 y(P\(C|\230A,B\)=0.6)317 2583 y(P\(C|A,\230B\)=0.1)317 2695 y(P\(C|\230A,\230B\)=0.9)268 2504 y tx@Dict begin PutEnd end 268 2504 a 268 2504 a tx@Dict begin PutEnd end 268 2504 a 268 2504 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@A /N@C InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 2504 a 268 2504 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@B /N@C InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 2504 a 1009 x Fl(\(b\))e Fi(P)14 b Fh(\(~)p Fi(A)p Fg(j)p Fi(B)5 b Fh(\))26 b(=)268 3671 y Fl(\(c\))f Fi(P)14 b Fh(\(~)p Fi(A)p Fg(j)p Fi(B)5 b(;)17 b Fh(~)p Fi(C)7 b Fh(\))26 b(=)268 3743 y tx@Dict begin { 136.57318 -34.1433 } PutCoor PutBegin end 268 3743 a 268 3838 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@A 11 {InitCnode } NewNode end end 268 3838 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 3838 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin 369 3838 a 333 3871 a Fl(A)369 3838 y tx@Dict begin PutEnd end 369 3838 a 268 3743 a end tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3743 a 268 3743 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 3743 a 23 x Fj(P\(A\)=0.2)268 3743 y tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3743 a 268 3743 a tx@Dict begin { 136.57318 0.0 } PutCoor PutBegin end 268 3743 a 268 3838 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@B 11 {InitCnode } NewNode end end 268 3838 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 3838 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 3838 a 336 3871 a Fl(B)369 3838 y tx@Dict begin PutEnd end 369 3838 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@B known { /N@B load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3743 a 268 3743 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 3743 a 23 x Fj(P\(B\)=0.4)268 3743 y tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3743 a 268 3743 a tx@Dict begin { -68.28659 -68.28659 } PutCoor PutBegin end 268 3743 a 268 3838 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@E 11 {InitCnode } NewNode end end 268 3838 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 3838 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 3838 a 339 3871 a Fl(E)369 3838 y tx@Dict begin PutEnd end 369 3838 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@E known { /N@E load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3743 a 268 3743 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 3743 a 317 3709 a Fj(P\(E|A\)=0.1)317 3822 y(P\(E|\230A\)=0.3)268 3743 y tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@B known { /N@B load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3743 a 268 3743 a tx@Dict begin { 68.28659 -68.28659 } PutCoor PutBegin end 268 3743 a 268 3838 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@F 11 {InitCnode } NewNode end end 268 3838 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 3838 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 3838 a 341 3871 a Fl(F)369 3838 y tx@Dict begin PutEnd end 369 3838 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@F known { /N@F load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3743 a 268 3743 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 3743 a 317 3709 a Fj(P\(F|B\)=0.8)317 3822 y(P\(F|\230B\)=0.4)268 3743 y tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3743 a 268 3743 a tx@Dict begin { 68.28659 -68.28659 } PutCoor PutBegin end 268 3743 a 268 3838 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@C 11 {InitCnode } NewNode end end 268 3838 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 3838 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 3838 a 336 3871 a Fl(C)369 3838 y tx@Dict begin PutEnd end 369 3838 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@C known { /N@C load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3743 a 268 3743 a tx@Dict begin { 18.20981 -10. PtoC } PutCoor PutBegin end 268 3743 a 317 3614 a Ff(P\(C|A,B\)=0.3)317 3713 y(P\(C|\230A,B\))49 b(=)g(0.6)317 3813 y(P\(C|A,\230B\)=0.1)317 3912 y (P\(C|\230A,\230B\)=0.9)268 3743 y tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@C known { /N@C load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3743 a 268 3743 a tx@Dict begin { 0.0 -68.28659 } PutCoor PutBegin end 268 3743 a 268 3838 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@D 11 {InitCnode } NewNode end end 268 3838 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 3838 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 3838 a 333 3871 a Fl(D)369 3838 y tx@Dict begin PutEnd end 369 3838 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@D known { /N@D load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3743 a 268 3743 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 3743 a 317 3709 a Fj(P\(D|C\)=0.4)317 3822 y(P\(D|\230C\)=0.4)268 3743 y tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin PutEnd end 268 3743 a 268 3743 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@A /N@C InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 3743 a 268 3743 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@B /N@C InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 3743 a 268 3743 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@A /N@E InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 3743 a 268 3743 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@B /N@F InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 3743 a 268 3743 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@C /N@D InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 3743 a Black 1918 5551 a Fl(1)p Black eop %%Page: 2 2 2 1 bop Black Black 268 248 a Fl(\(d\))25 b Fi(P)14 b Fh(\()p Fi(E)6 b Fg(j)p Fi(D)s Fh(\))26 b(=)268 323 y tx@Dict begin { 136.57318 -34.1433 } PutCoor PutBegin end 268 323 a 268 417 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@A 11 {InitCnode } NewNode end end 268 417 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 417 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 417 a 333 450 a Fl(A)369 417 y tx@Dict begin PutEnd end 369 417 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 323 a 23 x Fj(P\(A\)=0.2)268 323 y tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 136.57318 0.0 } PutCoor PutBegin end 268 323 a 268 417 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@B 11 {InitCnode } NewNode end end 268 417 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 417 a tx@Dict begin 369 417 a 336 tx@Dict begin 369 417 a 268 323 a tx@Dict begin 268 323 a 268 { -11.38109 11.38109 } PutCoor PutBegin 450 a Fl(B)369 417 y PutEnd end PutEnd 323 a end end tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@B known { /N@B load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 323 a 23 x Fj(P\(B\)=0.4)268 323 y tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { -68.28659 -68.28659 } PutCoor PutBegin end 268 323 a 268 417 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@E 11 {InitCnode } NewNode end end 268 417 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 417 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 417 a 339 450 a Fl(E)369 417 y tx@Dict begin PutEnd end 369 417 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@E known { /N@E load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 323 a 317 289 a Fj(P\(E|A\)=0.1)317 402 y(P\(E|\230A\)=0.3)268 323 y tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@B known { /N@B load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 68.28659 -68.28659 } PutCoor PutBegin end 268 323 a 268 417 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@F 11 {InitCnode } NewNode end end 268 417 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 417 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 417 a 341 450 a Fl(F)369 417 y tx@Dict begin PutEnd end 369 417 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@F known { /N@F load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 323 a 317 289 a Fj(P\(F|B\)=0.8)317 402 y(P\(F|\230B\)=0.4)268 323 y tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 68.28659 -68.28659 } PutCoor PutBegin end 268 323 a 268 417 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@C 11 {InitCnode } NewNode end end 268 417 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 417 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 417 a 336 450 a Fl(C)369 417 y tx@Dict begin PutEnd end 369 417 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@C known { /N@C load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 18.20981 -10. PtoC } PutCoor PutBegin end 268 323 a 317 193 a Ff(P\(C|A,B\)=0.3)317 293 y(P\(C|\230A,B\)=0.6)317 392 y(P\(C|A,\230B\)=0.1)317 492 y(P\(C|\230A,\230B\)=0.9)268 323 y tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@C known { /N@C load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 0.0 -68.28659 } PutCoor PutBegin end 268 323 a 268 417 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@D 11 {InitCnode } NewNode end end 268 417 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 417 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 417 a 333 450 a Fl(D)369 417 y tx@Dict begin PutEnd end 369 417 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@D known { /N@D load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 323 a 317 289 a Fj(P\(D|C\)=0.4)317 402 y(P\(D|\230C\)=0.4)268 323 y tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@E known { /N@E load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 0.0 -68.28659 } PutCoor PutBegin end 268 323 a 268 417 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@G 11 {InitCnode } NewNode end end 268 417 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 417 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 417 a 333 450 a Fl(G)369 417 y tx@Dict begin PutEnd end 369 417 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@G known { /N@G load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 323 a 317 289 a Fj(P\(G|E\)=0.6)317 402 y(P\(G|\230E\)=0.3)268 323 y tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@F known { /N@F load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 0.0 -68.28659 } PutCoor PutBegin end 268 323 a 268 417 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@H 11 {InitCnode } NewNode end end 268 417 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 417 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 417 a 333 450 a Fl(H)369 417 y tx@Dict begin PutEnd end 369 417 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@H known { /N@H load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 18.20981 0. PtoC } PutCoor PutBegin end 268 323 a 317 289 a Fj(P\(H|F\)=0.2)317 402 y(P\(H|\230F\)=0.7)268 323 y tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@G known { /N@G load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 68.28659 -68.28659 } PutCoor PutBegin end 268 323 a 268 417 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@I 11 {InitCnode } NewNode end end 268 417 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 417 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 417 a 352 450 a Fl(I)369 417 y tx@Dict begin PutEnd end 369 417 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@I known { /N@I load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 18.20981 -10. PtoC } PutCoor PutBegin end 268 323 a 317 193 a Ff(P\(I|D,G\)=0.1)317 293 y(P\(I|\230D,G\)=0.3)317 392 y(P\(I|D,\230G\)=0.4)317 492 y(P\(I|\230D,\230G\)=0.9)268 323 y tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@D known { /N@D load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 68.28659 -68.28659 } PutCoor PutBegin end 268 323 a 268 417 a tx@Dict begin tx@NodeDict begin {0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@J 11 {InitCnode } NewNode end end 268 417 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 22.76219 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 369 417 a tx@Dict begin { -11.38109 11.38109 } PutCoor PutBegin end 369 417 a 350 450 a Fl(J)369 417 y tx@Dict begin PutEnd end 369 417 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@J known { /N@J load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 323 a 268 323 a tx@Dict begin { 18.20981 -10. PtoC } PutCoor PutBegin end 268 323 a 317 193 a Ff(P\(J|D,H\)=0.6)317 293 y(P\(J|\230D,H\)=0.7)317 392 y(P\(J|D,\230H\)=0.3)317 492 y(P\(J|\230D,\230H\)=0.5)268 323 y tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin PutEnd end 268 323 a 268 323 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@A /N@C InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 323 a 268 323 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@B /N@C InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 323 a 268 323 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@A /N@E InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 323 a 268 323 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@B /N@F InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 323 a 268 323 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@C /N@D InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 323 a 268 323 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@E /N@G InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 323 a 268 323 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@G /N@I InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 323 a 268 323 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@F /N@H InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 323 a 268 323 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@H /N@J InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 323 a 268 323 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@D /N@I InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 323 a 268 323 a tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@D /N@J InitNC { NCLine } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore grestore end 268 323 a 2429 x Fl(\(e\))f Fi(P)14 b Fh(\(~)p Fi(G)p Fg(j)p Fh(~)p Fi(J)9 b Fh(\))26 b(=)268 3205 y tx@Dict begin { 91.04877 -22.76219 } PutCoor PutBegin end 268 3205 a 268 3323 a tx@Dict begin tx@NodeDict begin {0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@A 11 {InitCnode } NewNode end end 268 3323 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 392 3323 a tx@Dict begin { -14.22636 14.22636 } PutCoor PutBegin 392 3323 a 336 3349 a Fl(A)408 3364 y Fe(0)392 3323 y tx@Dict begin PutEnd end 392 3323 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a end tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3205 a 268 3205 a tx@Dict begin { 22.76227 90. PtoC } PutCoor PutBegin end 268 3205 a 30 3191 a Fj(P\(A)195 3205 y Fe(0)233 3191 y Fj(\)=0.2)268 3205 y tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@A known { /N@A load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3205 a 268 3205 a tx@Dict begin { 45.52438 0.0 } PutCoor PutBegin end 268 3205 a 268 3323 a tx@Dict begin tx@NodeDict begin {0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@B 11 {InitCnode } NewNode end end 268 3323 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 392 3323 a tx@Dict begin { -14.22636 14.22636 } PutCoor PutBegin end 392 3323 a 336 3349 a Fl(A)408 3364 y Fe(1)392 3323 y tx@Dict begin PutEnd end 392 3323 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@B known { /N@B load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3205 a 268 3205 a tx@Dict begin { 56.90547 0.0 } PutCoor PutBegin end 268 3205 a 149 3212 a tx@Dict begin tx@NodeDict begin {1.68 0.0 28.49974 14.24986 0.84 } false /N@C 16 {InitRnode } NewNode end end 149 3212 a 36 w Fd(:)e(:)g(:)268 3205 y tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@C known { /N@C load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3205 a 268 3205 a tx@Dict begin { 56.90547 0.0 } PutCoor PutBegin end 268 3205 a 268 3323 a tx@Dict begin tx@NodeDict begin {0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@D 11 {InitCnode } NewNode end end 268 3323 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 392 3323 a tx@Dict begin { -14.22636 14.22636 } PutCoor PutBegin end 392 3323 a 287 3345 a Fl(A)359 3360 y Fc(n)p Fb(\000)p Fe(1)392 3323 y tx@Dict begin PutEnd end 392 3323 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@D known { /N@D load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3205 a 268 3205 a tx@Dict begin { 45.52438 0.0 } PutCoor PutBegin end 268 3205 a 268 3323 a tx@Dict begin tx@NodeDict begin {0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@E 11 {InitCnode } NewNode end end 268 3323 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 392 3323 a tx@Dict begin { -14.22636 14.22636 } PutCoor PutBegin end 392 3323 a 333 3349 a Fl(A)405 3364 y Fc(n)392 3323 y tx@Dict begin PutEnd end 392 3323 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@E known { /N@E load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3205 a 268 3205 a tx@Dict begin { 56.90547 0.0 } PutCoor PutBegin end 268 3205 a 149 3212 a tx@Dict begin tx@NodeDict begin {1.68 0.0 28.49974 14.24986 0.84 } false /N@F 16 {InitRnode } NewNode end end 149 3212 a 36 w Fd(:)g(:)g(:)268 3205 y tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@B known { /N@B load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3205 a 268 3205 a tx@Dict begin { 0.0 -45.52438 } PutCoor PutBegin end 268 3205 a 268 3323 a tx@Dict begin tx@NodeDict begin {0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@G 11 {InitCnode } NewNode end end 268 3323 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 392 3323 a tx@Dict begin { -14.22636 14.22636 } PutCoor PutBegin end 392 3323 a 339 3349 a Fl(B)405 3364 y Fe(1)392 3323 y tx@Dict begin PutEnd end 392 3323 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@D known { /N@D load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3205 a 268 3205 a tx@Dict begin { 0.0 -45.52438 } PutCoor PutBegin end 268 3205 a 268 3323 a tx@Dict begin tx@NodeDict begin {0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@H 11 {InitCnode } NewNode end end 268 3323 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 392 3323 a tx@Dict begin { -14.22636 14.22636 } PutCoor PutBegin end 392 3323 a 291 3345 a Fl(B)357 3360 y Fc(n)p Fb(\000)p Fe(1)392 3323 y tx@Dict begin PutEnd end 392 3323 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@E known { /N@E load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3205 a 268 3205 a tx@Dict begin { 0.0 -45.52438 } PutCoor PutBegin end 268 3205 a 268 3323 a tx@Dict begin tx@NodeDict begin {0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add 0.8 add} false /N@I 11 {InitCnode } NewNode end end 268 3323 a @beginspecial @setspecial tx@Dict begin STP newpath 0.8 SLW 0 setgray 0.0 2 div 28.45274 0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.0 add CLW 2 div add 0 360 arc closepath gsave 1 setgray fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 392 3323 a tx@Dict begin { -14.22636 14.22636 } PutCoor PutBegin end 392 3323 a 335 3349 a Fl(B)401 3364 y Fc(n)392 3323 y tx@Dict begin PutEnd end 392 3323 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin PutEnd end 268 3205 a 268 3205 a tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@E known { /N@E load GetCenter } { 0 0 } ifelse end } PutCoor PutBegin end 268 3205 a 268 3205 a tx@Dict begin { 22.76227 90. PtoC } PutCoor PutBegin end 268 3205 a -124 3058 a Fj(P\(A)41 3072 y Fc(n)86 3058 y Fj(|A)196 3072 y Fc(n)p Fb(\000)p Fe(1)332 3058 y Fj(\)=0.9)-124 3171 y(P\(A)41 3185 y Fc(n)86 3171 y Fj(|\230A)251 3185 y Fc(n)p Fb(\000)p Fe(1)387 3171 y Fj(\)=0.1)2...

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Carnegie Mellon - CS - 15781
%!PS-Adobe-2.0 %Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %Title: hw5solution.dvi %CreationDate: Mon Nov 24 23:27:03 2003 %Pages: 5 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Bold Times-Roman Courier CMMI12 CM
Carnegie Mellon - CS - 15781
%!PS-Adobe-2.0 %Creator: dvips(k) 5.90a Copyright 2002 Radical Eye Software %Title: hw7.dvi %CreationDate: Sun Nov 23 00:39:57 2003 %Pages: 6 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Bold Times-Roman Courier Times-Italic CMM
Carnegie Mellon - CS - 15781
%!PS-Adobe-2.0 %Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %Title: final-solutions.dvi %Pages: 21 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -f final-solution
Carnegie Mellon - CS - 15781
Learning in Bayes Nets Bayes Nets: Learning Parameters and StructureMachine Learning 10-701 Anna Goldenberg1. Parameter Learning/Estimation: infer from data, given GParents ~L,~R ~L,R L,~R L,R P(W|Pa) P(~W|Pa)1 2 3 4=? =? =? =?1 1 1 2 1
Carnegie Mellon - CS - 15781
OutlineReducing Data DimensionRequired reading: Bishop, chapter 3.6, 8.6 Recommended reading: Wall et al., 2003 Feature selection Single feature scoring criteria Search strategies Unsupervised dimension reduction using all features Princip
Carnegie Mellon - CS - 781
Learning in Bayes Nets Bayes Nets: Learning Parameters and StructureMachine Learning 10-701 Anna Goldenberg1. Parameter Learning/Estimation: infer from data, given GParents ~L,~R ~L,R L,~R L,R P(W|Pa) P(~W|Pa)1 2 3 4=? =? =? =?1 1 1 2 1
Carnegie Mellon - CS - 781
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University of Texas - ARE - 383
Lecture Objectives: Review the previous lectures Prepare for the exam solve some example problems Discuss the midterm project assignmentReview Heat transfer Thermal analysis of building elements External and internal boundary conditions Wea
George Mason - ASTR - 402
4. Telescopes Light gathering power and resolution Optical and radio telescopes Limitations of Earth's atmosphere and satellite missions. Instruments (prism spectrographs and diffraction gratings), detection devices (CCDs) and methods (photometry
High Point - PHY - 221
Potential Energy GraphForce and Potential EnergyExamplePollHere is a graph of potential energy for two charged particles as a function of r. Are the charged particles attracting or repeling each other?1. Attracting 2. Repeling 3. Neither, be
Allan Hancock College - ABG - 110
@ title &quot;Pore Shape Factor Distribution&quot;@ subtitle &quot;Normalised - Volume Weighted - Mean: 0.0396055 StDev: 0.00724783&quot;@ xaxis label &quot;Pore Shape Factor&quot; @ yaxis label &quot;relative frequency&quot;# Mean 0.0396055# StDev 0.007247830.0275 0.09825030.028
Allan Hancock College - ABG - 110
@ title &quot;Pore Tortuosity Distribution&quot;@ subtitle &quot;Normalised - Mean: 2.55099 StDev: 1.06123&quot;@ xaxis label &quot;Pore Tortuosity&quot; @ yaxis label &quot;relative frequency&quot;# Mean 2.55099# StDev 1.061230.1785 0.0001680670.1795 00.1805 00.1815 00.1825
Allan Hancock College - ABG - 110
@ title &quot;Pore Tortuosity Distribution&quot;@ subtitle &quot;Normalised - Volume Weighted - Mean: 2.55099 StDev: 1.06123&quot;@ xaxis label &quot;Pore Tortuosity&quot; @ yaxis label &quot;relative frequency&quot;# Mean 2.55099# StDev 1.061230.1785 0.0001680670.1795 00.1805
Allan Hancock College - ABG - 110
@ title &quot;Grain Shape Factor Distribution&quot;@ subtitle &quot;Normalised - Volume Weighted - Mean: 0.0527908 StDev: 0.0070536&quot;@ xaxis label &quot;Grain Shape Factor&quot; @ yaxis label &quot;relative frequency&quot;# Mean 0.0527908# StDev 0.00705360.0395 0.00489250.040
Valdosta - MATH - 4161
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 90 0+0=0 1+0=1 2+0=2 3+0=3 4+0=4 5+0=5 6+0=6 7+0=7 8+0=8 9+0=9 0 0+0=0 1+0=1 2+0=2 3+0=3 4+0=4 5+0=5 6+0=6 7+0=7 8+0=8 9+0=9 0 0+0=0 1+0=1 2+0=2 3+0=3 4+0=4 5+0=5 6+0=6 7
Valdosta - MATH - 4161
MATH 4161Subtraction of Whole Numbers: Analyzing Students' WorkFor each section, decide if the student's work is correct. Show how the student would most likely complete the last exercise. Identify the process the student seems to be using, and w
Valdosta - MATH - 4161
MATH 4161Multiplication of Whole Numbers: Analyzing Students' WorkFor each section, decide if the student's work is correct. Show how the student would most likely complete the last exercise. Identify the process the student seems to be using, an
Valdosta - MATH - 4161
Einstein was one of the most famous persons to recognize that time is relative. From his thinking on this topic he formed his famous theory on relativity. Today we will examine our own perceptions of time in order to help us get in touch with som
Valdosta - MATH - 4161
MATH 4161Subtraction of Integers: Analyzing Students' WorkFor each section, decide if the student's work is correct. Show how the student would most likely complete the last exercise. Identify the process the student seems to be using, and write
Valdosta - MATH - 4161
Proportional ReasoningEquivalentsInteger Rods White1 cm x 1 cm Red 2 cm x 1 cm Lime 3 cm x 1 cm Purple 4 cm x 1 cm Yellow 5 cm x 1 cm Green 6 cm x 1 cm Black 7 cm x 1 cm Brown 8 cm x 1 cm Blue 9 cm x 1 cm Orange 10 cm x 1 cmW R
Valdosta - MATH - 3190
Technology (121 163)Calculator Comments (129-130) Calculators should be used as o Experimentation o Discovery tool o Instructional aid o Curriculum development Classroom usage o Checking work o Computational aid o Pattern exploration Calculator
Valdosta - MATH - 3190
TLP Investigation #1 Simply Enormous What is the largest number that can be written with only four digits and no other symbols? Initially did you think the answer was 9999? This activity takes a look at how enormous the evaluation of numbers can get
Valdosta - MATH - 3190
Matrices and Determinants (361-364) Technology becomes a valuable tool o Simplifies process o Allows students to concentrate on the meaning instead of focusing on the process Finding the determinant a b o = ( a d) - ( c b ) = ad - cb c d a b c
Valdosta - MATH - 3190
Functions (383-384) Definitions o According to Euler a function is a variable quantity that is dependent upon another variable quantity o Later a more precise definition was given: a function is a mapping from one set into another set such that to e
Valdosta - MATH - 3190
Unit 3 Practice QuizPascal's Triangle Questions 1. What is the 4th term in the expansion of (a + b)9? 2. What is the coefficient of the 4th term in the expansion of (a + b)9? 3. What are the variables of the 4th term in the expansion of (a + b)9? 4.
Valdosta - MATH - 5164
1 Developing Mathematical ThinkingLearning mathematics involves learning ways of thinking. Learning powerful mathematical ideas rather than disconnected procedures for carrying out calculations Entails learning how to o Generate those ideas o Expr
Valdosta - MATH - 2160
Name: _Rolling Doubles Activity How many rolls of a fair pair of random number generator cubes do you think it will take before you roll a double (both cubes showing the same number on the top face)? Write your estimate here: __ rolls (Estimate mu
Valdosta - MATH - 4161
Types of ReasoningHow we think about things.We See the Same Thing DifferentlyWe See the Same Thing DifferentlyWhat Do We See?Shapes?Symmetr y?Repetition ?Lines ?Curves?Stripes ?Squares &amp; Cubes?Rectangles &amp; Prisms?Stars?Ovoi
Valdosta - MATH - 2160
Venn DiagramsSets, Unions, Intersections, and Complements Venn DiagramsVocabulary Universe Element Set Subset Disjoint Mutually Exclusive Finite Infinite Intersection Union Compliment Empty Set Cardinality A Priori Ad
Valdosta - MATH - 2160
Percents Types of Percent ProblemsONLY Three types: Don't know C A% x B = CWhat is 27.37% of 123.4 to the nearest thousandth? 0.2737 x 123.4 = C C = 33.775 Types of Percent ProblemsA% x B = C Don't know A% What percent o
Valdosta - MATH - 2160
Equivalents PiagetConcrete SemiconcreteA manipulative Something I can move around and investigate things with A picture of the things I have been moving around If I have never moved it around before this becomes semiabstract for
Valdosta - MATH - 2160
Graphs Equivalent Representations Percents Decimals Ratios Fractions 25% = 0.25 = 25/100 = Need to be able to fill in missing equivalent values on a table Circle Graph Representations5/3 12.5% 1.25 All circles contain exactly
Valdosta - MATH - 2160
Mice on Two Islands Xray Island20,000 mice are on the Island Population of mice grows 3000 mice every year How many mice in 1 year? 5 years? 7 years? N years? Tango Island20,000 mice are on the Island Population of mi
Valdosta - MATH - 2160
Surface area: area of the bases plus the areas of the lateral faces 7 cm Example: There are 4 lateral faces: 2 lateral faces are 6 cm by 7 cm (A1= wh) and 2 lateral faces are 5 cm by 7 cm (A2 = lh). There are 2 bases 6 cm by 5 cm (A3 = lw) A1 = 6 cm
Valdosta - MATH - 2160
Weird Horse Race In this Weird Horse Race, which horse do you think will win? Horse # _ Place a bean on each horse. Roll the dice and subtract the lowest number from the highest number. Move the horse for the result one mark. Repeat until a horse r
Valdosta - MATH - 2160
Describing Measures of Central Tendency and Dispersion Different types of averages o arithmetic mean x + x 2 + x3 + + xn x= 1 n sum all terms x= number of terms o median put the list of numbers in order (low to high or high to low) when there a
Valdosta - MATH - 3161
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 90 0x0=0 1x0=0 2x0=0 3x0=0 4x0=0 5x0=0 6x0=0 7x0=0 8x0=0 9x0=0 0 0x0=0 1x0=0 2x0=0 3x0=0 4x0=0 5x0=0 6x0=0 7x0=0 8x0=0 9x0=0 0 0x0=0 1x0=0 2x0=0 3x0=0 4x0=0 5x0=0 6x0=0 7
Valdosta - MATH - 3161
Final Exam ReviewChapter 1: Viewing Mathematics Mathematics as Problem Solving o The Role of Problem Solving The Meaning of a Problem p. 38 p A problem is a situation for which the following conditions exist p It involves a question that represen
Valdosta - MATH - 3161
DATE Tuesday, August 16, 2005 Thursday, August 18, 2005 Tuesday, August 23, 2005 Thursday, August 25, 2005 Tuesday, August 30, 2005 Thursday, September 01, 2005 Tuesday, September 06, 2005 Thursday, September 08, 2005 Tuesday, September 13, 2005 Thur
Valdosta - MATH - 3162
Chapter 10: Introducing GeometryQuestions about 10.1? 10.2 Solving Problems in Geometry Will use basic geometric ideas and relationships Will solve and analyze real-world problems Look at mini-investigation 10.2 p. 534 Any questions? 10.2.1. Poi
Valdosta - MATH - 3162
Chapter 9: Probability9.4 Odds and Long Term Behavior 9.4.1. Odds in Favor and Odds Against P( A ) 9.4.1.1. Odds in favor of A = 1 - P( A ) 1- P( A ) 9.4.1.2. Odds against A = P( A ) 9.4.1.3. Alternate way of thinking about this: 9.4.1.3.1. let m be
Valdosta - MATH - 5164
MATH 5164 - Understanding Algebra for P-5 Teachers Summer 2005DATEThursday, June 09, 2005 Tuesday, June 14, 2005 Monday, June 20, 2005 Tuesday, June 21, 2005 Monday, June 27, 2005 Tuesday, June 28, 2005NH 2104TIME9:00 am - 12:00 pm 9:00 am - 12
Valdosta - MATH - 5164
3 Developing and Using Relational Thinking Use of the equal sign correctly, but still calculating important step Use of the equal sign correctly and realizing calculation not required, only need to compare both sides critical part of learning Goal
Valdosta - MATH - 5164
MATH 5164 - Understanding Algebra for P-5 TeachersSummer 2006DATE Monday, June 05, 2006EC 118READING Chapter 1: 1-8Tentative ScheduleTOPIC Syllabus; Introductions; Developing Mathematical ThinkingWednesday, June 07, 2006WEB - NO CLASS Web
Valdosta - MATH - 3162
MATH 3162C Spring 2006 Tentative ScheduleDATE Tuesday, January 10, 2006 Thursday, January 12, 2006 Tuesday, January 17, 2006 Thursday, January 19, 2006 Tuesday, January 24, 2006 Thursday, January 26, 2006 Tuesday, February 07, 2006 Thursday, Februar
Valdosta - MATH - 3162
Name: _ Matching: Column A 1. A type of continuous data 2. A type of discrete data 3. Discrete line graph 4. Continuous line graph 5. Positive correlationQuiz 8.2 Column B A. People B. m = -3 C. Dashed line D. m = 3 E. Solid line F. Temperatures G.
Valdosta - MATH - 3161
Chapter 3: Estimation and Computation3.1 Strategies and Procedures for Mental Computation 3.1.1. When to Use Mental Computation 3.1.1.1. Description of Mental Computation: Mental computation is the process of finding an exact answer to a computation
Valdosta - MATH - 3161
Chapter 6: Rational Number Operations and Properties6.1 Rational Number Ideas and Symbols 6.1.1. Rational Number Uses and Models 6.1.1.1. Models for rational numbers 6.1.1.1.1. Used to describe a quantity between 0 and 1 6.1.1.1.2. identify the whol
Valdosta - MATH - 3161
Chapter 4: Number Theory4.2 Prime and Composite Numbers 4.2.1. Defining Prime and Composite Numbers 4.2.1.1. Definition of Prime and Composite Numbers: A natural number that has exactly two distinct factors is called a prime number. A natural number
Valdosta - MATH - 3161
Chapter 7: Proportional Reasoning7.2 Proportional Variation and Solving Proportions 7.2.1. Recognizing proportional variation 7.2.1.1. ratio remains constant Fundamental Theorem of Fractions idea 7.2.1.2. Definition of quantities varying proportion
Valdosta - MATH - 3161
Chapter 7: Proportional Reasoning7.3 Solving Percent Problems 7.3.1. Definition of percent 7.3.1.1. Definition of percent: a percent is a ratio with a denominator of 100 7.3.1.2. represented by the symbol % 7.3.1.3. 100% means 100 or ALL of the amou
Valdosta - MATH - 3161
Chapter 2: Sets and Whole-Number Operations and Properties2.4 Numeration 2.4.1. Numeration Systems 2.4.1.1. 2 is a symbol, it is NOT a number numbers are abstract ideas 2.4.1.2. Symbol representing a number is numeral sometimes called the name of
Valdosta - MATH - 4161
Tentative Schedule MATH 4161A Amended 1/12/2004 14:56:13 PMDATE UNIT READING TOPIC ASSIGNMENT DUE1/12/041/14/04 1/19/04 1/21/04NO CLASS MLK JR Day NO CLASS1/26/041/28/042/2/04 2/4/04 2/9/04EXAM #1 EXAM #1 EXAM #12/11/042/16/042/18/
Valdosta - MATH - 4161
Chapter 1: Viewing Mathematics1.4 A Connected, Balanced View of Mathematics 1.4.1. Importance of a Connected View of Mathematics 1.4.1.1. Connected view of mathematics considers various ideas of mathematics as being integrated in meaningful ways 1.
Valdosta - MATH - 4161
Exam 2 ReviewTime Sequence of telling time o hour hand first o add minute hand later for precision Telling time on the number line using the hour hand only Telling time on a clock using the hour hand only Elapsed time Adding and subtracting in
Valdosta - MATH - 4161
Proportional ReasoningProportional reasoning is one of the four types of mathematical reasoning that we discussed in Unit 1 of this course. O'Daffer states, &quot;Proportional reasoning involves drawing conclusions or solving problems with either the for
Valdosta - MATH - 4161
Chapter 6: Rational Number Operations and Properties6.4 Dividing, Comparing, and Ordering Rational Numbers 6.4.1. Modeling rational number division 6.4.1.1. no remainders with rational number division 6.4.1.2. see example p. 320 6.4.1.3. Sharing mod
Valdosta - MATH - 5164
MATH 5164 T 17:00 19:45; NH 2104 Understanding Algebra for P-5 Teachers Spring 2006Instructor Office Phone Email Office Hours Options : Dr. Peggy L. Moch : Nevins Hall 1181 : 333-5785 : plmoch@valdosta.edu (best way to contact me) : MTWR 14:00 15:
Valdosta - MATH - 5166
MATH 5166 T 17:00 19:45 NH 2103 Understanding Data Analysis and Probability for P-5 Teachers Spring 2007Instructor Office Phone Email Office Hours Options : Dr. Peggy L. Moch : Nevins Hall 1181 : 333-5785 : plmoch@valdosta.edu (best way to contact
Valdosta - MATH - 5166
MATH 5166 - Understanding Data Analysis and Probability for P-5 Teachers Spring 2007 NH 2103DATE TIME TOPIC-Syllabus -Ice Breaker -Data and Where to Get It -Representations of Data -Venn Diagrams -Percentages -Circle Graphs -Line Plot -Bar Graph -L
Valdosta - MATH - 2160
MATH 2160 A &amp; BDATE Monday, January 08, 2007 Wednesday, January 10, 2007 Monday, January 15, 2007 Wednesday, January 17, 2007 Monday, January 22, 2007 Wednesday, January 24, 2007 Monday, January 29, 2007 Wednesday, January 31, 2007 Monday, February