(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 1422747, 37642]*) (*NotebookOutlinePosition[ 1423960, 37681]*) (* CellTagsIndexPosition[ 1423916, 37677]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Appendix D", FontSize->12, FontVariations->{"Underline"->False}], StyleBox["\n", FontVariations->{"Underline"->False}], StyleBox["\n"], StyleBox[ "STABLE DISTRIBUTIONS FOR INVESTMENT REAL ESTATE RETURNS\n IN TIER II", FontSize->12, FontVariations->{"Underline"->False}] }], "Title", PageWidth->PaperWidth, TextAlignment->Center, FontFamily->"Times New Roman", FontSize->18, FontVariations->{"Underline"->True}], Cell[BoxData[{\(<< Calculus`\), \(<< Statistics`\), \(<< Graphics`\n<< \ Graphics`FilledPlot`\), RowBox[{ RowBox[{\(<< Graphics`Arrow`\), "\n", StyleBox[\(Off[General::spell1]\), FontFamily->"Courier New"]}], StyleBox[";", FontFamily->"Courier New"], StyleBox["\n", FontFamily->"Courier New"], StyleBox[\(Off[General::spell]\), FontFamily->"Courier New"], StyleBox[";", FontFamily->"Courier New"]}]}], "Input", PageWidth->PaperWidth] }, Open ]], Cell[TextData[StyleBox[ "I. Mathematics of Expected Value with Stable, non-Normal Distributions"]], "Subtitle", PageWidth->PaperWidth, FontSize->16, FontSlant->"Plain", FontColor->GrayLevel[0]], Cell[TextData[{ "This monograph is intended to demonstrate that one may expect values of \ \[Alpha] between 1.2 and 1.8 and \[Beta] between 0 and .2 for distributions \ of investment returns on privately held real estate. It also extends the \ illustration contained in Appendix C to the case involving stable \ distributions. Finally, it attempts to provide more insight into the special \ form of discrete Fourier transforms used in this dissertation. This notebook \ was used to produce many of the illustrations in the text.\n\nIn general, the \ probability distribution function (pdf) and the characteristic function \ (ch.f.) of a random variable form a Fourier transform pair defined by the \ equations:\n\n", Cell[BoxData[ FormBox[ StyleBox[\(F \((u)\) = \ \[Integral]\_\(-\[Infinity]\)\%\[Infinity] f \((x)\) e\^\((iux)\)\ dx, \n\n f \((x)\) = \(1\/\(2 \[Pi]\)\) \(\[Integral]\_\(-\[Infinity]\)\%\ \[Infinity] F \((u)\) e\^\(-iux\)\ du\)\), FontColor->GrayLevel[0]], TextForm]], "Text", FontSize->14], "\n\nwhere x and u are respectively the probability distribution variable \ and the angular variable of the characteristic function.\n\nFor many \ distributions, including almost all of the stable distributions of interest \ here, the above integrations cannot be performed analytically and a closed \ analytical pdf is not defined. Therefore, stable distributions are usually \ defined by stating their ch.f.\n\nIt is sometimes desirable, as in our case, \ to study the effects on the pdf of varying the parameters of the cf. It is \ possible, subject the restrictions of sampling theory, to construct a sampled \ version of the ch.f. by evaluating the ch.f. at equally spaced values of the \ angle variable u. The usual procedure is to assign values to all parameters \ before sampling, which results in a numeric series. This series is then \ transformed into a numeric series in x using discrete fourier transform \ techniques. This can be accomplished to a high degree of accuracy provided \ the samples are properly spaced and cover all the significant range of the \ ch.f. \n\nOne of the drawbacks of using the numeric approach is that all \ parameters must be evaluated prior to the application of the transform \ procedure. We have elected to use a variation of the usual discrete transform \ which allows evaluation after transformation. This procedure is outlined \ below.\n\nWe will use the the S(\[Alpha],\[Beta],\[Gamma],\[Delta];0) \ parameterization as suggested by Nolan (1998 page 189 Eq. #3) substituting u \ for t, \[Gamma] for \[Sigma], and \[Delta] for \[Mu]. " }], "Text", PageWidth->PaperWidth, FontFamily->"Times New Roman", FontSize->12, FontSlant->"Plain", FontColor->GrayLevel[0]], Cell[BoxData[ \(fu := Exp[\((\(-\[Gamma]^\[Alpha]\)\ Abs[u]^\[Alpha]\ \((1 + I\ \[Beta]\ \ Sign[ u]\ Tan[\[Pi]\ \[Alpha]/ 2]\ \((\[Gamma]\ Abs[u]^\((1 - \[Alpha])\) - 1)\))\) + \[Delta]\ u\ I)\)]\)], "Input", PageWidth->PaperWidth], Cell[TextData[StyleBox["Although fu is not directly integratable, we can \ apply the transform at the selected sampling points by use of an impulse \ function, DiracDelta[u-u1], which has value only when u= u1. The integration \ is performed over a band of +/- \[Epsilon] about each point where u= u1, then \ the limit is calculated as \[Epsilon]\[Rule]0. The result is a list of terms \ which are the Fourier transforms of each sample of u. x is now the \ independent variable. The pdf is the sum of these terms, ffx1 below. \ Mathematica performs a change of variable (u1\[Rule]2 \[Pi] f, to correct the \ scaling), evaluates the terms at selected points, -5<=f <=5 in steps of .01, \ and sums the terms in the ffx1 operation below.", FontSize->12, FontSlant->"Plain"]], "Text", PageWidth->PaperWidth, FontColor->GrayLevel[0]], Cell[CellGroupData[{ Cell[BoxData[ \(idf = Limit[1\/\(2\ \[Pi]\)\ \(\[Integral]\_\(u1 - \[Epsilon]\)\%\(u1 + \ \[Epsilon]\)DiracDelta[ u - u1] \((fu /. u -> u1)\)\ \(E\^\(\(-I\)\ u1\ x\)\) \[DifferentialD]u\), \ \[Epsilon] -> 0]\)], "Input", PageWidth->PaperWidth], Cell[BoxData[ \(\[ExponentialE]\^\(\(-\[ImaginaryI]\)\ u1\ x + \[ImaginaryI]\ u1\ \ \[Delta] - \[Gamma]\^\[Alpha]\ Abs[u1]\^\[Alpha]\ \((1 + \[ImaginaryI]\ \ \[Beta]\ \((\(-1\) + \[Gamma]\ Abs[u1]\^\(1 - \[Alpha]\))\)\ Sign[u1]\ Tan[\(\ \[Pi]\ \[Alpha]\)\/2])\)\)\/\(2\ \[Pi]\)\)], "Output", PageWidth->PaperWidth] }, Open ]], Cell[TextData[{ StyleBox["Note, below, that a table of values, ", FontSlant->"Plain"], "ffx1,", StyleBox[" is produced with a specific range, {-5,5}, and step value (.01). \ ", FontSlant->"Plain"] }], "Text", PageWidth->PaperWidth, FontSize->12, FontColor->GrayLevel[0]], Cell[BoxData[ \(\(ffx1 = Apply[Plus, Table[\((idf /. u1 -> 2\ \[Pi]\ f)\), {f, \(-5\), 5, .01}]];\)\)], "Input", PageWidth->PaperWidth], Cell[TextData[{ StyleBox["To correct amplitude scaling, we make use of the fact that ", FontSize->12, FontColor->GrayLevel[0]], Cell[BoxData[ \(\[Integral]\_\(-\[Infinity]\)\%\[Infinity] x \[DifferentialD]x = 1. \)], PageWidth->PaperWidth, CellMargins->{{Inherited, 0}, {Inherited, Inherited}}, CellSize->{483.188, Inherited}, FontSize->12, FontSlant->"Plain", FontColor->GrayLevel[0]], "\n", StyleBox["We can perform the integration numerically after assigning \ values to the parameters. The scaling factor is independent of the assigned \ parameters so long as the integration is performed over a range which covers \ all significant values of the pdf.", FontSize->12, FontColor->GrayLevel[0]] }], "Text", PageWidth->PaperWidth, FontSlant->"Plain"], Cell[CellGroupData[{ Cell[BoxData[ \(m1 = NIntegrate[ Evaluate[ Abs[ffx1 /. {\[Alpha] \[Rule] 2, \[Beta] \[Rule] 0, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}]], {x, \(-30\), 30}]\)], "Input", PageWidth->PaperWidth], Cell[BoxData[ \(15.915494309191605`\)], "Output", PageWidth->PaperWidth] }, Open ]], Cell[TextData[{ StyleBox["The value of the constant term \"m1\" above is ONLY useful for \ that certain range and step value (in ", FontSize->12, FontSlant->"Plain", FontColor->GrayLevel[0]], StyleBox["ffx1", FontSize->12, FontColor->GrayLevel[0]], StyleBox[") specified above. This constant, a divisor of the function that \ creates the \"simulated\" pdf, must be reset if range or step value changes.\n\ \nAfter application of the scaling factor, we are able to plot the pdf for a \ wide range of parameters. The \"simulated\" probability distribution \ function, above, is now operational within the bounds of the range and step \ value leading to the m1 constant above. Below, a stable distribution is \ plotted using input values for \[Alpha], \[Beta], \[Gamma] and \[Delta].", FontSize->12, FontSlant->"Plain", FontColor->GrayLevel[0]] }], "Text", PageWidth->PaperWidth, FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(pf1 = Plot[Evaluate[{Abs[ ffx1\/m1] /. {\[Alpha] \[Rule] 2, \[Beta] \[Rule] 0, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}, Abs[ffx1\/m1] /. {\[Alpha] \[Rule] 1.4, \[Beta] \[Rule] 1, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}}], {x, \(-5\), 25}, PlotStyle -> {Hue[ .6], Hue[ .9]}, PlotRange -> All, GridLines -> Automatic]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.18254 0.031746 0.0147151 2.08655 [ [.02381 .00222 -6 -9 ] [.02381 .00222 6 0 ] [.34127 .00222 -3 -9 ] [.34127 .00222 3 0 ] [.5 .00222 -6 -9 ] [.5 .00222 6 0 ] [.65873 .00222 -6 -9 ] [.65873 .00222 6 0 ] [.81746 .00222 -6 -9 ] [.81746 .00222 6 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.17004 .11904 -24 -4.5 ] [.17004 .11904 0 4.5 ] [.17004 .22337 -18 -4.5 ] [.17004 .22337 0 4.5 ] [.17004 .3277 -24 -4.5 ] [.17004 .3277 0 4.5 ] [.17004 .43202 -18 -4.5 ] [.17004 .43202 0 4.5 ] [.17004 .53635 -24 -4.5 ] [.17004 .53635 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 .5 r .25 Mabswid [ ] 0 setdash .02381 0 m .02381 .61803 L s .18254 0 m .18254 .61803 L s .34127 0 m .34127 .61803 L s .5 0 m .5 .61803 L s .65873 0 m .65873 .61803 L s .81746 0 m .81746 .61803 L s .97619 0 m .97619 .61803 L s 0 .01472 m 1 .01472 L s 0 .11904 m 1 .11904 L s 0 .22337 m 1 .22337 L s 0 .3277 m 1 .3277 L s 0 .43202 m 1 .43202 L s 0 .53635 m 1 .53635 L s 0 g .02381 .01472 m .02381 .02097 L s [(-5)] .02381 .00222 0 1 Mshowa .34127 .01472 m .34127 .02097 L s [(5)] .34127 .00222 0 1 Mshowa .5 .01472 m .5 .02097 L s [(10)] .5 .00222 0 1 Mshowa .65873 .01472 m .65873 .02097 L s [(15)] .65873 .00222 0 1 Mshowa .81746 .01472 m .81746 .02097 L s [(20)] .81746 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(25)] .97619 .00222 0 1 Mshowa .125 Mabswid .05556 .01472 m .05556 .01847 L s .0873 .01472 m .0873 .01847 L s .11905 .01472 m .11905 .01847 L s .15079 .01472 m .15079 .01847 L s .21429 .01472 m .21429 .01847 L s .24603 .01472 m .24603 .01847 L s .27778 .01472 m .27778 .01847 L s .30952 .01472 m .30952 .01847 L s .37302 .01472 m .37302 .01847 L s .40476 .01472 m .40476 .01847 L s .43651 .01472 m .43651 .01847 L s .46825 .01472 m .46825 .01847 L s .53175 .01472 m .53175 .01847 L s .56349 .01472 m .56349 .01847 L s .59524 .01472 m .59524 .01847 L s .62698 .01472 m .62698 .01847 L s .69048 .01472 m .69048 .01847 L s .72222 .01472 m .72222 .01847 L s .75397 .01472 m .75397 .01847 L s .78571 .01472 m .78571 .01847 L s .84921 .01472 m .84921 .01847 L s .88095 .01472 m .88095 .01847 L s .9127 .01472 m .9127 .01847 L s .94444 .01472 m .94444 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .18254 .11904 m .18879 .11904 L s [(0.05)] .17004 .11904 1 0 Mshowa .18254 .22337 m .18879 .22337 L s [(0.1)] .17004 .22337 1 0 Mshowa .18254 .3277 m .18879 .3277 L s [(0.15)] .17004 .3277 1 0 Mshowa .18254 .43202 m .18879 .43202 L s [(0.2)] .17004 .43202 1 0 Mshowa .18254 .53635 m .18879 .53635 L s [(0.25)] .17004 .53635 1 0 Mshowa .125 Mabswid .18254 .03558 m .18629 .03558 L s .18254 .05645 m .18629 .05645 L s .18254 .07731 m .18629 .07731 L s .18254 .09818 m .18629 .09818 L s .18254 .13991 m .18629 .13991 L s .18254 .16077 m .18629 .16077 L s .18254 .18164 m .18629 .18164 L s .18254 .2025 m .18629 .2025 L s .18254 .24424 m .18629 .24424 L s .18254 .2651 m .18629 .2651 L s .18254 .28597 m .18629 .28597 L s .18254 .30683 m .18629 .30683 L s .18254 .34856 m .18629 .34856 L s .18254 .36943 m .18629 .36943 L s .18254 .39029 m .18629 .39029 L s .18254 .41116 m .18629 .41116 L s .18254 .45289 m .18629 .45289 L s .18254 .47376 m .18629 .47376 L s .18254 .49462 m .18629 .49462 L s .18254 .51549 m .18629 .51549 L s .18254 .55722 m .18629 .55722 L s .18254 .57808 m .18629 .57808 L s .18254 .59895 m .18629 .59895 L s .25 Mabswid .18254 0 m .18254 .61803 L s 0 .4 1 r .5 Mabswid .02381 .01585 m .02846 .01634 L .03279 .01697 L .03754 .01791 L .04262 .01929 L .04795 .0213 L .053 .02388 L .05753 .02691 L .06244 .03116 L .06751 .03681 L .07308 .04485 L .0789 .0557 L .08435 .06857 L .0941 .09927 L .10458 .14505 L .11468 .20256 L .12571 .27892 L .1458 .43587 L .15593 .50853 L .16548 .56231 L .17076 .58341 L .17374 .59212 L .17515 .59541 L .17648 .59798 L .17769 .59989 L .17879 .60127 L .18001 .60239 L .18133 .6031 L .18259 .60332 L .1833 .60324 L .18396 .60303 L .18517 .60231 L .18645 .60109 L .18759 .59961 L .18883 .59757 L .19134 .59212 L .19366 .58554 L .19582 .57812 L .2007 .55707 L .20592 .52868 L .2242 .3974 L .24411 .24454 L .2546 .17706 L .2657 .1206 L .2756 .08338 L .28123 .06725 L .2865 .05503 L .29575 .03921 L .30094 .0329 L .30568 .0284 L Mistroke .31046 .02488 L .31555 .02202 L .32035 .02001 L .3247 .01863 L .32984 .01742 L .33273 .0169 L .33539 .01651 L .34028 .01594 L .34274 .01573 L .34544 .01553 L .34796 .01538 L .3507 .01524 L .35311 .01515 L .35567 .01506 L .35798 .015 L .36051 .01494 L .36499 .01487 L .3677 .01483 L .37019 .01481 L .37287 .01479 L .37579 .01477 L .37835 .01476 L .38073 .01475 L .38343 .01474 L .38592 .01474 L .38838 .01473 L .39098 .01473 L .3936 .01472 L .39647 .01472 L .39895 .01472 L .40161 .01472 L .40412 .01472 L .40641 .01472 L .40879 .01472 L .41099 .01472 L .4134 .01472 L .41596 .01472 L .41818 .01472 L .42026 .01472 L .42255 .01472 L .42501 .01472 L .42741 .01472 L .42996 .01472 L .43238 .01472 L .43457 .01472 L .43715 .01472 L .43995 .01472 L .44259 .01472 L .44503 .01472 L .44755 .01472 L Mistroke .44991 .01472 L .45249 .01472 L .45527 .01472 L .45666 .01472 L .45818 .01472 L .45951 .01472 L .46094 .01472 L .46235 .01472 L .46363 .01472 L .46612 .01472 L .46845 .01472 L .471 .01472 L .47229 .01472 L .47367 .01472 L .47486 .01472 L .47616 .01472 L .47864 .01472 L .48098 .01472 L .48327 .01472 L .48538 .01472 L .48658 .01472 L .48786 .01472 L .49019 .01472 L .49153 .01472 L .49295 .01472 L .49548 .01472 L .49677 .01472 L .49814 .01472 L .50061 .01472 L .50212 .01472 L .50354 .01472 L .50483 .01472 L .50621 .01472 L .50746 .01472 L .5086 .01472 L .51084 .01472 L .5121 .01472 L .51346 .01472 L .51594 .01472 L .5173 .01472 L .51853 .01472 L .51985 .01472 L .52128 .01472 L .52262 .01472 L .52384 .01472 L .525 .01472 L .52624 .01472 L .5274 .01472 L .52846 .01472 L .53052 .01472 L Mistroke .53168 .01472 L .53294 .01472 L .53522 .01472 L .53636 .01472 L .53761 .01472 L .53883 .01472 L .54015 .01472 L .54137 .01472 L .54249 .01472 L .54469 .01472 L .54598 .01472 L .54719 .01472 L .54946 .01472 L .55073 .01472 L .5519 .01472 L .55318 .01472 L .55382 .01472 L .55453 .01472 L .55573 .01472 L .55681 .01472 L .55926 .01472 L .56034 .01472 L .56152 .01472 L .56264 .01472 L .56367 .01472 L .56616 .01472 L .56747 .01472 L .56813 .01472 L .56885 .01472 L .57017 .01472 L .57139 .01472 L .57251 .01472 L .57372 .01472 L .57437 .01472 L .57508 .01472 L .57637 .01472 L .57763 .01472 L .57879 .01472 L .58008 .01472 L .58082 .01472 L .58151 .01472 L .58224 .01472 L .5829 .01472 L .58366 .01472 L .58439 .01472 L .58564 .01472 L .58634 .01472 L .58699 .01472 L .58818 .01472 L .58943 .01472 L Mistroke .59048 .01472 L .59161 .01472 L .59284 .01472 L .594 .01472 L .59532 .01472 L .59606 .01472 L .59675 .01472 L .59799 .01472 L .59869 .01472 L .59935 .01472 L .60049 .01472 L .60172 .01472 L .60303 .01472 L .60423 .01472 L .6053 .01472 L .60645 .01472 L .60753 .01472 L .60851 .01472 L .61319 .01472 L .61536 .01472 L .61658 .01472 L .61769 .01472 L .619 .01472 L .62024 .01472 L .62138 .01472 L .62262 .01472 L .62385 .01472 L .62515 .01472 L .62748 .01472 L .62876 .01472 L .62948 .01472 L .63013 .01472 L .63263 .01472 L .63364 .01472 L .63471 .01472 L .6359 .01472 L .637 .01472 L .63823 .01472 L .63936 .01472 L .64063 .01472 L .64184 .01472 L .64304 .01472 L .64436 .01472 L .64502 .01472 L .64574 .01472 L .64703 .01472 L .64831 .01472 L .64953 .01472 L .65062 .01472 L .65182 .01472 L Mistroke .65255 .01472 L .65324 .01472 L .65454 .01472 L .65526 .01472 L .65593 .01472 L .65666 .01472 L .65743 .01472 L .65872 .01472 L .65992 .01472 L .66123 .01472 L .66197 .01472 L .66265 .01472 L .66384 .01472 L .66513 .01472 L .66634 .01472 L .66745 .01472 L .66861 .01472 L .66988 .01472 L .67119 .01472 L .6719 .01472 L .67256 .01472 L .67376 .01472 L .67489 .01472 L .67591 .01472 L .677 .01472 L .67818 .01472 L .67927 .01472 L .68045 .01472 L .68174 .01472 L .6824 .01472 L .68312 .01472 L .68444 .01472 L .68572 .01472 L .68691 .01472 L .68764 .01472 L .68832 .01472 L .6896 .01472 L .69032 .01472 L .69098 .01472 L .6917 .01472 L .69246 .01472 L .69366 .01472 L .69494 .01472 L .69615 .01472 L .69725 .01472 L .69854 .01472 L .69927 .01472 L .69995 .01472 L .70119 .01472 L .7025 .01472 L Mistroke .7037 .01472 L .70501 .01472 L .70625 .01472 L .70741 .01472 L .70855 .01472 L .70958 .01472 L .71077 .01472 L .7119 .01472 L .71313 .01472 L .71443 .01472 L .71554 .01472 L .71676 .01472 L .71807 .01472 L .7188 .01472 L .71948 .01472 L .72078 .01472 L .72201 .01472 L .72306 .01472 L .72422 .01472 L .72543 .01472 L .72656 .01472 L .72755 .01472 L .72859 .01472 L .72973 .01472 L .73077 .01472 L .73191 .01472 L .73313 .01472 L .73428 .01472 L .73533 .01472 L .73656 .01472 L .73725 .01472 L .73789 .01472 L .73906 .01472 L .74031 .01472 L .74152 .01472 L .74283 .01472 L .74408 .01472 L .74523 .01472 L .74638 .01472 L .74741 .01472 L .74973 .01472 L .75986 .01472 L .77817 .01472 L .78302 .01472 L .78754 .01472 L .78871 .01472 L .78982 .01472 L .7911 .01472 L .79226 .01472 L .79355 .01472 L Mistroke .79474 .01472 L .79605 .01472 L .79744 .01472 L .8026 .01472 L .80329 .01472 L .80393 .01472 L .8046 .01472 L .80534 .01472 L .80608 .01472 L .80688 .01472 L .80762 .01472 L .80829 .01472 L .80956 .01472 L .81028 .01472 L .81094 .01472 L .81215 .01472 L .81344 .01472 L .81463 .01472 L .81574 .01472 L .81696 .01472 L .81827 .01472 L .82318 .01472 L .82386 .01472 L .8246 .01472 L .82529 .01472 L .82593 .01472 L .82714 .01472 L .82841 .01472 L .8291 .01472 L .82983 .01472 L .83115 .01472 L .83196 .01472 L .83272 .01472 L .83415 .01472 L .83946 .01472 L .84414 .01472 L .8491 .01472 L .85035 .01472 L .85105 .01472 L .85169 .01472 L .85245 .01472 L .85317 .01472 L .85383 .01472 L .85455 .01472 L .85581 .01472 L .85651 .01472 L .85715 .01472 L .8584 .01472 L .85957 .01472 L .87964 .01472 L Mistroke .89812 .01472 L .90797 .01472 L .91853 .01472 L .92365 .01472 L .92617 .01472 L .92851 .01472 L .9296 .01472 L .93062 .01472 L .93168 .01472 L .93286 .01472 L .93395 .01472 L .93512 .01472 L .93641 .01472 L .9376 .01472 L .93885 .01472 L .94003 .01472 L .94109 .01472 L .94224 .01472 L .94348 .01472 L .94478 .01472 L .9459 .01472 L .94713 .01472 L .94827 .01472 L .94931 .01472 L .95051 .01472 L .95164 .01472 L .95269 .01472 L .95367 .01472 L .95473 .01472 L .95587 .01472 L .96602 .01472 L .97061 .01472 L .97319 .01472 L .97435 .01472 L .97557 .01472 L .97619 .01472 L Mfstroke 1 0 .6 r .02381 .01475 m .02846 .01475 L .03068 .01475 L .03279 .01475 L .03398 .01475 L .03527 .01475 L .03645 .01475 L .03754 .01475 L .03871 .01475 L .04 .01475 L .04065 .01475 L .04135 .01475 L .04262 .01475 L .04393 .01475 L .04516 .01475 L .04586 .01475 L .0465 .01475 L .04793 .01475 L .04917 .01475 L .05052 .01475 L .0518 .01475 L .05297 .01475 L .05411 .01476 L .05517 .01476 L .05633 .01476 L .05758 .01477 L .05889 .01477 L .06012 .01478 L .06124 .01479 L .06244 .01481 L .0637 .01482 L .06505 .01485 L .06632 .01488 L .06749 .01491 L .06878 .01496 L .0702 .01502 L .07168 .01511 L .07306 .01521 L .07453 .01535 L .07591 .01551 L .07851 .01592 L .07996 .01623 L .0813 .01658 L .08433 .01764 L .08675 .01885 L .08901 .02034 L .0915 .0225 L .09417 .02556 L .09696 .02978 L .09961 .03496 L Mistroke .10458 .04847 L .10718 .05788 L .10962 .06842 L .11419 .0929 L .11911 .12674 L .12442 .17202 L .14282 .37523 L .15316 .48556 L .15821 .52845 L .1628 .55889 L .1653 .57166 L .16766 .58123 L .17015 .58867 L .17156 .59168 L .17286 .5937 L .17417 .59503 L .1754 .59562 L .17611 .59569 L .17675 .59558 L .17746 .59527 L .17821 .59473 L .17889 .59406 L .17961 .59316 L .18092 .59106 L .18247 .5878 L .18388 .58416 L .18874 .5671 L .19389 .54276 L .2031 .48844 L .22391 .35274 L .24375 .24481 L .26185 .17439 L .27186 .14549 L .28134 .12339 L .29147 .10441 L .30225 .0884 L .31169 .07716 L .32213 .06712 L .34054 .05392 L .35062 .0485 L .35987 .04436 L .38071 .03721 L .39961 .0326 L .42031 .02891 L .43989 .02631 L .46083 .02421 L .48216 .02257 L .5023 .02137 L .54073 .01969 L .56059 .01905 L Mistroke .58162 .01849 L .61948 .01771 L .65978 .01711 L .69858 .01669 L .73982 .01634 L .77955 .01608 L .81776 .01589 L .85843 .01572 L .89758 .01559 L .93918 .01548 L .97619 .01539 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol001=oo`D006=oo`D002moo`03001oogoo00=oo`@002aoo`03001oogoo00=oo`D0 02Uoo`<000Eoo`@002Yoo`<000Eoo`D000aoo`00ogooJGoo003oOomYOol00?moofUoo`004Goo00<0 3gooOol0Ool0 0`0?Oomoo`02Ool3O18^Ool00`0?Oomoo`0cOol00`0?Oomoo`0cOol00`0?Oomoo`0cOol00`0?Oomo o`0@Ool0015oo`0300moogoo00eoo`030Imoogoo00Qoo`03O19oogoo01Qoo`03001oogoo025oo`03 0Imoogoo00moo`0300moogoo009l4S5oo`0300moogoo03=oo`0300moogoo03=oo`0300moogoo03=o o`0300moogoo011oo`004Goo00<03gooOol03Woo00<1WgooOol01goo00=l4WooOol067oo00<007oo Ool08Goo00<1WgooOol03goo00<03g`BO180Ool00`6OOomoo`08Ool00g`BOomoo`0GOol0 0`00Oomoo`0POol00`6OOomoo`0@Ool00g`BOomoo`0cOol00`0?Oomoo`0cOol00`0?Oomoo`0cOol0 0`0?Oomoo`0cOol00`0?Oomoo`0@Ool0015oo`0300moogoo00moo`030Imoogoo00Moo`03O19oogoo 01Moo`80025oo`030Imoogoo00ioo`9l4P0300moogoo03=oo`0300moogoo03=oo`0300moogoo03=o o`0300moogoo03=oo`0300moogoo011oo`004Goo00<03gooOol03goo00<1WgooOol01goo00=l4Woo Ool05goo00<007ooOol07goo00<1WgooOol03Woo00Al4WooOol03cEoo`0300moogoo03=oo`0300mo ogoo03=oo`0300moogoo03=oo`0300moogoo011oo`004Goo00<03gooOol047oo00<1WgooOol01Woo 00=l4WooOol05goo00<007ooOol07goo00<1WgooOol03Goo00El4WooOomoo`0?03Eoo`0300moogoo 03=oo`0300moogoo03=oo`0300moogoo03=oo`0300moogoo011oo`004Goo00<03gooOol047oo00<1 WgooOol01goo00=l4WooOol05Woo00<007ooOol07Woo00<1WgooOol037oo0W`B17oo00<03gooOol0 Ool00`0?Oomoo`0cOol00`0?Oomoo`0cOol00`0?Oomoo`0cOol00`0? Oomoo`0cOol00`0?Oomoo`0@Ool0015oo`0300moogoo01Ioo`030Imoogoo00=oo`03O19oogoo01Ao o`03001oogoo01Yoo`030Imoogoo00Aoo`03O19oogoo00moo`0300moogoo03=oo`0300moogoo03=o o`0300moogoo03=oo`0300moogoo03=oo`0300moogoo011oo`004Goo00<03gooOol047oo10000Woo 00<1WgooOol00P0000=oog`BOol00Woo100017oo10001goo00<007ooOol06Woo00<1WgooOol017oo 00=l4WooOol03goo00<03gooOol0Ool00g`B0Imoo`0ROol00`0?Oomoo`0c Ool00`0?Oomoo`0cOol00`0?Oomoo`0cOol00`0?Oomoo`0cOol00`0?Oomoo`0@Ool0015oo`0300mo ogoo021oo`040ImoogooO18?Ool00`00Oomoo`0>Ool00g`B0Imoo`0ROol00`0?Oomoo`0cOol00`0? Oomoo`0cOol00`0?Oomoo`0cOol00`0?Oomoo`0cOol00`0?Oomoo`0@Ool0015oo`0300moogoo021o o`040ImoogooO18?Ool2000?Ool00g`B0Imoo`0ROol00`0?Oomoo`0cOol00`0?Oomoo`0cOol00`0? Oomoo`0cOol00`0?Oomoo`0cOol00`0?Oomoo`0@Ool0015oo`0300moogoo021oo`040ImoogooO18? Ool00`00Oomoo`0>Ool00g`B0Imoo`0ROol00`0?Oomoo`0cOol00`0?Oomoo`0cOol00`0?Oomoo`0c Ool00`0?Oomoo`0cOol00`0?Oomoo`0@Ool0015oo`0300moogoo021oo`040ImoogooO18?Ool00`00 Oomoo`0>Ool00g`B0Imoo`0ROol00`0?Oomoo`0cOol00`0?Oomoo`0cOol00`0?Oomoo`0cOol00`0? Oomoo`0cOol00`0?Oomoo`0@Ool0015oo`0300moogoo025oo`030Imoog`B00moo`03001oogoo00eo o`03O19oo`6O02=oo`0300moogoo03=oo`0300moogoo03=oo`0300moogoo03=oo`0300moogoo03=o o`0300moogoo011oo`004Goo00<03gooOol047oo10001Goo0P001Goo00D0006O001l4P0000=oo`@0 00Moo`03001oogoo00eoo`03O19oo`6O02=oo`0300moogoo03=oo`0300moogoo03=oo`0300moogoo 03=oo`0300moogoo03=oo`0300moogoo011oo`004Goo00<03gooOol03goo00<007ooOol00Woo00<0 07ooOol00Woo0P001Woo00<1W`00O1800goo00<007ooOol00Woo00<007ooOol017oo00<007ooOol0 3Goo00=l4P6OOol08goo00<03gooOol0Ool00`00Oomoo`0Ool2000"], ImageRangeCache->{{{127.438, 356.813}, {517.25, 375.938}} -> {-25.0213, 0.805476, 0.115713, 0.00176053}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth] }, Open ]], Cell[TextData[StyleBox["We can represent the approximation to the normal \ using \[Alpha] = 2 and \[Beta] = 0", FontSize->12, FontColor->GrayLevel[0]]], "Text", PageWidth->PaperWidth, FontSlant->"Plain"], Cell[CellGroupData[{ Cell[BoxData[ \(pdfplt = Plot[Evaluate[{Abs[ ffx1\/m1] /. {\[Alpha] \[Rule] 2, \[Beta] \[Rule] 0, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}}], {x, \(-5\), 5}, PlotStyle -> {Hue[ .6], Hue[ .9]}, PlotRange -> All, GridLines -> Automatic]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0952381 0.0135766 2.09059 [ [.11905 .00108 -6 -9 ] [.11905 .00108 6 0 ] [.30952 .00108 -6 -9 ] [.30952 .00108 6 0 ] [.69048 .00108 -3 -9 ] [.69048 .00108 3 0 ] [.88095 .00108 -3 -9 ] [.88095 .00108 3 0 ] [.4875 .11811 -24 -4.5 ] [.4875 .11811 0 4.5 ] [.4875 .22264 -18 -4.5 ] [.4875 .22264 0 4.5 ] [.4875 .32716 -24 -4.5 ] [.4875 .32716 0 4.5 ] [.4875 .43169 -18 -4.5 ] [.4875 .43169 0 4.5 ] [.4875 .53622 -24 -4.5 ] [.4875 .53622 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 .5 r .25 Mabswid [ ] 0 setdash .11905 0 m .11905 .61803 L s .30952 0 m .30952 .61803 L s .5 0 m .5 .61803 L s .69048 0 m .69048 .61803 L s .88095 0 m .88095 .61803 L s 0 .01358 m 1 .01358 L s 0 .11811 m 1 .11811 L s 0 .22264 m 1 .22264 L s 0 .32716 m 1 .32716 L s 0 .43169 m 1 .43169 L s 0 .53622 m 1 .53622 L s 0 g .11905 .01358 m .11905 .01983 L s [(-4)] .11905 .00108 0 1 Mshowa .30952 .01358 m .30952 .01983 L s [(-2)] .30952 .00108 0 1 Mshowa .69048 .01358 m .69048 .01983 L s [(2)] .69048 .00108 0 1 Mshowa .88095 .01358 m .88095 .01983 L s [(4)] .88095 .00108 0 1 Mshowa .125 Mabswid .16667 .01358 m .16667 .01733 L s .21429 .01358 m .21429 .01733 L s .2619 .01358 m .2619 .01733 L s .35714 .01358 m .35714 .01733 L s .40476 .01358 m .40476 .01733 L s .45238 .01358 m .45238 .01733 L s .54762 .01358 m .54762 .01733 L s .59524 .01358 m .59524 .01733 L s .64286 .01358 m .64286 .01733 L s .7381 .01358 m .7381 .01733 L s .78571 .01358 m .78571 .01733 L s .83333 .01358 m .83333 .01733 L s .07143 .01358 m .07143 .01733 L s .02381 .01358 m .02381 .01733 L s .92857 .01358 m .92857 .01733 L s .97619 .01358 m .97619 .01733 L s .25 Mabswid 0 .01358 m 1 .01358 L s .5 .11811 m .50625 .11811 L s [(0.05)] .4875 .11811 1 0 Mshowa .5 .22264 m .50625 .22264 L s [(0.1)] .4875 .22264 1 0 Mshowa .5 .32716 m .50625 .32716 L s [(0.15)] .4875 .32716 1 0 Mshowa .5 .43169 m .50625 .43169 L s [(0.2)] .4875 .43169 1 0 Mshowa .5 .53622 m .50625 .53622 L s [(0.25)] .4875 .53622 1 0 Mshowa .125 Mabswid .5 .03448 m .50375 .03448 L s .5 .05539 m .50375 .05539 L s .5 .07629 m .50375 .07629 L s .5 .0972 m .50375 .0972 L s .5 .13901 m .50375 .13901 L s .5 .15992 m .50375 .15992 L s .5 .18082 m .50375 .18082 L s .5 .20173 m .50375 .20173 L s .5 .24354 m .50375 .24354 L s .5 .26445 m .50375 .26445 L s .5 .28535 m .50375 .28535 L s .5 .30626 m .50375 .30626 L s .5 .34807 m .50375 .34807 L s .5 .36898 m .50375 .36898 L s .5 .38988 m .50375 .38988 L s .5 .41079 m .50375 .41079 L s .5 .4526 m .50375 .4526 L s .5 .47351 m .50375 .47351 L s .5 .49441 m .50375 .49441 L s .5 .51532 m .50375 .51532 L s .5 .55713 m .50375 .55713 L s .5 .57804 m .50375 .57804 L s .5 .59894 m .50375 .59894 L s .25 Mabswid .5 0 m .5 .61803 L s 0 .4 1 r .5 Mabswid .02381 .01472 m .03279 .01501 L .04262 .01542 L .06244 .01659 L .07298 .01745 L .08426 .01861 L .10458 .0215 L .1148 .02345 L .12589 .02603 L .14603 .03223 L .16586 .04075 L .18689 .05313 L .20643 .0684 L .22473 .08663 L .2635 .1398 L .30472 .21974 L .34443 .31624 L .38262 .41699 L .40394 .47089 L .42327 .51498 L .44365 .5539 L .4624 .58078 L .47176 .5905 L .47653 .59444 L .48165 .59787 L .48433 .59934 L .48678 .60049 L .48927 .60145 L .49157 .60217 L .49425 .60278 L .49566 .60302 L .49639 .60311 L .49717 .60319 L .49847 .60328 L .49969 .60332 L .50039 .60332 L .50114 .6033 L .50177 .60327 L .50247 .60322 L .50379 .60309 L .505 .60291 L .50634 .60267 L .50775 .60234 L .51013 .60166 L .51274 .60069 L .51756 .59833 L .52208 .59545 L .53218 .58673 L .54303 .57398 L .5642 .53999 L Mistroke .5843 .49841 L .62255 .40342 L .66325 .2965 L .70243 .20419 L .72244 .16437 L .74406 .12777 L .7632 .10096 L .78418 .07725 L .80416 .05963 L .82524 .04553 L .84479 .03584 L .86571 .02836 L .87591 .02558 L .88699 .02308 L .89657 .02131 L .90713 .01969 L .92694 .01746 L .93779 .01657 L .94796 .01591 L .9627 .01519 L .97619 .01472 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggoo1@00 NGoo1@00?goo0`00<7oo000fOol00`00Oomoo`0jOol01@00Oomoogoo0000NGoo00D007ooOomoo`00 041oo`03001oogoo02moo`00=Woo00<007ooOol0>goo00<007ooOol0Ngoo00<007ooOol0@Goo00<0 07ooOol0;goo000ZOol60002Ool6000cOol60004Ool00`00Oomoo`1kOol00`00Oomoo`0lOol6000` Ool003=oo`04001oogoo000oOol00`00Oomoo`1kOol00`00Oomoo`0lOol01000Oomoo`00goo00@007ooOol0035oo`00=7oo00<0 07oo0000?7oo00D007ooOomoo`0007Uoo`05001oogooOol0000nOol00`00Ool0000aOol003Eoo`80 03eoo`<007]oo`<0041oo`80035oo`00ogooJGoo003oOomYOol00?moofUoo`00Ool20Il^Ool00`0?Oomoo`0nOol0 0`00Oomoo`0nOol00`0?Oomoo`0/Ool20Il@Ool00`0?Oomoo`0`Ool0035oo`0300moogoo011oo`81 Wbaoo`0300moogoo03ioo`03001oogoo03ioo`0300moogoo02]oo`030Imoogoo011oo`0300moogoo 031oo`00Ool00`0?Oomoo`0nOol00`00Oomoo`0nOol00`0?Oomoo`0>Ool00`6OOomoo`0]Ool0 0`0?Oomoo`0`Ool0035oo`0300moogoo02eoo`030Imoogoo00ioo`0300moogoo03ioo`8003moo`03 00moogoo00eoo`030Imoogoo02ioo`0300moogoo031oo`007oo00<03gooOol0<7oo000aOol00`0?Oomoo`0hOol00`6OOomoo`03 Ool00`0?Oomoo`0nOol00`00Oomoo`0nOol00`0?Oomoo`02Ool00`6OOomoo`0iOol00`0?Oomoo`0` Ool0035oo`0300moogoo03Qoo`030Imoogoo00=oo`0300moogoo03ioo`03001oogoo03ioo`0300mo ogoo009oo`030Imoogoo03Uoo`0300moogoo031oo`00Goo00<1WgooOol00Woo 00<03gooOol0?Woo0P00?goo00D03gooOomoo`6O03aoo`0300moogoo031oo`00Goo00<1WgooOol00Woo00<03gooOol0?Woo00<007ooOol0?Woo00D03gooOomoo`6O03aoo`0300mo ogoo031oo`00Woo00D1WgooOomoo`0?041oo`03001oogoo03ioo`0500moogoo Ool1W`0lOol00`0?Oomoo`0`Ool0035oo`0300moogoo03Yoo`050ImoogooOol03`10Ool00`00Oomo o`0nOol0100?Oomoo`6O?Goo00<03gooOol0<7oo000aOol00`0?Oomoo`0kOol0106OOomoo`0?9Woo 10001Goo0P001Goo1@001Goo00<007ooOol0?Woo00@03gooOol1Wceoo`0300moogoo031oo`00goo00@1WgooOol03bEoo`03001oogoo009oo`03001oogoo009oo`8000Moo`03001o ogoo00Eoo`03001oogoo03ioo`0300moo`6O03ioo`0300moogoo031oo`00goo00@1WgooOol03d1oo`0300moogoo031oo`00goo00D1WgooOomoo`0?041oo`0300mo ogoo031oo`00Goo00<007ooOol0>Goo 00<1WgooOol00Woo00<03gooOol0?Woo00<03gooOol0<7oo000aOol00`0?Oomoo`0nOol00`0?Oomo o`02Ool00`6OOomoo`0iOol00`00Oomoo`0iOol00`6OOomoo`02Ool00`0?Oomoo`0nOol00`0?Oomo o`0`Ool0035oo`0300moogoo03ioo`0300moogoo00=oo`030Imoogoo03Qoo`03001oogoo03Qoo`03 0Imoogoo00=oo`0300moogoo03ioo`0300moogoo031oo`007oo00<007ooOol0>7oo00<1WgooOol00goo00<03gooOol0?Woo00<03gooOol0 <7oo000aOol00`0?Oomoo`0nOol00`0?Oomoo`03Ool00`6OOomoo`0hOol00`00Oomoo`0hOol00`6O Oomoo`03Ool00`0?Oomoo`0nOol00`0?Oomoo`0`Ool0035oo`0300moogoo03ioo`0300moogoo00Ao o`030Imoogoo03Moo`03001oogoo03Moo`030Imoogoo00Aoo`0300moogoo03ioo`0300moogoo031o o`007oo00<1WgooOol017oo 00<03gooOol0?Woo00<03gooOol0<7oo000aOol00`0?Oomoo`0nOol00`0?Oomoo`05Ool00`6OOomo o`0fOol00`00Oomoo`0fOol00`6OOomoo`05Ool00`0?Oomoo`0nOol00`0?Oomoo`0`Ool0035oo`03 00moogoo03ioo`0300moogoo00Eoo`030Imoogoo03Ioo`03001oogoo03Ioo`030Imoogoo00Eoo`03 00moogoo03ioo`0300moogoo031oo`00Ool00`00Oomoo`02Ool00`00Oomoo`0;Ool00`00Oomoo`07Ool00`00Oomo o`03Ool00`00Oomoo`0aOol00`6OOomoo`0:Ool00`0?Oomoo`0nOol00`0?Oomoo`0`Ool000UoogH0 3`030Il03`0?00h03`0300003`0?00803`0300003`0?00/03`0300003`0?00L03`0300003`0?00<0 3`<003403`030Il03`0?07@03`Yoo`00Ool00`6OOomoo`0]Ool00`00Oomoo`0]Ool00`6OOomoo`0>Ool00`0?Oomoo`0nOol0 0`0?Oomoo`0`Ool0035oo`0300moogoo03ioo`0300moogoo00moo`030Imoogoo02aoo`03001oogoo 02aoo`030Imoogoo00moo`0300moogoo03ioo`0300moogoo031oo`00Ool00`00Oomoo`0>Ool00`6OOomoo`0]Ool0 0`0?Oomoo`0nOol00`0?Oomoo`0`Ool0035oo`0300moogoo03ioo`0300moogoo02ioo`030Imoogoo 00eoo`03001oogoo00eoo`030Imoogoo02ioo`0300moogoo03ioo`0300moogoo031oo`00"], ImageRangeCache->{{{127.438, 356.813}, {287.813, 146.5}} -> {-11.6954, 0.300547, 0.0386424, 0.00176038}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth] }, Open ]], Cell[TextData[StyleBox["Repeating the above without the gridlines and axes \ produces the illustration in Chapter 1.", FontSlant->"Plain", FontColor->GrayLevel[0]]], "Text", PageWidth->PaperWidth, FontSize->12], Cell[CellGroupData[{ Cell[BoxData[ \(bmppdf2 = Plot[Evaluate[{Abs[ ffx1\/m1] /. {\[Alpha] \[Rule] 2, \[Beta] \[Rule] 0, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}}], {x, \(-5\), 5}, Frame -> None, FrameTicks -> {False, False}, PlotStyle -> {Hue[ .6], Hue[ .9]}, PlotRange -> All, GridLines -> None, \ Axes -> None]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0952381 0.0135766 2.09059 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 .4 1 r .5 Mabswid [ ] 0 setdash .02381 .01472 m .03279 .01501 L .04262 .01542 L .06244 .01659 L .07298 .01745 L .08426 .01861 L .10458 .0215 L .1148 .02345 L .12589 .02603 L .14603 .03223 L .16586 .04075 L .18689 .05313 L .20643 .0684 L .22473 .08663 L .2635 .1398 L .30472 .21974 L .34443 .31624 L .38262 .41699 L .40394 .47089 L .42327 .51498 L .44365 .5539 L .4624 .58078 L .47176 .5905 L .47653 .59444 L .48165 .59787 L .48433 .59934 L .48678 .60049 L .48927 .60145 L .49157 .60217 L .49425 .60278 L .49566 .60302 L .49639 .60311 L .49717 .60319 L .49847 .60328 L .49969 .60332 L .50039 .60332 L .50114 .6033 L .50177 .60327 L .50247 .60322 L .50379 .60309 L .505 .60291 L .50634 .60267 L .50775 .60234 L .51013 .60166 L .51274 .60069 L .51756 .59833 L .52208 .59545 L .53218 .58673 L .54303 .57398 L .5642 .53999 L Mistroke .5843 .49841 L .62255 .40342 L .66325 .2965 L .70243 .20419 L .72244 .16437 L .74406 .12777 L .7632 .10096 L .78418 .07725 L .80416 .05963 L .82524 .04553 L .84479 .03584 L .86571 .02836 L .87591 .02558 L .88699 .02308 L .89657 .02131 L .90713 .01969 L .92694 .01746 L .93779 .01657 L .94796 .01591 L .9627 .01519 L .97619 .01472 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgWoo0P6OkGoo0`6O?7oo000lOol2 0IoYOol20IloOol003ioo`81WnEoo`81Wd5oo`00@7oo0P6OhWoo00<1WgooOol0@Goo0012Ool20IoO Ool00`6OOomoo`12Ool004Aoo`030Imoogoo0=Yoo`81WdEoo`00AGoo00<1WgooOol0f7oo00<1Wgoo Ool0AGoo0016Ool20IoGOol00`6OOomoo`16Ool004Qoo`030Imoogoo0==oo`030Imoogoo04Moo`00 BGoo00<1WgooOol0dGoo00<1WgooOol0B7oo001:Ool00`6OOomoo`3?Ool00`6OOomoo`19Ool004]o o`030Imoogoo0goo00<1WgooOol0Tgoo002EOol00`6OOomoo`0iOol00`6OOomoo`2DOol009Eoo`03 0Imoogoo03Uoo`030Imoogoo09Aoo`00UWoo00<1WgooOol0>7oo00<1WgooOol0U7oo002FOol00`6O Oomoo`0gOol00`6OOomoo`2EOol009Moo`030Imoogoo03Ioo`030Imoogoo09Eoo`00Ugoo00<1Wgoo Ool0=Goo00<1WgooOol0UWoo002HOol00`6OOomoo`0dOol00`6OOomoo`2FOol009Qoo`030Imoogoo 03=oo`030Imoogoo09Moo`00V7oo00<1WgooOol0"], ImageRangeCache->{{{127.438, 356.813}, {562, 420.688}} -> {-11.1189, 0.873588, 0.0367378, 0.00167361}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth] }, Open ]], Cell[TextData[StyleBox["Below is a symmetric, stable distribution", FontSlant->"Plain", FontColor->GrayLevel[0]]], "Text", PageWidth->PaperWidth, FontSize->12], Cell[CellGroupData[{ Cell[BoxData[ \(skew0 = Plot[Evaluate[{Abs[ ffx1\/m1] /. {\[Alpha] \[Rule] 1.1, \[Beta] \[Rule] 0, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}}], {x, \(-6\), 6}, PlotRange -> All, GridLines -> None, Frame -> None, Axes -> None, PlotStyle -> {Hue[1]}]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0793651 -0.000792581 1.96647 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 1 0 0 r .5 Mabswid [ ] 0 setdash .02381 .01472 m .06244 .01769 L .10458 .022 L .14415 .02753 L .18221 .03489 L .20178 .0398 L .22272 .04619 L .24259 .05367 L .26416 .06386 L .28492 .07637 L .30409 .0911 L .32282 .10946 L .34344 .13581 L .36285 .1685 L .38373 .2151 L .40486 .27757 L .42495 .35281 L .46315 .51853 L .47328 .55593 L .47825 .57116 L .48282 .5829 L .4881 .59337 L .49088 .59744 L .4923 .59912 L .49382 .60061 L .49511 .60162 L .49628 .60233 L .49746 .60286 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60291 L .50306 .60265 L .50379 .6023 L .50501 .60153 L .50614 .60064 L .50871 .59795 L .51121 .59447 L .51389 .58984 L .52314 .56715 L .53407 .52951 L .544 .48862 L .58398 .3175 L .6023 .25451 L .62244 .1999 L .64232 .1589 L .66336 .12628 L .68281 .10346 L .7037 .08468 L .72488 .07008 L Mistroke .74498 .05924 L .78322 .04424 L .80294 .03853 L .82392 .03353 L .86556 .02601 L .90568 .02083 L .94428 .01712 L .97619 .01472 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgmoo`El03Uoo`00>goo17`0igoo17`0?Woo000o Ool6O03MOol4O012Ool004Eoo`El0=Eoo`=l04Ioo`00BWoo0W`0cgoo17`0BGoo001Ool00g`0Oomoo`17Ool00g`0Oomoo`2=Ool008io o`03O01oogoo04Moo`03O01oogoo08eoo`00Sgoo00=l07ooOol0AGoo00=l07ooOol0SWoo002?Ool0 0g`0Oomoo`15Ool00g`0Oomoo`2>Ool008moo`03O01oogoo04Eoo`03O01oogoo08ioo`00T7oo00=l 07ooOol0@goo00=l07ooOol0Sgoo002@Ool00g`0Oomoo`13Ool00g`0Oomoo`2?Ool0091oo`03O01o ogoo04=oo`03O01oogoo08moo`00TGoo00=l07ooOol0@Woo00=l07ooOol0Sgoo002AOol00g`0Oomo o`11Ool00g`0Oomoo`2@Ool0095oo`03O01oogoo045oo`03O01oogoo091oo`00TWoo00=l07ooOol0 @7oo00=l07ooOol0T7oo002BOol00g`0Oomoo`0oOol00g`0Oomoo`2AOol0099oo`03O01oogoo03mo o`03O01oogoo095oo`00TWoo00=l07ooOol0?goo00=l07ooOol0TGoo002COol00g`0Oomoo`0mOol0 0g`0Oomoo`2BOol009=oo`03O01oogoo03eoo`03O01oogoo099oo`00Tgoo00=l07ooOol0?Goo00=l 07ooOol0TWoo002COol00g`0Oomoo`0mOol00g`0Oomoo`2BOol009Aoo`03O01oogoo03]oo`03O01o ogoo09=oo`00U7oo00=l07ooOol0>goo00=l07ooOol0Tgoo002DOol00g`0Oomoo`0kOol00g`0Oomo o`2COol009Aoo`03O01oogoo03Yoo`03O01oogoo09Aoo`00UGoo00=l07ooOol0>Goo00=l07ooOol0 U7oo002EOol00g`0Oomoo`0iOol00g`0Oomoo`2DOol009Eoo`03O01oogoo03Uoo`03O01oogoo09Ao o`00UWoo00=l07ooOol0=goo00=l07ooOol0UGoo002FOol00g`0Oomoo`0gOol00g`0Oomoo`2EOol0 09Ioo`03O01oogoo03Moo`03O01oogoo09Eoo`00UWoo00=l07ooOol0=goo00=l07ooOol0UGoo002G Ool00g`0Oomoo`0eOol00g`0Oomoo`2FOol009Moo`03O01oogoo03Eoo`03O01oogoo09Ioo`00Ugoo 00=l07ooOol0=Goo00=l07ooOol0UWoo002GOol00g`0Oomoo`0eOol00g`0Oomoo`2FOol009Qoo`03 O01oogoo03=oo`03O01oogoo09Moo`00V7oo00=l07ooOol0Ool00g`0Oomoo`2ZOol00:Yoo`03O01oogoo00ioo`03O01oogoo 0:Yoo`00Zgoo00=l07ooOol03Goo00=l07ooOol0ZWoo002[Ool00g`0Oomoo`0"], ImageRangeCache->{{{127.438, 356.813}, {287.813, 146.5}} -> {-13.3427, 0.326226, 0.0440853, 0.00177925}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth] }, Open ]], Cell[TextData[StyleBox["We can change the parameters to show a right \"fat \ tail\" fpr the stable distribution with a positive skew, below.", FontSlant->"Plain", FontColor->GrayLevel[0]]], "Text", PageWidth->PaperWidth, FontSize->12], Cell[CellGroupData[{ Cell[BoxData[ \(bmppdf3 = Plot[Evaluate[{Abs[ ffx1\/m1] /. {\[Alpha] \[Rule] 1.1, \[Beta] \[Rule] .75, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}}], {x, \(-6\), 6}, Frame -> None, FrameTicks -> {False, False}, PlotStyle -> {Hue[ .6], Hue[ .9]}, PlotRange -> All, GridLines -> None, \ Axes -> None]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0793651 0.0110312 2.0411 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 .4 1 r .5 Mabswid [ ] 0 setdash .02381 .01472 m .06244 .01543 L .08255 .01589 L .10458 .01649 L .14415 .01792 L .16372 .01885 L .18466 .02009 L .20597 .02171 L .22611 .0237 L .24608 .02633 L .26452 .02965 L .28325 .0344 L .29389 .03807 L .30387 .04248 L .31425 .04849 L .32412 .05618 L .33298 .0655 L .34264 .07937 L .35296 .1001 L .36232 .12575 L .37311 .16502 L .38329 .21195 L .42184 .43953 L .43215 .49515 L .44178 .53817 L .45182 .57181 L .45714 .58467 L .4599 .58999 L .46284 .59463 L .46535 .59779 L .46669 .59917 L .46813 .60043 L .46944 .60138 L .47065 .60208 L .4718 .6026 L .47302 .603 L .47371 .60315 L .47434 .60325 L .47507 .60331 L .47575 .60332 L .47698 .60322 L .47767 .60309 L .4783 .60294 L .47964 .60248 L .48111 .60179 L .48265 .60085 L .48408 .59979 L .48915 .59464 L .49378 .58819 L .5042 .56864 L Mistroke .52323 .52047 L .54396 .45964 L .58466 .34469 L .62384 .25716 L .64386 .22196 L .66548 .1902 L .7056 .14518 L .72557 .12804 L .74665 .11288 L .78468 .09146 L .82515 .07478 L .86411 .06286 L .90553 .05332 L .94542 .04628 L .97619 .04193 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00`6OOomoo`19Ool00`6OOomoo`2;Ool008ioo`030Imoogoo04Uoo`030Imo ogoo08]oo`00SWoo00<1WgooOol0B7oo00<1WgooOol0S7oo002>Ool00`6OOomoo`18Ool00`6OOomo o`2goo00<1WgooOol0UGoo002BOol00`6OOomoo`0k Ool00`6OOomoo`2EOol0099oo`030Imoogoo03]oo`030Imoogoo09Eoo`00TWoo00<1WgooOol0>Woo 00<1WgooOol0UWoo002BOol00`6OOomoo`0jOol00`6OOomoo`2FOol0099oo`030Imoogoo03Yoo`03 0Imoogoo09Ioo`00Tgoo00<1WgooOol0>7oo00<1WgooOol0Ugoo002COol00`6OOomoo`0hOol00`6O Oomoo`2GOol009=oo`030Imoogoo03Qoo`030Imoogoo09Moo`00Tgoo00<1WgooOol0=goo00<1Wgoo Ool0V7oo002COol00`6OOomoo`0gOol00`6OOomoo`2HOol009=oo`030Imoogoo03Moo`030Imoogoo 09Qoo`00U7oo00<1WgooOol0=Goo00<1WgooOol0VGoo002DOol00`6OOomoo`0eOol00`6OOomoo`2I Ool009Aoo`030Imoogoo03Eoo`030Imoogoo09Uoo`00U7oo00<1WgooOol0=7oo00<1WgooOol0VWoo 002DOol00`6OOomoo`0dOol00`6OOomoo`2JOol009Aoo`030Imoogoo03Aoo`030Imoogoo09Yoo`00 UGoo00<1WgooOol0"], ImageRangeCache->{{{127.438, 356.813}, {578.75, 437.438}} -> {-13.3427, 0.931908, 0.0440853, 0.00171419}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth] }, Open ]], Cell["\<\ Plotting them together, we can illustrate the additional variation exposed by \ heavy tails that is \"cut off\" by the normal tails\ \>", "Text", PageWidth->PaperWidth, FontSize->12, FontSlant->"Plain", FontColor->GrayLevel[0]], Cell[CellGroupData[{ Cell[BoxData[ \(hvysym = FilledPlot[{Evaluate[{Abs[ ffx1\/m1] /. {\[Alpha] \[Rule] 2, \[Beta] \[Rule] 0, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}}\ ], Evaluate[{Abs[ ffx1\/m1] /. {\[Alpha] \[Rule] 1.1, \[Beta] \[Rule] 0, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}}]}, {x, \(-6\), 6}, PlotRange -> All, Epilog\ -> \ {Arrow[{4, \ .13}, \ {4, .01}], Arrow[{\(-4\), \ .13}, \ {\(-4\), .01}], Arrow[{\(-3\), .25}, \ {\(-1.4\), .18}], Arrow[{ .5, \ .04}, \ {1, .15}], \n\ \ \ \ \ Text["\", \ {3.7, \ .17}, \ {0, \ \(- .5\)}], Text["\", \ {3.7, \ .15}, \ {0, \ \(- .5\)}], \n\ \ \ \ \ \ Text["\", \ {\(-3.7\), \ .17}, \ {0, \ \(- .5\)}], Text["\", \ {\(-3.7\), \ .15}, \ {0, \ \(- .5\)}], Text["\", {\(-3\), .25}, {0, \(- .5\)}], Text["\", { .4, .02}, {0, \(- .5\)}]}, GridLines -> None, \ Frame -> None, Axes -> None, PlotStyle -> {{Hue[ .3], Hue[1]}}]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0 1 0 0.618034 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.05 0.0125 moveto 0 0 lineto -0.05 -0.0125 lineto fill -0.05 0.0125 moveto 0 0 lineto -0.05 -0.0125 lineto -0.05 0.0125 lineto stroke } ifelse grestore } def % End of user PostScript % Start of sub-graphic p 0 0 1 0.618034 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0793651 0.0146484 1.91621 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 1 0 0 r .5 Mabswid [ ] 0 setdash .02381 .01472 m .03279 .01474 L .04262 .01478 L .05288 .01484 L .06244 .01492 L .0731 .01504 L .0828 .01519 L .094 .01543 L .10458 .01574 L .11428 .01612 L .12455 .01666 L .13333 .01725 L .14299 .01808 L .15313 .01921 L .1624 .02051 L .17311 .02243 L .18328 .02474 L .19287 .02744 L .20309 .03099 L .22147 .03952 L .23176 .04574 L .24289 .05385 L .26306 .07287 L .283 .09804 L .30406 .13243 L .34203 .21542 L .38246 .32703 L .42136 .43756 L .44118 .48583 L .45162 .50725 L .46273 .5262 L .47256 .53929 L .47816 .54507 L .48342 .54934 L .48576 .55087 L .48823 .55224 L .49036 .55321 L .49264 .55404 L .49392 .55441 L .49509 .55469 L .49627 .5549 L .49738 .55505 L .49868 .55516 L .49987 .5552 L .50118 .55517 L .50184 .55513 L .50257 .55506 L .50386 .55488 L .50506 .55465 L .50638 .55433 L Mistroke .50778 .5539 L .51038 .55289 L .51273 .55173 L .51752 .54866 L .52202 .5449 L .53206 .53359 L .54291 .51711 L .56289 .47667 L .58397 .42326 L .62199 .3141 L .66247 .20426 L .70143 .12266 L .72271 .09014 L .74284 .06669 L .76279 .04952 L .78122 .03807 L .79992 .02986 L .81056 .02641 L .82054 .02381 L .8304 .02175 L .84076 .02003 L .85047 .01878 L .85928 .01787 L .86885 .01709 L .87906 .01645 L .88852 .016 L .89744 .01567 L .90719 .0154 L .91749 .01518 L .92629 .01505 L .93596 .01493 L .94611 .01485 L .95537 .01479 L .96049 .01477 L .96606 .01475 L .97619 .01472 L Mfstroke .02381 .02976 m .06244 .03266 L .10458 .03686 L .14415 .04225 L .18221 .04942 L .20178 .0542 L .22272 .06043 L .24259 .06772 L .26416 .07764 L .28492 .08984 L .30409 .10419 L .32282 .12208 L .34344 .14775 L .36285 .17961 L .38373 .22503 L .40486 .2859 L .42495 .35921 L .46315 .5207 L .47328 .55714 L .47825 .57198 L .48282 .58342 L .4881 .59363 L .49088 .59759 L .4923 .59923 L .49382 .60068 L .49511 .60166 L .49628 .60236 L .49746 .60287 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60292 L .50306 .60267 L .50379 .60232 L .50501 .60158 L .50614 .60071 L .50871 .59809 L .51121 .5947 L .51389 .59018 L .52314 .56807 L .53407 .5314 L .544 .49155 L .58398 .3248 L .6023 .26343 L .62244 .21021 L .64232 .17026 L .66336 .13847 L .68281 .11624 L .7037 .09794 L .72488 .0837 L Mistroke .74498 .07314 L .78322 .05853 L .80294 .05297 L .82392 .0481 L .86556 .04076 L .90568 .03572 L .94428 .0321 L .97619 .02976 L Mfstroke 0 1 1 r .02381 .01472 m .03279 .01474 L .04262 .01478 L .05288 .01484 L .06244 .01492 L .0731 .01504 L .0828 .01519 L .094 .01543 L .10458 .01574 L .11428 .01612 L .12455 .01666 L .13333 .01725 L .14299 .01808 L .15313 .01921 L .1624 .02051 L .17311 .02243 L .18328 .02474 L .19287 .02744 L .20309 .03099 L .22147 .03952 L .23176 .04574 L .24289 .05385 L .26306 .07287 L .283 .09804 L .30406 .13243 L .34203 .21542 L .38246 .32703 L .42136 .43756 L .44118 .48583 L .45162 .50725 L .46273 .5262 L .47256 .53929 L .47816 .54507 L .48342 .54934 L .48576 .55087 L .48823 .55224 L .49036 .55321 L .49264 .55404 L .49392 .55441 L .49509 .55469 L .49627 .5549 L .49738 .55505 L .49868 .55516 L .49987 .5552 L .50118 .55517 L .50184 .55513 L .50257 .55506 L .50386 .55488 L .50506 .55465 L .50638 .55433 L .50778 .5539 L .51038 .55289 L .51273 .55173 L .51752 .54866 L .52202 .5449 L .53206 .53359 L .54291 .51711 L .56289 .47667 L .58397 .42326 L .62199 .3141 L .66247 .20426 L .70143 .12266 L .72271 .09014 L .74284 .06669 L .76279 .04952 L .78122 .03807 L .79992 .02986 L .81056 .02641 L .82054 .02381 L .8304 .02175 L .84076 .02003 L .85047 .01878 L .85928 .01787 L .86885 .01709 L .87906 .01645 L .88852 .016 L .89744 .01567 L .90719 .0154 L .91749 .01518 L .92629 .01505 L .93596 .01493 L .94611 .01485 L .95537 .01479 L .96049 .01477 L .96606 .01475 L .97619 .01472 L .97619 .02976 L .94428 .0321 L .90568 .03572 L .86556 .04076 L .82392 .0481 L .80294 .05297 L .78322 .05853 L .74498 .07314 L .72488 .0837 L .7037 .09794 L .68281 .11624 L .66336 .13847 L .64232 .17026 L .62244 .21021 L .6023 .26343 L .58398 .3248 L .544 .49155 L .53407 .5314 L .52314 .56807 L .51389 .59018 L .51121 .5947 L .50871 .59809 L .50614 .60071 L .50501 .60158 L .50379 .60232 L .50306 .60267 L .50239 .60292 L .50107 .60324 L .49987 .60332 L .49857 .60318 L .49746 .60287 L .49628 .60236 L .49511 .60166 L .49382 .60068 L .4923 .59923 L .49088 .59759 L .4881 .59363 L .48282 .58342 L .47825 .57198 L .47328 .55714 L .46315 .5207 L .42495 .35921 L .40486 .2859 L .38373 .22503 L .36285 .17961 L .34344 .14775 L .32282 .12208 L .30409 .10419 L .28492 .08984 L .26416 .07764 L .24259 .06772 L .22272 .06043 L .20178 .0542 L .18221 .04942 L .14415 .04225 L .10458 .03686 L .06244 .03266 L .02381 .02976 L F 1 0 0 r .02381 .01472 m .03279 .01474 L .04262 .01478 L .05288 .01484 L .06244 .01492 L .0731 .01504 L .0828 .01519 L .094 .01543 L .10458 .01574 L .11428 .01612 L .12455 .01666 L .13333 .01725 L .14299 .01808 L .15313 .01921 L .1624 .02051 L .17311 .02243 L .18328 .02474 L .19287 .02744 L .20309 .03099 L .22147 .03952 L .23176 .04574 L .24289 .05385 L .26306 .07287 L .283 .09804 L .30406 .13243 L .34203 .21542 L .38246 .32703 L .42136 .43756 L .44118 .48583 L .45162 .50725 L .46273 .5262 L .47256 .53929 L .47816 .54507 L .48342 .54934 L .48576 .55087 L .48823 .55224 L .49036 .55321 L .49264 .55404 L .49392 .55441 L .49509 .55469 L .49627 .5549 L .49738 .55505 L .49868 .55516 L .49987 .5552 L .50118 .55517 L .50184 .55513 L .50257 .55506 L .50386 .55488 L .50506 .55465 L .50638 .55433 L Mistroke .50778 .5539 L .51038 .55289 L .51273 .55173 L .51752 .54866 L .52202 .5449 L .53206 .53359 L .54291 .51711 L .56289 .47667 L .58397 .42326 L .62199 .3141 L .66247 .20426 L .70143 .12266 L .72271 .09014 L .74284 .06669 L .76279 .04952 L .78122 .03807 L .79992 .02986 L .81056 .02641 L .82054 .02381 L .8304 .02175 L .84076 .02003 L .85047 .01878 L .85928 .01787 L .86885 .01709 L .87906 .01645 L .88852 .016 L .89744 .01567 L .90719 .0154 L .91749 .01518 L .92629 .01505 L .93596 .01493 L .94611 .01485 L .95537 .01479 L .96049 .01477 L .96606 .01475 L .97619 .01472 L Mfstroke .02381 .02976 m .06244 .03266 L .10458 .03686 L .14415 .04225 L .18221 .04942 L .20178 .0542 L .22272 .06043 L .24259 .06772 L .26416 .07764 L .28492 .08984 L .30409 .10419 L .32282 .12208 L .34344 .14775 L .36285 .17961 L .38373 .22503 L .40486 .2859 L .42495 .35921 L .46315 .5207 L .47328 .55714 L .47825 .57198 L .48282 .58342 L .4881 .59363 L .49088 .59759 L .4923 .59923 L .49382 .60068 L .49511 .60166 L .49628 .60236 L .49746 .60287 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60292 L .50306 .60267 L .50379 .60232 L .50501 .60158 L .50614 .60071 L .50871 .59809 L .51121 .5947 L .51389 .59018 L .52314 .56807 L .53407 .5314 L .544 .49155 L .58398 .3248 L .6023 .26343 L .62244 .21021 L .64232 .17026 L .66336 .13847 L .68281 .11624 L .7037 .09794 L .72488 .0837 L Mistroke .74498 .07314 L .78322 .05853 L .80294 .05297 L .82392 .0481 L .86556 .04076 L .90568 .03572 L .94428 .0321 L .97619 .02976 L Mfstroke 0 g .81746 .26376 m .81746 .03381 L s % Start of user PostScript 4. 0.13 4. 0.01 MAarrowhead1 % End of user PostScript .18254 .26376 m .18254 .03381 L s % Start of user PostScript -4. 0.13 -4. 0.01 MAarrowhead1 % End of user PostScript .2619 .4937 m .38889 .35957 L s % Start of user PostScript -3. 0.25 -1.4 0.18 MAarrowhead1 % End of user PostScript .53968 .0913 m .57937 .30208 L s % Start of user PostScript 0.5 0.04 1. 0.15 MAarrowhead1 % End of user PostScript gsave .79365 .3404 -93.0938 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.188 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (Additional) show 123.188 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .79365 .30208 -90 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (Variation) show 117.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .20635 .3404 -93.0938 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.188 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (Additional) show 123.188 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .20635 .30208 -90 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (Variation) show 117.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .2619 .4937 -81 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (normal) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .53175 .05297 -93 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (heavy) show 99.000 13.000 moveto (tail) show 123.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0 0 1 0.618034 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0793651 0.0146484 1.91621 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgQoo`Al0383o`Yoo`00 27oo>0?o17`0hGoo0g`0=P?o2Woo0008Ooll0ol3O03JOol4O00i0ol:Ool000Qoo`Ml03P3o`=l0=Ao o`=l03P3o`Il00Uoo`003goo3g`08`?o00<000?o0ol01P?o0W`0d7oo0W`01`?o00<000?o0ol090?o 3G`03goo000NOol;O00H0ol00`000ol3o`080ol2O030ol2O031Ool2O00>0ol30004 0ol8O00eOol003]oo`Al00040ol00000000@0ol00g`0Oomoo`2lOol2O00@0ol30004O00mOol003mo o`03O000000000800103o`9l0;]oo`03O003o`?o00h3o`03O00000000080045oo`00?goo1@000g`0 3`?o0W`0Hgoo0`00DWoo00=l00?o0ol02`?o17`000=oo`0000000`00@7oo000oOol50003Ool3O00> 0ol00g`0Oomoo`1ROol00`00Oomoo`1?Ool00g`00ol3o`080ol4O005Ool50010Ool003moo`D000Io o`Al00/3o`03O01oogoo03ioo`<00004Ool000000002Ool50003Ool300000goo00000003Ool20007 Ool00`00Oomoo`09Ool30004Ool300000goo00000002Ool50003Ool5000XOol2O0080ol3O008Ool6 0010Ool003moo`H000Uoo`Al00P3o`03O01oogoo03ioo`05001oogooOol00002Ool00`00Oomoo`05 Ool01000Oomoogoo0P0017oo0P001Woo00<007oo00002Goo00D007ooOomoo`00009oo`04001oogoo Ool20005Ool00`00Oomoo`05Ool00`00Oomoo`0WOol00g`00ol3o`060ol2O00;Ool60010Ool003mo o`H000eoo`Al00D3o`03O01oogoo03eoo`05001oogooOol00002Ool00`00Oomoo`05Ool00`00Oomo o`02Ool01@00Oomoogoo00000Woo00<007ooOol00goo00<007oo00002Goo00<007ooOol017oo00<0 07ooOol00Woo00<007ooOol00goo00<007ooOol01Goo00<007ooOol09Woo00=l00?o0ol010?o0g`0 3Goo1P00@7oo000nOol7000AOol2O0040ol00g`0Oomoo`0lOol01@00Oomoogoo00000Woo1P000goo 1@000goo00@007ooOol000Aoo`05001oogooOol00008Ool00`00Oomoo`05Ool50005Ool00`00Oomo o`05Ool00`00Oomoo`0UOol00g`00ol3o`020ol3O00@Ool7000oOol003ioo`P0019oo`9l00<3o`03 O01oogoo03]oo`80009oo`04001oogoo0004Ool01000Oomoo`0017oo00@007ooOol000Aoo`05001o ogooOol00003Ool00`00Oomoo`06Ool00`00Oomoo`04Ool00`00Oomoo`02Ool00`00Oomoo`03Ool0 0`00Oomoo`05Ool00`00Oomoo`0TOol017`00ol3o`?o0W`04Woo2000?goo000nOol8000DOol2O002 0ol00g`0Oomoo`0jOol01000Ool0000017oo100017oo10000Woo0`000Woo0`0000Eoo`00000007oo 00<000Ioo`D000Aoo`@000Aoo`<000Moo`03001oogoo02=oo`03O003o`?o009l01Aoo`P003moo`00 ?Woo20005Woo0W`000<3og`0Ool0>Woo00<007ooOol0:Woo00<007ooOol05goo00<007ooOol08Woo 00Al00?oO01l01Ioo`P003moo`00?Goo2@0067oo00=l00?oO000>Goo0P00?Woo00<007ooOol017oo 0P008goo0g`067oo2@00?Woo000mOol:000HOol2O02TOol2O00IOol:000nOol003eoo`X001Yoo`9l 0:5oo`9l01Yoo`X003ioo`00@Goo00<007ooOol07Woo0g`0WGoo0g`087oo00<007ooOol0@7oo0011 Ool00`00Oomoo`0OOol017`00oml07`0VWoo00=l00?oO0008Goo00<007ooOol0@7oo0011Ool00`00 Oomoo`0OOol017`00ol3o`?o0W`0F7oo00<007ooOol0>goo0W`000<3og`0Ool08Goo00<007ooOol0 @7oo0011Ool00`00Oomoo`0POol00g`00ol3o`020ol00g`0Oomoo`1EOol00`00Oomoo`0iOol2O003 0ol00g`0Oomoo`0POol00`00Oomoo`10Ool0045oo`03001oogoo025oo`03O003o`?o0083o`03O01o ogoo05Aoo`03001oogoo03Qoo`03O003o`?o0083o`03O01oogoo025oo`03001oogoo041oo`00@Goo 00<007ooOol08Woo00=l00?o0ol00P?o0W`0EGoo00<007ooOol0=Woo00=l00?o0ol00P?o00=l07oo Ool08Woo00<007ooOol0@7oo0011Ool00`00Oomoo`0ROol00g`00ol3o`040ol00g`0Oomoo`1BOol0 0`00Oomoo`0eOol00g`00ol3o`030ol00g`0Oomoo`0ROol00`00Oomoo`10Ool0045oo`03001oogoo 02=oo`03O003o`?o00@3o`03O01oogoo055oo`03001oogoo03Aoo`03O003o`?o00<3o`03O01oogoo 02=oo`03001oogoo041oo`00@Goo00<007ooOol08goo00=l00?o0ol01@?o00=l07ooOol0D7oo00<0 07ooOol07oo00<007ooOol0@7oo0011 Ool00`00Oomoo`0hOol00g`00ol3o`0:0ol00g`0Oomoo`0nOol00`00Oomoo`0?Ool00g`00ol3o`0; 0ol00g`0Oomoo`0hOol00`00Oomoo`10Ool0045oo`03001oogoo03Qoo`03O003o`?o00/3o`03O01o ogoo03eoo`03001oogoo00moo`03O003o`?o00X3o`03O01oogoo03Uoo`03001oogoo041oo`00@Goo 00<007ooOol0>Goo00=l00?o0ol02P?o00=l07ooOol0?Woo00<007ooOol03Woo00=l00?o0ol02P?o 00=l07ooOol0>Goo00<007ooOol0@7oo0011Ool00`00Oomoo`0iOol00g`00ol3o`0:0ol00g`0Oomo o`0nOol00`00Oomoo`0=Ool00g`00ol3o`0;0ol00g`0Oomoo`0iOol00`00Oomoo`10Ool0045oo`03 001oogoo03Uoo`03O003o`?o00/3o`03O01oogoo03eoo`03001oogoo00eoo`03O003o`?o00X3o`03 O01oogoo03Yoo`03001oogoo041oo`00@Goo00<007ooOol0>Woo00=l00?o0ol02P?o00=l07ooOol0 ?Goo00<007ooOol03Goo00=l00?o0ol02P?o00=l07ooOol0>Woo00<007ooOol0@7oo0011Ool00`00 Oomoo`0jOol00g`00ol3o`0;0ol00g`0Oomoo`0lOol00`00Oomoo`0goo00=l00?o0ol02P?o00=l07ooOol0?Goo00<007ooOol00P0027oo00=l00?o0ol02`?o00=l 07ooOol0>goo00<007ooOol0@7oo0011Ool00`00Oomoo`0kOol00g`00ol3o`0;0ol00g`0Oomoo`0k Ool60008Ool00g`00ol3o`0;0ol00g`0Oomoo`0kOol00`00Oomoo`10Ool0045oo`03001oogoo03ao o`03O003o`?o00X3o`03O01oogoo03Qoo`T000Qoo`03O003o`?o00X3o`03O01oogoo03aoo`03001o ogoo041oo`00@Goo00<007ooOol0?7oo00=l00?o0ol02P?o00=l07ooOol0>7oo2@001goo00=l00?o 0ol02`?o00=l07ooOol0?7oo00<007ooOol0@7oo0011Ool00`00Oomoo`0lOol00g`00ol3o`0;0ol0 0g`0Oomoo`0hOol80007Ool00g`00ol3o`0;0ol00g`0Oomoo`0lOol00`00Oomoo`10Ool0045oo`03 001oogoo03eoo`03O003o`?o00X3o`03O01oogoo03Qoo`P000Moo`03O003o`?o00X3o`03O01oogoo 03eoo`03001oogoo041oo`00PGoo00=l00?o0ol02P?o00=l07ooOol0>Goo1`001Woo00=l00?o0ol0 2`?o00=l07ooOol0P7oo0021Ool00g`00ol3o`0;0ol00g`0Oomoo`0hOol70006Ool00g`00ol3o`0; 0ol00g`0Oomoo`20Ool0089oo`03O003o`?o00X3o`03O01oogoo03Uoo`H000Ioo`03O003o`?o00X3 o`03O01oogoo085oo`00PWoo00=l00?o0ol02`?o00=l07ooOol0>7oo1@001Woo00=l00?o0ol02`?o 00=l07ooOol0PGoo0023Ool00g`00ol3o`0:0ol00g`0Oomoo`0hOol50006Ool00g`00ol3o`0;0ol0 0g`0Oomoo`21Ool008=oo`03O003o`?o00X3o`03O01oogoo03Uoo`@000Ioo`03O003o`?o00X3o`03 O01oogoo089oo`00Pgoo00=l00?o0ol02`?o00=l07ooOol0>7oo10001Goo00=l00?o0ol02`?o00=l 07ooOol0PWoo0024Ool00g`00ol3o`0:0ol00g`0Oomoo`0iOol30005Ool00g`00ol3o`0:0ol00g`0 Oomoo`23Ool008Aoo`03O003o`?o00X3o`03O01oogoo03Uoo`<000Eoo`03O003o`?o00X3o`03O01o ogoo08=oo`00Q7oo00=l00?o0ol02`?o00=l07ooOol0>Goo0P0017oo00=l00?o0ol02`?o00=l07oo Ool0Pgoo0025Ool00g`00ol3o`0:0ol00g`0Oomoo`0iOol20004Ool00g`00ol3o`0:0ol00g`0Oomo o`24Ool008Eoo`03O003o`?o00X3o`03O01oogoo03Yoo`03001oogoo009oo`03O003o`?o00X3o`03 O01oogoo08Aoo`00QWoo00=l00?o0ol02@?o00=l07ooOol0>Woo00<007ooOol00Woo00=l00?o0ol0 2P?o00=l07ooOol0Q7oo0026Ool00g`00ol3o`0:0ol00g`0Oomoo`0mOol00g`00ol3o`0:0ol00g`0 Oomoo`25Ool002]oo`8000Eoo`<00004Ool00000Ool50004Ool50003Ool300000goo00000003Ool3 0004Ool50003Ool40003Ool3000017oo000000005Woo00=l00?o0ol02P?o00=l07ooOol0?Goo00=l 00?o0ol02P?o00=l07ooOol06Woo0P001Goo0`0000Aoo`00001oo`D000Aoo`D000=oo`<00003Ool0 000000=oo`<000Aoo`D000=oo`@000=oo`<00004Ool00000000VOol002]oo`8000Aoo`04001oogoo Ool20003Ool00`00Oomoo`07Ool00`00Oomoo`02Ool01000Oomoogoo0P000goo00D007ooOomoo`00 00Eoo`03001oogoo009oo`03001oogoo009oo`05001oogooOol00003Ool00`00Oomoo`0FOol00g`0 0ol3o`090ol00g`0Oomoo`0mOol00g`00ol3o`0:0ol00g`0Oomoo`0JOol20004Ool01000Oomoogoo 0P000goo00<007ooOol01goo00<007ooOol00Woo00@007ooOomoo`8000=oo`05001oogooOol00005 Ool00`00Oomoo`02Ool00`00Oomoo`02Ool01@00Oomoogoo00000goo00<007ooOol09Goo000ZOol0 1000Oomoo`000goo00<007ooOol00Woo00D007ooOomoo`0000Uoo`03001oogoo009oo`03001oogoo 009oo`05001oogooOol00009Ool00`00Oomoo`02Ool00`00Oomoo`02Ool01@00Oomoogoo00000goo 00<007ooOol05Woo00=l00?o0ol02@?o00=l07ooOol0?7oo00=l00?o0ol02P?o00=l07ooOol06Woo 00@007ooOol000=oo`03001oogoo009oo`05001oogooOol00009Ool00`00Oomoo`02Ool00`00Oomo o`02Ool01@00Oomoogoo00002Goo00<007ooOol00Woo00<007ooOol00Woo00D007ooOomoo`0000=o o`03001oogoo02Eoo`00:Woo00@007ooOol000Aoo`D000=oo`03001oogoo00Moo`03001oogoo00=o o`D000=oo`03001oogoo00Moo`03001oogoo009oo`03001oogoo009oo`05001oogooOol00003Ool0 0`00Oomoo`0FOol00g`00ol3o`0:0ol00g`0Oomoo`0kOol00g`00ol3o`0:0ol00g`0Oomoo`0JOol0 1000Oomoo`0017oo1@000goo00<007ooOol01goo00<007ooOol00goo1@000goo00<007ooOol01goo 00<007ooOol00Woo00<007ooOol00Woo00D007ooOomoo`0000=oo`03001oogoo02Eoo`00:Woo00@0 07ooOol000=oo`03001oogoo009oo`04001oogooOol20008Ool00`00Oomoo`02Ool00`00Oomoo`02 Ool01@00Oomoogoo00002Goo00<007ooOol00Woo00<007ooOol00Woo00@007ooOomoo`80009oo`03 001oogoo01Moo`03O003o`?o00T3o`03O01oogoo03]oo`03O003o`?o00X3o`03O01oogoo01Yoo`04 001oogoo0003Ool00`00Oomoo`02Ool01000Oomoogoo0P0027oo00<007ooOol00Woo00<007ooOol0 0Woo00D007ooOomoo`0000Uoo`03001oogoo009oo`03001oogoo009oo`04001oogooOol20002Ool0 0`00Oomoo`0UOol002Uoo`03001oogoo009oo`04001oogooOol40003Ool2000017oo000000000goo 0`001Goo10000goo1@0017oo0`001Goo10000goo0P0000=oo`0000006Woo00=l00?o0ol02@?o00=l 07ooOol0>Woo00=l00?o0ol02P?o00=l07ooOol06Woo00<007ooOol00Woo00@007ooOomoo`@000=o o`800004Ool000000003Ool30005Ool40003Ool50004Ool30005Ool40003Ool200000goo0000000X Ool002Uoo`03001oogoo009oo`03001oogoo025oo`03001oogoo03Aoo`03O003o`?o00P3o`03O01o ogoo03Yoo`03O003o`?o00X3o`03O01oogoo01Yoo`03001oogoo009oo`03001oogoo025oo`03001o ogoo045oo`00:7oo0`000Woo0`0057oo00<007ooOol05Goo00<007ooOol0:Woo00=l00?o0ol02@?o 00=l07ooOol0>Goo00=l00?o0ol02P?o00=l07ooOol06Goo0`000Woo0`0057oo00<007ooOol05Goo 00<007ooOol0=goo0029Ool00g`00ol3o`090ol00g`0Oomoo`0iOol00g`00ol3o`090ol00g`0Oomo o`28Ool008Yoo`03O003o`?o00P3o`03O01oogoo03Qoo`03O003o`?o00X3o`03O01oogoo08Qoo`00 RWoo00=l00?o0ol02@?o00=l07ooOol0=goo00=l00?o0ol02@?o00=l07ooOol0RGoo002:Ool00g`0 0ol3o`090ol00g`0Oomoo`0gOol00g`00ol3o`090ol00g`0Oomoo`29Ool008]oo`03O003o`?o00P3 o`03O01oogoo03Moo`03O003o`?o00T3o`03O01oogoo08Uoo`00Rgoo00=l00?o0ol020?o00=l07oo Ool0=Woo00=l00?o0ol02@?o00=l07ooOol0RWoo000UOol3000017oo000000000Woo0`0000=oo`00 00000Woo0`0000=oo`0000000Woo1@0017oo0`0017oo1@000goo10000goo0`0000Aoo`000000009o o`<00003Ool00000009oo`D001Qoo`03O003o`?o00T3o`03O01oogoo03Eoo`03O003o`?o00T3o`03 O01oogoo01Yoo`<00004Ool000000002Ool300000goo00000002Ool300000goo00000002Ool50004 Ool30004Ool50003Ool40003Ool3000017oo000000000Woo0`0000=oo`0000000Woo1@008Woo000V Ool01@00Oomoogoo00000Woo00@007ooOomoo`80009oo`04001oogooOol20005Ool00`00Oomoo`03 Ool01@00Oomoogoo00001Goo00<007ooOol00Woo00<007ooOol00Woo00D007ooOomoo`0000=oo`04 001oogoo0003Ool20005Ool00`00Oomoo`0IOol00g`00ol3o`080ol00g`0Oomoo`0eOol00g`00ol3 o`090ol00g`0Oomoo`0KOol01@00Oomoogoo00000Woo00@007ooOomoo`80009oo`04001oogooOol2 0005Ool00`00Oomoo`03Ool01@00Oomoogoo00001Goo00<007ooOol00Woo00<007ooOol00Woo00D0 07ooOomoo`0000=oo`04001oogoo0003Ool20005Ool00`00Oomoo`0ROol002Moo`<000=oo`03001o ogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomoo`03Ool00`00Oomoo`07Ool00`00 Oomoo`02Ool00`00Oomoo`02Ool01@00Oomoogoo00000goo00@007ooOol000Aoo`03001oogoo00=o o`03001oogoo01Uoo`03O003o`?o00P3o`03O01oogoo03Eoo`03O003o`?o00P3o`03O01oogoo01eo o`<000=oo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomoo`03Ool00`00 Oomoo`07Ool00`00Oomoo`02Ool00`00Oomoo`02Ool01@00Oomoogoo00000goo00@007ooOol000Ao o`03001oogoo00=oo`03001oogoo029oo`009goo00<007oo00000goo00<007ooOol00Woo00@007oo Ool000Aoo`03001oogoo00=oo`03001oogoo00=oo`03001oogoo00Moo`03001oogoo009oo`03001o ogoo009oo`05001oogooOol00003Ool01000Oomoogoo1@001Goo00<007ooOol06Goo00=l00?o0ol0 20?o00=l07ooOol0=7oo00=l00?o0ol02@?o00=l07ooOol07Goo00<007oo00000goo00<007ooOol0 0Woo00@007ooOol000Aoo`03001oogoo00=oo`03001oogoo00=oo`03001oogoo00Moo`03001oogoo 009oo`03001oogoo009oo`05001oogooOol00003Ool01000Oomoogoo1@001Goo00<007ooOol08Woo 000WOol00`00Ool00003Ool01000Oomoogoo0P000Woo00@007ooOomoo`8000Eoo`03001oogoo00=o o`03001oogoo00Moo`03001oogoo009oo`03001oogoo009oo`04001oogooOol20002Ool01000Oomo o`0017oo00<007ooOol00goo00<007ooOol06Woo00=l00?o0ol020?o00=l07ooOol0Ool007moo`P000Uoo`03O003o`?o00L3o`03O01oogoo02moo`03 O003o`?o00L3o`03O01oogoo08moo`00OGoo2P002Goo00=l00?o0ol01`?o00=l07ooOol0;goo00=l 00?o0ol01`?o00=l07ooOol0Sgoo001lOol:000;Ool00g`00ol3o`060ol00g`0Oomoo`0_Ool00g`0 0ol3o`070ol00g`0Oomoo`2?Ool007eoo`T000]oo`03O003o`?o00L3o`03O01oogoo02eoo`03O003 o`?o00L3o`03O01oogoo091oo`00OWoo1`0037oo00=l00?o0ol01`?o00=l07ooOol0;Goo00=l00?o 0ol01`?o00=l07ooOol0T7oo001oOol6000=Ool00g`00ol3o`060ol00g`0Oomoo`0]Ool00g`00ol3 o`070ol00g`0Oomoo`2@Ool007ioo`03001oo`0000<000ioo`03O003o`?o00H3o`03O01oogoo02eo o`03O003o`?o00H3o`03O01oogoo095oo`00OGoo00@007ooOomoo`<000ioo`03O003o`?o00L3o`03 O01oogoo02]oo`03O003o`?o00L3o`03O01oogoo095oo`00O7oo00<007ooOol00goo00<007ooOol0 3Woo00=l00?o0ol01P?o00=l07ooOol0:goo00=l00?o0ol01`?o00=l07ooOol0TGoo001kOol00`00 Oomoo`0EOol00g`00ol3o`060ol00g`0Oomoo`0[Ool00g`00ol3o`060ol00g`0Oomoo`2BOol007Yo o`03001oogoo01Ioo`03O003o`?o00H3o`03O01oogoo02]oo`03O003o`?o00H3o`03O01oogoo099o o`00NGoo00<007ooOol067oo00=l00?o0ol01P?o00=l07ooOol0:Woo00=l00?o0ol01@?o00=l07oo Ool0Tgoo001hOol00`00Oomoo`0IOol00g`00ol3o`060ol00g`0Oomoo`0YOol00g`00ol3o`060ol0 0g`0Oomoo`2COol007Moo`03001oogoo01]oo`03O003o`?o00D3o`03O01oogoo02Uoo`03O003o`?o 00H3o`03O01oogoo09=oo`00MWoo00<007ooOol077oo00=l00?o0ol01@?o00=l07ooOol0:Goo00=l 00?o0ol01@?o00=l07ooOol0U7oo001eOol00`00Oomoo`0MOol00g`00ol3o`060ol00g`0Oomoo`0X Ool00g`00ol3o`050ol00g`0Oomoo`2DOol007Aoo`03001oogoo01moo`03O003o`?o00D3o`03O01o ogoo02Moo`03O003o`?o00H3o`03O01oogoo09Aoo`00M7oo00<007ooOol07goo00=l00?o0ol01@?o 00=l07ooOol09goo00=l00?o0ol01@?o00=l07ooOol0UGoo001cOol00`00Oomoo`0POol00g`00ol3 o`050ol00g`0Oomoo`0WOol00g`00ol3o`050ol00g`0Oomoo`2EOol0079oo`03001oogoo029oo`03 O003o`?o00D3o`03O01oogoo02Ioo`03O003o`?o00@3o`03O01oogoo09Ioo`00LGoo00<007ooOol0 8goo00=l00?o0ol01@?o00=l07ooOol09Goo00=l00?o0ol01@?o00=l07ooOol0UWoo001`Ool00`00 Oomoo`0TOol00g`00ol3o`050ol00g`0Oomoo`0UOol00g`00ol3o`040ol00g`0Oomoo`2GOol006mo o`03001oogoo02Ioo`03O003o`?o00@3o`03O01oogoo02Eoo`03O003o`?o00@3o`03O01oogoo09Mo o`00KWoo00<007ooOol09goo00=l00?o0ol010?o00=l07ooOol09Goo00=l00?o0ol010?o00=l07oo Ool0Ugoo001]Ool00`00Oomoo`0YOol00g`00ol3o`040ol00g`0Oomoo`0SOol00g`00ol3o`040ol0 0g`0Oomoo`2HOol006aoo`03001oogoo02Yoo`03O003o`?o00@3o`03O01oogoo02=oo`03O003o`?o 00@3o`03O01oogoo09Qoo`00Jgoo00<007ooOol0:goo00=l00?o0ol010?o00=l07ooOol08goo00=l 00?o0ol00`?o00=l07ooOol0VGoo001ZOol00`00Oomoo`0]Ool00g`00ol3o`030ol00g`0Oomoo`0S Ool00g`00ol3o`030ol00g`0Oomoo`2IOol006Uoo`03001oogoo02ioo`03O003o`?o00@3o`03O01o ogoo029oo`03O003o`?o00<3o`03O01oogoo09Uoo`00J7oo00<007ooOol0<7oo00=l00?o0ol00`?o 00=l07ooOol08Goo00=l00?o0ol00`?o00=l07ooOol0VWoo001WOol00`00Oomoo`0aOol00g`00ol3 o`030ol00g`0Oomoo`0QOol00g`00ol3o`030ol00g`0Oomoo`2JOol006Ioo`03001oogoo03=oo`03 O003o`?o0083o`03O01oogoo025oo`03O003o`?o0083o`03O01oogoo09]oo`00IGoo00<007ooOol0 =7oo00=l00?o0ol00`?o00=l07ooOol087oo00=l00?o0ol00P?o00=l07ooOol0Vgoo001UOol00`00 Oomoo`0dOol00g`00ol3o`030ol00g`0Oomoo`0OOol00g`00ol3o`020ol00g`0Oomoo`2LOol006Ao o`03001oogoo03Ioo`03O003o`?o0083o`03O01oogoo01moo`03O003o`?o0083o`03O01oogoo09ao o`00Hgoo00<007ooOol0=goo00=l00?o0ol00P?o00=l07ooOol07goo00El00?o0ol3og`009moo`00 HWoo00<007ooOol0>Goo00=l00?o0ol00P?o00=l07ooOol07Woo00El00?o0ol3og`009moo`00HGoo 00<007ooOol0>Woo00=l00?o0ol00P?o00=l07ooOol07Goo00El00?o0ol3og`00:1oo`00H7oo00<0 07ooOol0>goo00=l00?o0ol00P?o00=l07ooOol07Goo00El00?o0ol3og`00:1oo`00Ggoo00<007oo Ool0?Goo00El00?o0ol3og`001moo`04O003o`?oO02QOol005ioo`03001oogoo03ioo`03O003o`?o 0083o`03O01oogoo01aoo`04O003o`?oO02QOol00:1oo`05O003o`?o0oml000MOol017`00ol3og`0 XWoo0018Ool3000017oo000000000Woo10000goo1@000Woo0`0000Eoo`00001oo`00009oo`<00003 Ool00000009oo`D002Yoo`05O003o`?o0oml000MOol017`00ol3og`0XWoo0019Ool01@00Oomoogoo 00000Woo00<007ooOol00Woo00D007ooOomoo`0000Ioo`04001oogoo0002Ool00`00Ool00003Ool2 0005Ool00`00Oomoo`0[Ool017`00ol3og`07Goo00=l00?oO000Xgoo0019Ool01@00Oomoogoo0000 0Woo00<007ooOol00Woo00D007ooOomoo`0000Ioo`04001oogoo0002Ool00`00Ool00004Ool00`00 Oomoo`03Ool00`00Oomoo`0[Ool01G`00ol3o`?oO00077oo00=l00?oO000Xgoo0019Ool01@00Oomo ogoo00000Woo00<007ooOol00Woo00D007ooOomoo`0000Ioo`04001oogoo0002Ool00`00Oomoo`05 0005Ool00`00Oomoo`0/Ool017`00ol3og`06goo00=l00?oO000Y7oo0019Ool20002Ool01000Oomo o`0017oo00@007ooOomoo`8000Eoo`800007Ool00000Ool007oo000017oo00<007ooOol00goo00<0 07ooOol0;Goo00=l00?oO0006goo00=l00?oO000Y7oo0018Ool200000goo00000004Ool40003Ool2 00001Goo00000000Ool00P0000Eoo`00Oomoo`0000=oo`@000Ioo`03001oogoo02eoo`03O003og`0 01]oo`9l0:Eoo`00Lgoo00<007ooOol0;Woo00=l00?oO0006Goo00=l00?oO000YGoo001bOol2000` Ool00g`00oml000IOol2O02VOol00:Eoo`9l01Uoo`9l0:Ioo`00YGoo0W`06Goo00=l07ooOol0YGoo 002VOol00g`0Oomoo`0FOol00g`0Oomoo`2VOol00:Moo`03O01oogoo01Eoo`03O01oogoo0:Ioo`00 Ygoo00=l07ooOol057oo0W`0Z7oo002WOol2O00DOol2O02YOol00:Moo`03O003og`0019oo`03O003 og`00:Uoo`00Z7oo00=l00?oO0004Goo00=l00?oO000ZGoo002XOol017`00ol3og`03goo00Al00?o 0oml0:Uoo`00Z7oo00El00?o0ol3og`000eoo`04O003o`?oO02ZOol00:Qoo`03O003o`?o0083o`9l 00Yoo`05O003o`?o0oml002ZOol00:Uoo`03O003o`?o00<3o`9l00Ioo`9l00@3o`03O01oogoo0:Qo o`00ZGoo00=l00?o0ol010?o1g`01@?o00=l07ooOol0ZGoo002YOol00g`00ol3o`0@0ol00g`0Oomo o`2YOol00:Uoo`03O003o`?o0103o`03O01oogoo0:Uoo`00ZWoo00=l00?o0ol03`?o00=l07ooOol0 ZGoo002ZOol00g`00ol3o`0>0ol00g`0Oomoo`2ZOol00:]oo`03O003o`?o00d3o`03O01oogoo0:Yo o`00Zgoo00=l00?o0ol03@?o00=l07ooOol0ZWoo002[Ool00g`00ol3o`0<0ol00g`0Oomoo`2[Ool0 0:aoo`03O003o`?o00/3o`03O01oogoo0:]oo`00[7oo00=l00?o0ol02P?o00=l07ooOol0[7oo002] Ool00g`00ol3o`090ol00g`0Oomoo`2/Ool00:eoo`03O003o`?o00T3o`03O01oogoo0:aoo`00[Woo 00=l00?o0ol01`?o00=l07ooOol0[Goo002^Ool00g`00ol3o`070ol00g`0Oomoo`2]Ool00:moo`03 O003o`?o00D3o`03O01oogoo0:ioo`00/7oo00=l00?o0ol00`?o00=l07ooOol0[goo002`Ool2O003 0ol00g`0Oomoo`2`Ool00;5oo`El0;9oo`00ogooJGoo003oOomYOol00?moofUoo`00ogooJGoo003o OomYOol00001\ \>"], ImageRangeCache->{{{127.438, 356.813}, {417.438, 276.125}} -> {-0.558944, 1.954, 0.00349883, 0.00566123}, {{127.75, 356.438}, {417.438, 276.125}} -> {-13.341, 0.622579, 0.0440853, 0.00182591}, {{127.75, 356.438}, {417.438, 276.125}} -> {-13.341, 0.622579, 0.0440853, 0.00182591}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth] }, Open ]], Cell["\<\ We can combine a symmetric and skewed stable plot illustrate how variation is \ moved from the left to the right as \[Beta] increases.\ \>", "Text", PageWidth->PaperWidth], Cell[CellGroupData[{ Cell[BoxData[ \(tradeoff = FilledPlot[{Evaluate[\ {Abs[ ffx1\/m1] /. {\[Alpha] \[Rule] 2, \[Beta] \[Rule] 0, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}}], Evaluate[{Abs[ ffx1\/m1] /. {\[Alpha] \[Rule] 1.1, \[Beta] \[Rule] 0, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}}\ ], Evaluate[{Abs[ ffx1\/m1] /. {\[Alpha] \[Rule] 1.1, \[Beta] \[Rule] .75, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}}]}, {x, \(-6\), 6}, PlotRange -> All, Epilog\ -> \ {Arrow[{4, \ .2}, \ {4, .03}], Arrow[{\(-3.6\), \ .25}, \ {\(-1.3\), .2}], Arrow[{ .5, \ .05}, \ {\(-1.7\), .06}], \n\ \ \ \ \ \ Text["\", \ {3.7, \ .22}, \ {0, \ \(- .5\)}], Text["\", \ {3.8, \ .2}, \ {0, \ \(- .5\)}], Text["\", {\(-3.5\), .25}, {0, \(- .5\)}], Text["\", { .15, .03}, {0, \(- .5\)}], Text["\", { .05, .01}, {0, \(- .5\)}]}, GridLines -> None, \ Frame -> None, Axes -> None, PlotStyle -> {{Hue[ .3], Hue[1]}}]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0 1 0 0.618034 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.05 0.0125 moveto 0 0 lineto -0.05 -0.0125 lineto fill -0.05 0.0125 moveto 0 0 lineto -0.05 -0.0125 lineto -0.05 0.0125 lineto stroke } ifelse grestore } def % End of user PostScript % Start of sub-graphic p 0 0 1 0.618034 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0793651 0.0146484 1.91621 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 1 0 0 r .5 Mabswid [ ] 0 setdash .02381 .01472 m .03279 .01474 L .04262 .01478 L .05288 .01484 L .06244 .01492 L .0731 .01504 L .0828 .01519 L .094 .01543 L .10458 .01574 L .11428 .01612 L .12455 .01666 L .13333 .01725 L .14299 .01808 L .15313 .01921 L .1624 .02051 L .17311 .02243 L .18328 .02474 L .19287 .02744 L .20309 .03099 L .22147 .03952 L .23176 .04574 L .24289 .05385 L .26306 .07287 L .283 .09804 L .30406 .13243 L .34203 .21542 L .38246 .32703 L .42136 .43756 L .44118 .48583 L .45162 .50725 L .46273 .5262 L .47256 .53929 L .47816 .54507 L .48342 .54934 L .48576 .55087 L .48823 .55224 L .49036 .55321 L .49264 .55404 L .49392 .55441 L .49509 .55469 L .49627 .5549 L .49738 .55505 L .49868 .55516 L .49987 .5552 L .50118 .55517 L .50184 .55513 L .50257 .55506 L .50386 .55488 L .50506 .55465 L .50638 .55433 L Mistroke .50778 .5539 L .51038 .55289 L .51273 .55173 L .51752 .54866 L .52202 .5449 L .53206 .53359 L .54291 .51711 L .56289 .47667 L .58397 .42326 L .62199 .3141 L .66247 .20426 L .70143 .12266 L .72271 .09014 L .74284 .06669 L .76279 .04952 L .78122 .03807 L .79992 .02986 L .81056 .02641 L .82054 .02381 L .8304 .02175 L .84076 .02003 L .85047 .01878 L .85928 .01787 L .86885 .01709 L .87906 .01645 L .88852 .016 L .89744 .01567 L .90719 .0154 L .91749 .01518 L .92629 .01505 L .93596 .01493 L .94611 .01485 L .95537 .01479 L .96049 .01477 L .96606 .01475 L .97619 .01472 L Mfstroke .02381 .02976 m .06244 .03266 L .10458 .03686 L .14415 .04225 L .18221 .04942 L .20178 .0542 L .22272 .06043 L .24259 .06772 L .26416 .07764 L .28492 .08984 L .30409 .10419 L .32282 .12208 L .34344 .14775 L .36285 .17961 L .38373 .22503 L .40486 .2859 L .42495 .35921 L .46315 .5207 L .47328 .55714 L .47825 .57198 L .48282 .58342 L .4881 .59363 L .49088 .59759 L .4923 .59923 L .49382 .60068 L .49511 .60166 L .49628 .60236 L .49746 .60287 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60292 L .50306 .60267 L .50379 .60232 L .50501 .60158 L .50614 .60071 L .50871 .59809 L .51121 .5947 L .51389 .59018 L .52314 .56807 L .53407 .5314 L .544 .49155 L .58398 .3248 L .6023 .26343 L .62244 .21021 L .64232 .17026 L .66336 .13847 L .68281 .11624 L .7037 .09794 L .72488 .0837 L Mistroke .74498 .07314 L .78322 .05853 L .80294 .05297 L .82392 .0481 L .86556 .04076 L .90568 .03572 L .94428 .0321 L .97619 .02976 L Mfstroke .02381 .01811 m .06244 .01878 L .08255 .01921 L .10458 .01978 L .14415 .02111 L .16372 .02199 L .18466 .02315 L .20597 .02467 L .22611 .02654 L .24608 .02901 L .26452 .03213 L .28325 .03659 L .29389 .04004 L .30387 .04417 L .31425 .04981 L .32412 .05704 L .33298 .06578 L .34264 .07881 L .35296 .09827 L .36232 .12235 L .37311 .15922 L .38329 .20328 L .42184 .41693 L .43215 .46915 L .44178 .50954 L .45182 .54112 L .45714 .55319 L .4599 .55818 L .46284 .56254 L .46535 .56551 L .46669 .5668 L .46813 .56798 L .46944 .56887 L .47065 .56953 L .4718 .57002 L .47302 .57039 L .47371 .57054 L .47434 .57063 L .47507 .57069 L .47575 .5707 L .47698 .5706 L .47767 .57048 L .4783 .57034 L .47964 .56991 L .48111 .56926 L .48265 .56838 L .48408 .56738 L .48915 .56255 L .49378 .5565 L .5042 .53814 L Mistroke .52323 .49292 L .54396 .43581 L .58466 .32789 L .62384 .24572 L .64386 .21267 L .66548 .18285 L .7056 .14059 L .72557 .1245 L .74665 .11027 L .78468 .09016 L .82515 .07449 L .86411 .06331 L .90553 .05435 L .94542 .04774 L .97619 .04366 L Mfstroke 0 1 0 r .02381 .01472 m .03279 .01474 L .04262 .01478 L .05288 .01484 L .06244 .01492 L .0731 .01504 L .0828 .01519 L .094 .01543 L .10458 .01574 L .11428 .01612 L .12455 .01666 L .13333 .01725 L .14299 .01808 L .15313 .01921 L .1624 .02051 L .17311 .02243 L .18328 .02474 L .19287 .02744 L .20309 .03099 L .22147 .03952 L .23176 .04574 L .24289 .05385 L .26306 .07287 L .283 .09804 L .30406 .13243 L .34203 .21542 L .38246 .32703 L .42136 .43756 L .44118 .48583 L .45162 .50725 L .46273 .5262 L .47256 .53929 L .47816 .54507 L .48342 .54934 L .48576 .55087 L .48823 .55224 L .49036 .55321 L .49264 .55404 L .49392 .55441 L .49509 .55469 L .49627 .5549 L .49738 .55505 L .49868 .55516 L .49987 .5552 L .50118 .55517 L .50184 .55513 L .50257 .55506 L .50386 .55488 L .50506 .55465 L .50638 .55433 L .50778 .5539 L .51038 .55289 L .51273 .55173 L .51752 .54866 L .52202 .5449 L .53206 .53359 L .54291 .51711 L .56289 .47667 L .58397 .42326 L .62199 .3141 L .66247 .20426 L .70143 .12266 L .72271 .09014 L .74284 .06669 L .76279 .04952 L .78122 .03807 L .79992 .02986 L .81056 .02641 L .82054 .02381 L .8304 .02175 L .84076 .02003 L .85047 .01878 L .85928 .01787 L .86885 .01709 L .87906 .01645 L .88852 .016 L .89744 .01567 L .90719 .0154 L .91749 .01518 L .92629 .01505 L .93596 .01493 L .94611 .01485 L .95537 .01479 L .96049 .01477 L .96606 .01475 L .97619 .01472 L .97619 .02976 L .94428 .0321 L .90568 .03572 L .86556 .04076 L .82392 .0481 L .80294 .05297 L .78322 .05853 L .74498 .07314 L .72488 .0837 L .7037 .09794 L .68281 .11624 L .66336 .13847 L .64232 .17026 L .62244 .21021 L .6023 .26343 L .58398 .3248 L .544 .49155 L .53407 .5314 L .52314 .56807 L .51389 .59018 L .51121 .5947 L .50871 .59809 L .50614 .60071 L .50501 .60158 L .50379 .60232 L .50306 .60267 L .50239 .60292 L .50107 .60324 L .49987 .60332 L .49857 .60318 L .49746 .60287 L .49628 .60236 L .49511 .60166 L .49382 .60068 L .4923 .59923 L .49088 .59759 L .4881 .59363 L .48282 .58342 L .47825 .57198 L .47328 .55714 L .46315 .5207 L .42495 .35921 L .40486 .2859 L .38373 .22503 L .36285 .17961 L .34344 .14775 L .32282 .12208 L .30409 .10419 L .28492 .08984 L .26416 .07764 L .24259 .06772 L .22272 .06043 L .20178 .0542 L .18221 .04942 L .14415 .04225 L .10458 .03686 L .06244 .03266 L .02381 .02976 L F 1 0 0 r .02381 .01472 m .03279 .01474 L .04262 .01478 L .05288 .01484 L .06244 .01492 L .0731 .01504 L .0828 .01519 L .094 .01543 L .10458 .01574 L .11428 .01612 L .12455 .01666 L .13333 .01725 L .14299 .01808 L .15313 .01921 L .1624 .02051 L .17311 .02243 L .18328 .02474 L .19287 .02744 L .20309 .03099 L .22147 .03952 L .23176 .04574 L .24289 .05385 L .26306 .07287 L .283 .09804 L .30406 .13243 L .34203 .21542 L .38246 .32703 L .42136 .43756 L .44118 .48583 L .45162 .50725 L .46273 .5262 L .47256 .53929 L .47816 .54507 L .48342 .54934 L .48576 .55087 L .48823 .55224 L .49036 .55321 L .49264 .55404 L .49392 .55441 L .49509 .55469 L .49627 .5549 L .49738 .55505 L .49868 .55516 L .49987 .5552 L .50118 .55517 L .50184 .55513 L .50257 .55506 L .50386 .55488 L .50506 .55465 L .50638 .55433 L Mistroke .50778 .5539 L .51038 .55289 L .51273 .55173 L .51752 .54866 L .52202 .5449 L .53206 .53359 L .54291 .51711 L .56289 .47667 L .58397 .42326 L .62199 .3141 L .66247 .20426 L .70143 .12266 L .72271 .09014 L .74284 .06669 L .76279 .04952 L .78122 .03807 L .79992 .02986 L .81056 .02641 L .82054 .02381 L .8304 .02175 L .84076 .02003 L .85047 .01878 L .85928 .01787 L .86885 .01709 L .87906 .01645 L .88852 .016 L .89744 .01567 L .90719 .0154 L .91749 .01518 L .92629 .01505 L .93596 .01493 L .94611 .01485 L .95537 .01479 L .96049 .01477 L .96606 .01475 L .97619 .01472 L Mfstroke .02381 .02976 m .06244 .03266 L .10458 .03686 L .14415 .04225 L .18221 .04942 L .20178 .0542 L .22272 .06043 L .24259 .06772 L .26416 .07764 L .28492 .08984 L .30409 .10419 L .32282 .12208 L .34344 .14775 L .36285 .17961 L .38373 .22503 L .40486 .2859 L .42495 .35921 L .46315 .5207 L .47328 .55714 L .47825 .57198 L .48282 .58342 L .4881 .59363 L .49088 .59759 L .4923 .59923 L .49382 .60068 L .49511 .60166 L .49628 .60236 L .49746 .60287 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60292 L .50306 .60267 L .50379 .60232 L .50501 .60158 L .50614 .60071 L .50871 .59809 L .51121 .5947 L .51389 .59018 L .52314 .56807 L .53407 .5314 L .544 .49155 L .58398 .3248 L .6023 .26343 L .62244 .21021 L .64232 .17026 L .66336 .13847 L .68281 .11624 L .7037 .09794 L .72488 .0837 L Mistroke .74498 .07314 L .78322 .05853 L .80294 .05297 L .82392 .0481 L .86556 .04076 L .90568 .03572 L .94428 .0321 L .97619 .02976 L Mfstroke 0 0 1 r .02381 .02976 m .06244 .03266 L .10458 .03686 L .14415 .04225 L .18221 .04942 L .20178 .0542 L .22272 .06043 L .24259 .06772 L .26416 .07764 L .28492 .08984 L .30409 .10419 L .32282 .12208 L .34344 .14775 L .36285 .17961 L .38373 .22503 L .40486 .2859 L .42495 .35921 L .46315 .5207 L .47328 .55714 L .47825 .57198 L .48282 .58342 L .4881 .59363 L .49088 .59759 L .4923 .59923 L .49382 .60068 L .49511 .60166 L .49628 .60236 L .49746 .60287 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60292 L .50306 .60267 L .50379 .60232 L .50501 .60158 L .50614 .60071 L .50871 .59809 L .51121 .5947 L .51389 .59018 L .52314 .56807 L .53407 .5314 L .544 .49155 L .58398 .3248 L .6023 .26343 L .62244 .21021 L .64232 .17026 L .66336 .13847 L .68281 .11624 L .7037 .09794 L .72488 .0837 L .74498 .07314 L .78322 .05853 L .80294 .05297 L .82392 .0481 L .86556 .04076 L .90568 .03572 L .94428 .0321 L .97619 .02976 L .97619 .04366 L .94542 .04774 L .90553 .05435 L .86411 .06331 L .82515 .07449 L .78468 .09016 L .74665 .11027 L .72557 .1245 L .7056 .14059 L .66548 .18285 L .64386 .21267 L .62384 .24572 L .58466 .32789 L .54396 .43581 L .52323 .49292 L .5042 .53814 L .49378 .5565 L .48915 .56255 L .48408 .56738 L .48265 .56838 L .48111 .56926 L .47964 .56991 L .4783 .57034 L .47767 .57048 L .47698 .5706 L .47575 .5707 L .47507 .57069 L .47434 .57063 L .47371 .57054 L .47302 .57039 L .4718 .57002 L .47065 .56953 L .46944 .56887 L .46813 .56798 L .46669 .5668 L .46535 .56551 L .46284 .56254 L .4599 .55818 L .45714 .55319 L .45182 .54112 L .44178 .50954 L .43215 .46915 L .42184 .41693 L .38329 .20328 L .37311 .15922 L .36232 .12235 L .35296 .09827 L .34264 .07881 L .33298 .06578 L .32412 .05704 L .31425 .04981 L .30387 .04417 L .29389 .04004 L .28325 .03659 L .26452 .03213 L .24608 .02901 L .22611 .02654 L .20597 .02467 L .18466 .02315 L .16372 .02199 L .14415 .02111 L .10458 .01978 L .08255 .01921 L .06244 .01878 L .02381 .01811 L F 1 0 0 r .02381 .02976 m .06244 .03266 L .10458 .03686 L .14415 .04225 L .18221 .04942 L .20178 .0542 L .22272 .06043 L .24259 .06772 L .26416 .07764 L .28492 .08984 L .30409 .10419 L .32282 .12208 L .34344 .14775 L .36285 .17961 L .38373 .22503 L .40486 .2859 L .42495 .35921 L .46315 .5207 L .47328 .55714 L .47825 .57198 L .48282 .58342 L .4881 .59363 L .49088 .59759 L .4923 .59923 L .49382 .60068 L .49511 .60166 L .49628 .60236 L .49746 .60287 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60292 L .50306 .60267 L .50379 .60232 L .50501 .60158 L .50614 .60071 L .50871 .59809 L .51121 .5947 L .51389 .59018 L .52314 .56807 L .53407 .5314 L .544 .49155 L .58398 .3248 L .6023 .26343 L .62244 .21021 L .64232 .17026 L .66336 .13847 L .68281 .11624 L .7037 .09794 L .72488 .0837 L Mistroke .74498 .07314 L .78322 .05853 L .80294 .05297 L .82392 .0481 L .86556 .04076 L .90568 .03572 L .94428 .0321 L .97619 .02976 L Mfstroke .02381 .01811 m .06244 .01878 L .08255 .01921 L .10458 .01978 L .14415 .02111 L .16372 .02199 L .18466 .02315 L .20597 .02467 L .22611 .02654 L .24608 .02901 L .26452 .03213 L .28325 .03659 L .29389 .04004 L .30387 .04417 L .31425 .04981 L .32412 .05704 L .33298 .06578 L .34264 .07881 L .35296 .09827 L .36232 .12235 L .37311 .15922 L .38329 .20328 L .42184 .41693 L .43215 .46915 L .44178 .50954 L .45182 .54112 L .45714 .55319 L .4599 .55818 L .46284 .56254 L .46535 .56551 L .46669 .5668 L .46813 .56798 L .46944 .56887 L .47065 .56953 L .4718 .57002 L .47302 .57039 L .47371 .57054 L .47434 .57063 L .47507 .57069 L .47575 .5707 L .47698 .5706 L .47767 .57048 L .4783 .57034 L .47964 .56991 L .48111 .56926 L .48265 .56838 L .48408 .56738 L .48915 .56255 L .49378 .5565 L .5042 .53814 L Mistroke .52323 .49292 L .54396 .43581 L .58466 .32789 L .62384 .24572 L .64386 .21267 L .66548 .18285 L .7056 .14059 L .72557 .1245 L .74665 .11027 L .78468 .09016 L .82515 .07449 L .86411 .06331 L .90553 .05435 L .94542 .04774 L .97619 .04366 L Mfstroke 0 g .81746 .39789 m .81746 .07213 L s % Start of user PostScript 4. 0.2 4. 0.03 MAarrowhead1 % End of user PostScript .21429 .4937 m .39683 .39789 L s % Start of user PostScript -3.6 0.25 -1.3 0.2 MAarrowhead1 % End of user PostScript .53968 .11046 m .36508 .12962 L s % Start of user PostScript 0.5 0.05 -1.7 0.06 MAarrowhead1 % End of user PostScript gsave .79365 .43621 -90 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (variation) show 117.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .80159 .39789 -78 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (added) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .22222 .4937 -81 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (normal) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .5119 .07213 -90 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (variation) show 117.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .50397 .03381 -84 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (removed) show 105.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0 0 1 0.618034 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0793651 0.0146484 1.91621 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg9oo`Al0383h0Yo o`0027oo?P0O27`0egoo0g`0=P?P2Woo0008Oom601l7O0301l00g`0 Oomoo`1dOol2O00C01l2O00COol8000oOol006Qoo`03O003h0?P00D3h003O0007`0O00d07`03O01o ogoo011oo`8002Qoo`D003Aoo`03O0007`0O01807`03O01oogoo01=oo`P003moo`00JGoo00=l00?P 0n001@?P00=l000O01l03@0O00=l07ooOol03Goo10007goo2@00>7oo00=l000O01l04@0O0W`05Woo 2000?goo001YOol00g`00n03h0060n000g`001l07`0<01l00g`0Oomoo`0:Ool7000FOol90010Ool0 0g`001l07`0A01l00g`0Oomoo`0FOol9000nOol006Yoo`03O003h0?P00H3h003O0007`0O00`07`03 O01oogoo00Moo`T000ioo`P004Qoo`03O0007`0O01407`03O01oogoo01Ioo`X003ioo`00Jgoo00=l 00?P0n001P?P00=l000O01l02`0O00=l07ooOol01Goo2`001Goo2@00Cgoo00=l000O01l0400O0W`0 6Goo2P00?Woo001[Ool00g`00n03h0070n000g`001l07`0:01l00g`0Oomoo`02OolC001GOol00g`0 01l07`0@01l00g`0Oomoo`0NOol00`00Oomoo`10Ool006aoo`03O003h0?P00L3h003O0007`0O00X0 7`03O01oo`00010005Yoo`03O0007`0O00l07`9l025oo`03001oogoo041oo`00K7oo00=l00?P0n00 1`?P00=l000O01l02P0O4`00FWoo00=l000O01l03P0O00=l07ooOol08Goo00<007ooOol0@7oo001] Ool00g`00n03h0070n000g`001l07`0901l00g`0Oomoo`02Ool>001IOol00g`001l07`0>01l00g`0 Oomoo`0ROol00`00Oomoo`10Ool006eoo`03O003h0?P00P3h003O0007`0O00T07`03O01oogoo00Yo o`D005Qoo`03O0007`0O00d07`9l02Eoo`03001oogoo041oo`00KWoo00=l00?P0n0020?P00=l000O 01l0200O00=l07ooOol0IWoo00=l000O01l03@0O00=l07ooOol09Goo00<007ooOol0@7oo001^Ool0 0g`00n03h0080n000g`001l07`0801l00g`0Oomoo`1UOol00g`001l07`0=01l00g`0Oomoo`0VOol0 0`00Oomoo`10Ool006moo`03O003h0?P00P3h003O0007`0O00L07`03O01oogoo06Eoo`03O0007`0O 00`07`03O01oogoo02Moo`03001oogoo041oo`00Kgoo00=l00?P0n002@?P00=l000O01l01`0O00=l 07ooOol0Hgoo00=l000O01l0300O00=l07ooOol0:7oo00<007ooOol0@7oo001`Ool00g`00n03h009 0n000g`001l07`0601l00g`0Oomoo`1ROol00g`001l07`0<01l00g`0Oomoo`0YOol00`00Oomoo`10 Ool0071oo`03O003h0?P00T3h003O0007`0O00H07`03O01oogoo069oo`03O0007`0O00/07`03O01o ogoo02Yoo`03001oogoo041oo`00LGoo00=l00?P0n002@?P00=l000O01l01P0O00=l07ooOol0H7oo 00=l000O01l02`0O00=l07ooOol0:goo00<007ooOol0@7oo001aOol00g`00n03h00:0n000g`001l0 7`0501l00g`0Oomoo`1POol00g`001l07`0:01l00g`0Oomoo`0/Ool00`00Oomoo`10Ool0075oo`03 O003h0?P00X3h003O0007`0O00D07`03O01oogoo05moo`03O0007`0O00X07`03O01oogoo02eoo`03 001oogoo041oo`00LWoo00=l00?P0n002P?P00=l000O01l0100O00=l07ooOol0GWoo00=l000O01l0 2`0O00=l07ooOol0;Goo00<007ooOol0@7oo001bOol00g`00n03h00:0n000g`001l07`0501l00g`0 Oomoo`1MOol00g`001l07`0:01l00g`0Oomoo`0^Ool00`00Oomoo`10Ool007=oo`03O003h0?P00X3 h003O0007`0O00@07`03O01oogoo05aoo`03O0007`0O00X07`03O01oogoo02moo`03001oogoo041o o`00Lgoo00=l00?P0n002`?P00=l000O01l00`0O00=l07ooOol0Fgoo00=l000O01l02P0O00=l07oo Ool0<7oo00<007ooOol0@7oo001dOol00g`00n03h00:0n000g`001l07`0301l00g`0Oomoo`1KOol0 0g`001l07`0901l2O00bOol00`00Oomoo`10Ool007Aoo`03O003h0?P00/3h003O0007`0O00807`03 O01oogoo05Yoo`03O0007`0O00T07`9l03=oo`03001oogoo041oo`00MGoo00=l00?P0n002P?P00=l 000O01l00P0O00=l07ooOol0FWoo00=l000O01l0200O00=l00?PO000Goo00<007ooOol0@7oo001mOol00g`00n03h00:0n02O01@Ool00g`001l07`0201l00g`0 0n03h0050n000g`0Oomoo`0iOol00`00Oomoo`10Ool007eoo`03O003h0?P00X3h09l04moo`03O000 7`0O00<07`03O003h0?P00D3h003O01oogoo03Uoo`03001oogoo041oo`00OGoo00=l00?P0n002`?P 00=l07ooOol0CGoo00=l000O01l00P0O00=l00?P0n001@?P00=l07ooOol0>Woo00<007ooOol0@7oo 001nOol00g`00n03h00:0n02O01>Ool00g`001l07`0201l00g`00n03h0050n000g`0Oomoo`0jOol0 0`00Oomoo`10Ool007ioo`03O003h0?P00/3h003O01oogoo04]oo`03O0007`0O00807`03O003h0?P 00H3h003O01oogoo03Yoo`03001oogoo041oo`00OWoo00=l00?P0n002`?P00=l07ooOol0Bgoo00=l 000O01l00P0O00=l00?P0n001@?P00=l07ooOol0>goo00<007ooOol0@7oo001oOol00g`00n03h00: 0n000g`0Oomoo`1:Ool00g`001l07`0201l00g`00n03h0060n000g`0Oomoo`0kOol00`00Oomoo`10 Ool007moo`03O003h0?P00X3h09l04]oo`03O0007`0O00807`03O003h0?P00H3h003O01oogoo03]o o`03001oogoo041oo`00P7oo00=l00?P0n002@?P0W`0Bgoo00El000O01l07g`000P3h003O01oogoo 03aoo`03001oogoo041oo`00P7oo00=l00?P0n002P?P00=l07ooOol0B7oo00=l000O01l00P0O00=l 00?P0n001P?P00=l07ooOol0?7oo00<007ooOol0@7oo0020Ool00g`00n03h00:0n02O019Ool01G`0 01l07`0OO0002@?P00=l07ooOol0?7oo00<007ooOol0@7oo0021Ool00g`00n03h0090n02O019Ool0 1G`001l07`0OO00020?P00=l07ooOol0?Goo00<007ooOol0@7oo0021Ool00g`00n03h0090n02O018 Ool01G`001l07`0OO0002@?P00=l07ooOol0?Goo00<007ooOol0@7oo0021Ool00g`00n03h0090n00 0g`001ml0017Ool01G`001l07`0OO0002@?P00=l07ooOol0?Goo00<007ooOol0@7oo0022Ool00g`0 0n03h0090n02O017Ool017`001l07g`02@?P00=l07ooOol0?Woo00<007ooOol0@7oo0022Ool00g`0 0n03h0090n000g`001ml0015Ool01G`001l07`0OO0002@?P00=l07ooOol0?Woo00<007ooOol0@7oo 0023Ool00g`00n03h0080n000g`001ml0015Ool017`001l07g`02P?P00=l07ooOol0?Woo00<007oo Ool0@7oo0023Ool00g`00n03h0080n000g`001ml0015Ool017`001l07g`02@?P00=l07ooOol0?goo 00<007ooOol0@7oo0023Ool00g`00n03h0080n0017`001l07g`0@goo00Al000O01ml00X3h003O01o ogoo03moo`03001oogoo041oo`00Q7oo00=l00?P0n0020?P00=l000OO000@goo00Al000O01ml00T3 h003O01oogoo041oo`03001oogoo041oo`00Q7oo00=l00?P0n0020?P00=l000OO000@goo00Al000O 01ml00T3h003O01oogoo041oo`03001oogoo041oo`00Q7oo00=l00?P0n0020?P00Al000O01ml045o o`04O0007`0OO00:0n000g`0Oomoo`10Ool00`00Oomoo`10Ool008Eoo`03O003h0?P00L3h004O000 7`0OO011Ool017`001l07g`02@?P00=l07ooOol0@Goo00<007ooOol0@7oo0025Ool00g`00n03h007 0n0017`001l07g`0@Goo00=l000OO0002P?P00=l07ooOol0@Goo00<007ooOol0@7oo0026Ool00g`0 0n03h0060n0017`001l07g`0@Goo00=l000OO0002P?P00=l07ooOol0@Goo00<007ooOol0@7oo0026 Ool00g`00n03h0070n0017`001l07g`0?goo00=l000OO0002P?P00=l07ooOol0@Woo00<007ooOol0 @7oo0026Ool00g`00n03h0070n0017`001l07g`0?goo00=l000OO0002P?P00=l07ooOol0@Woo00<0 07ooOol0@7oo0027Ool00g`00n03h0060n0017`001l07g`0?goo0W`02`?P00=l07ooOol0@Woo00<0 07ooOol0@7oo0027Ool00g`00n03h0060n0017`001l07g`0?Woo00=l000OO0002P?P00=l07ooOol0 @goo00<007ooOol0@7oo0027Ool00g`00n03h0060n001G`001l07`0OO000?Goo0W`02`?P00=l07oo Ool0@goo00<007ooOol0@7oo0028Ool00g`00n03h0060n0017`001l07g`0?Goo0W`02`?P00=l07oo Ool0@goo00<007ooOol0@7oo0028Ool00g`00n03h0060n0017`001l07g`0?7oo0W`02`?P00=l07oo Ool0A7oo00<007ooOol0@7oo0029Ool00g`00n03h0050n0017`001l07g`0?7oo0W`02`?P00=l07oo Ool0A7oo00<007ooOol0@7oo0029Ool00g`00n03h0050n001G`001l07`0OO000>goo00=l00?P0n00 2P?P00=l07ooOol0A7oo00<007ooOol0@7oo0029Ool00g`00n03h0050n001G`001l07`0OO000>goo 00=l00?P0n002@?P00=l07ooOol0AGoo00<007ooOol0@7oo002:Ool00g`00n03h0040n001G`001l0 7`0OO000>Woo0W`02`?P00=l07ooOol0AGoo00<007ooOol0@7oo002:Ool00g`00n03h0050n001G`0 01l07`0OO000>Goo00=l00?P0n002@?P00=l07ooOol0AWoo00<007ooOol0@7oo002:Ool00g`00n03 h0050n001G`001l07`0OO000>Goo00=l00?P0n002@?P00=l07ooOol0AWoo00<007ooOol0@7oo002; Ool00g`00n03h0040n001G`001l07`0OO000>Goo00=l00?P0n002@?P00=l07ooOol0AWoo00<007oo Ool0@7oo002;Ool00g`00n03h0040n001G`001l07`0OO000>7oo00=l00?P0n002@?P00=l07ooOol0 Agoo00<007ooOol0@7oo002;Ool00g`00n03h0040n000g`001l07`0201l00g`0Oomoo`0eOol00g`0 0n03h0090n000g`0Oomoo`17Ool00`00Oomoo`10Ool008aoo`03O003h0?P00@3h005O0007`0O01ml 000fOol2O00;0n000g`0Oomoo`17Ool00`00Oomoo`10Ool008aoo`03O003h0?P00@3h005O0007`0O 01ml000fOol2O00:0n000g`0Oomoo`18Ool00`00Oomoo`10Ool008aoo`03O003h0?P00@3h005O000 7`0O01ml000fOol00g`00n03h0090n000g`0Oomoo`18Ool00`00Oomoo`10Ool008eoo`03O003h0?P 00<3h003O0007`0O00807`03O01oogoo039oo`9l00/3h003O01oogoo04Qoo`03001oogoo041oo`00 SGoo00=l00?P0n000`?P00=l000O01l00P0O00=l07ooOol0Ool00g`00n03h0020n000g`001l07`0201l00g`0Oomoo`0bOol2O00:0n000g`0 Oomoo`19Ool00`00Oomoo`10Ool008ioo`03O003h0?P00<3h005O0007`0O01ml000cOol2O00;0n00 0g`0Oomoo`19Ool00`00Oomoo`10Ool008ioo`03O003h0?P00<3h003O0007`0O00807`03O01oogoo 031oo`9l00X3h003O01oogoo04Yoo`03001oogoo041oo`00Sgoo00=l00?P0n000P?P00=l000O01l0 0P0O00=l07ooOol0;goo00=l000OO0002P?P00=l07ooOol0BWoo00<007ooOol0@7oo002?Ool00g`0 0n03h0020n000g`001l07`0201l00g`0Oomoo`0_Ool00g`001ml00090n000g`0Oomoo`1;Ool00`00 Oomoo`10Ool008moo`03O003h0?P0083h003O0007`0O00807`03O01oogoo02moo`03O0007g`000T3 h003O01oogoo04]oo`03001oogoo041oo`00T7oo00=l00?P0n000P?P00=l000O01l00P0O00=l07oo Ool0;Goo00=l000OO0002P?P00=l07ooOol0Bgoo00<007ooOol0@7oo002@Ool00g`00n03h0020n00 0g`001l07`0201l00g`0Oomoo`0]Ool00g`001ml00090n000g`0Oomoo`1Ool2000eOol007aoo`T0011oo`04O003h0?PO005 01l00g`0Oomoo`0SOol00g`001l07`0201l00g`00n03h0050n000g`0Oomoo`2DOol007Yoo`8000=o o`@001=oo`03O003h7`000D07`03O01oogoo02=oo`05O0007`0O01ml00080n000g`0Oomoo`2DOol0 07Uoo`03001oogoo00=oo`<001Aoo`03O003h7`000D07`03O01oogoo02=oo`05O0007`0O01ml0007 0n000g`0Oomoo`2EOol007Moo`8000Moo`03001oogoo01=oo`03O003h7`000D07`03O01oogoo029o o`03O0007`0O00807`03O003h0?P00D3h003O01oogoo09Eoo`00MGoo0P0087oo0W`01P0O00=l07oo Ool08Goo00=l000O01l00P0O00=l00?P0n0010?P00=l07ooOol0UWoo001cOol2000ROol00g`00n1l 000501l00g`0Oomoo`0QOol01G`001l07`0OO0001`?P00=l07ooOol0UWoo001aOol2000TOol00g`0 0n1l000501l00g`0Oomoo`0POol00g`001l07`0201l00g`00n03h0040n000g`0Oomoo`0/Ool20005 Ool3000017oo000007oo1@0017oo1@000goo0`0000=oo`0000000goo0`0017oo1@000goo10000goo 0`0000Aoo`00000002Ioo`00Kgoo0P009goo0W`01@0O00=l07ooOol087oo00=l000O01l00P0O00=l 00?P0n0010?P00=l07ooOol0;7oo0P0017oo00@007ooOomoo`8000=oo`03001oogoo00Moo`03001o ogoo009oo`04001oogooOol20003Ool01@00Oomoogoo00001Goo00<007ooOol00Woo00<007ooOol0 0Woo00D007ooOomoo`0000=oo`03001oogoo02Eoo`00KGoo0P00:Goo0W`01@0O00=l07ooOol07goo 00=l000O01l00`0O00=l00?P0n0010?P00=l07ooOol0:goo00@007ooOol000=oo`03001oogoo009o o`05001oogooOol00009Ool00`00Oomoo`02Ool00`00Oomoo`02Ool01@00Oomoogoo00002Goo00<0 07ooOol00Woo00<007ooOol00Woo00D007ooOomoo`0000=oo`03001oogoo02Eoo`00Jgoo0P00;7oo 0W`01@0O00=l07ooOol07Woo00=l000O01l00P0O00=l00?P0n0010?P00=l07ooOol0;7oo00@007oo Ool000Aoo`D000=oo`03001oogoo00Moo`03001oogoo00=oo`D000=oo`03001oogoo00Moo`03001o ogoo009oo`03001oogoo009oo`05001oogooOol00003Ool00`00Oomoo`0UOol006Uoo`8002ioo`9l 00D07`03O01oogoo01ioo`03O0007`0O00807`03O003h0?P00@3h003O01oogoo02]oo`03001oogoo 009oo`04001oogoo0004Ool01000Oomoogoo0P0027oo00<007ooOol00Woo00<007ooOol00Woo00D0 07ooOomoo`0000Uoo`03001oogoo009oo`03001oogoo009oo`04001oogooOol20002Ool00`00Oomo o`0UOol006Moo`80031oo`9l00D07`03O01oogoo01eoo`03O0007`0O00<07`03O003h0?P00<3h003 O01oogoo02]oo`<0009oo`<0009oo`@000=oo`800004Ool000000003Ool30005Ool40003Ool50004 Ool30005Ool40003Ool200000goo0000000XOol006Eoo`8003=oo`03O0007`0O00<07`03O01oogoo 01eoo`03O0007`0O00<07`03O003h0?P00<3h003O01oogoo05Eoo`03001oogoo045oo`00Hgoo0P00 =Goo00=l000O01l0100O00=l07ooOol077oo00=l000O01l00`0O00=l00?P0n000`?P00=l07ooOol0 Agoo00<007ooOol05Goo00<007ooOol0=goo001ROol00`00Oomoo`0fOol00g`001l07`0301l00g`0 Oomoo`0KOol00g`001l07`0301l00g`00n03h0030n000g`0Oomoo`2JOol0061oo`8003Uoo`03O000 7`0O00<07`03O01oogoo01]oo`03O0007`0O00<07`03O003h0?P00<3h003O01oogoo09Yoo`00GWoo 0P00>goo00=l000O01l00`0O00=l07ooOol06Woo00=l000O01l0100O00=l00?P0n000P?P00=l07oo Ool0Vgoo001LOol2000mOol00g`001l07`0401l00g`0Oomoo`0IOol00g`001l07`0401l00g`00n03 h0020n000g`0Oomoo`2KOol005Yoo`8003moo`03O0007`0O00@07`03O01oogoo01Uoo`03O0007`0O 00<07`03O003h0?P0083h003O01oogoo09aoo`00F7oo0P00@Woo00=l000O01l00`0O00=l07ooOol0 67oo00=l000O01l0100O00=l00?P0n000P?P00=l07ooOol0W7oo001FOol20014Ool00g`001l07`03 01l00g`0Oomoo`0HOol00g`001l07`0401l01G`00n03h0?PO000Wgoo001DOol20016Ool00g`001l0 7`0401l00g`0Oomoo`0GOol00g`001l07`0401l01G`00n03h0?PO000Wgoo001BOol20018Ool00g`0 01l07`0401l00g`0Oomoo`0FOol00g`001l07`0401l01G`00n03h0?PO000X7oo001@Ool2001:Ool0 0g`001l07`0401l00g`0Oomoo`0FOol00g`001l07`0401l01G`00n03h0?PO000X7oo001>Ool2001= Ool00g`001l07`0301l00g`0Oomoo`0EOol00g`001l07`0501l017`00n03h7`0XGoo001=Ool00`00 Oomoo`1=Ool00g`001l07`0401l00g`0Oomoo`0DOol00g`001l07`0501l017`00n03h7`0XGoo002M Ool00g`001l07`0401l00g`0Oomoo`0DOol00g`001l07`0401l017`00n03h7`0XWoo000jOol30000 17oo000000000Woo10000goo1@000Woo0`0000Eoo`00001oo`00009oo`<00003Ool00000009oo`D0 03Eoo`03O0007`0O00@07`03O01oogoo01=oo`03O0007`0O00D07`04O003h0?PO02ROol003]oo`05 001oogooOol00002Ool00`00Oomoo`02Ool01@00Oomoogoo00001Woo00@007ooOol0009oo`03001o o`0000=oo`8000Eoo`03001oogoo03Eoo`03O0007`0O00@07`03O01oogoo01=oo`03O0007`0O00D0 7`03O003h7`00:=oo`00>goo00D007ooOomoo`00009oo`03001oogoo009oo`05001oogooOol00006 Ool01000Oomoo`000Woo00<007oo000017oo00<007ooOol00goo00<007ooOol0=Woo00=l000O01l0 100O00=l07ooOol04Goo00=l000O01l01P0O00=l00?PO000Xgoo000kOol01@00Oomoogoo00000Woo 00<007ooOol00Woo00D007ooOomoo`0000Ioo`04001oogoo0002Ool00`00Oomoo`050005Ool00`00 Oomoo`0fOol00g`001l07`0401l00g`0Oomoo`0AOol00g`001l07`0501l00g`00n1l002TOol003]o o`80009oo`04001oogoo0004Ool01000Oomoogoo0P001Goo0P0000Moo`00001oo`00Ool00004Ool0 0`00Oomoo`03Ool00`00Oomoo`0fOol00g`001l07`0401l00g`0Oomoo`0@Ool00g`001l07`0601l0 0g`00n1l002TOol003Yoo`800003Ool0000000Aoo`@000=oo`800005Ool00000001oo`0200001Goo 001oogoo00000goo10001Woo00<007ooOol0=Woo00=l000O01l0100O00=l07ooOol047oo00=l000O 01l01P0O0W`0YGoo001UOol00`00Oomoo`0gOol00g`001l07`0401l00g`0Oomoo`0>Ool00g`001l0 7`0601l00g`00n1l002UOol006Aoo`8003Uoo`03O0007`0O00@07`03O01oogoo00ioo`03O0007`0O 00H07`9l0:Ioo`00Wgoo00=l000O01l0100O00=l07ooOol03Woo00=l000O01l01P0O0W`0YWoo002P Ool00g`001l07`0301l00g`0Oomoo`0=Ool00g`001l07`0701l00g`0Oomoo`2UOol00:1oo`03O000 7`0O00<07`03O01oogoo00eoo`03O0007`0O00H07`03O01oogoo0:Ioo`00XGoo00=l000O01l00`0O 00=l07ooOol02goo00=l000O01l01`0O00=l07ooOol0YWoo002QOol00g`001l07`0301l00g`0Oomo o`0;Ool00g`001l07`0701l00g`0Oomoo`2VOol00:5oo`03O0007`0O00<07`9l00]oo`03O0007`0O 00L07`03O01oogoo0:Moo`00XWoo00=l000O01l00P0O00=l00?PO0002Woo00=l000O01l01`0O00=l 07ooOol0Ygoo002ROol00g`001l07`0301l00g`00n1l0008Ool00g`001l07`0801l00g`0Oomoo`2W Ool00:9oo`03O0007`0O00<07`04O003h0?PO007Ool00g`001l07`0801l00g`0Oomoo`2WOol00:=o o`03O0007`0O00807`05O003h0?P0n1l0005Ool00g`001l07`0801l00g`0Oomoo`2XOol00:=oo`03 O0007`0O00807`03O003h0?P0083h09l00=oo`03O0007`0O00P07`03O01oogoo0:Qoo`00Y7oo00=l 000O01l00P0O00=l00?P0n000`?P0g`02`0O00=l07ooOol0Z7oo002TOol00g`001l07`0201l00g`0 0n03h0040n02O00:01l00g`0Oomoo`2YOol00:Eoo`05O0007`0O01ml00060n000g`001l07`0901l0 0g`0Oomoo`2YOol00:Eoo`05O0007`0O01ml00060n000g`001l07`0901l00g`0Oomoo`2YOol00:Io o`05O0007`0O01ml00040n000g`001l07`0:01l00g`0Oomoo`2YOol00:Moo`04O0007`0OO0020n02 O00<01l00g`0Oomoo`2ZOol00:Qoo`Il00d07`03O01oogoo0:Yoo`00ZWoo0W`03`0O00=l07ooOol0 ZWoo002[Ool00g`001l07`0<01l00g`0Oomoo`2[Ool00:aoo`03O0007`0O00/07`03O01oogoo0:]o o`00[7oo00=l000O01l02P0O00=l07ooOol0[7oo002]Ool00g`001l07`0901l00g`0Oomoo`2/Ool0 0:eoo`03O0007`0O00T07`03O01oogoo0:aoo`00[Woo00=l000O01l01`0O00=l07ooOol0[Goo002^ Ool00g`001l07`0701l00g`0Oomoo`2]Ool00:moo`03O0007`0O00D07`03O01oogoo0:ioo`00/7oo 00=l000O01l00`0O00=l07ooOol0[goo002`Ool2O00301l00g`0Oomoo`2`Ool00;5oo`El0;9oo`00 ogooJGoo003oOomYOol00?moofUoo`00ogooJGoo003oOomYOol00001\ \>"], ImageRangeCache->{{{127.438, 356.813}, {431.938, 290.625}} -> {-0.558944, 2.05661, 0.00349883, 0.00566123}, {{127.75, 356.438}, {431.938, 290.625}} -> {-13.341, 0.655674, 0.0440853, 0.00182591}, {{127.75, 356.438}, {431.938, 290.625}} -> {-13.341, 0.655674, 0.0440853, 0.00182591}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth] }, Open ]], Cell["\<\ Below, we remove the normal from the background to reveal only the two stable \ plots.\ \>", "Text", PageWidth->PaperWidth], Cell[CellGroupData[{ Cell[BoxData[ \(stbl2plt = FilledPlot[{Evaluate[{Abs[ ffx1\/m1] /. {\[Alpha] \[Rule] 1.1, \[Beta] \[Rule] 0, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}}\ ], Evaluate[{Abs[ ffx1\/m1] /. {\[Alpha] \[Rule] 1.1, \[Beta] \[Rule] .75, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}}]}, {x, \(-6\), 6}, PlotRange -> All, Epilog\ -> \ {Arrow[{4, \ .2}, \ {4, .03}], Arrow[{\(-3.6\), \ .25}, \ {\(-1.3\), .2}], Arrow[{ .5, \ .05}, \ {\(-1.7\), .06}], \n\ \ \ \ \ \ Text["\", \ {3.7, \ .22}, \ {0, \ \(- .5\)}], Text["\", \ {3.8, \ .2}, \ {0, \ \(- .5\)}], Text["\", {\(-3.5\), .25}, {0, \(- .5\)}], Text["\", { .15, .03}, {0, \(- .5\)}], Text["\", { .05, .01}, {0, \(- .5\)}]}, GridLines -> None, \ Frame -> None, Axes -> None, PlotStyle -> {{Hue[ .3], Hue[1]}}]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0 1 0 0.618034 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.05 0.0125 moveto 0 0 lineto -0.05 -0.0125 lineto fill -0.05 0.0125 moveto 0 0 lineto -0.05 -0.0125 lineto -0.05 0.0125 lineto stroke } ifelse grestore } def % End of user PostScript % Start of sub-graphic p 0 0 1 0.618034 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0793651 0.0112366 1.92732 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 1 0 0 r .5 Mabswid [ ] 0 setdash .02381 .02644 m .06244 .02935 L .10458 .03358 L .14415 .039 L .18221 .04621 L .20178 .05102 L .22272 .05728 L .24259 .06462 L .26416 .0746 L .28492 .08686 L .30409 .1013 L .32282 .11929 L .34344 .14511 L .36285 .17716 L .38373 .22283 L .40486 .28406 L .42495 .3578 L .46315 .52022 L .47328 .55687 L .47825 .5718 L .48282 .58331 L .4881 .59357 L .49088 .59756 L .4923 .5992 L .49382 .60066 L .49511 .60165 L .49628 .60235 L .49746 .60287 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60292 L .50306 .60267 L .50379 .60232 L .50501 .60157 L .50614 .60069 L .50871 .59806 L .51121 .59465 L .51389 .59011 L .52314 .56787 L .53407 .53098 L .544 .49091 L .58398 .32319 L .6023 .26146 L .62244 .20793 L .64232 .16775 L .66336 .13578 L .68281 .11341 L .7037 .09501 L .72488 .08069 L Mistroke .74498 .07007 L .78322 .05537 L .80294 .04978 L .82392 .04488 L .86556 .0375 L .90568 .03243 L .94428 .02879 L .97619 .02644 L Mfstroke .02381 .01472 m .06244 .01539 L .08255 .01583 L .10458 .01639 L .14415 .01774 L .16372 .01862 L .18466 .01979 L .20597 .02132 L .22611 .0232 L .24608 .02568 L .26452 .02882 L .28325 .0333 L .29389 .03677 L .30387 .04093 L .31425 .0466 L .32412 .05387 L .33298 .06267 L .34264 .07577 L .35296 .09534 L .36232 .11956 L .37311 .15665 L .38329 .20096 L .42184 .41585 L .43215 .46837 L .44178 .50899 L .45182 .54076 L .45714 .5529 L .4599 .55792 L .46284 .5623 L .46535 .56529 L .46669 .56659 L .46813 .56778 L .46944 .56867 L .47065 .56934 L .4718 .56983 L .47302 .5702 L .47371 .57035 L .47434 .57044 L .47507 .5705 L .47575 .57051 L .47698 .57041 L .47767 .57029 L .4783 .57015 L .47964 .56972 L .48111 .56907 L .48265 .56818 L .48408 .56717 L .48915 .56231 L .49378 .55623 L .5042 .53776 L Mistroke .52323 .49228 L .54396 .43483 L .58466 .3263 L .62384 .24364 L .64386 .2104 L .66548 .18042 L .7056 .13791 L .72557 .12172 L .74665 .10741 L .78468 .08718 L .82515 .07143 L .86411 .06018 L .90553 .05116 L .94542 .04452 L .97619 .04041 L Mfstroke 0 1 1 r .02381 .02644 m .06244 .02935 L .10458 .03358 L .14415 .039 L .18221 .04621 L .20178 .05102 L .22272 .05728 L .24259 .06462 L .26416 .0746 L .28492 .08686 L .30409 .1013 L .32282 .11929 L .34344 .14511 L .36285 .17716 L .38373 .22283 L .40486 .28406 L .42495 .3578 L .46315 .52022 L .47328 .55687 L .47825 .5718 L .48282 .58331 L .4881 .59357 L .49088 .59756 L .4923 .5992 L .49382 .60066 L .49511 .60165 L .49628 .60235 L .49746 .60287 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60292 L .50306 .60267 L .50379 .60232 L .50501 .60157 L .50614 .60069 L .50871 .59806 L .51121 .59465 L .51389 .59011 L .52314 .56787 L .53407 .53098 L .544 .49091 L .58398 .32319 L .6023 .26146 L .62244 .20793 L .64232 .16775 L .66336 .13578 L .68281 .11341 L .7037 .09501 L .72488 .08069 L .74498 .07007 L .78322 .05537 L .80294 .04978 L .82392 .04488 L .86556 .0375 L .90568 .03243 L .94428 .02879 L .97619 .02644 L .97619 .04041 L .94542 .04452 L .90553 .05116 L .86411 .06018 L .82515 .07143 L .78468 .08718 L .74665 .10741 L .72557 .12172 L .7056 .13791 L .66548 .18042 L .64386 .2104 L .62384 .24364 L .58466 .3263 L .54396 .43483 L .52323 .49228 L .5042 .53776 L .49378 .55623 L .48915 .56231 L .48408 .56717 L .48265 .56818 L .48111 .56907 L .47964 .56972 L .4783 .57015 L .47767 .57029 L .47698 .57041 L .47575 .57051 L .47507 .5705 L .47434 .57044 L .47371 .57035 L .47302 .5702 L .4718 .56983 L .47065 .56934 L .46944 .56867 L .46813 .56778 L .46669 .56659 L .46535 .56529 L .46284 .5623 L .4599 .55792 L .45714 .5529 L .45182 .54076 L .44178 .50899 L .43215 .46837 L .42184 .41585 L .38329 .20096 L .37311 .15665 L .36232 .11956 L .35296 .09534 L .34264 .07577 L .33298 .06267 L .32412 .05387 L .31425 .0466 L .30387 .04093 L .29389 .03677 L .28325 .0333 L .26452 .02882 L .24608 .02568 L .22611 .0232 L .20597 .02132 L .18466 .01979 L .16372 .01862 L .14415 .01774 L .10458 .01639 L .08255 .01583 L .06244 .01539 L .02381 .01472 L F 1 0 0 r .02381 .02644 m .06244 .02935 L .10458 .03358 L .14415 .039 L .18221 .04621 L .20178 .05102 L .22272 .05728 L .24259 .06462 L .26416 .0746 L .28492 .08686 L .30409 .1013 L .32282 .11929 L .34344 .14511 L .36285 .17716 L .38373 .22283 L .40486 .28406 L .42495 .3578 L .46315 .52022 L .47328 .55687 L .47825 .5718 L .48282 .58331 L .4881 .59357 L .49088 .59756 L .4923 .5992 L .49382 .60066 L .49511 .60165 L .49628 .60235 L .49746 .60287 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60292 L .50306 .60267 L .50379 .60232 L .50501 .60157 L .50614 .60069 L .50871 .59806 L .51121 .59465 L .51389 .59011 L .52314 .56787 L .53407 .53098 L .544 .49091 L .58398 .32319 L .6023 .26146 L .62244 .20793 L .64232 .16775 L .66336 .13578 L .68281 .11341 L .7037 .09501 L .72488 .08069 L Mistroke .74498 .07007 L .78322 .05537 L .80294 .04978 L .82392 .04488 L .86556 .0375 L .90568 .03243 L .94428 .02879 L .97619 .02644 L Mfstroke .02381 .01472 m .06244 .01539 L .08255 .01583 L .10458 .01639 L .14415 .01774 L .16372 .01862 L .18466 .01979 L .20597 .02132 L .22611 .0232 L .24608 .02568 L .26452 .02882 L .28325 .0333 L .29389 .03677 L .30387 .04093 L .31425 .0466 L .32412 .05387 L .33298 .06267 L .34264 .07577 L .35296 .09534 L .36232 .11956 L .37311 .15665 L .38329 .20096 L .42184 .41585 L .43215 .46837 L .44178 .50899 L .45182 .54076 L .45714 .5529 L .4599 .55792 L .46284 .5623 L .46535 .56529 L .46669 .56659 L .46813 .56778 L .46944 .56867 L .47065 .56934 L .4718 .56983 L .47302 .5702 L .47371 .57035 L .47434 .57044 L .47507 .5705 L .47575 .57051 L .47698 .57041 L .47767 .57029 L .4783 .57015 L .47964 .56972 L .48111 .56907 L .48265 .56818 L .48408 .56717 L .48915 .56231 L .49378 .55623 L .5042 .53776 L Mistroke .52323 .49228 L .54396 .43483 L .58466 .3263 L .62384 .24364 L .64386 .2104 L .66548 .18042 L .7056 .13791 L .72557 .12172 L .74665 .10741 L .78468 .08718 L .82515 .07143 L .86411 .06018 L .90553 .05116 L .94542 .04452 L .97619 .04041 L Mfstroke 0 g .81746 .3967 m .81746 .06906 L s % Start of user PostScript 4. 0.2 4. 0.03 MAarrowhead1 % End of user PostScript .21429 .49307 m .39683 .3967 L s % Start of user PostScript -3.6 0.25 -1.3 0.2 MAarrowhead1 % End of user PostScript .53968 .1076 m .36508 .12688 L s % Start of user PostScript 0.5 0.05 -1.7 0.06 MAarrowhead1 % End of user PostScript gsave .79365 .43525 -90 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (variation) show 117.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .80159 .3967 -78 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (added) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .22222 .49307 -81 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (normal) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .5119 .06906 -90 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (variation) show 117.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .50397 .03051 -84 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (removed) show 105.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0 0 1 0.618034 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0793651 0.0112366 1.92732 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgO03oOolSOol000Qooch3o`ml0?mooaAoo`0027ooC@?o1g`0ogoo3Goo0008Ool7O01=0ol5 O03^Ool@O009Ool000moo`ml04<3o`=l0>Aoo`Ml00l3o`Yoo`007Woo2g`0>`?o0g`0fWoo1g`05P?o 2Woo000YOol8O00f0ol3O00aOol50004Ool500001Goo00000000Ool00P0000Aoo`00Oomoo`@000Eo o`8000Eoo`D000=oo`<00003Ool0000006Qoo`Ml01d3o`Yoo`00goo17`0 ;`?o0W`0;7oo00<007ooOol017oo1P000Woo00@007ooOol0009oo`03001oo`0000Aoo`05001oogoo Ool00002Ool01000Oomoogoo1P000Woo00<007ooOol00Woo00<007ooOol0Dgoo1G`09@?o2G`03goo 000oOol6O00[0ol00g`0Oomoo`0YOol20005Ool00`00Oomoo`02Ool00`00Oomoo`0200001goo0000 07oo001oo`0000Aoo`04001oogoo0004Ool01000Oomoo`0017oo00@007ooOol000=oo`80055oo`Al 0283o`Ql01Qoo`00AGoo1G`09`?o0W`0:7oo0P0000Aoo`00000000=oo`@0009oo`800005Ool007oo Ool00003Ool40002Ool30002Ool30002Ool40004Ool300000goo001oo`10ol00g`0 Oomoo`1dOol2O00C0ol2O00COol8000oOol0071oo`03O003o`?o00d3o`03O01oogoo011oo`8002Qo o`D003Aoo`03O003o`?o0183o`03O01oogoo01=oo`P003moo`00LGoo00=l00?o0ol03@?o00=l07oo Ool03Goo10007goo2@00>7oo00=l00?o0ol04@?o0W`05Woo2000?goo001bOol00g`00ol3o`0<0ol0 0g`0Oomoo`0:Ool7000FOol90010Ool00g`00ol3o`0A0ol00g`0Oomoo`0FOol9000nOol007=oo`03 O003o`?o00`3o`03O01oogoo00Moo`T000ioo`P004Qoo`03O003o`?o0143o`03O01oogoo01Ioo`X0 03ioo`00M7oo00=l00?o0ol02`?o00=l07ooOol01Goo2`001Goo2@00Cgoo00=l00?o0ol040?o0W`0 6Goo2P00?Woo001eOol00g`00ol3o`0:0ol00g`0Oomoo`02OolC001GOol00g`00ol3o`0@0ol00g`0 Oomoo`0NOol00`00Oomoo`10Ool007Ioo`03O003o`?o00X3o`03O01oo`00010005Yoo`03O003o`?o 0103o`03O01oogoo01moo`03001oogoo041oo`00MWoo00=l00?o0ol02P?o4`00FWoo00=l00?o0ol0 3`?o00=l07ooOol087oo00<007ooOol0@7oo001gOol00g`00ol3o`090ol00g`0Oomoo`02Ool>001I Ool00g`00ol3o`0>0ol2O00SOol00`00Oomoo`10Ool007Qoo`03O003o`?o00T3o`03O01oogoo00Yo o`D005Qoo`03O003o`?o00h3o`03O01oogoo02=oo`03001oogoo041oo`00NGoo00=l00?o0ol020?o 00=l07ooOol0IWoo00=l00?o0ol03P?o00=l07ooOol097oo00<007ooOol0@7oo001iOol00g`00ol3 o`080ol00g`0Oomoo`1UOol00g`00ol3o`0>0ol00g`0Oomoo`0UOol00`00Oomoo`10Ool007Yoo`03 O003o`?o00L3o`03O01oogoo06Eoo`03O003o`?o00d3o`03O01oogoo02Ioo`03001oogoo041oo`00 Ngoo00=l00?o0ol01`?o00=l07ooOol0Hgoo00=l00?o0ol03@?o00=l07ooOol09goo00<007ooOol0 @7oo001lOol00g`00ol3o`060ol00g`0Oomoo`1ROol00g`00ol3o`0=0ol00g`0Oomoo`0XOol00`00 Oomoo`10Ool007aoo`03O003o`?o00H3o`03O01oogoo069oo`03O003o`?o00`3o`03O01oogoo02Uo o`03001oogoo041oo`00OGoo00=l00?o0ol01P?o00=l07ooOol0H7oo00=l00?o0ol030?o00=l07oo Ool0:Woo00<007ooOol0@7oo001mOol00g`00ol3o`060ol00g`0Oomoo`1POol00g`00ol3o`0;0ol0 0g`0Oomoo`0[Ool00`00Oomoo`10Ool007ioo`03O003o`?o00D3o`03O01oogoo05moo`03O003o`?o 00/3o`03O01oogoo02aoo`03001oogoo041oo`00OWoo00=l00?o0ol01@?o00=l07ooOol0GWoo00=l 00?o0ol02`?o00=l07ooOol0;Goo00<007ooOol0@7oo001oOol00g`00ol3o`050ol00g`0Oomoo`1M Ool00g`00ol3o`0:0ol00g`0Oomoo`0^Ool00`00Oomoo`10Ool0081oo`03O003o`?o00@3o`03O01o ogoo05aoo`03O003o`?o00X3o`03O01oogoo02moo`03001oogoo041oo`00P7oo00=l00?o0ol010?o 00=l07ooOol0G7oo00=l00?o0ol02@?o00=l07ooOol0<7oo00<007ooOol0@7oo0021Ool00g`00ol3 o`030ol00g`0Oomoo`1KOol00g`00ol3o`090ol00g`0Oomoo`0aOol00`00Oomoo`10Ool0085oo`03 O003o`?o00<3o`03O01oogoo05]oo`03O003o`?o00P3o`03O01oogoo039oo`03001oogoo041oo`00 PWoo00=l00?o0ol00P?o00=l07ooOol0FWoo00=l00?o0ol020?o00=l07ooOol07oo00<0 07ooOol0@7oo0025Ool01G`00ol3o`?oO000Egoo00=l00?o0ol01@?o00=l07ooOol0>Goo00<007oo Ool0@7oo0025Ool01G`00ol3o`?oO000EWoo00=l00?o0ol01@?o00=l07ooOol0>Woo00<007ooOol0 @7oo0026Ool017`00ol3og`0EWoo00=l00?o0ol01@?o00=l07ooOol0>Woo00<007ooOol0@7oo0026 Ool017`00ol3og`0EGoo00=l00?o0ol01@?o00=l07ooOol0>goo00<007ooOol0@7oo0027Ool017`0 0ol3og`0E7oo00=l00?o0ol010?o00=l07ooOol0?7oo00<007ooOol0@7oo0027Ool017`00ol3og`0 E7oo00=l00?o0ol00`?o00=l07ooOol0?Goo00<007ooOol0@7oo0028Ool00g`00oml001COol00g`0 0ol3o`040ol00g`0Oomoo`0mOol00`00Oomoo`10Ool008Qoo`03O003og`005=oo`03O003o`?o00<3 o`03O01oogoo03ioo`03001oogoo041oo`00RGoo0W`0Dgoo00=l00?o0ol00`?o00=l07ooOol0?Woo 00<007ooOol0@7oo0029Ool2O01BOol00g`00ol3o`030ol00g`0Oomoo`0oOol00`00Oomoo`10Ool0 08Uoo`03O003og`0055oo`03O003o`?o0083o`03O01oogoo041oo`03001oogoo041oo`00RWoo0W`0 D7oo00=l00?o0ol00`?o00=l07ooOol0@7oo00<007ooOol0@7oo002:Ool2O01@Ool00g`00ol3o`02 0ol00g`0Oomoo`11Ool00`00Oomoo`10Ool008Yoo`9l051oo`03O003o`?o0083o`03O01oogoo045o o`03001oogoo041oo`00Rgoo00=l07ooOol0CGoo00=l00?o0ol00P?o00=l07ooOol0@Woo00<007oo Ool0@7oo002;Ool2O01>Ool00g`00ol3o`020ol00g`0Oomoo`12Ool00`00Oomoo`10Ool008aoo`03 O01oogoo04aoo`05O003o`?o0oml0015Ool00`00Oomoo`10Ool008aoo`03O01oogoo04]oo`03O003 o`?o0083o`03O01oogoo04=oo`03001oogoo041oo`00S7oo00=l07ooOol0Bgoo00El00?o0ol3og`0 04Ioo`03001oogoo041oo`00S7oo0W`0Bgoo00=l00?o0ol00P?o00=l07ooOol0A7oo00<007ooOol0 @7oo002Ool2O017Ool017`00ol3og`0BWoo00<007ooOol0@7oo002>Ool00g`00oml0016Ool0 17`00ol3og`0BWoo00<007ooOol0@7oo002>Ool00g`00oml0015Ool017`00ol3og`0Bgoo00<007oo Ool0@7oo002>Ool00g`00oml0015Ool017`00ol3og`0Bgoo00<007ooOol0@7oo002>Ool017`00ol3 og`0A7oo00=l00?oO000C7oo00<007ooOol0@7oo002>Ool017`00ol3og`0@goo00Al00?o0oml04ao o`03001oogoo041oo`00Sgoo00=l00?oO000@goo00Al00?o0oml04aoo`03001oogoo041oo`00Sgoo 00Al00?o0oml049oo`03O003og`004eoo`03001oogoo041oo`00Sgoo00Al00?o0oml045oo`04O003 o`?oO01=Ool00`00Oomoo`10Ool008moo`04O003o`?oO011Ool00g`00oml001>Ool00`00Oomoo`10 Ool008moo`04O003o`?oO011Ool00g`00oml001>Ool00`00Oomoo`10Ool0091oo`04O003o`?oO010 Ool2O01?Ool00`00Oomoo`10Ool0091oo`04O003o`?oO00oOol00g`00oml001?Ool00`00Oomoo`10 Ool0091oo`04O003o`?oO00oOol2O01@Ool00`00Oomoo`10Ool0091oo`04O003o`?oO00oOol2O01@ Ool00`00Oomoo`10Ool0091oo`05O003o`?o0oml000mOol2O01AOol00`00Oomoo`10Ool0091oo`05 O003o`?o0oml000mOol2O01AOol00`00Oomoo`10Ool0095oo`04O003o`?oO00mOol00g`0Oomoo`1@ Ool00`00Oomoo`10Ool0095oo`04O003o`?oO00lOol2O01BOol00`00Oomoo`10Ool0095oo`05O003 o`?o0oml000kOol00g`0Oomoo`1AOol00`00Oomoo`10Ool0095oo`05O003o`?o0oml000kOol00g`0 Oomoo`1AOol00`00Oomoo`10Ool0095oo`05O003o`?o0oml000kOol00g`0Oomoo`1AOol00`00Oomo o`10Ool0099oo`05O003o`?o0oml000iOol00g`0Oomoo`1BOol00`00Oomoo`10Ool0099oo`05O003 o`?o0oml000iOol00g`0Oomoo`1BOol00`00Oomoo`10Ool0099oo`05O003o`?o0oml000iOol00g`0 Oomoo`1BOol00`00Oomoo`10Ool0099oo`05O003o`?o0oml000hOol2O01DOol00`00Oomoo`10Ool0 099oo`03O003o`?o0083o`03O01oogoo03Eoo`03O01oogoo05=oo`03001oogoo041oo`00TWoo00=l 00?o0ol00P?o00=l07ooOol0=7oo0W`0EGoo00<007ooOol0@7oo002COol01G`00ol3o`?oO000=Woo 0W`0EGoo00<007ooOol0@7oo002COol01G`00ol3o`?oO000=Woo0W`0EGoo00<007ooOol0@7oo002C Ool00g`00ol3o`020ol00g`0Oomoo`0bOol2O01FOol00`00Oomoo`10Ool009=oo`03O003o`?o0083 o`03O01oogoo039oo`9l05Ioo`03001oogoo041oo`00Tgoo00=l00?o0ol00P?o00=l07ooOol0Ool00g`00ol3o`030ol00g`0Oomoo`0V Ool01G`00ol3o`?oO000@Woo00<007ooOol00Woo00@007ooOol000=oo`80009oo`04001oogooOol2 0002Ool00`00Oomoo`02Ool01000Oomoo`000goo0P00=Goo001mOol;000?Ool00g`00ol3o`030ol0 0g`0Oomoo`0VOol017`00ol3og`0A7oo100017oo0`0000=oo`00Ool00Woo0`0000=oo`00Ool00Woo 100017oo0`0000=oo`00Ool0=7oo001mOol9000AOol00g`00ol3o`030ol00g`0Oomoo`0UOol01G`0 0ol3o`?oO000D7oo00<007ooOol01Goo00<007ooOol03Goo00<007ooOol0goo00D007ooOomoo`00009oo`03001oogoo 009oo`05001oogooOol00006Ool01000Oomoo`000Woo00<007ooOol01@001Goo00<007ooOol0=Woo 00=l00?o0ol010?o00=l07ooOol04Goo00=l00?o0ol01@?o00=l07ooOol0Y7oo000kOol20002Ool0 1000Oomoo`0017oo00@007ooOomoo`8000Eoo`800007Ool00000Ool007oo000017oo00<007ooOol0 0goo00<007ooOol0=Woo00=l00?o0ol010?o00=l07ooOol047oo00=l00?o0ol01P?o00=l07ooOol0 Y7oo000jOol200000goo00000004Ool40003Ool200001Goo00000000Ool00P0000Eoo`00Oomoo`00 00=oo`@000Ioo`03001oogoo03Moo`03O003o`?o00@3o`03O01oogoo00moo`03O003o`?o00H3o`03 O01oogoo0:Aoo`00IGoo00<007ooOol0=goo00=l00?o0ol010?o00=l07ooOol03Woo00=l00?o0ol0 1P?o00=l07ooOol0YGoo001TOol2000iOol00g`00ol3o`040ol00g`0Oomoo`0>Ool00g`00ol3o`06 0ol00g`0Oomoo`2UOol00:1oo`03O003o`?o00<3o`03O01oogoo00eoo`03O003o`?o00L3o`03O01o ogoo0:Eoo`00X7oo00=l00?o0ol00`?o00=l07ooOol03Goo00=l00?o0ol01`?o00=l07ooOol0YGoo 002POol00g`00ol3o`040ol00g`0Oomoo`0"], ImageRangeCache->{{{127.438, 356.813}, {405.813, 264.5}} -> {-0.558944, 1.87174, 0.00349883, 0.00566123}, {{127.75, 356.438}, {405.813, 264.5}} -> {-13.341, 0.594381, 0.0440853, 0.00181539}, {{127.75, 356.438}, { 405.813, 264.5}} -> {-13.341, 0.594381, 0.0440853, 0.00181539}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth] }, Open ]], Cell["\<\ The prior illustration may be clearer with the only the normal plot in the \ background, behind the filled plot of the two stable distributions.\ \>", "Text", PageWidth->PaperWidth], Cell[CellGroupData[{ Cell[BoxData[ \(rtskew = Show[bmppdf2, stbl2plt, Epilog\ -> \ {Arrow[{4, \ .2}, \ {4, .03}], Arrow[{\(-3.6\), \ .25}, \ {\(-1.3\), .2}], Arrow[{ .5, \ .05}, \ {\(-1.7\), .06}], \n\ \ \ \ \ \ Text["\", \ {3.7, \ .22}, \ {0, \ \(- .5\)}], Text["\", \ {3.8, \ .2}, \ {0, \ \(- .5\)}], Text["\", {\(-3.5\), .25}, {0, \(- .5\)}], Text["\", { .15, .03}, {0, \(- .5\)}], Text["\", { .05, .01}, {0, \(- .5\)}]}]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0793651 0.0136698 1.9194 [ [.79365 .43594 -29 -3.21875 ] [.79365 .43594 29 9.65625 ] [.80159 .39755 -17 -3.21875 ] [.80159 .39755 17 9.65625 ] [.22222 .49352 -20 -3.21875 ] [.22222 .49352 20 9.65625 ] [.5119 .07125 -29 -3.21875 ] [.5119 .07125 29 9.65625 ] [.50397 .03286 -23 -3.21875 ] [.50397 .03286 23 9.65625 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.05 0.0125 moveto 0 0 lineto -0.05 -0.0125 lineto fill -0.05 0.0125 moveto 0 0 lineto -0.05 -0.0125 lineto -0.05 0.0125 lineto stroke } ifelse grestore } def % End of user PostScript 0 .4 1 r .5 Mabswid [ ] 0 setdash .10317 .01472 m .11065 .01499 L .11885 .01537 L .13537 .01644 L .14415 .01723 L .15355 .01829 L .17048 .02095 L .179 .02274 L .18824 .0251 L .20502 .0308 L .22155 .03862 L .23908 .04998 L .25536 .06401 L .27061 .08074 L .30292 .12956 L .33727 .20295 L .37036 .29155 L .40219 .38405 L .41995 .43353 L .43606 .47402 L .45304 .50975 L .46867 .53443 L .47647 .54335 L .48044 .54696 L .48471 .55012 L .48694 .55147 L .48898 .55252 L .49106 .55341 L .49298 .55406 L .49521 .55463 L .49639 .55484 L .49699 .55493 L .49764 .555 L .49872 .55509 L .49974 .55512 L .50033 .55512 L .50095 .5551 L .50148 .55507 L .50206 .55503 L .50315 .55491 L .50417 .55475 L .50528 .55452 L .50646 .55423 L .50844 .55359 L .51062 .5527 L .51464 .55054 L .5184 .5479 L .52681 .53989 L .53586 .52819 L .5535 .49697 L Mistroke .57025 .4588 L .60212 .37159 L .63604 .27342 L .66869 .18868 L .68537 .15211 L .70339 .11851 L .71933 .0939 L .73682 .07213 L .75347 .05595 L .77103 .043 L .78732 .03411 L .80476 .02724 L .81326 .02469 L .82249 .0224 L .83048 .02077 L .83927 .01929 L .85578 .01723 L .86482 .01642 L .8733 .01582 L .88558 .01515 L .89683 .01472 L Mfstroke 1 0 0 r .02381 .02881 m .06244 .03171 L .10458 .03592 L .14415 .04132 L .18221 .0485 L .20178 .05329 L .22272 .05953 L .24259 .06683 L .26416 .07677 L .28492 .08898 L .30409 .10336 L .32282 .12128 L .34344 .147 L .36285 .17891 L .38373 .2244 L .40486 .28537 L .42495 .35881 L .46315 .52056 L .47328 .55706 L .47825 .57193 L .48282 .58339 L .4881 .59361 L .49088 .59758 L .4923 .59922 L .49382 .60067 L .49511 .60166 L .49628 .60236 L .49746 .60287 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60292 L .50306 .60267 L .50379 .60232 L .50501 .60158 L .50614 .6007 L .50871 .59808 L .51121 .59468 L .51389 .59016 L .52314 .56802 L .53407 .53128 L .544 .49137 L .58398 .32434 L .6023 .26286 L .62244 .20955 L .64232 .16954 L .66336 .1377 L .68281 .11543 L .7037 .0971 L .72488 .08284 L Mistroke .74498 .07226 L .78322 .05762 L .80294 .05205 L .82392 .04717 L .86556 .03983 L .90568 .03477 L .94428 .03115 L .97619 .02881 L Mfstroke .02381 .01713 m .06244 .01781 L .08255 .01824 L .10458 .01881 L .14415 .02015 L .16372 .02102 L .18466 .02219 L .20597 .02371 L .22611 .02558 L .24608 .02806 L .26452 .03118 L .28325 .03565 L .29389 .0391 L .30387 .04324 L .31425 .04889 L .32412 .05613 L .33298 .06489 L .34264 .07794 L .35296 .09743 L .36232 .12155 L .37311 .15848 L .38329 .20261 L .42184 .41662 L .43215 .46893 L .44178 .50938 L .45182 .54102 L .45714 .55311 L .4599 .55811 L .46284 .56247 L .46535 .56544 L .46669 .56674 L .46813 .56793 L .46944 .56882 L .47065 .56948 L .4718 .56997 L .47302 .57034 L .47371 .57048 L .47434 .57058 L .47507 .57063 L .47575 .57064 L .47698 .57055 L .47767 .57043 L .4783 .57028 L .47964 .56986 L .48111 .56921 L .48265 .56833 L .48408 .56732 L .48915 .56248 L .49378 .55642 L .5042 .53803 L Mistroke .52323 .49273 L .54396 .43553 L .58466 .32743 L .62384 .24512 L .64386 .21202 L .66548 .18215 L .7056 .13982 L .72557 .1237 L .74665 .10945 L .78468 .0893 L .82515 .07362 L .86411 .06241 L .90553 .05343 L .94542 .04682 L .97619 .04273 L Mfstroke 0 1 1 r .02381 .02881 m .06244 .03171 L .10458 .03592 L .14415 .04132 L .18221 .0485 L .20178 .05329 L .22272 .05953 L .24259 .06683 L .26416 .07677 L .28492 .08898 L .30409 .10336 L .32282 .12128 L .34344 .147 L .36285 .17891 L .38373 .2244 L .40486 .28537 L .42495 .35881 L .46315 .52056 L .47328 .55706 L .47825 .57193 L .48282 .58339 L .4881 .59361 L .49088 .59758 L .4923 .59922 L .49382 .60067 L .49511 .60166 L .49628 .60236 L .49746 .60287 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60292 L .50306 .60267 L .50379 .60232 L .50501 .60158 L .50614 .6007 L .50871 .59808 L .51121 .59468 L .51389 .59016 L .52314 .56802 L .53407 .53128 L .544 .49137 L .58398 .32434 L .6023 .26286 L .62244 .20955 L .64232 .16954 L .66336 .1377 L .68281 .11543 L .7037 .0971 L .72488 .08284 L .74498 .07226 L .78322 .05762 L .80294 .05205 L .82392 .04717 L .86556 .03983 L .90568 .03477 L .94428 .03115 L .97619 .02881 L .97619 .04273 L .94542 .04682 L .90553 .05343 L .86411 .06241 L .82515 .07362 L .78468 .0893 L .74665 .10945 L .72557 .1237 L .7056 .13982 L .66548 .18215 L .64386 .21202 L .62384 .24512 L .58466 .32743 L .54396 .43553 L .52323 .49273 L .5042 .53803 L .49378 .55642 L .48915 .56248 L .48408 .56732 L .48265 .56833 L .48111 .56921 L .47964 .56986 L .4783 .57028 L .47767 .57043 L .47698 .57055 L .47575 .57064 L .47507 .57063 L .47434 .57058 L .47371 .57048 L .47302 .57034 L .4718 .56997 L .47065 .56948 L .46944 .56882 L .46813 .56793 L .46669 .56674 L .46535 .56544 L .46284 .56247 L .4599 .55811 L .45714 .55311 L .45182 .54102 L .44178 .50938 L .43215 .46893 L .42184 .41662 L .38329 .20261 L .37311 .15848 L .36232 .12155 L .35296 .09743 L .34264 .07794 L .33298 .06489 L .32412 .05613 L .31425 .04889 L .30387 .04324 L .29389 .0391 L .28325 .03565 L .26452 .03118 L .24608 .02806 L .22611 .02558 L .20597 .02371 L .18466 .02219 L .16372 .02102 L .14415 .02015 L .10458 .01881 L .08255 .01824 L .06244 .01781 L .02381 .01713 L F 1 0 0 r .02381 .02881 m .06244 .03171 L .10458 .03592 L .14415 .04132 L .18221 .0485 L .20178 .05329 L .22272 .05953 L .24259 .06683 L .26416 .07677 L .28492 .08898 L .30409 .10336 L .32282 .12128 L .34344 .147 L .36285 .17891 L .38373 .2244 L .40486 .28537 L .42495 .35881 L .46315 .52056 L .47328 .55706 L .47825 .57193 L .48282 .58339 L .4881 .59361 L .49088 .59758 L .4923 .59922 L .49382 .60067 L .49511 .60166 L .49628 .60236 L .49746 .60287 L .49857 .60318 L .49987 .60332 L .50107 .60324 L .50239 .60292 L .50306 .60267 L .50379 .60232 L .50501 .60158 L .50614 .6007 L .50871 .59808 L .51121 .59468 L .51389 .59016 L .52314 .56802 L .53407 .53128 L .544 .49137 L .58398 .32434 L .6023 .26286 L .62244 .20955 L .64232 .16954 L .66336 .1377 L .68281 .11543 L .7037 .0971 L .72488 .08284 L Mistroke .74498 .07226 L .78322 .05762 L .80294 .05205 L .82392 .04717 L .86556 .03983 L .90568 .03477 L .94428 .03115 L .97619 .02881 L Mfstroke .02381 .01713 m .06244 .01781 L .08255 .01824 L .10458 .01881 L .14415 .02015 L .16372 .02102 L .18466 .02219 L .20597 .02371 L .22611 .02558 L .24608 .02806 L .26452 .03118 L .28325 .03565 L .29389 .0391 L .30387 .04324 L .31425 .04889 L .32412 .05613 L .33298 .06489 L .34264 .07794 L .35296 .09743 L .36232 .12155 L .37311 .15848 L .38329 .20261 L .42184 .41662 L .43215 .46893 L .44178 .50938 L .45182 .54102 L .45714 .55311 L .4599 .55811 L .46284 .56247 L .46535 .56544 L .46669 .56674 L .46813 .56793 L .46944 .56882 L .47065 .56948 L .4718 .56997 L .47302 .57034 L .47371 .57048 L .47434 .57058 L .47507 .57063 L .47575 .57064 L .47698 .57055 L .47767 .57043 L .4783 .57028 L .47964 .56986 L .48111 .56921 L .48265 .56833 L .48408 .56732 L .48915 .56248 L .49378 .55642 L .5042 .53803 L Mistroke .52323 .49273 L .54396 .43553 L .58466 .32743 L .62384 .24512 L .64386 .21202 L .66548 .18215 L .7056 .13982 L .72557 .1237 L .74665 .10945 L .78468 .0893 L .82515 .07362 L .86411 .06241 L .90553 .05343 L .94542 .04682 L .97619 .04273 L Mfstroke 0 g .81746 .39755 m .81746 .07125 L s % Start of user PostScript 4. 0.2 4. 0.03 MAarrowhead1 % End of user PostScript .21429 .49352 m .39683 .39755 L s % Start of user PostScript -3.6 0.25 -1.3 0.2 MAarrowhead1 % End of user PostScript .53968 .10964 m .36508 .12883 L s % Start of user PostScript 0.5 0.05 -1.7 0.06 MAarrowhead1 % End of user PostScript gsave .79365 .43594 -90 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (variation) show 117.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .80159 .39755 -78 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (added) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .22222 .49352 -81 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (normal) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .5119 .07125 -90 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (variation) show 117.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .50397 .03286 -84 -7.21875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (removed) show 105.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg1oo`H1Wcaoo`0027oo?P?o 3g`0cGoo106O@Woo0008Ool7O0160ol7O033Ool30IlgOol6O009Ool000moo`]l0483o`El0;]oo`<1 Wc1oo`Yl00D3o`Yoo`006Woo27`0?`?o0g`0]Woo0P6O;7oo1g`03`?o2Woo000ROol7O00k0ol3O02a Ool20IlTOol:O00F0ol:Ool002Uoo`Ql03H3o`=l035oo`D000Aoo`D00005Ool00000001oo`020000 17oo001oogoo10001Goo0P001Goo1@000goo0`0000=oo`000000AGoo00<1WgooOol06Woo2W`080?o 2Woo000aOol7O00b0ol2O00`Ool00`00Oomoo`04Ool00`00Oomoo`05Ool01000Oomoo`000Woo00<0 07oo000017oo00<007ooOol00Woo0P0017oo00<007ooOol01Goo00@007ooOomoo`8004Aoo`81WaQo o`El02P3o`=l00Uoo`00>7oo1W`0;P?o0W`0;Woo00<007ooOol017oo00<007ooOol01Goo00@007oo Ool0009oo`03001oo`0000Aoo`05001oogooOol00002Ool01@00Oomoogoo00001goo00<007ooOol0 0Woo00<007ooOol0@Goo00<1WgooOol04goo1G`09`?o1W`037oo000nOol5O00[0ol2O00/Ool00`00 Oomoo`04Ool60002Ool01000Oomoo`000Woo00<007oo000017oo00D007ooOomoo`00009oo`04001o ogooOol60002Ool00`00Oomoo`02Ool00`00Oomoo`0oOol20IlBOol4O00V0ol6O00BOol004=oo`Al 02T3o`03O01oogoo02Uoo`8000Eoo`03001oogoo009oo`03001oogoo00800007Ool00000Ool007oo 000017oo00@007ooOol000Aoo`04001oogoo0004Ool01000Oomoo`000goo0P00@7oo00<1WgooOol0 3Woo17`08P?o27`067oo0017Ool3O00W0ol2O00XOol2000017oo000000000goo10000Woo0P0000Eo o`00Oomoo`0000=oo`@0009oo`<0009oo`<0009oo`@000Aoo`<00003Ool007oo03eoo`81W`ioo`=l 0203o`Il021oo`00BWoo17`09@?o0W`0Fgoo00<007ooOol0>goo00<1WgooOol02Woo17`07P?o1G`0 9Woo001>Ool4O00S0ol00g`0Oomoo`1GOol2000lOol00`6OOomoo`07Ool4O00M0ol5O00[Ool0059o o`9l0283o`03O01oogoo09=oo`030Imoogoo00Ioo`9l01d3o`Al031oo`00E7oo0W`08@?o00=l07oo Ool0TGoo00<1WgooOol017oo0g`06`?o17`0=7oo001FOol2O00P0ol00g`0Oomoo`2?Ool00`6OOomo o`02Ool3O00K0ol3O00hOol005Qoo`9l01l3o`03O01oogoo08eoo`040ImoogooOol2O00J0ol4O00k Ool005Yoo`9l01d3o`03O01oogoo08aoo`030Imoogoo009l01P3o`04001l07`0O00oOol005aoo`9l 01`3o`03O01oogoo01aoo`8000Eoo`<00004Ool00000Ool50004Ool50003Ool300000goo00000003 Ool30004Ool50003Ool40003Ool3000017oo00000000:Goo00@1WgooO01l01T3o`03O00007oo045o o`00GWoo0W`06`?o00=l07ooOol06goo0P0017oo00@007ooOomoo`8000=oo`03001oogoo00Moo`03 001oogoo009oo`04001oogooOol20003Ool01@00Oomoogoo00001Goo00<007ooOol00Woo00<007oo Ool00Woo00D007ooOomoo`0000=oo`03001oogoo02Moo`030Iml07`001T3o`9l0080049oo`00H7oo 0W`06@?o00=l07ooOol06Woo00@007ooOol000=oo`03001oogoo009oo`05001oogooOol00009Ool0 0`00Oomoo`02Ool00`00Oomoo`02Ool01@00Oomoogoo00002Goo00<007ooOol00Woo00<007ooOol0 0Woo00D007ooOomoo`0000=oo`03001oogoo02Ioo`9l01P3o`=l009oo`<0045oo`00HWoo0W`060?o 00=l07ooOol06Goo00@007ooOol000Aoo`D000=oo`03001oogoo00Moo`03001oogoo00=oo`D000=o o`03001oogoo00Moo`03001oogoo009oo`03001oogoo009oo`05001oogooOol00003Ool00`00Oomo o`0UOol00g`00ol3o`0F0ol2O005Ool30011Ool0069oo`040Imoog`0O00F0ol00g`0Oomoo`0HOol0 0`00Oomoo`02Ool01000Oomoo`0017oo00@007ooOomoo`8000Qoo`03001oogoo009oo`03001oogoo 009oo`05001oogooOol00009Ool00`00Oomoo`02Ool00`00Oomoo`02Ool01000Oomoogoo0P000Woo 00<007ooOol08goo0W`05`?o0W`01goo0`00@Goo001SOol0106OOomoog`05P?o00=l07ooOol05Woo 0`000Woo0`000Woo10000goo0P0000Aoo`00000000=oo`<000Eoo`@000=oo`D000Aoo`<000Eoo`@0 00=oo`800003Ool0000002Eoo`03O003o`?o01D3o`9l00Qoo`@0045oo`00Hgoo00@1WgooOomoo`9l 01@3o`03O01oogoo041oo`03001oogoo03aoo`9l01H3o`9l00Yoo`D0041oo`00I7oo00<1WgooOol0 0Woo00=l00?o0ol04P?o00=l07ooOol00ol00g`0Oomoo`1fOol00g`00ol3 o`0B0ol2O00COol7000oOol006Moo`030Imoogoo00Eoo`03O003o`?o00h3o`03O01oogoo03Yoo`D0 03Eoo`03O003o`?o0143o`9l01Aoo`P003moo`00J7oo00<1WgooOol01Goo00=l00?o0ol03@?o00=l 07ooOol047oo0P007goo2@00>7oo0W`04P?o0W`05Woo2000?goo001XOol00`6OOomoo`06Ool00g`0 0ol3o`0=0ol00g`0Oomoo`00ol2O00SOol00`00Oomoo`10Ool006aoo`030Imoogoo00Qo o`03O003o`?o00T3o`03O01oogoo00Ioo`X005Uoo`03O003o`?o00d3o`03O01oogoo02=oo`03001o ogoo041oo`00KGoo00<1WgooOol027oo00=l00?o0ol02@?o00=l07ooOol02goo1000F7oo00=l00?o 0ol03@?o00=l07ooOol097oo00<007ooOol0@7oo001]Ool00`6OOomoo`09Ool00g`00ol3o`080ol0 0g`0Oomoo`1VOol00g`00ol3o`0=0ol00g`0Oomoo`0UOol00`00Oomoo`10Ool006ioo`030Imoogoo 00Qoo`03O003o`?o00P3o`03O01oogoo06Ioo`03O003o`?o00`3o`03O01oogoo02Ioo`03001oogoo 041oo`00KWoo00<1WgooOol02Goo00=l00?o0ol01`?o00=l07ooOol0IGoo00=l00?o0ol030?o00=l 07ooOol09goo00<007ooOol0@7oo001_Ool00`6OOomoo`09Ool00g`00ol3o`070ol00g`0Oomoo`1S Ool00g`00ol3o`0<0ol00g`0Oomoo`0XOol00`00Oomoo`10Ool006moo`030Imoogoo00Yoo`03O003 o`?o00H3o`03O01oogoo06=oo`03O003o`?o00/3o`03O01oogoo02Uoo`03001oogoo041oo`00L7oo 00<1WgooOol02Goo00=l00?o0ol01P?o00=l07ooOol0HWoo00=l00?o0ol02`?o00=l07ooOol0:Woo 00<007ooOol0@7oo001`Ool00`6OOomoo`0:Ool00g`00ol3o`060ol00g`0Oomoo`1POol00g`00ol3 o`0;0ol00g`0Oomoo`0[Ool00`00Oomoo`10Ool0075oo`030Imoogoo00Yoo`03O003o`?o00D3o`03 O01oogoo061oo`03O003o`?o00X3o`03O01oogoo02aoo`03001oogoo041oo`00LGoo00<1WgooOol0 2Woo00=l00?o0ol01@?o00=l07ooOol0Ggoo00=l00?o0ol02P?o00=l07ooOol0;Goo00<007ooOol0 @7oo001bOol00`6OOomoo`0:Ool00g`00ol3o`040ol00g`0Oomoo`1NOol00g`00ol3o`0:0ol00g`0 Oomoo`0^Ool00`00Oomoo`10Ool0079oo`030Imoogoo00Yoo`03O003o`?o00D3o`03O01oogoo05eo o`03O003o`?o00T3o`03O01oogoo02moo`03001oogoo041oo`00Lgoo00<1WgooOol02Woo00=l00?o 0ol010?o00=l07ooOol0G7oo00=l00?o0ol02@?o00=l07ooOol0<7oo00<007ooOol0@7oo001cOol0 0`6OOomoo`0;Ool00g`00ol3o`030ol00g`0Oomoo`1KOol00g`00ol3o`090ol00g`00Imoo`0aOol0 0`00Oomoo`10Ool007Aoo`030Imoogoo00Yoo`03O003o`?o00<3o`03O01oogoo05]oo`03O003o`?o 00P3o`03O001Wgoo039oo`03001oogoo041oo`00M7oo00<1WgooOol02goo00=l00?o0ol00P?o00=l 07ooOol0FWoo00=l00?o0ol020?o00=l07oo0Il07oo00<007ooOol0@7oo001lOol00`6OOomoo`0: Ool00g`00oml001@Ool00g`00ol3o`040ol00g`0Oomoo`04Ool00`6OOomoo`0hOol00`00Oomoo`10 Ool007eoo`030Imoogoo00Yoo`9l051oo`03O003o`?o00<3o`03O01oogoo00Aoo`030Imoogoo03Uo o`03001oogoo041oo`00OGoo00<1WgooOol02Woo0W`0D7oo00=l00?o0ol00`?o00=l07ooOol017oo 00<1WgooOol0>Goo00<007ooOol0@7oo001mOol00`6OOomoo`0;Ool00g`0Oomoo`1=Ool00g`00ol3 o`030ol00g`0Oomoo`05Ool00`6OOomoo`0iOol00`00Oomoo`10Ool007ioo`030Imoogoo00Yoo`03 O01oogoo04eoo`03O003o`?o0083o`03O01oogoo00Eoo`030Imoogoo03Yoo`03001oogoo041oo`00 OWoo00<1WgooOol02Woo0W`0CWoo00=l00?o0ol00P?o00=l07ooOol01Goo00<1WgooOol0>Woo00<0 07ooOol0@7oo001oOol00`6OOomoo`0:Ool00g`0Oomoo`1;Ool00g`00ol3o`020ol00g`0Oomoo`06 Ool00`6OOomoo`0jOol00`00Oomoo`10Ool007moo`030Imoogoo00Yoo`03O01oogoo04]oo`03O003 o`?o0083o`03O01oogoo00Eoo`030Imoogoo03]oo`03001oogoo041oo`00Ogoo00<1WgooOol02Woo 00=l07ooOol0BWoo00=l00?o0ol00P?o00=l07ooOol01Woo00<1WgooOol0>goo00<007ooOol0@7oo 0020Ool00`6OOomoo`09Ool2O01;Ool00g`00ol3o`020ol00g`0Oomoo`06Ool00`6OOomoo`0kOol0 0`00Oomoo`10Ool0081oo`030Imoogoo00Uoo`9l04]oo`05O003o`?o0oml0008Ool00`6OOomoo`0l Ool00`00Oomoo`10Ool0081oo`030Imoogoo00Yoo`9l04Uoo`03O003o`?o0083o`03O01oogoo00Io o`030Imoogoo03aoo`03001oogoo041oo`00PGoo00<1WgooOol02Goo0W`0BGoo00El00?o0ol3og`0 00Qoo`030Imoogoo03eoo`03001oogoo041oo`00PGoo00<1WgooOol02Goo0W`0BGoo00El00?o0ol3 og`000Qoo`030Imoogoo03eoo`03001oogoo041oo`00PWoo00<1WgooOol027oo00=l00?oO000Agoo 00El00?o0ol3og`000Uoo`030Imoogoo03eoo`03001oogoo041oo`00PWoo00<1WgooOol027oo00=l 00?oO000Agoo00El00?o0ol3og`000Qoo`030Imoogoo03ioo`03001oogoo041oo`00PWoo00<1Wgoo Ool02Goo0W`0Agoo00Al00?o0oml00Uoo`030Imoogoo03ioo`03001oogoo041oo`00Pgoo00<1Wgoo Ool027oo00=l00?oO000AGoo00El00?o0ol3og`000Uoo`030Imoogoo03ioo`03001oogoo041oo`00 Pgoo00<1WgooOol027oo00=l00?oO000AGoo00Al00?o0oml00Uoo`030Imoogoo03moo`03001oogoo 041oo`00Pgoo00<1WgooOol027oo00Al00?o0oml04Aoo`04O003o`?oO009Ool00`6OOomoo`0oOol0 0`00Oomoo`10Ool008Aoo`030Imoogoo00Moo`04O003o`?oO013Ool017`00ol3og`02Woo00<1Wgoo Ool0?goo00<007ooOol0@7oo0024Ool00`6OOomoo`08Ool00g`00oml0013Ool017`00ol3og`02Goo 00<1WgooOol0@7oo00<007ooOol0@7oo0025Ool00`6OOomoo`07Ool017`00ol3og`0@Woo00=l00?o O0002Woo00<1WgooOol0@7oo00<007ooOol0@7oo0025Ool00`6OOomoo`07Ool017`00ol3og`0@Goo 00Al00?o0oml00Yoo`030Imoogoo041oo`03001oogoo041oo`00QGoo00<1WgooOol01goo00Al00?o 0oml045oo`03O003og`000Yoo`030Imoogoo045oo`03001oogoo041oo`00QWoo00<1WgooOol01Woo 00Al00?o0oml045oo`03O003og`000Yoo`030Imoogoo045oo`03001oogoo041oo`00QWoo00<1Wgoo Ool01Woo00El00?o0ol3og`0041oo`9l00]oo`030Imoogoo045oo`03001oogoo041oo`00QWoo00<1 WgooOol01goo00Al00?o0oml03moo`03O003og`000Yoo`030Imoogoo049oo`03001oogoo041oo`00 Qgoo00<1WgooOol01Woo00Al00?o0oml03moo`9l00]oo`030Imoogoo049oo`03001oogoo041oo`00 Qgoo00<1WgooOol01Woo00Al00?o0oml03moo`9l00]oo`030Imoogoo049oo`03001oogoo041oo`00 Qgoo00<1WgooOol01Woo00El00?o0ol3og`003eoo`9l00]oo`030Imoogoo04=oo`03001oogoo041o o`00R7oo00<1WgooOol01Goo00El00?o0ol3og`003eoo`9l00]oo`030Imoogoo04=oo`03001oogoo 041oo`00R7oo00<1WgooOol01Woo00Al00?o0oml03eoo`03O01oogoo00Yoo`030Imoogoo04=oo`03 001oogoo041oo`00R7oo00<1WgooOol01Woo00Al00?o0oml03aoo`9l00]oo`030Imoogoo04Aoo`03 001oogoo041oo`00RGoo00<1WgooOol01Goo00El00?o0ol3og`003]oo`03O01oogoo00Yoo`030Imo ogoo04Aoo`03001oogoo041oo`00RGoo00<1WgooOol01Goo00El00?o0ol3og`003]oo`03O01oogoo 00Uoo`030Imoogoo04Eoo`03001oogoo041oo`00RGoo00<1WgooOol01Goo00El00?o0ol3og`003]o o`03O01oogoo00Uoo`030Imoogoo04Eoo`03001oogoo041oo`00RWoo00<1WgooOol017oo00El00?o 0ol3og`003Yoo`03O01oogoo00Yoo`030Imoogoo04Eoo`03001oogoo041oo`00RWoo00<1WgooOol0 1Goo00El00?o0ol3og`003Uoo`03O01oogoo00Uoo`030Imoogoo04Ioo`03001oogoo041oo`00RWoo 00<1WgooOol01Goo00El00?o0ol3og`003Uoo`03O01oogoo00Uoo`030Imoogoo04Ioo`03001oogoo 041oo`00Rgoo00<1WgooOol017oo00El00?o0ol3og`003Qoo`9l00]oo`030Imoogoo04Ioo`03001o ogoo041oo`00Rgoo00<1WgooOol017oo00El00?o0ol3og`003Qoo`03O01oogoo00Uoo`030Imoogoo 04Moo`03001oogoo041oo`00Rgoo00<1WgooOol017oo00=l00?o0ol00P?o00=l07ooOol0=7oo0W`0 2goo00<1WgooOol0Agoo00<007ooOol0@7oo002Ool00`6OOomoo`03Ool01G`00ol3o`?oO000Ool00`6OOomoo`03Ool00g`00ol3o`020ol00g`0Oomoo`0`Ool2 O00:Ool00`6OOomoo`1:Ool00`00Oomoo`10Ool008ioo`030Imoogoo00=oo`03O003o`?o0083o`03 O01oogoo02moo`03O003og`000Yoo`030Imoogoo04Yoo`03001oogoo041oo`00Sgoo00<1WgooOol0 0Woo00=l00?o0ol00P?o00=l07ooOol0;goo00=l00?oO0002Woo00<1WgooOol0BWoo00<007ooOol0 @7oo002?Ool00`6OOomoo`02Ool00g`00ol3o`020ol00g`0Oomoo`0_Ool00g`00oml0009Ool00`6O Oomoo`1;Ool00`00Oomoo`10Ool008moo`030Imoogoo00=oo`03O003o`?o0083o`03O01oogoo02eo o`03O003og`000Yoo`030Imoogoo04]oo`03001oogoo041oo`00T7oo00<1WgooOol00Woo00=l00?o 0ol00P?o00=l07ooOol0;Goo00=l00?oO0002Goo00<1WgooOol0C7oo00<007ooOol0@7oo002@Ool0 0`6OOomoo`02Ool00g`00ol3o`020ol00g`0Oomoo`0/Ool017`00ol3og`02Goo00<1WgooOol0C7oo 00<007ooOol0@7oo002@Ool00`6OOomoo`02Ool00g`00ol3o`020ol00g`0Oomoo`0/Ool017`00ol3 og`02Goo00<1WgooOol0C7oo00<007ooOol0@7oo002AOol01@6OOomoogooO0001@?o00=l07ooOol0 :goo00=l00?oO0002Goo00<1WgooOol0CGoo00<007ooOol0@7oo002AOol00`6OOomoo`02Ool00g`0 0ol3o`020ol00g`0Oomoo`0ZOol017`00ol3og`02Goo00<1WgooOol0CGoo00<007ooOol0@7oo002A Ool00`6OOomoo`02Ool00g`00ol3o`020ol00g`0Oomoo`0ZOol017`00ol3og`02Goo00<1WgooOol0 CGoo00<007ooOol0@7oo0027oo1@000Woo00<007ooOol00Woo00@007ooOol000Aoo`03001o ogoo00H0009oo`03001oogoo009oo`03001oogoo03=oo`00O7oo3@002goo00@1WgooOoml00D3o`03 O01oogoo02Ioo`05O003o`?o0oml0007Ool00`6OOomoo`0hOol00`00Oomoo`02Ool01000Oomoo`00 0goo0P000Woo00@007ooOomoo`80009oo`03001oogoo009oo`04001oogoo0003Ool2000eOol007eo o`/000aoo`040ImoogooO0050ol00g`0Oomoo`0VOol017`00ol3og`027oo00<1WgooOol0>Goo1000 17oo0`0000=oo`00Ool00Woo0`0000=oo`00Ool00Woo100017oo0`0000=oo`00Ool0=7oo001mOol: 000=Ool0106OOomoog`01@?o00=l07ooOol09Goo00El00?o0ol3og`000Moo`030Imoogoo04Ioo`03 001oogoo00Eoo`03001oogoo00eoo`03001oogoo03=oo`00OWoo20003goo00<1WgooO0001@?o00=l 07ooOol09Goo00El00?o0ol3og`000Moo`030Imoogoo04Eoo`8000Ioo`8000ioo`8003Eoo`00O7oo 2@0047oo00@1WgooOoml00D3o`03O01oogoo02=oo`03O003o`?o0083o`03O01oogoo00Eoo`030Imo ogoo09Aoo`00NWoo0P000goo10004Woo00@1WgooOoml00D3o`03O01oogoo02=oo`05O003o`?o0oml 0007Ool00`6OOomoo`2EOol007Uoo`03001oogoo00=oo`<001Aoo`030Imoog`000D3o`03O01oogoo 02=oo`05O003o`?o0oml0007Ool00`6OOomoo`2EOol007Moo`8000Moo`03001oogoo01=oo`030Imo og`000D3o`03O01oogoo029oo`03O003o`?o0083o`03O01oogoo00Aoo`030Imoogoo09Ioo`00MGoo 0P007goo00<1WgooO0001P?o00=l07ooOol08Goo00=l00?o0ol00P?o00=l07ooOol017oo00<1Wgoo Ool0UWoo001cOol2000ROol00`6OOoml00050ol00g`0Oomoo`0QOol01G`00ol3o`?oO0001goo00<1 WgooOol0UWoo001aOol2000TOol00`6OOoml00050ol00g`0Oomoo`0POol00g`00ol3o`020ol00g`0 Oomoo`04Ool00`6OOomoo`0/Ool20005Ool3000017oo000007oo1@0017oo1@000goo0`0000=oo`00 00000goo0`0017oo1@000goo10000goo0`0000Aoo`00000002Ioo`00Kgoo0P009goo00<1Wg`00ol0 10?o00=l07ooOol087oo00=l00?o0ol00P?o00=l07ooOol017oo00<1WgooOol0;7oo0P0017oo00@0 07ooOomoo`8000=oo`03001oogoo00Moo`03001oogoo009oo`04001oogooOol20003Ool01@00Oomo ogoo00001Goo00<007ooOol00Woo00<007ooOol00Woo00D007ooOomoo`0000=oo`03001oogoo02Eo o`00KGoo0P00:Goo00<1Wg`00ol010?o00=l07ooOol07goo00=l00?o0ol00`?o00=l07ooOol017oo 00<1WgooOol0:goo00@007ooOol000=oo`03001oogoo009oo`05001oogooOol00009Ool00`00Oomo o`02Ool00`00Oomoo`02Ool01@00Oomoogoo00002Goo00<007ooOol00Woo00<007ooOol00Woo00D0 07ooOomoo`0000=oo`03001oogoo02Eoo`00Jgoo0P00:goo00<1WgooO0001@?o00=l07ooOol07Woo 00=l00?o0ol00P?o00=l07ooOol017oo00<1WgooOol0;7oo00@007ooOol000Aoo`D000=oo`03001o ogoo00Moo`03001oogoo00=oo`D000=oo`03001oogoo00Moo`03001oogoo009oo`03001oogoo009o o`05001oogooOol00003Ool00`00Oomoo`0UOol006Uoo`8002ioo`030Iml00?o00@3o`03O01oogoo 01ioo`03O003o`?o0083o`03O01oogoo00Aoo`030Imoogoo02]oo`03001oogoo009oo`04001oogoo 0004Ool01000Oomoogoo0P0027oo00<007ooOol00Woo00<007ooOol00Woo00D007ooOomoo`0000Uo o`03001oogoo009oo`03001oogoo009oo`04001oogooOol20002Ool00`00Oomoo`0UOol006Moo`80 031oo`030Iml00?o00@3o`03O01oogoo01eoo`03O003o`?o00<3o`03O01oogoo00=oo`030Imoogoo 02]oo`<0009oo`<0009oo`@000=oo`800004Ool000000003Ool30005Ool40003Ool50004Ool30005 Ool40003Ool200000goo0000000XOol006Eoo`8003=oo`03O003o`?o00<3o`03O01oogoo01eoo`03 O003o`?o00<3o`03O01oogoo00=oo`030Imoogoo05Eoo`03001oogoo045oo`00Hgoo0P00=Goo00=l 00?o0ol010?o00=l07ooOol077oo00=l00?o0ol00`?o00=l07ooOol00goo00<1WgooOol0Agoo00<0 07ooOol05Goo00<007ooOol0=goo001ROol00`00Oomoo`0eOol00`6OO003o`040ol00g`0Oomoo`0K Ool00g`00ol3o`030ol00g`0Oomoo`03Ool00`6OOomoo`2JOol0061oo`8003Uoo`03O003o`?o00<3 o`03O01oogoo01]oo`03O003o`?o00<3o`03O01oogoo00=oo`030Imoogoo09Yoo`00GWoo0P00>goo 00=l00?o0ol00`?o00=l07ooOol06Woo00=l00?o0ol010?o00=l07ooOol00Woo00<1WgooOol0Vgoo 001LOol2000mOol00g`00ol3o`040ol00g`0Oomoo`0IOol00g`00ol3o`040ol00g`0Oomoo`02Ool0 0`6OOomoo`2KOol005Yoo`8003moo`03O003o`?o00@3o`03O01oogoo01Uoo`03O003o`?o00<3o`03 O01oogoo009oo`030Imoogoo09aoo`00F7oo0P00@Woo00=l00?o0ol00`?o00=l07ooOol067oo00=l 00?o0ol010?o00=l07ooOol00Woo00<1WgooOol0W7oo001FOol20014Ool00g`00ol3o`030ol00g`0 Oomoo`0HOol00g`00ol3o`040ol00g`0Oomoo`02Ool00`6OOomoo`2LOol005Aoo`8004Ioo`03O003 o`?o00@3o`03O01oogoo01Moo`03O003o`?o00@3o`05O01oogooOol1W`2OOol0059oo`8004Qoo`03 O003o`?o00@3o`03O01oogoo01Ioo`03O003o`?o00@3o`03O01oogoo009oo`030Imoogoo09eoo`00 D7oo0P00BWoo00=l00?o0ol010?o00=l07ooOol05Woo00=l00?o0ol010?o00El07ooOomoo`6O0:1o o`00CWoo0P00CGoo00=l00?o0ol00`?o00=l07ooOol05Goo00=l00?o0ol01@?o00El07ooOomoo`6O 0:1oo`00CGoo00<007ooOol0CGoo00=l00?o0ol010?o00=l07ooOol057oo00=l00?o0ol01@?o00Al 07ooOol1Wj5oo`00WGoo00=l00?o0ol010?o00=l07ooOol057oo00=l00?o0ol010?o00El07ooOomo o`6O0:5oo`00>Woo0`0000Aoo`000000009oo`@000=oo`D0009oo`<00005Ool00000Ool00002Ool3 00000goo00000002Ool5000eOol00g`00ol3o`040ol00g`0Oomoo`0COol00g`00ol3o`050ol017`0 Oomoo`6OXWoo000kOol01@00Oomoogoo00000Woo00<007ooOol00Woo00D007ooOomoo`0000Ioo`04 001oogoo0002Ool00`00Ool00003Ool20005Ool00`00Oomoo`0eOol00g`00ol3o`040ol00g`0Oomo o`0COol00g`00ol3o`050ol017`0Oomoo`6OXWoo000kOol01@00Oomoogoo00000Woo00<007ooOol0 0Woo00D007ooOomoo`0000Ioo`04001oogoo0002Ool00`00Ool00004Ool00`00Oomoo`03Ool00`00 Oomoo`0fOol00g`00ol3o`040ol00g`0Oomoo`0AOol00g`00ol3o`060ol00g`0Ool1W`2SOol003]o o`05001oogooOol00002Ool00`00Oomoo`02Ool01@00Oomoogoo00001Woo00@007ooOol0009oo`03 001oogoo00D000Eoo`03001oogoo03Ioo`03O003o`?o00@3o`03O01oogoo015oo`03O003o`?o00D3 o`04O01oogoo0InSOol003]oo`80009oo`04001oogoo0004Ool01000Oomoogoo0P001Goo0P0000Mo o`00001oo`00Ool00004Ool00`00Oomoo`03Ool00`00Oomoo`0fOol00g`00ol3o`040ol00g`0Oomo o`0AOol00g`00ol3o`050ol00g`0Ool1W`2TOol003Yoo`800003Ool0000000Aoo`@000=oo`800005 Ool00000001oo`0200001Goo001oogoo00000goo10001Woo00<007ooOol0=Woo00=l00?o0ol010?o 00=l07ooOol047oo00=l00?o0ol01P?o00=l07oo0Il0Y7oo001UOol00`00Oomoo`0gOol00g`00ol3 o`040ol00g`0Oomoo`0?Ool00g`00ol3o`050ol00g`0Ool1W`2UOol006Aoo`8003Uoo`03O003o`?o 00@3o`03O01oogoo00moo`03O003o`?o00D3o`03O01oo`6O0:Eoo`00Wgoo00=l00?o0ol010?o00=l 07ooOol03Woo00=l00?o0ol01P?o00=l006OOol0YGoo002POol00g`00ol3o`030ol00g`0Oomoo`0> Ool00g`00ol3o`060ol00g`00Imoo`2UOol00:1oo`03O003o`?o00<3o`03O01oogoo00eoo`03O003 o`?o00H3o`03O001Wgoo0:Ioo`00XGoo00=l00?o0ol00`?o00=l07ooOol037oo00=l00?o0ol01P?o 00=l07ooOol0YWoo002QOol00g`00ol3o`030ol00g`0Oomoo`0"], ImageRangeCache->{{{127.438, 356.813}, {313.063, 171.75}} -> {-13.3427, 0.384226, 0.0440853, 0.00182288}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth] }, Open ]], Cell["\<\ Two factors are critical to the successful application of these procedures: \ the sampling range and interval in the ch.f. domain. As in any sampled data \ process, aliasing occurs if the sampling interval exceeds that required for \ the necessary range of the transformed variable. The sampling range in the \ ch.f. domain must include all significant values for the parameters of \ interest. Because of the characteristics of the transformation (rapid convergence in \ the ch.f. domain implies a wide range in the pdf domain and visa versa), the \ number of samples required tends to be constant - about 1000 samples are \ adequate for most sceneros, but more samples may be required for a wide range \ of parameters. If a larger range of x is required, the sampling interval may \ be increased in proportion, i.e. {f,-5,5,.01} or {f,-0.5,0.5,.001} or \ {f,-50,50,.1}, provided the f range as determined below is adequate. The f range can be readily tested by assigning the mininum values of interest \ to \[Alpha] and \[Gamma] (the rate of convergence is relatively insensitive \ to \[Beta] and \[Delta], but values must be provided), then evaluating the \ function |fu| over a range of f sufficient to include all significant values \ of |fu|. To illustrate:\ \>", "Text", PageWidth->PaperWidth], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[ Evaluate[{Abs[ fu] /. {\[Alpha] \[Rule] 1.1, \[Beta] \[Rule] \(-1\), \[Gamma] \[Rule] .2, \[Delta] \ \[Rule] 0, u -> 2\ \[Pi]\ f}, Abs[fu] /. {\[Alpha] \[Rule] 1.1, \[Beta] \[Rule] \(-1\), \[Gamma] \[Rule] .1, \[Delta] \ \[Rule] 0, u -> 2\ \[Pi]\ f}}], {f, \(-5\), 5}, PlotStyle -> {Hue[ .6], Hue[ .9]}, GridLines -> Automatic]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0952381 0.0147151 0.589273 [ [.11905 .00222 -6 -9 ] [.11905 .00222 6 0 ] [.30952 .00222 -6 -9 ] [.30952 .00222 6 0 ] [.69048 .00222 -3 -9 ] [.69048 .00222 3 0 ] [.88095 .00222 -3 -9 ] [.88095 .00222 3 0 ] [.4875 .13257 -18 -4.5 ] [.4875 .13257 0 4.5 ] [.4875 .25042 -18 -4.5 ] [.4875 .25042 0 4.5 ] [.4875 .36828 -18 -4.5 ] [.4875 .36828 0 4.5 ] [.4875 .48613 -18 -4.5 ] [.4875 .48613 0 4.5 ] [.4875 .60399 -6 -4.5 ] [.4875 .60399 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 .5 r .25 Mabswid [ ] 0 setdash .11905 0 m .11905 .61803 L s .30952 0 m .30952 .61803 L s .5 0 m .5 .61803 L s .69048 0 m .69048 .61803 L s .88095 0 m .88095 .61803 L s 0 .01472 m 1 .01472 L s 0 .13257 m 1 .13257 L s 0 .25042 m 1 .25042 L s 0 .36828 m 1 .36828 L s 0 .48613 m 1 .48613 L s 0 .60399 m 1 .60399 L s 0 g .11905 .01472 m .11905 .02097 L s [(-4)] .11905 .00222 0 1 Mshowa .30952 .01472 m .30952 .02097 L s [(-2)] .30952 .00222 0 1 Mshowa .69048 .01472 m .69048 .02097 L s [(2)] .69048 .00222 0 1 Mshowa .88095 .01472 m .88095 .02097 L s [(4)] .88095 .00222 0 1 Mshowa .125 Mabswid .16667 .01472 m .16667 .01847 L s .21429 .01472 m .21429 .01847 L s .2619 .01472 m .2619 .01847 L s .35714 .01472 m .35714 .01847 L s .40476 .01472 m .40476 .01847 L s .45238 .01472 m .45238 .01847 L s .54762 .01472 m .54762 .01847 L s .59524 .01472 m .59524 .01847 L s .64286 .01472 m .64286 .01847 L s .7381 .01472 m .7381 .01847 L s .78571 .01472 m .78571 .01847 L s .83333 .01472 m .83333 .01847 L s .07143 .01472 m .07143 .01847 L s .02381 .01472 m .02381 .01847 L s .92857 .01472 m .92857 .01847 L s .97619 .01472 m .97619 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .5 .13257 m .50625 .13257 L s [(0.2)] .4875 .13257 1 0 Mshowa .5 .25042 m .50625 .25042 L s [(0.4)] .4875 .25042 1 0 Mshowa .5 .36828 m .50625 .36828 L s [(0.6)] .4875 .36828 1 0 Mshowa .5 .48613 m .50625 .48613 L s [(0.8)] .4875 .48613 1 0 Mshowa .5 .60399 m .50625 .60399 L s [(1)] .4875 .60399 1 0 Mshowa .125 Mabswid .5 .04418 m .50375 .04418 L s .5 .07364 m .50375 .07364 L s .5 .10311 m .50375 .10311 L s .5 .16203 m .50375 .16203 L s .5 .1915 m .50375 .1915 L s .5 .22096 m .50375 .22096 L s .5 .27989 m .50375 .27989 L s .5 .30935 m .50375 .30935 L s .5 .33882 m .50375 .33882 L s .5 .39774 m .50375 .39774 L s .5 .42721 m .50375 .42721 L s .5 .45667 m .50375 .45667 L s .5 .5156 m .50375 .5156 L s .5 .54506 m .50375 .54506 L s .5 .57452 m .50375 .57452 L s .25 Mabswid .5 0 m .5 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 .4 1 r .5 Mabswid .02381 .01502 m .04262 .01514 L .06244 .01532 L .08255 .01557 L .09396 .01576 L .10458 .01597 L .125 .01649 L .14357 .01715 L .16272 .01808 L .1835 .01948 L .20334 .02135 L .22437 .02412 L .2439 .02768 L .2622 .0322 L .28245 .03898 L .30098 .04739 L .31996 .05891 L .34068 .07595 L .36036 .09783 L .38133 .12929 L .40274 .17281 L .42291 .22744 L .44299 .29838 L .46146 .38109 L .48188 .49373 L .49186 .55545 L .49415 .5698 L .49658 .58481 L .49866 .59706 L .49984 .60332 L .50095 .59924 L .50208 .59279 L .50312 .58662 L .50546 .57225 L .51036 .54153 L .51928 .48676 L .53892 .37918 L .55945 .28876 L .57855 .22297 L .59697 .17348 L .61665 .13285 L .638 .09996 L .65815 .07707 L .67817 .06024 L .69662 .04867 L .71538 .03985 L .73602 .03271 L .75547 .02781 L .77636 .024 L .79754 .02125 L Mistroke .81764 .01939 L .83748 .01806 L .85588 .01717 L .87645 .01645 L .89507 .01597 L .91435 .01562 L .93518 .01535 L .95514 .01516 L .96518 .01509 L .97619 .01502 L Mfstroke 1 0 .6 r .02381 .03211 m .06244 .03851 L .10458 .04808 L .14415 .06041 L .18221 .07635 L .22272 .09912 L .26171 .12847 L .30316 .17009 L .34309 .22324 L .3815 .28953 L .42237 .3797 L .46172 .48757 L .48147 .54842 L .49012 .57546 L .49468 .58939 L .49719 .5967 L .49842 .60011 L .49955 .60302 L .50085 .60202 L .50154 .60023 L .50226 .59825 L .50471 .59118 L .5095 .57664 L .51896 .54705 L .53984 .48293 L .57781 .37926 L .61824 .29005 L .65714 .2229 L .6985 .16818 L .73835 .12842 L .77668 .09952 L .81746 .07651 L .85673 .0601 L .89448 .04834 L .93468 .03907 L .97337 .03252 L .97619 .03211 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgWoo1@00 NGoo1@00?Woo0`00Woo00<007ooOol0Ngoo00<007ooOol0@7oo00<0 07ooOol0<7oo000[Ool60002Ool6000bOol60004Ool00`00Oomoo`1kOol00`00Oomoo`0kOol6000a Ool003Aoo`04001oogoo000nOol00`00Oomoo`1kOol00`00Oomoo`0kOol01000Oomoo`00Woo00@007ooOol0039oo`00=Goo00<0 07oo0000>goo00D007ooOomoo`0007Uoo`05001oogooOol0000mOol00`00Ool0000bOol003Ioo`80 03aoo`<007]oo`<003moo`80039oo`00ogooJGoo003oOomYOol00?moofUoo`00Ool40Il[Ool00`0?Oomoo`0aOol0015oo`Al4Qeoo`03 00moogoo02aoo`<1W`ioo`0300moogoo03ioo`03001oogoo03ioo`0300moogoo00]oo`<1Wbmoo`03 00moogoo01Yoo`El4Q9oo`005Goo1W`B5goo00<03gooOol0;goo106O2Woo00<03gooOol0?Woo00<0 07ooOol0?Woo00<03gooOol01goo106OOol6O18MOol0025oo`El4Paoo`0300moogoo03Eoo`81W`Ioo`0300moogoo03ioo`03001o ogoo03ioo`0300moogoo00=oo`81WcQoo`0300moogoo00Yoo`Al4R=oo`009Woo1G`B1goo00<03goo Ool0=goo0P6O17oo00<03gooOol0?Woo0P00?goo00@03gooOomoo`81WcYoo`0300moogoo00Eoo`El 4RMoo`00:goo17`B0goo00<03gooOol0>Goo0P6O0Woo00<03gooOol0?Woo00<007ooOol0?Woo00@0 3goo0Il1Wcaoo`0400moogooOol4O18/Ool002moo`=l4P0300moogoo03]oo`81W`0300moogoo03io o`03001oogoo03ioo`81Wcioo`0400ml4W`BO18`Ool0039oo`Al4Saoo`81Wcmoo`03001oogoo03eo o`030Il03goo03]oo`Al4S=oo`00 Ool00`0?Oomoo`0JOol2O18QOol00`0?Oomoo`0aOol0039oo`0300moogoo025oo`03O19oogoo01Uo o`0300moogoo011oo`030Imoogoo02]oo`03001oogoo02aoo`030Imoogoo00moo`0300moogoo01Uo o`03O19oogoo025oo`0300moogoo035oo`00Ool00`0?Oomoo`0EOol00`6OOomoo`0Ool00g`BOomoo`0/Ool00`0?Oomo o`0aOol0039oo`0300moogoo02eoo`03O19oogoo00eoo`0300moogoo01Eoo`030Imoogoo00]oo`03 001oogoo009oo`03001oogoo009oo`8000Aoo`05001oogooOol00006Ool00`00Oomoo`0VOol00`6O Oomoo`0EOol00`0?Oomoo`0=Ool00g`BOomoo`0]Ool00`0?Oomoo`0aOol0039oo`0300moogoo02io o`03O19oogoo00aoo`0300moogoo01Ioo`030Imoogoo00Yoo`03001oogoo009oo`03001oogoo00Uo o`03001oogoo00Moo`03001oogoo02Ioo`030Imoogoo01Eoo`0300moogoo00aoo`03O19oogoo02io o`0300moogoo035oo`002GooF`0?00=l4P0?00l0900?00<1W`0?00l02P0?00<0000?00l00P0?00<0 000?00l02P0?00<0000?00l01P0?0`009@0?00<1W`0?00l0900?00=l4P0?00l0F@0?2Woo000bOol0 0`0?Oomoo`0`Ool00g`BOomoo`0:Ool00`0?Oomoo`0GOol00`6OOomoo`09Ool00`00Oomoo`02Ool0 0`00Oomoo`0;Ool00`00Oomoo`05Ool00`00Oomoo`0TOol00`6OOomoo`0GOol00`0?Oomoo`0:Ool0 0g`BOomoo`0`Ool00`0?Oomoo`0aOol0039oo`0300moogoo035oo`03O19oogoo00Uoo`0300moogoo 01Moo`030Imoogoo00Uoo`03001oogoo009oo`03001oogoo00aoo`03001oogoo00Aoo`03001oogoo 02Aoo`030Imoogoo01Moo`0300moogoo00Uoo`03O19oogoo035oo`0300moogoo035oo`00Goo00El4WooOomoo`0?01eoo`030Imoogoo021oo`80025oo`030Imoogoo01]oo`05 00moogooOoml4P0kOol00`0?Oomoo`0aOol0039oo`0300moogoo03Yoo`04O19oogoo00lNOol00`6O Oomoo`0OOol00`00Oomoo`0OOol00`6OOomoo`0LOol0100?Oomoog`B?7oo00<03gooOol0Ool00g`BOomoo`0BOol01P00Oomoo`6OOol000ioo`03001oogoo00Aoo`03 001oogoo01Eoo`030Imoogoo01Eoo`03O19oogoo00ioo`0300moogoo03eoo`0300moogoo035oo`00 2GooN`0?00=l4P0?00l04@0?00H0000?00l1W`0?000:00l6000500l3000E00l00`6O00l03`0D00l0 0g`B00l03`1i00l:Ool0039oo`0300moogoo03eoo`0300moogoo00moo`03O19oogoo015oo`06001o ogooOol1W`002goo00@007ooOol000Ioo`03001oogoo01Eoo`030Imoogoo01Aoo`03O19oogoo00mo o`0300moogoo03eoo`0300moogoo035oo`00Ool00`6OOomoo`0?Ool00`00Oomoo`0?Ool00`6OOomoo`0>Ool00g`BOomoo`0KOol0 0`0?Oomoo`0mOol00`0?Oomoo`0aOol0039oo`0300moogoo03eoo`0300moogoo01]oo`03O19oogoo 00moo`030Imoogoo00ioo`03001oogoo00ioo`030Imoogoo00moo`03O19oogoo01]oo`0300moogoo 03eoo`0300moogoo035oo`00Ool00`6OOomoo`0> Ool00`00Oomoo`0>Ool00`6OOomoo`0>Ool00g`BOomoo`0LOol00`0?Oomoo`0mOol00`0?Oomoo`0a Ool0039oo`0300moogoo03eoo`0300moogoo01aoo`03O19oogoo00ioo`030Imoogoo00ioo`03001o ogoo00ioo`030Imoogoo00ioo`03O19oogoo01aoo`0300moogoo03eoo`0300moogoo035oo`00Ool00`6OOomoo`0=Ool00`00Oomoo`0=Ool00`6OOomo o`0>Ool00g`BOomoo`0MOol00`0?Oomoo`0mOol00`0?Oomoo`0aOol0039oo`0300moogoo03eoo`03 00moogoo01ioo`03O19oogoo00eoo`030Imoogoo00eoo`8000ioo`030Imoogoo00eoo`03O19oogoo 01ioo`0300moogoo03eoo`0300moogoo035oo`0000l00g`B00003`0300l00`00 00l03`0500l01@6O00l03`0?00000`0?00<0000?00l00`0?0`002`0?00<1W`0?00l02`0?00=l4P0? 00l0S00?2Woo000bOol00`0?Oomoo`0mOol00`0?Oomoo`0SOol00g`BOomoo`02Ool00`00Oomoo`05 Ool0106OOomoogoo10001Woo00<007ooOol02Woo00<1WgooOol02goo00=l4WooOol08goo00<03goo Ool0?Goo00<03gooOol0Woo00<03gooOol0?Goo00<03gooOol07oo00<03gooOol0?Goo00<03gooOol0Goo00=l4Woo0Il00Woo00H007ooOol1WgooO18kOol00`0?Oomoo`0m Ool00`0?Oomoo`0aOol0039oo`0300moogoo03eoo`0300moogoo03Uoo`03O19oo`6O009oo`06001o ogoo0Imoog`B>goo00<03gooOol0?Goo00<03gooOol0goo00<03gooOol0?Goo00<03gooOol0goo 00Ql4P6OOol007oo0Imoog`B?7oo00<03gooOol0?Goo00<03gooOol0"], ImageRangeCache->{{{127.438, 356.813}, {274.25, 132.938}} -> {-11.7223, 0.962646, 0.0387313, 0.00625974}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth] }, Open ]], Cell[TextData[{ "The plot above shows that the range f +/- 5 is adequate for \[Gamma]= .2, \ but marginal for \[Gamma]= .1. \n\nThe unaliased range of x is equal to 1/df, \ where df is the sampling interval of f, which, in our example, is 1/.01 or \ 100 or +/- 50. Actually, df*dx= 1/n where n is the number of samples, but the \ number of samples of x is the same as the number of samples of f so the total \ range of", StyleBox[" x = n*dx = 1/df).", Background->None], "\n\nThe effect of aliasing is shown when we plot x over the range of 0 to \ 100 for df= .01. Note that the plot 50-100 is a mirror image of 0-50. This \ type of plot is the easiest test test for aliasing." }], "Text", PageWidth->PaperWidth], Cell[CellGroupData[{ Cell[BoxData[ \(pf1 = Plot[Evaluate[ Abs[ffx1\/m1] /. {\[Alpha] \[Rule] 2, \[Beta] \[Rule] 0, \[Gamma] \[Rule] 1, \[Delta] \[Rule] 0}], {x, 0, 100}, PlotRange -> All, GridLines -> Automatic]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00952381 0.0147151 2.08655 [ [.21429 .00222 -6 -9 ] [.21429 .00222 6 0 ] [.40476 .00222 -6 -9 ] [.40476 .00222 6 0 ] [.59524 .00222 -6 -9 ] [.59524 .00222 6 0 ] [.78571 .00222 -6 -9 ] [.78571 .00222 6 0 ] [.97619 .00222 -9 -9 ] [.97619 .00222 9 0 ] [.01131 .11904 -24 -4.5 ] [.01131 .11904 0 4.5 ] [.01131 .22337 -18 -4.5 ] [.01131 .22337 0 4.5 ] [.01131 .3277 -24 -4.5 ] [.01131 .3277 0 4.5 ] [.01131 .43202 -18 -4.5 ] [.01131 .43202 0 4.5 ] [.01131 .53635 -24 -4.5 ] [.01131 .53635 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 .5 r .25 Mabswid [ ] 0 setdash .02381 0 m .02381 .61803 L s .21429 0 m .21429 .61803 L s .40476 0 m .40476 .61803 L s .59524 0 m .59524 .61803 L s .78571 0 m .78571 .61803 L s .97619 0 m .97619 .61803 L s 0 .01472 m 1 .01472 L s 0 .11904 m 1 .11904 L s 0 .22337 m 1 .22337 L s 0 .3277 m 1 .3277 L s 0 .43202 m 1 .43202 L s 0 .53635 m 1 .53635 L s 0 g .21429 .01472 m .21429 .02097 L s [(20)] .21429 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(40)] .40476 .00222 0 1 Mshowa .59524 .01472 m .59524 .02097 L s [(60)] .59524 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(80)] .78571 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(100)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .2619 .01472 m .2619 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .45238 .01472 m .45238 .01847 L s .5 .01472 m .5 .01847 L s .54762 .01472 m .54762 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .7381 .01472 m .7381 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .11904 m .03006 .11904 L s [(0.05)] .01131 .11904 1 0 Mshowa .02381 .22337 m .03006 .22337 L s [(0.1)] .01131 .22337 1 0 Mshowa .02381 .3277 m .03006 .3277 L s [(0.15)] .01131 .3277 1 0 Mshowa .02381 .43202 m .03006 .43202 L s [(0.2)] .01131 .43202 1 0 Mshowa .02381 .53635 m .03006 .53635 L s [(0.25)] .01131 .53635 1 0 Mshowa .125 Mabswid .02381 .03558 m .02756 .03558 L s .02381 .05645 m .02756 .05645 L s .02381 .07731 m .02756 .07731 L s .02381 .09818 m .02756 .09818 L s .02381 .13991 m .02756 .13991 L s .02381 .16077 m .02756 .16077 L s .02381 .18164 m .02756 .18164 L s .02381 .2025 m .02756 .2025 L s .02381 .24424 m .02756 .24424 L s .02381 .2651 m .02756 .2651 L s .02381 .28597 m .02756 .28597 L s .02381 .30683 m .02756 .30683 L s .02381 .34856 m .02756 .34856 L s .02381 .36943 m .02756 .36943 L s .02381 .39029 m .02756 .39029 L s .02381 .41116 m .02756 .41116 L s .02381 .45289 m .02756 .45289 L s .02381 .47376 m .02756 .47376 L s .02381 .49462 m .02756 .49462 L s .02381 .51549 m .02756 .51549 L s .02381 .55722 m .02756 .55722 L s .02381 .57808 m .02756 .57808 L s .02381 .59895 m .02756 .59895 L s .25 Mabswid .02381 0 m .02381 .61803 L s .5 Mabswid .02381 .60332 m .02499 .60108 L .02605 .5952 L .02729 .584 L .02846 .56931 L .03053 .53438 L .03279 .4861 L .04262 .23674 L .04762 .13805 L .05015 .10172 L .05293 .0716 L .05529 .05302 L .0566 .04511 L .05784 .0389 L .05899 .03414 L .06025 .02988 L .06244 .02433 L .06382 .02186 L .0653 .01983 L .0667 .01841 L .06799 .01743 L .06916 .01675 L .07044 .01619 L .07177 .01575 L .07302 .01546 L .07372 .01533 L .07448 .01521 L .07515 .01513 L .07587 .01505 L .07651 .01499 L .07721 .01494 L .07846 .01487 L .07922 .01484 L .07991 .01482 L .08065 .01479 L .08147 .01478 L .08285 .01475 L .0836 .01475 L .08429 .01474 L .08556 .01473 L .08628 .01473 L .08694 .01473 L .08815 .01472 L .08943 .01472 L .09058 .01472 L .09166 .01472 L .09284 .01472 L .0941 .01472 L .0948 .01472 L .09545 .01472 L Mistroke .09616 .01472 L .09691 .01472 L .09763 .01472 L .09831 .01472 L .09958 .01472 L .10083 .01472 L .10198 .01472 L .10325 .01472 L .10388 .01472 L .10458 .01472 L .10589 .01472 L .1071 .01472 L .10773 .01472 L .10843 .01472 L .10916 .01472 L .10984 .01472 L .11109 .01472 L .11223 .01472 L .11349 .01472 L .11481 .01472 L .11593 .01472 L .11712 .01472 L .11824 .01472 L .11926 .01472 L .12047 .01472 L .12177 .01472 L .123 .01472 L .12413 .01472 L .12534 .01472 L .12663 .01472 L .12786 .01472 L .12898 .01472 L .13028 .01472 L .13102 .01472 L .13171 .01472 L .13297 .01472 L .1336 .01472 L .1343 .01472 L .13498 .01472 L .13569 .01472 L .13697 .01472 L .13768 .01472 L .13834 .01472 L .13907 .01472 L .13985 .01472 L .14052 .01472 L .14125 .01472 L .14194 .01472 L .14257 .01472 L .14378 .01472 L Mistroke .14506 .01472 L .14626 .01472 L .14758 .01472 L .14882 .01472 L .14998 .01472 L .15112 .01472 L .15216 .01472 L .15335 .01472 L .15448 .01472 L .15571 .01472 L .15701 .01472 L .15812 .01472 L .15934 .01472 L .1621 .01472 L .1633 .01472 L .16461 .01472 L .16583 .01472 L .16695 .01472 L .16803 .01472 L .16918 .01472 L .1717 .01472 L .17294 .01472 L .17408 .01472 L .17506 .01472 L .1761 .01472 L .17714 .01472 L .17828 .01472 L .18291 .01472 L .18545 .01472 L .18615 .01472 L .18688 .01472 L .1882 .01472 L .19058 .01472 L .19123 .01472 L .19193 .01472 L .1932 .01472 L .1944 .01472 L .1957 .01472 L .19808 .01472 L .20254 .01472 L .20525 .01472 L .2059 .01472 L .20658 .01472 L .20781 .01472 L .20848 .01472 L .20922 .01472 L .20996 .01472 L .21075 .01472 L .21147 .01472 L .21213 .01472 L Mistroke .21341 .01472 L .21462 .01472 L .2159 .01472 L .21656 .01472 L .2173 .01472 L .21859 .01472 L .21982 .01472 L .22113 .01472 L .22349 .01472 L .22479 .01472 L .22597 .01472 L .22664 .01472 L .22737 .01472 L .22868 .01472 L .23362 .01472 L .23804 .01472 L .24289 .01472 L .24421 .01472 L .24563 .01472 L .24818 .01472 L .2489 .01472 L .24968 .01472 L .25037 .01472 L .2511 .01472 L .25176 .01472 L .25248 .01472 L .25376 .01472 L .25506 .01472 L .25625 .01472 L .25752 .01472 L .2582 .01472 L .25892 .01472 L .26014 .01472 L .26128 .01472 L .26377 .01472 L .26874 .01472 L .26995 .01472 L .27125 .01472 L .27199 .01472 L .27267 .01472 L .274 .01472 L .27474 .01472 L .27542 .01472 L .27617 .01472 L .27697 .01472 L .27773 .01472 L .27844 .01472 L .27908 .01472 L .27978 .01472 L .281 .01472 L Mistroke .28232 .01472 L .28307 .01472 L .28376 .01472 L .28445 .01472 L .2851 .01472 L .28638 .01472 L .28755 .01472 L .28884 .01472 L .28949 .01472 L .29021 .01472 L .29155 .01472 L .29225 .01472 L .29299 .01472 L .29364 .01472 L .29436 .01472 L .2956 .01472 L .30525 .01472 L .3078 .01472 L .30914 .01472 L .31055 .01472 L .31179 .01472 L .31249 .01472 L .31315 .01472 L .31555 .01472 L .32034 .01472 L .32271 .01472 L .32374 .01472 L .32489 .01472 L .32612 .01472 L .32742 .01472 L .32811 .01472 L .32884 .01472 L .32954 .01472 L .33018 .01472 L .3313 .01472 L .33253 .01472 L .3338 .01472 L .335 .01472 L .33568 .01472 L .33642 .01472 L .33772 .01472 L .34062 .01472 L .34314 .01472 L .34585 .01472 L .34716 .01472 L .3484 .01472 L .34951 .01472 L .35073 .01472 L .3553 .01472 L .35791 .01472 L Mistroke .35866 .01472 L .35937 .01472 L .36 .01472 L .36069 .01472 L .36196 .01472 L .3626 .01472 L .3633 .01472 L .36454 .01472 L .3657 .01472 L .367 .01472 L .36774 .01472 L .36842 .01472 L .36968 .01472 L .37031 .01472 L .37101 .01472 L .37221 .01472 L .3735 .01472 L .37585 .01472 L .37857 .01472 L .37929 .01472 L .38007 .01472 L .38081 .01472 L .38148 .01472 L .38282 .01472 L .38349 .01472 L .38423 .01472 L .38552 .01472 L .38673 .01472 L .39173 .01472 L .3963 .01472 L .39754 .01472 L .39824 .01472 L .39889 .01472 L .40008 .01472 L .40135 .01472 L .40206 .01472 L .40282 .01472 L .40354 .01472 L .4042 .01472 L .40545 .01472 L .40677 .01472 L .40807 .01472 L .40929 .01472 L .40997 .01472 L .4107 .01472 L .41198 .01472 L .41684 .01472 L .41962 .01472 L .4203 .01472 L .42103 .01472 L Mistroke .42183 .01472 L .42258 .01472 L .42325 .01472 L .42399 .01472 L .42534 .01472 L .42788 .01472 L .43318 .01472 L .43445 .01472 L .43514 .01472 L .43578 .01472 L .43693 .01472 L .43818 .01472 L .43931 .01472 L .44035 .01472 L .44154 .01472 L .44267 .01472 L .44388 .01472 L .445 .01472 L .44623 .01472 L .44753 .01472 L .44882 .01472 L .45 .01472 L .45267 .01472 L .45502 .01472 L .4562 .01472 L .45749 .01472 L .45823 .01472 L .45894 .01472 L .46025 .01472 L .46319 .01472 L .4685 .01472 L .47091 .01472 L .47351 .01472 L .47596 .01472 L .47713 .01472 L .47821 .01472 L .47941 .01472 L .48072 .01472 L .48187 .01472 L .4831 .01472 L .4838 .01472 L .48456 .01472 L .48593 .01472 L .48849 .01472 L .49317 .01472 L .4943 .01472 L .49552 .01472 L .49622 .01472 L .49686 .01472 L .4981 .01472 L Mistroke .49923 .01472 L .50028 .01472 L .50142 .01472 L .50264 .01472 L .50468 .01472 L .50694 .01472 L .51186 .01472 L .51306 .01472 L .51434 .01472 L .51507 .01472 L .51574 .01472 L .51704 .01472 L .51824 .01472 L .51933 .01472 L .52054 .01472 L .52181 .01472 L .52395 .01472 L .52631 .01472 L .5319 .01472 L .53721 .01472 L .53952 .01472 L .54079 .01472 L .54198 .01472 L .54266 .01472 L .54339 .01472 L .54467 .01472 L .54717 .01472 L .54973 .01472 L .55097 .01472 L .55211 .01472 L .55331 .01472 L .55459 .01472 L .55601 .01472 L .55732 .01472 L .55843 .01472 L .55961 .01472 L .5608 .01472 L .56211 .01472 L .56664 .01472 L .5673 .01472 L .56803 .01472 L .56871 .01472 L .56935 .01472 L .57055 .01472 L .57183 .01472 L .57471 .01472 L .57613 .01472 L .57743 .01472 L .57866 .01472 L .57997 .01472 L Mistroke .58129 .01472 L .58273 .01472 L .58523 .01472 L .58632 .01472 L .58754 .01472 L .58875 .01472 L .59005 .01472 L .59072 .01472 L .59145 .01472 L .59277 .01472 L .59404 .01472 L .59467 .01472 L .59536 .01472 L .59659 .01472 L .59774 .01472 L .59895 .01472 L .60009 .01472 L .60112 .01472 L .60224 .01472 L .60704 .01472 L .60977 .01472 L .61233 .01472 L .61361 .01472 L .61433 .01472 L .61499 .01472 L .61792 .01472 L .62278 .01472 L .62399 .01472 L .62527 .01472 L .62594 .01472 L .62667 .01472 L .62796 .01472 L .62862 .01472 L .62934 .01472 L .63062 .01472 L .63194 .01472 L .63313 .01472 L .63429 .01472 L .63554 .01472 L .63673 .01472 L .63782 .01472 L .63891 .01472 L .63994 .01472 L .64106 .01472 L .64226 .01472 L .64698 .01472 L .6495 .01472 L .65019 .01472 L .65092 .01472 L .65162 .01472 L Mistroke .65225 .01472 L .65297 .01472 L .65362 .01472 L .65511 .01472 L .6578 .01472 L .66262 .01472 L .66379 .01472 L .66504 .01472 L .66577 .01472 L .66642 .01472 L .66771 .01472 L .66892 .01472 L .6702 .01472 L .67086 .01472 L .67159 .01472 L .67288 .01472 L .67409 .01472 L .67539 .01472 L .67661 .01472 L .67773 .01472 L .67898 .01472 L .67968 .01472 L .68033 .01472 L .68152 .01472 L .68279 .01472 L .68407 .01472 L .68479 .01472 L .68545 .01472 L .68623 .01472 L .68696 .01472 L .68764 .01472 L .68838 .01472 L .68968 .01472 L .6909 .01472 L .69319 .01472 L .69831 .01472 L .70273 .01472 L .70395 .01472 L .70523 .01472 L .70632 .01472 L .70752 .01472 L .70866 .01472 L .70987 .01472 L .7105 .01472 L .7112 .01472 L .71243 .01472 L .71359 .01472 L .71483 .01472 L .716 .01472 L .71708 .01472 L Mistroke .71774 .01472 L .71843 .01472 L .71969 .01472 L .72101 .01472 L .72176 .01472 L .72244 .01472 L .72365 .01472 L .72496 .01472 L .72618 .01472 L .72733 .01472 L .72955 .01472 L .732 .01472 L .73695 .01472 L .73914 .01472 L .74122 .01472 L .74237 .01472 L .74362 .01472 L .74469 .01472 L .74581 .01472 L .74645 .01472 L .74715 .01472 L .74838 .01472 L .74907 .01472 L .74981 .01472 L .75051 .01472 L .75115 .01472 L .75373 .01472 L .75617 .01472 L .76554 .01472 L .76807 .01472 L .77077 .01472 L .77187 .01472 L .77307 .01472 L .77437 .01472 L .7756 .01472 L .77852 .01472 L .77996 .01472 L .7813 .01472 L .78251 .01472 L .7838 .01472 L .78454 .01472 L .78523 .01472 L .78653 .01472 L .78769 .01472 L .78893 .01472 L .7901 .01472 L .79117 .01472 L .79243 .01472 L .79314 .01472 L .7938 .01472 L Mistroke .795 .01472 L .79628 .01472 L .8016 .01472 L .80287 .01472 L .8035 .01472 L .8042 .01472 L .80544 .01472 L .80659 .01472 L .80766 .01472 L .80863 .01472 L .81081 .01472 L .81196 .01472 L .81318 .01472 L .81422 .01472 L .81537 .01472 L .81776 .01472 L .81901 .01472 L .81971 .01472 L .82035 .01472 L .8216 .01472 L .82278 .01472 L .82387 .01472 L .82506 .01472 L .82571 .01472 L .82639 .01472 L .82762 .01472 L .83038 .01472 L .83154 .01472 L .83277 .01472 L .83413 .01472 L .8354 .01472 L .83791 .01472 L .84029 .01472 L .84133 .01472 L .84243 .01472 L .84364 .01472 L .84476 .01472 L .84968 .01472 L .85098 .01472 L .85171 .01472 L .85237 .01472 L .85365 .01472 L .85486 .01472 L .85616 .01472 L .8569 .01472 L .85757 .01472 L .85826 .01472 L .85901 .01472 L .8598 .01472 L .86054 .01472 L Mistroke .86185 .01472 L .86305 .01472 L .86371 .01472 L .86443 .01472 L .86574 .01472 L .86694 .01472 L .86807 .01472 L .86931 .01472 L .87 .01472 L .87064 .01472 L .87186 .01472 L .87254 .01472 L .87318 .01472 L .87448 .01472 L .8752 .01472 L .87586 .01472 L .87706 .01472 L .87817 .01472 L .87939 .01472 L .88068 .01472 L .8818 .01472 L .88285 .01472 L .884 .01472 L .88524 .01472 L .88645 .01472 L .88758 .01472 L .88882 .01472 L .89013 .01472 L .89139 .01472 L .89257 .01472 L .89364 .01472 L .89479 .01472 L .89584 .01472 L .897 .01472 L .89821 .01472 L .89934 .01472 L .9004 .01472 L .90136 .01472 L .90247 .01472 L .90353 .01472 L .90466 .01472 L .90589 .01472 L .90705 .01472 L .90812 .01472 L .90929 .01472 L .91058 .01472 L .91123 .01472 L .91193 .01472 L .91318 .01473 L .91387 .01473 L Mistroke .91451 .01473 L .91519 .01474 L .91594 .01474 L .91721 .01476 L .91791 .01477 L .91855 .01478 L .91978 .01481 L .92091 .01484 L .92221 .01491 L .92344 .01499 L .9246 .0151 L .92565 .01523 L .92687 .01544 L .92801 .01569 L .92907 .01601 L .93005 .01638 L .93112 .01689 L .93225 .01759 L .9334 .0185 L .93462 .01974 L .93578 .02125 L .93683 .02295 L .93807 .02544 L .93942 .02887 L .94069 .03297 L .94186 .03756 L .94383 .04753 L .94595 .06203 L .94782 .07871 L .94978 .10082 L .95396 .16541 L .95852 .26356 L .97619 .60332 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggoo00<03gooOol0?7oo00<0 3gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>goo00<03gooOol02Woo000ROol00`00Oomoo`0k Ool00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0kOol00`0?Oomoo`0: Ool0029oo`03001oogoo03]oo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300mo ogoo03]oo`0300moogoo00Yoo`008Woo00<007ooOol0>goo00<03gooOol0?7oo00<03gooOol0?7oo 00<03gooOol0?7oo00<03gooOol0>goo00<03gooOol02Woo000JOooo001;0004Ool0029oo`03001o ogoo00]oo`8000moo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00eo o`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eo o`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00eoo`03001oogoo00eo o`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00eoo`8000eoo`03001oogoo00Yoo`008Woo 00<007ooOol02Woo00<007ooOol0;Woo00<007ooOol0?7oo00<007ooOol0?7oo00<007ooOol0?7oo 00<007ooOol0;Woo00<007ooOol02Woo00<007ooOol02Woo000ROol00`00Oomoo`09Ool2000`Ool0 0`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0^Ool00`00Oomoo`0:Ool0 0`0?Oomoo`0:Ool0029oo`03001oogoo00Uoo`03001oogoo02moo`0300moogoo03aoo`0300moogoo 03aoo`0300moogoo03aoo`0300moogoo02moo`03001oogoo00Uoo`0300moogoo00Yoo`008Woo00<0 07ooOol02Goo00<007ooOol0;goo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<0 3gooOol0;goo00<007ooOol02Goo00<03gooOol02Woo000ROol00`00Oomoo`08Ool00`00Oomoo`0` Ool00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0`Ool00`00Oomoo`08 Ool00`0?Oomoo`0:Ool0029oo`8000Uoo`03001oogoo031oo`0300moogoo03aoo`0300moogoo03ao o`0300moogoo03aoo`0300moogoo031oo`03001oogoo00Qoo`0300moogoo00Yoo`008Woo00<007oo Ool027oo00<007ooOol0<7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03goo Ool0<7oo00<007ooOol027oo00<03gooOol02Woo000ROol00`00Oomoo`07Ool00`00Oomoo`0aOol0 0`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0`Ool00`00Oomoo`08Ool0 0`0?Oomoo`0:Ool0029oo`03001oogoo00Moo`03001oogoo035oo`0300moogoo03aoo`0300moogoo 03aoo`0300moogoo03aoo`0300moogoo035oo`03001oogoo00Moo`0300moogoo00Yoo`008Woo00<0 07ooOol01goo00<007ooOol0Ool00`00Oomoo`05Ool0 0`00Oomoo`03Ool00`00Oomoo`0eOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol0 0`0?Oomoo`0eOol00`00Oomoo`03Ool00`0?Oomoo`0:Ool0029oo`03001oogoo00=oo`03001oogoo 03Eoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Eoo`03001oogoo 00=oo`0300moogoo00Yoo`008Woo00<007ooOol00goo00<007ooOol0=Goo00<03gooOol0?7oo00<0 3gooOol0?7oo00<03gooOol0?7oo00<03gooOol0=Goo00<007ooOol00goo00<03gooOol02Woo000R Ool20004Ool00`00Oomoo`0eOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0? Oomoo`0eOol00`00Oomoo`03Ool00`0?Oomoo`0:Ool0029oo`03001oogoo00=oo`03001oogoo03Eo o`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Eoo`03001oogoo00=o o`0300moogoo00Yoo`008Woo00<007ooOol00goo00<007ooOol0=Goo00<03gooOol0?7oo00<03goo Ool0?7oo00<03gooOol0?7oo00<03gooOol0=Goo00<007ooOol00goo00<03gooOol02Woo000ROol0 0`00Oomoo`03Ool00`00Oomoo`0eOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol0 0`0?Oomoo`0eOol00`00Oomoo`03Ool00`0?Oomoo`0:Ool0029oo`03001oogoo00=oo`03001oogoo 03Eoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Eoo`03001oogoo 00=oo`0300moogoo00Yoo`008Woo00<007ooOol00goo00<007ooOol0=Goo00<03gooOol0?7oo00<0 3gooOol0?7oo00<03gooOol0?7oo00<03gooOol0=Goo00<007ooOol00goo00<03gooOol02Woo000R Ool00`00Oomoo`03Ool00`00Oomoo`0eOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0l Ool00`0?Oomoo`0eOol00`00Oomoo`03Ool00`0?Oomoo`0:Ool0029oo`8000Aoo`03001oogoo03Eo o`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Eoo`03001oogoo00=o o`0300moogoo00Yoo`008Woo00<007ooOol00goo00<007ooOol0=Goo00<03gooOol0?7oo00<03goo Ool0?7oo00<03gooOol0?7oo00<03gooOol0=Goo00<007ooOol00goo00<03gooOol02Woo000ROol0 0`00Oomoo`03Ool00`00Oomoo`0eOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol0 0`0?Oomoo`0eOol00`00Oomoo`03Ool00`0?Oomoo`0:Ool0029oo`03001oogoo00=oo`03001oogoo 03Eoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Eoo`03001oogoo 00=oo`0300moogoo00Yoo`008Woo00<007ooOol00Woo00<007ooOol0=Woo00<03gooOol0?7oo00<0 3gooOol0?7oo00<03gooOol0?7oo00<03gooOol0=Goo00<007ooOol00goo00<03gooOol02Woo000R Ool00`00Oomoo`02Ool00`00Oomoo`0fOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0l Ool00`0?Oomoo`0eOol00`00Oomoo`03Ool00`0?Oomoo`0:Ool0029oo`8000=oo`03001oogoo03Io o`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Eoo`03001oogoo00=o o`0300moogoo00Yoo`008Woo00<007ooOol00Woo00<007ooOol0=Woo00<03gooOol0?7oo00<03goo Ool0?7oo00<03gooOol0?7oo00<03gooOol0=Goo00<007ooOol00goo00<03gooOol02Woo000ROol0 0`00Oomoo`02Ool00`00Oomoo`0fOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol0 0`0?Oomoo`0eOol00`00Oomoo`03Ool00`0?Oomoo`0:Ool0029oo`03001oogoo009oo`03001oogoo 03Ioo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Ioo`03001oogoo 009oo`0300moogoo00Yoo`008Woo00<007ooOol00Woo00<007ooOol0=Woo00<03gooOol0?7oo00<0 3gooOol0?7oo00<03gooOol0?7oo00<03gooOol0=Woo00<007ooOol00Woo00<03gooOol02Woo000R Ool00`00Oomoo`02Ool00`00Oomoo`0fOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0l Ool00`0?Oomoo`0fOol00`00Oomoo`02Ool00`0?Oomoo`0:Ool0029oo`03001oogoo009oo`03001o ogoo03Ioo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Ioo`03001o ogoo009oo`0300moogoo00Yoo`008Woo0P000goo00<007ooOol0=Woo00<03gooOol0?7oo00<03goo Ool0?7oo00<03gooOol0?7oo00<03gooOol0=Woo00<007ooOol00Woo00<03gooOol02Woo000ROol0 0`00Oomoo`02Ool00`00Oomoo`0fOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol0 0`0?Oomoo`0fOol00`00Oomoo`02Ool00`0?Oomoo`0:Ool0029oo`03001oogoo009oo`03001oogoo 03Ioo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Ioo`03001oogoo 009oo`0300moogoo00Yoo`008Woo00<007ooOol00Woo00<007ooOol0=Woo00<03gooOol0?7oo00<0 3gooOol0?7oo00<03gooOol0?7oo00<03gooOol0=Woo00<007ooOol00Woo00<03gooOol02Woo0004 0005Ool20005Ool50003Ool40006Ool00`00Oomoo`02Ool00`00Oomoo`0fOol00`0?Oomoo`0lOol0 0`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0fOol00`00Oomoo`02Ool00`0?Oomoo`0:Ool0 00Aoo`03001oogoo009oo`8000Moo`03001oogoo009oo`03001oogoo009oo`03001oogoo00=oo`03 001oogoo009oo`03001oogoo03Ioo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`03 00moogoo03Ioo`03001oogoo009oo`0300moogoo00Yoo`0017oo00<007ooOol02goo00<007ooOol0 1goo00<007ooOol00goo00<007ooOol00Woo00<007ooOol0=Woo00<03gooOol0?7oo00<03gooOol0 ?7oo00<03gooOol0?7oo00<03gooOol0=Woo00<007ooOol00Woo00<03gooOol02Woo0004Ool00`00 Oomoo`0;Ool00`00Oomoo`05Ool200l00`0000l03`0300l3000200l00`0000l03`3o00l]00l00`00 00l03`0;00l4Ool000Aoo`03001oogoo00]oo`03001oogoo00=oo`@000Ioo`03001oogoo009oo`03 001oogoo03Ioo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Ioo`03 001oogoo009oo`0300moogoo00Yoo`0017oo00<007ooOol02goo00<007ooOol00goo00<007ooOol0 1goo00<007ooOol00Woo00<007ooOol0=Woo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0 ?7oo00<03gooOol0=Woo00<007ooOol00Woo00<03gooOol02Woo0004Ool00`00Oomoo`09Ool30005 Ool00`00Oomoo`07Ool00`00Oomoo`02Ool00`00Oomoo`0fOol00`0?Oomoo`0lOol00`0?Oomoo`0l Ool00`0?Oomoo`0lOol00`0?Oomoo`0fOol00`00Oomoo`02Ool00`0?Oomoo`0:Ool000@000ioo`03 001oogoo00=oo`D000Eoo`03001oogoo009oo`03001oogoo03Ioo`0300moogoo03aoo`0300moogoo 03aoo`0300moogoo03aoo`0300moogoo03Ioo`03001oogoo009oo`0300moogoo00Yoo`008Woo00<0 07ooOol00Woo00<007ooOol0=Woo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<0 3gooOol0=Woo00<007ooOol00Woo00<03gooOol02Woo000ROol00`00Oomoo`02Ool00`00Oomoo`0f Ool00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0fOol00`00Oomoo`02 Ool00`0?Oomoo`0:Ool0029oo`8000=oo`03001oogoo03Ioo`0300moogoo03aoo`0300moogoo03ao o`0300moogoo03aoo`0300moogoo03Ioo`03001oogoo009oo`0300moogoo00Yoo`008Woo00<007oo Ool00Woo00<007ooOol0=Woo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03goo Ool0=goo00D007ooOomoo`0?00aoo`008Woo00<007ooOol00Woo00<007ooOol0=Woo00<03gooOol0 ?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0=goo00D007ooOomoo`0?00aoo`008Woo 00<007ooOol00Woo00<007ooOol0=Woo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo 00<03gooOol0=goo00D007ooOomoo`0?00aoo`008Woo00D007ooOomoo`0003Uoo`0300moogoo03ao o`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Moo`05001oogooOol03`0Goo00<03gooOol0?7oo00<03gooOol0 ?7oo00<03gooOol0?7oo00<03gooOol0=goo00D007ooOomoo`0?00aoo`008Woo0P000Woo00<007oo Ool0=goo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0=goo00D007oo Oomoo`0?00aoo`008Woo00D007ooOomoo`0003Uoo`0300moogoo03aoo`0300moogoo03aoo`0300mo ogoo03aoo`0300moogoo03Moo`05001oogooOol03`0Goo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<0 3gooOol0=goo00D007ooOomoo`0?00aoo`008Woo00D007ooOomoo`0003Uoo`0300moogoo03aoo`03 00moogoo03aoo`0300moogoo03aoo`0300moogoo03Moo`05001oogooOol03`0Goo00<03gooOol0?7oo00<03gooOol0?7oo 00<03gooOol0?7oo00<03gooOol0=goo00D007ooOomoo`0?00aoo`008Woo0P000Woo00<007ooOol0 =goo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0=goo00D007ooOomo o`0?00aoo`008Woo00D007ooOomoo`0003Uoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo 03aoo`0300moogoo03Moo`05001oogooOol03`0Goo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03goo Ool0=goo00D007ooOomoo`0?00aoo`008Woo00D007ooOomoo`0003Uoo`0300moogoo03aoo`0300mo ogoo03aoo`0300moogoo03aoo`0300moogoo03Moo`05001oogooOol03`0Goo00<03gooOol0?7oo00<03gooOol0?7oo00<03goo Ool0?7oo00<03gooOol0>7oo00@007ooOol03`aoo`008Woo0P000Woo00<007ooOol0=goo00<03goo Ool0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>7oo00@007ooOol03`aoo`008Woo 00D007ooOomoo`0003Uoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo 03Qoo`04001oogoo00lGoo 00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>7oo00@007ooOol03`ao o`0027oo10001Goo0P0017oo1@001Woo00D007ooOomoo`0003Uoo`0300moogoo03aoo`0300moogoo 03aoo`0300moogoo03aoo`0300moogoo03Qoo`04001oogoo00lGoo00<03gooOol0?7oo 00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>7oo00@007ooOol03`aoo`001goo00<007oo Ool00Woo00<007ooOol02Goo00<007ooOol01goo00D007ooOomoo`0003Uoo`0300moogoo03aoo`03 00moogoo03aoo`0300moogoo03aoo`0300moogoo03Qoo`04001oogoo00lWoo00<03gooOol0?7oo 00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>7oo00@007ooOol03`aoo`008Woo0P0000=o o`00Ool0>Goo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>7oo00@0 07ooOol03`aoo`008Woo00@007ooOol003Yoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo 03aoo`0300moogoo03Qoo`04001oogoo00lWoo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>7oo00@007oo Ool03`aoo`008Woo00@007ooOol003Yoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03ao o`0300moogoo03Uoo`03001oo`0?00aoo`008Woo00@007ooOol003Yoo`0300moogoo03aoo`0300mo ogoo03aoo`0300moogoo03aoo`0300moogoo03Uoo`03001oo`0?00aoo`008Woo00@007ooOol003Yo o`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Uoo`03001oo`0?00ao o`008Woo0P0000=oo`00Ool0>Goo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<0 3gooOol0>Goo00<007oo00l037oo000ROol01000Oomoo`00>Woo00<03gooOol0?7oo00<03gooOol0 ?7oo00<03gooOol0?7oo00<03gooOol0>Goo00<007oo00l037oo000ROol01000Oomoo`00>Woo00<0 3gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>Goo00<007oo00l037oo000R Ool01000Oomoo`00>Woo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0 >Goo00<007oo00l037oo000ROol01000Oomoo`00>Woo00<03gooOol0?7oo00<03gooOol0?7oo00<0 3gooOol0?7oo00<03gooOol0>Goo00<007oo00l037oo000ROol01000Oomoo`00>Woo00<03gooOol0 ?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>Goo00<007oo00l037oo000ROol01000 Oomoo`00>Woo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>Goo00<0 07oo00l037oo000ROol200000goo001oo`0iOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomo o`0lOol00`0?Oomoo`0iOol00`00Ool03`0goo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0 >Goo00<007oo00l037oo000ROol3000kOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0l Ool00`0?Oomoo`0iOol00`00Ool03`0goo 00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>Woo00<0000?Ool02goo 000ROol00`00Ool0000kOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomo o`0jOol00`0000moo`0;Ool000@000Eoo`8000Aoo`D000Aoo`@000Ioo`03001oo`0003]oo`0300mo ogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Yoo`0300003goo00]oo`0017oo 00<007ooOol00Woo0P0017oo00D007ooOomoo`0000=oo`03001oogoo009oo`03001oogoo00=oo`03 001oo`0003]oo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Yoo`03 00003goo00]oo`0017oo00<007ooOol02Goo00<007ooOol02Goo00<007ooOol00goo00<007oo0000 >goo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>Woo00<0000?Ool0 2goo0004Ool00`00Oomoo`0:Ool00`00Oomoo`06Ool200l00`0000l03`0300l3003o00lf00l00`00 00l03`0700l4Ool000Aoo`03001oogoo00]oo`03001oogoo00=oo`@000Ioo`03001oo`0003]oo`03 00moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Yoo`0300003goo00]oo`00 17oo00<007ooOol037oo00<007ooOol00Woo00<007ooOol01goo00<007oo0000>goo00<03gooOol0 ?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>Woo00<0000?Ool02goo0004Ool00`00 Oomoo`08Ool01@00Oomoogoo000017oo00<007ooOol01goo00<007oo0000>goo00<03gooOol0?7oo 00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>Woo00<0000?Ool02goo0004000Woo00<0000?Ool02goo000ROol2000lOol00`0?Oomo o`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0jOol00`0000moo`0;Ool0029oo`80 03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03Yoo`0300003goo 00]oo`008Woo0P00?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0 >Woo00<0000?Ool02goo000ROol2000lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0l Ool00`0?Oomoo`0jOol00`0000moo`0;Ool0029oo`8003aoo`0300moogoo03aoo`0300moogoo03ao o`0300moogoo03aoo`0300moogoo03Yoo`0300003goo00]oo`008Woo0P00?7oo00<03gooOol0?7oo 00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>Woo00<0000?Ool02goo000ROol2000lOol0 0`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0kOol00`00Oomoo`0:Ool0 029oo`8003aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03]oo`03 001oogoo00Yoo`008Woo0P00?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<0 3gooOol0>goo00<007ooOol02Woo000ROol2000lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0? Oomoo`0lOol00`0?Oomoo`0kOol00`00Oomoo`0:Ool0029oo`8003aoo`0300moogoo03aoo`0300mo ogoo03aoo`0300moogoo03aoo`0300moogoo03]oo`03001oogoo00Yoo`008Woo00<007ooOol0>goo 00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>goo00<007ooOol02Woo 000ROol00`00Oomoo`0kOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomo o`0kOol00`00Oomoo`0:Ool0029oo`03001oogoo03]oo`0300moogoo03aoo`0300moogoo03aoo`03 00moogoo03aoo`0300moogoo03]oo`03001oogoo00Yoo`008Woo0P00?7oo00<03gooOol0?7oo00<0 3gooOol0?7oo00<03gooOol0?7oo00<03gooOol0>goo00<007ooOol02Woo000ROol00`00Oomoo`0k Ool00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0kOol00`00Oomoo`0: Ool0029oo`03001oogoo03]oo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300mo ogoo03]oo`0300moogoo00Yoo`008Woo00<007ooOol0>goo00<03gooOol0?7oo00<03gooOol0?7oo 00<03gooOol0?7oo00<03gooOol0>goo00<03gooOol02Woo000ROol00`00Oomoo`0kOol00`0?Oomo o`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0lOol00`0?Oomoo`0kOol00`0?Oomoo`0:Ool0029oo`03 001oogoo03]oo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03aoo`0300moogoo03]oo`03 00moogoo00Yoo`008Woo00<007ooOol0>goo00<03gooOol0?7oo00<03gooOol0?7oo00<03gooOol0 ?7oo00<03gooOol0>goo00<03gooOol02Woo003oOomYOol00?moofUoo`00ogooJGoo0000\ \>"], ImageRangeCache->{{{127.438, 356.813}, {622.313, 481}} -> {-74.5059, 1.06825, 0.399314, 0.00182262}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth] }, Open ]], Cell[CellGroupData[{ Cell["\<\ A. Plotting Expected Values against \[Alpha] for different \[Beta] values\ \>", "Text", PageWidth->PaperWidth, FontSize->16, FontSlant->"Plain", FontColor->GrayLevel[0]], Cell[TextData[{ StyleBox["Using the tools at hand, we now wish to investigate expected \ values under differing stable distributions. To make this manageable, \ \[Gamma] and \[Delta] are fixed at, respectively, 3 and .06 leaving only \ \[Alpha] and \[Beta] varying. The plot below shows expected values for {\ \[Alpha], 1.2,1.8} and {\[Beta], -1, 1}.", FontFamily->"Times New Roman"], StyleBox["\n\n", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox["The steps are:\n\n1. Define the pdf with fixed \[Gamma] and \ \[Delta] (", FontFamily->"Times New Roman"], StyleBox["pdf1", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox["); \n\n2. From the definition of expected value for a continuous \ random variable, numerically integrate the product of x f(x) where f(x) is \ the pdf (", FontFamily->"Times New Roman"], StyleBox["pdf1", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[") ; \n\n3. Create a table (", FontFamily->"Times New Roman"], StyleBox["tvs1", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[") using a range of values for \[Alpha] and \[Beta], here \ {\[Alpha], 1.2,1.8} in steps of .1 and {\[Beta], -1, 1} in steps of .2;\n\n4. \ Working from the list created by the table, produce an object (", FontFamily->"Times New Roman"], StyleBox["tvf1", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[") that can be plotted.", FontFamily->"Times New Roman"] }], "Text", PageWidth->PaperWidth, FontSize->12, FontSlant->"Plain", FontColor->GrayLevel[0]], Cell[BoxData[ StyleBox[\(pdf[\[Alpha]_, \[Beta]_, \[Gamma]_, \[Delta]_] = Abs[ffx1\/m1];\), Background->None]], "Input", PageWidth->PaperWidth], Cell[BoxData[{ \(\[IndentingNewLine]\(pdf1 = pdf[\[Alpha], \[Beta], 3, .06];\)\), "\n", \(\(pvs1 := NIntegrate[Evaluate[x\ pdf1\ \ ], {x, \(-30\), 30}];\)\), "\n", \(\(tvs1 = Table[pvs1, {\[Alpha], 1.2, 1.8, .1}, {\[Beta], \(-1\), 1, .2}];\)\)}], "Input", PageWidth->PaperWidth], Cell[BoxData[ \(\(tvf1 = ListInterpolation[tvs1, {{1.2, 1.8}, {\(-1\), 1}}, InterpolationOrder \[Rule] {6, 9}];\)\)], "Input", PageWidth->PaperWidth], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["[Mathematica", FontSlant->"Italic", FontColor->GrayLevel[0]], StyleBox["'s explanation of the functions used above are shown below. \ Double click on far right cell bracket if not visible.]", FontColor->GrayLevel[0]] }], "Text", PageWidth->PaperWidth, FontSize->10], Cell[CellGroupData[{ Cell[BoxData[ \(\(?ListInterpolation\)\)], "Input", PageWidth->PaperWidth], Cell[BoxData[ \("ListInterpolation[array] constructs an InterpolatingFunction object \ which represents an approximate function that interpolates the array of \ values given. ListInterpolation[array, {{xmin, xmax}, {ymin, ymax}, ... }] \ specifies the domain of the grid from which the values in array are assumed \ to come."\)], "Print", PageWidth->PaperWidth] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(?InterpolationOrder\)\)], "Input", PageWidth->PaperWidth], Cell[BoxData[ \("InterpolationOrder is an option to Interpolation and \ ListInterpolation. InterpolationOrder-> n specifies interpolating polynomials \ of order n. InterpolationOrder -> {n1,n2,...} specifies interpolating \ polynomials of order n1, n2, ... for dimensions 1,2,..., respectively."\)], \ "Print", PageWidth->PaperWidth] }, Open ]] }, Open ]], Cell["\<\ Below the upper and lower \"corners\" of the plane are turned in when the \ range of \[Alpha] is 1.2 < \[Alpha] < 1.8. Changing that range to 1.3 < \ \[Alpha] < 1.7 overcomes that problem. To view the plot delete \ \"DisplayFunction\[RightArrow]Identity\" from the statement.\ \>", "Text", PageWidth->PaperWidth], Cell[CellGroupData[{ Cell[BoxData[ \(Plot3D[ tvf1[\[Alpha], \[Beta]], {\[Alpha], 1.2, 1.8}, {\[Beta], \(-1\), 1}, BoxRatios -> {1, 1, 1}, AxesLabel -> {"\", "\", "\"}, DisplayFunction \[Rule] Identity]\)], "Input", PageWidth->PaperWidth], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] SurfaceGraphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth] }, Open ]], Cell[TextData[{ "Continuing to work with the ", StyleBox["Mathematica", FontSlant->"Italic"], " object created above from the table (", StyleBox["tvs1", FontSlant->"Italic"], "), we can plot expected values over a range of \[Alpha] between 1.2 and \ 1.8 for different values of \[Beta] over its feasible range, 0 to .2 in this \ case. Here, \[Gamma] remains at a value of 3." }], "Text", PageWidth->PaperWidth, FontSlant->"Plain", FontColor->GrayLevel[0]], Cell[CellGroupData[{ Cell[BoxData[ \(pu\[Alpha]1 = Plot[{tvf1[\[Alpha], 0], tvf1[\[Alpha], .04], tvf1[\[Alpha], .08], tvf1[\[Alpha], .1], tvf1[\[Alpha], .14], tvf1[\[Alpha], .18], tvf1[\[Alpha], .2], .06}, {\[Alpha], 1.2, 1.8}, GridLines -> Automatic, \ TextStyle -> {FontSize -> 12, FontFamily \[Rule] Times}, PlotStyle -> {{Hue[ .1], AbsoluteThickness[3]}, {Hue[ .2], AbsoluteThickness[3]}, {Hue[ .3], AbsoluteThickness[3]}, {Hue[ .4], AbsoluteThickness[3]}, {Hue[ .5], AbsoluteThickness[3]}, {Hue[ .6], AbsoluteThickness[3]}, {Hue[ .7], AbsoluteThickness[3]}, {Hue[ .9], AbsoluteThickness[3]}}, PlotLegend -> {"\<\[Beta]=0\>", .04, .08, .10, .14, 1.8, .2, "\"}, LegendPosition -> {1.2, \(- .5\)}, LegendSize -> { .6, .8}, PlotLabel -> "\<[\[Alpha],\[Beta],3,.06]\>", Frame -> Automatic, FrameLabel -> {alpha, expected\ value}]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .43371 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.357978 0.334169 0.216854 0.334169 [ [ 0 0 0 0 ] [ 1 .43371 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath % Start of sub-graphic p 0.0238095 0.0103264 0.692147 0.423382 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -1.88095 1.5873 0.0147151 0.113654 [ [.02381 -0.0125 -9.5625 -15.75 ] [.02381 -0.0125 9.5625 0 ] [.18254 -0.0125 -9.5625 -15.75 ] [.18254 -0.0125 9.5625 0 ] [.34127 -0.0125 -9.5625 -15.75 ] [.34127 -0.0125 9.5625 0 ] [.5 -0.0125 -9.5625 -15.75 ] [.5 -0.0125 9.5625 0 ] [.65873 -0.0125 -9.5625 -15.75 ] [.65873 -0.0125 9.5625 0 ] [.81746 -0.0125 -9.5625 -15.75 ] [.81746 -0.0125 9.5625 0 ] [.97619 -0.0125 -9.5625 -15.75 ] [.97619 -0.0125 9.5625 0 ] [ 0 0 -0.125 0 ] [.5 -0.0125 -14.6563 -31.5 ] [.5 -0.0125 14.6563 -15.75 ] [-0.0125 .01472 -10 -7.875 ] [-0.0125 .01472 0 7.875 ] [-0.0125 .12837 -10 -7.875 ] [-0.0125 .12837 0 7.875 ] [-0.0125 .24202 -10 -7.875 ] [-0.0125 .24202 0 7.875 ] [-0.0125 .35568 -10 -7.875 ] [-0.0125 .35568 0 7.875 ] [-0.0125 .46933 -10 -7.875 ] [-0.0125 .46933 0 7.875 ] [-0.0125 .58298 -10 -7.875 ] [-0.0125 .58298 0 7.875 ] [ 0 0 -0.125 0 ] [-0.01875 .30902 -25.75 -37.0625 ] [-0.01875 .30902 -10 37.0625 ] [ 0 .61803 .125 0 ] [ 1 0 .125 0 ] [.5 .63053 -28.5625 0 ] [.5 .63053 28.5625 15.75 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 .5 r .25 Mabswid [ ] 0 setdash .18254 0 m .18254 .61803 L s .34127 0 m .34127 .61803 L s .5 0 m .5 .61803 L s .65873 0 m .65873 .61803 L s .81746 0 m .81746 .61803 L s 0 .12837 m 1 .12837 L s 0 .24202 m 1 .24202 L s 0 .35568 m 1 .35568 L s 0 .46933 m 1 .46933 L s 0 .58298 m 1 .58298 L s 0 g .02381 0 m .02381 .00625 L s gsave .02381 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.2) show 1.000 setlinewidth grestore .18254 0 m .18254 .00625 L s gsave .18254 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.3) show 1.000 setlinewidth grestore .34127 0 m .34127 .00625 L s gsave .34127 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.4) show 1.000 setlinewidth grestore .5 0 m .5 .00625 L s gsave .5 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.5) show 1.000 setlinewidth grestore .65873 0 m .65873 .00625 L s gsave .65873 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.6) show 1.000 setlinewidth grestore .81746 0 m .81746 .00625 L s gsave .81746 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.7) show 1.000 setlinewidth grestore .97619 0 m .97619 .00625 L s gsave .97619 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.8) show 1.000 setlinewidth grestore .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .15079 0 m .15079 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .27778 0 m .27778 .00375 L s .30952 0 m .30952 .00375 L s .37302 0 m .37302 .00375 L s .40476 0 m .40476 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .53175 0 m .53175 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .78571 0 m .78571 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .9127 0 m .9127 .00375 L s .94444 0 m .94444 .00375 L s .25 Mabswid 0 0 m 1 0 L s gsave .5 -0.0125 -75.6563 -35.5 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (alpha) show 1.000 setlinewidth grestore 0 .01472 m .00625 .01472 L s gsave -0.0125 .01472 -71 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 1.000 setlinewidth grestore 0 .12837 m .00625 .12837 L s gsave -0.0125 .12837 -71 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 1.000 setlinewidth grestore 0 .24202 m .00625 .24202 L s gsave -0.0125 .24202 -71 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 1.000 setlinewidth grestore 0 .35568 m .00625 .35568 L s gsave -0.0125 .35568 -71 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (3) show 1.000 setlinewidth grestore 0 .46933 m .00625 .46933 L s gsave -0.0125 .46933 -71 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (4) show 1.000 setlinewidth grestore 0 .58298 m .00625 .58298 L s gsave -0.0125 .58298 -71 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (5) show 1.000 setlinewidth grestore .125 Mabswid 0 .03745 m .00375 .03745 L s 0 .06018 m .00375 .06018 L s 0 .08291 m .00375 .08291 L s 0 .10564 m .00375 .10564 L s 0 .1511 m .00375 .1511 L s 0 .17383 m .00375 .17383 L s 0 .19656 m .00375 .19656 L s 0 .21929 m .00375 .21929 L s 0 .26475 m .00375 .26475 L s 0 .28748 m .00375 .28748 L s 0 .31022 m .00375 .31022 L s 0 .33295 m .00375 .33295 L s 0 .37841 m .00375 .37841 L s 0 .40114 m .00375 .40114 L s 0 .42387 m .00375 .42387 L s 0 .4466 m .00375 .4466 L s 0 .49206 m .00375 .49206 L s 0 .51479 m .00375 .51479 L s 0 .53752 m .00375 .53752 L s 0 .56025 m .00375 .56025 L s 0 .60572 m .00375 .60572 L s .25 Mabswid 0 0 m 0 .61803 L s gsave -0.01875 .30902 -115.938 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate 98.0625 11.875 translate 90 rotate -98.0625 -11.875 translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (expected) show 107.813 15.875 moveto (value) show 1.000 setlinewidth grestore .02381 .61178 m .02381 .61803 L s .18254 .61178 m .18254 .61803 L s .34127 .61178 m .34127 .61803 L s .5 .61178 m .5 .61803 L s .65873 .61178 m .65873 .61803 L s .81746 .61178 m .81746 .61803 L s .97619 .61178 m .97619 .61803 L s .125 Mabswid .05556 .61428 m .05556 .61803 L s .0873 .61428 m .0873 .61803 L s .11905 .61428 m .11905 .61803 L s .15079 .61428 m .15079 .61803 L s .21429 .61428 m .21429 .61803 L s .24603 .61428 m .24603 .61803 L s .27778 .61428 m .27778 .61803 L s .30952 .61428 m .30952 .61803 L s .37302 .61428 m .37302 .61803 L s .40476 .61428 m .40476 .61803 L s .43651 .61428 m .43651 .61803 L s .46825 .61428 m .46825 .61803 L s .53175 .61428 m .53175 .61803 L s .56349 .61428 m .56349 .61803 L s .59524 .61428 m .59524 .61803 L s .62698 .61428 m .62698 .61803 L s .69048 .61428 m .69048 .61803 L s .72222 .61428 m .72222 .61803 L s .75397 .61428 m .75397 .61803 L s .78571 .61428 m .78571 .61803 L s .84921 .61428 m .84921 .61803 L s .88095 .61428 m .88095 .61803 L s .9127 .61428 m .9127 .61803 L s .94444 .61428 m .94444 .61803 L s .25 Mabswid 0 .61803 m 1 .61803 L s .99375 .01472 m 1 .01472 L s .99375 .12837 m 1 .12837 L s .99375 .24202 m 1 .24202 L s .99375 .35568 m 1 .35568 L s .99375 .46933 m 1 .46933 L s .99375 .58298 m 1 .58298 L s .125 Mabswid .99625 .03745 m 1 .03745 L s .99625 .06018 m 1 .06018 L s .99625 .08291 m 1 .08291 L s .99625 .10564 m 1 .10564 L s .99625 .1511 m 1 .1511 L s .99625 .17383 m 1 .17383 L s .99625 .19656 m 1 .19656 L s .99625 .21929 m 1 .21929 L s .99625 .26475 m 1 .26475 L s .99625 .28748 m 1 .28748 L s .99625 .31022 m 1 .31022 L s .99625 .33295 m 1 .33295 L s .99625 .37841 m 1 .37841 L s .99625 .40114 m 1 .40114 L s .99625 .42387 m 1 .42387 L s .99625 .4466 m 1 .4466 L s .99625 .49206 m 1 .49206 L s .99625 .51479 m 1 .51479 L s .99625 .53752 m 1 .53752 L s .99625 .56025 m 1 .56025 L s .99625 .60572 m 1 .60572 L s .25 Mabswid 1 0 m 1 .61803 L s gsave .5 .63053 -89.5625 -4 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto %%IncludeResource: font Math2 %%IncludeFont: Math2 /Math2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 63.000 15.875 moveto (@) show 67.063 15.875 moveto %%IncludeResource: font Math1 %%IncludeFont: Math1 /Math1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (a) show 74.313 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (,) show 78.625 15.875 moveto %%IncludeResource: font Math1 %%IncludeFont: Math1 /Math1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (b) show 84.688 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (,) show 87.813 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (3) show 93.813 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (,) show 96.938 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (.06) show %%IncludeResource: font Math2 %%IncludeFont: Math2 /Math2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 112.063 15.875 moveto (D) show 116.125 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 1 .6 0 r 3 Mabswid .02381 .02098 m .06244 .02101 L .10458 .02104 L .14415 .02107 L .18221 .0211 L .22272 .02113 L .26171 .02116 L .30316 .02119 L .34309 .02121 L .3815 .02123 L .42237 .02126 L .46172 .02128 L .49955 .0213 L .53984 .02132 L .57861 .02133 L .61984 .02135 L .65954 .02137 L .69774 .02138 L .73838 .0214 L .77751 .02141 L .81909 .02143 L .85916 .02144 L .89771 .02145 L .93871 .02146 L .97619 .02147 L s .8 1 0 r .02381 .13807 m .06244 .12967 L .10458 .12207 L .14415 .11609 L .18221 .11115 L .22272 .10658 L .26171 .10268 L .30316 .09896 L .34309 .09567 L .3815 .09272 L .42237 .08976 L .46172 .08703 L .49955 .08449 L .53984 .08186 L .57861 .07937 L .61984 .07675 L .65954 .07423 L .69774 .0718 L .73838 .06917 L .77751 .06659 L .81909 .06376 L .85916 .06096 L .89771 .05817 L .93871 .05511 L .97619 .05225 L s .2 1 0 r .02381 .25501 m .06244 .23821 L .10458 .223 L .14415 .21101 L .18221 .20113 L .22272 .19196 L .26171 .18416 L .30316 .17669 L .34309 .1701 L .3815 .16418 L .42237 .15823 L .46172 .15275 L .49955 .14766 L .53984 .14238 L .57861 .13739 L .61984 .13213 L .65954 .12708 L .69774 .1222 L .73838 .11693 L .77751 .11175 L .81909 .1061 L .85916 .10047 L .89771 .09488 L .93871 .08876 L .97619 .08303 L s 0 1 .4 r .02381 .31338 m .06244 .2924 L .10458 .27339 L .14415 .25842 L .18221 .24607 L .22272 .23462 L .26171 .22486 L .30316 .21552 L .34309 .20729 L .3815 .19989 L .42237 .19245 L .46172 .1856 L .49955 .17924 L .53984 .17263 L .57861 .16639 L .61984 .15982 L .65954 .1535 L .69774 .1474 L .73838 .14081 L .77751 .13433 L .81909 .12726 L .85916 .12023 L .89771 .11324 L .93871 .10558 L .97619 .09842 L s 0 1 1 r .02381 .42979 m .06244 .40051 L .10458 .37398 L .14415 .35308 L .18221 .33582 L .22272 .31982 L .26171 .30618 L .30316 .29312 L .34309 .2816 L .3815 .27125 L .42237 .26084 L .46172 .25126 L .49955 .24235 L .53984 .2331 L .57861 .22436 L .61984 .21517 L .65954 .20633 L .69774 .19778 L .73838 .18855 L .77751 .17949 L .81909 .16958 L .85916 .15973 L .89771 .14995 L .93871 .13922 L .97619 .12919 L s 0 .4 1 r .02381 .54565 m .06244 .50819 L .10458 .47423 L .14415 .44745 L .18221 .42534 L .22272 .40482 L .26171 .38733 L .30316 .37057 L .34309 .35579 L .3815 .3425 L .42237 .32914 L .46172 .31684 L .49955 .3054 L .53984 .29352 L .57861 .2823 L .61984 .27048 L .65954 .25912 L .69774 .24813 L .73838 .23627 L .77751 .22462 L .81909 .21189 L .85916 .19923 L .89771 .18665 L .93871 .17286 L .97619 .15996 L s .2 0 1 r .02381 .60332 m .06244 .56182 L .10458 .52418 L .14415 .49451 L .18221 .46998 L .22272 .44723 L .26171 .42782 L .30316 .40924 L .34309 .39282 L .3815 .37808 L .42237 .36325 L .46172 .34959 L .49955 .33689 L .53984 .32371 L .57861 .31124 L .61984 .29812 L .65954 .2855 L .69774 .27329 L .73838 .26012 L .77751 .24718 L .81909 .23304 L .85916 .21897 L .89771 .205 L .93871 .18968 L .97619 .17535 L s 1 0 .6 r .02381 .02153 m .06244 .02153 L .10458 .02153 L .14415 .02153 L .18221 .02153 L .22272 .02153 L .26171 .02153 L .30316 .02153 L .34309 .02153 L .3815 .02153 L .42237 .02153 L .46172 .02153 L .49955 .02153 L .53984 .02153 L .57861 .02153 L .61984 .02153 L .65954 .02153 L .69774 .02153 L .73838 .02153 L .77751 .02153 L .81909 .02153 L .85916 .02153 L .89771 .02153 L .93871 .02153 L .97619 .02153 L s MathSubEnd P % End of sub-graphic 0 g .77569 .03306 m .77569 .3004 L .97619 .3004 L .97619 .03306 L F 1 g .75898 .04977 m .75898 .3171 L .95948 .3171 L .95948 .04977 L F 0 g .001 w [ ] 0 setdash .75898 .04977 m .95948 .04977 L .95948 .3171 L .75898 .3171 L .75898 .04977 L s % Start of sub-graphic p 0.758981 0.0497697 0.959482 0.317105 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0297619 0.297619 0.0140647 0.140647 [ [ 0 0 0 0 ] [ 1 1.33333 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.33333 L 0 1.33333 L closepath clip newpath % Start of sub-graphic p 0.0535714 0.0253165 0.35119 0.165963 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 1 0 .6 r 3 Mabswid [ ] 0 setdash .02381 .30902 m .97619 .30902 L s MathSubEnd P % End of sub-graphic 0 g gsave .38988 .09564 -61 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (ev) show 75.063 13.000 moveto %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (=) show 81.063 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (.06) show 99.063 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore % Start of sub-graphic p 0.0535714 0.188467 0.35119 0.329114 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .2 0 1 r 3 Mabswid [ ] 0 setdash .02381 .30902 m .97619 .30902 L s MathSubEnd P % End of sub-graphic 0 g [(0.2)] .38988 .25879 -1 0 Mshowa % Start of sub-graphic p 0.0535714 0.351617 0.35119 0.492264 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 .4 1 r 3 Mabswid [ ] 0 setdash .02381 .30902 m .97619 .30902 L s MathSubEnd P % End of sub-graphic 0 g [(1.8)] .38988 .42194 -1 0 Mshowa % Start of sub-graphic p 0.0535714 0.514768 0.35119 0.655415 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 1 1 r 3 Mabswid [ ] 0 setdash .02381 .30902 m .97619 .30902 L s MathSubEnd P % End of sub-graphic 0 g [(0.14)] .38988 .58509 -1 0 Mshowa % Start of sub-graphic p 0.0535714 0.677918 0.35119 0.818565 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 1 .4 r 3 Mabswid [ ] 0 setdash .02381 .30902 m .97619 .30902 L s MathSubEnd P % End of sub-graphic 0 g [(0.1)] .38988 .74824 -1 0 Mshowa % Start of sub-graphic p 0.0535714 0.841069 0.35119 0.981716 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .2 1 0 r 3 Mabswid [ ] 0 setdash .02381 .30902 m .97619 .30902 L s MathSubEnd P % End of sub-graphic 0 g [(0.08)] .38988 .91139 -1 0 Mshowa % Start of sub-graphic p 0.0535714 1.00422 0.35119 1.14487 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .8 1 0 r 3 Mabswid [ ] 0 setdash .02381 .30902 m .97619 .30902 L s MathSubEnd P % End of sub-graphic 0 g [(0.04)] .38988 1.07454 -1 0 Mshowa % Start of sub-graphic p 0.0535714 1.16737 0.35119 1.30802 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 1 .6 0 r 3 Mabswid [ ] 0 setdash .02381 .30902 m .97619 .30902 L s MathSubEnd P % End of sub-graphic 0 g gsave .38988 1.23769 -61 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (b) show 69.000 13.000 moveto %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (=) show 75.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore MathSubEnd P % End of sub-graphic 0 0 m 1 0 L 1 .43371 L 0 .43371 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{407.75, 176.75}, ImageMargins->{{7, 0}, {0, 4}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggoo0030Ool00`00Oomoo`3oOolkOol00;Moo`P00003Ool007oo 0080009oo`<00004Ool000000002Ool5003oOolZOol00;Ioo`05001oogooOol00002Ool00`00Oomo o`020002Ool01000Oomoo`000goo00@007ooOol000=oo`03001oogoo0?moobUoo`00]Woo00D007oo Oomoo`00009oo`04001oogoo0003Ool01000Oomoo`000goo00@007ooOol000=oo`03001oogoo0?mo obUoo`00]goo10000Woo00@007ooOol000=oo`04001oogoo0003Ool01000Oomoogoo1000ogoo:goo 002jOol01000Oomoo`000Woo00D007ooOomoo`00009oo`05001oogooOol00006Ool00`00Oomoo`3o OolYOol00;Ioo`05001oogooOol00002Ool00`00Ool000020002Ool00`00Oomoo`020002Ool01000 Oomoo`000goo00<007ooOol0ogoo:Goo002gOol30003Ool01@00Oomoo`00Ool00P000goo00@007oo 000000Aoo`<00;QoofD000ioo`00_Goo00<007ooOol01goo00<007ooOol0`7ooI@003Woo002mOol0 0`00Oomoo`07Ool00`00Oomoo`30OomU000>Ool00;aoo`8000Qoo`800<9oofD000ioo`00_Goo00<0 07ooOol01goo00<007ooOol0`7ooI@003Woo003oOon;OomU000>Ool00?mooh]oofD000ioo`00ogoo RgooI@003Woo003oOon2Oom^000>Ool00?mooh9oo`03001oogoo06=oo`P000ioo`00ogooPWoo00<0 07ooOol0Hgoo20003Woo003oOon2Ool00`00Oomoo`1SOol8000>Ool00?mooh9oo`03001oogoo06=o o`P000ioo`00CWoo0`000goo00@007ooOomoo`D001Ioo`<000=oo`04001oogooOol4000GOol30003 Ool00`00Oomoo`04Ool00`00Oomoo`0EOol30003Ool01000Oomoogoo0`006Goo0`000goo00<007oo Ool00Woo0`005goo0`000goo00<007ooOol00goo00<007ooOol05Woo0`000goo00<007ooOol00Woo 0`00AWoo00<007ooOol0Hgoo20003Woo001?Ool00`00Oomoo`06Ool01@00Oomoogoo00005goo00<0 07ooOol02Woo00<007ooOol05Goo00<007ooOol02Goo00<007ooOol05Woo00<007ooOol02Goo00<0 07ooOol05goo00<007ooOol01Woo00D007ooOomoo`0001Moo`03001oogoo00Qoo`03001oogoo01Mo o`03001oogoo00Ioo`05001oogooOol00015Ool00`00Oomoo`1SOol8000>Ool004moo`03001oogoo 00Moo`03001oogoo01Qoo`03001oogoo00Yoo`03001oogoo01Eoo`03001oogoo00Uoo`03001oogoo 01Ioo`03001oogoo00Yoo`03001oogoo01Ioo`03001oogoo00Ioo`05001oogooOol0000GOol00`00 Oomoo`09Ool00`00Oomoo`0FOol00`00Oomoo`06Ool01@00Oomoogoo0000AGoo00<007ooOol0:Goo 1@0017oo0P003Goo0P001Goo10001Goo0`003goo20003Woo001?Ool00`00Oomoo`08Ool00`00Oomo o`0GOol00`00Oomoo`0:Ool00`00Oomoo`0EOol00`00Oomoo`05Ool6000GOol00`00Oomoo`0:Ool0 0`00Oomoo`0FOol00`00Oomoo`06Ool01@00Oomoogoo00005goo00<007ooOol02Goo00<007ooOol0 5Woo00<007ooOol01Woo00D007ooOomoo`0004Eoo`03001oogoo02Qoo`03001oogoo00Moo`8000=o o`H000Aoo`8000Aoo`03001oogoo009oo`05001oogooOol00003Ool00`00Oomoo`0Ool0 04moo`03001oogoo00Uoo`03001oogoo01Ioo`03001oogoo00Yoo`03001oogoo01Eoo`03001oogoo 00Eoo`05001oogooOol0000HOol00`00Oomoo`0:Ool00`00Oomoo`0FOol00`00Oomoo`06Ool01@00 Oomoogoo00005goo00<007ooOol02Goo00<007ooOol05Woo00<007ooOol01goo00<007oo0000AWoo 00<007ooOol01Woo6G`B2Goo00<007ooOol01Woo00@007ooOol0019oo`03001oogoo009oo`05001o ogooOol00003Ool00`00Oomoo`0Ool004moo`03001oogoo00Uoo`03001oogoo01Ioo`03 001oogoo00Qoo`8001Qoo`03001oogoo00Ioo`04001oogoo000HOol00`00Oomoo`09Ool00`00Oomo o`0GOol00`00Oomoo`06Ool20002Ool00`00Oomoo`0EOol00`00Oomoo`0:Ool00`00Oomoo`0EOol0 0`00Oomoo`08Ool00`00Oomoo`15Ool00`00Oomoo`06OolIO189Ool60003Ool01000Oomoo`000Woo 1P002Woo00<007ooOol00Woo00D007ooOomoo`0000=oo`03001oogoo00aoo`P000ioo`00Cgoo00<0 07ooOol02Woo00<007ooOol05Goo00<007ooOol02Goo00<007ooOol05Woo00<007ooOol01goo00<0 07oo000067oo00<007ooOol01Woo0`006Woo00<007ooOol01Woo00@007oo000001Qoo`03001oogoo 00Yoo`03001oogoo01Eoo`03001oogoo00Moo`03001oo`0004Ioo`03001oogoo00IooaUl4PUoo`03 001oogoo009oo`04001oogoo0004Ool00`00Oomoo`0?Ool00`00Oomoo`02Ool01000Oomoogoo1000 3goo20003Woo001?Ool00`00Oomoo`0:Ool00`00Oomoo`0EOol00`00Oomoo`0:Ool00`00Oomoo`0E Ool00`00Oomoo`07Ool00`00Ool0000HOol00`00Oomoo`07Ool00`00Oomoo`0IOol00`00Oomoo`07 Ool00`00Oomoo`0HOol00`00Oomoo`0:Ool00`00Oomoo`0EOol00`00Oomoo`06Ool01@00Oomoogoo 0000AGoo00<007ooOol0:Goo10000Woo0`000Woo0`0047oo00<007ooOol00Woo00D007ooOomoo`00 019oo`P000ioo`00CWoo0P0027oo00D007ooOomoo`0001Ioo`8000Qoo`05001oogooOol0000FOol2 000:Ool2000GOol20009Ool00`00Oomoo`0HOol2000:Ool00`00Oomoo`0FOol20007Ool00`00Oomo o`03Ool00`00Oomoo`0COol20008Ool01@00Oomoogoo0000AGoo00<007ooOol0Agoo00<007ooOol0 0Woo00<007ooOol00Woo00<007ooOol03goo20003Woo001?Ool00`00Oomoo`07Ool3000HOol00`00 Oomoo`07Ool3000HOol00`00Oomoo`09Ool00`00Oomoo`0FOol00`00Oomoo`08Ool3000HOol00`00 Oomoo`09Ool2000GOol00`00Oomoo`06Ool6000FOol00`00Oomoo`07Ool30016Ool00`00Oomoo`18 Ool40006Ool3000>Ool8000>Ool00?mooh9oo`03001oogoo06=oo`P000ioo`00ogooPWoo00<007oo Ool0Hgoo20003Woo003oOon2Ool00`00Oomoo`1SOol8000>Ool00?mooh9oo`03001oogoo06=oo`P0 00ioo`00ogooPWoo00<007ooOol0Hgoo20003Woo003oOon2Ool00`00Oomoo`1SOol8000>Ool00?mo oh9oo`03001oogoo06=oo`P000ioo`00AGoo0`0027ooj`00AWoo00<007ooOol0Hgoo20003Woo0014 Ool01@00Oomoogoo00001goo00<007ooOol00Woo00<007ooOol01Goo00<007ooOol017oo00<007oo Ool01Goo00<007ooOol017oo00<007ooOol01Goo00<007ooOol017oo00<007ooOol017oo00<007oo Ool01Goo00<007ooOol017oo00<007ooOol01Goo00<007ooOol017oo00<007ooOol01Goo00<007oo Ool017oo00<007ooOol017oo00<007ooOol01Goo00<007ooOol017oo00<007ooOol01Goo00<007oo Ool017oo00<007ooOol01Goo00<007ooOol017oo00<007ooOol017oo00<007ooOol01Goo00<007oo Ool017oo00<007ooOol01Goo00<007ooOol017oo00<007ooOol01Goo00<007ooOol017oo00<007oo Ool017oo00<007ooOol01Goo00<007ooOol017oo00<007ooOol00goo00<007ooOol0A7oo00<007oo Ool09goo10001Goo0P0017oo1@00:7oo20003Woo0014Ool01@00Oomoogoo00001goo00<007ooOol0 0Woo00<007ooOol08goo00<007ooOol08Woo00<007ooOol08Woo00<007ooOol08Woo00<007ooOol0 8Woo00<007ooOol08Woo00<007ooOol00goo00<007ooOol0A7oo00<007ooOol09Woo00<007ooOol0 0Woo00<007ooOol00Woo0P0017oo00D007ooOomoo`0002Qoo`P000ioo`00A7oo00D007ooOomoo`00 00Moo`03001oogoo02Qoo`0300moogoo029oo`0300moogoo029oo`0300moogoo029oo`0300moogoo 029oo`0300moogoo02Qoo`03001oogoo04Aoo`03001oogoo00IooaTD7`Moo`03001oogoo009oo`03 001oogoo00Uoo`03001oogoo02Uoo`P000ioo`00A7oo00D007ooOomoo`0000Moo`80009oon9l4P9o o`<004Ioo`03001oogoo00IooaTD7`Moo`03001oogoo009oo`03001oogoo00Yoo`03001oogoo02Qo o`P000ioo`00A7oo00D007ooOomoo`0000Moo`04001oogooOooRO184Ool00`00Oomoo`14Ool00`00 Oomoo`06OolI51l7Ool00`00Oomoo`02Ool00`00Oomoo`0;Ool00`00Oomoo`0WOol8000>Ool004Ao o`05001oogooOol00007Ool01000OomoogoohW`B17oo00<007ooOol0A7oo00<007ooOol09Woo00<0 07ooOol00Woo00<007ooOol037oo00<007ooOol09Woo20003Woo0014Ool01@00Oomoogoo00001goo 00<007ooOol0:7oo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol08Woo 00<03gooOol0:7oo00<007ooOol0A7oo00<007ooOol09Woo00<007ooOol00Woo00<007ooOol027oo 00D007ooOomoo`0002Qoo`P000ioo`00A7oo00D007ooOomoo`0000Moo`03001oogoo02Qoo`0300mo ogoo029oo`0300moogoo029oo`0300moogoo029oo`0300moogoo029oo`0300moogoo02Qoo`03001o ogoo04Aoo`03001oogoo02Moo`@000aoo`<002Uoo`P000ioo`00AGoo0`0027oo0P00:Goo00<03goo Ool08Woo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol09goo0P00AWoo 00<007ooOol0Hgoo20003Woo001@Ool00`00Oomoo`0XOol00`0?Oomoo`0ROol00`0?Oomoo`0ROol0 0`0?Oomoo`0ROol00`0?Oomoo`0ROol00`0?Oomoo`0XOol00`00Oomoo`14Ool00`00Oomoo`1SOol8 000>Ool0051oo`03001oogoo02Qoo`0300moogoo029oo`0300moogoo029oo`0300moogoo029oo`03 00moogoo029oo`0300moogoo01ioo`IWh0Aoo`03001oogoo04Aoo`03001oogoo06=oo`P000ioo`00 D7oo00<007ooOol0:7oo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol0 8Woo00<03gooOol05Goo3fOP17oo00<007ooOol0A7oo00<007ooOol0Hgoo20003Woo001@Ool00`00 Oomoo`0XOol00`0?Oomoo`0ROol00`0?Oomoo`0ROol00`0?Oomoo`0ROol00`0?Oomoo`0ROol00`0? Oomoo`03OolQIn04Ool00`00Oomoo`14Ool00`00Oomoo`1SOol8000>Ool0051oo`8002Uoo`0300mo ogoo029oo`0300moogoo029oo`0300moogoo029oo`0300moogoo01ioobEWh0Uoo`8004Ioo`03001o ogoo06=oo`P000ioo`00D7oo00<007ooOol0:7oo00<03gooOol08Woo00<03gooOol08Woo00<03goo Ool08Woo00<03gooOol02goo;fOP4goo00<007ooOol0A7oo00<007ooOol0Hgoo20003Woo001@Ool0 0`00Oomoo`0XOol00`0?Oomoo`0ROol00`0?Oomoo`0ROol00`0?Oomoo`0NOol_In0UOol00`00Oomo o`14Ool00`00Oomoo`1SOol8000>Ool0051oo`03001oogoo02Qoo`0300moogoo029oo`0300moogoo 029oo`0300moogoo01AoobmWh0Aoo`0300moogoo02Qoo`03001oogoo04Aoo`03001oogoo06=oo`P0 00ioo`00D7oo00<007ooOol0:7oo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol00Woo;VOP 5goo00<03gooOol0:7oo00<007ooOol0A7oo00<007ooOol09goo1@0017oo0P001Goo1000:7oo2000 3Woo001@Ool00`00Oomoo`0XOol00`0?Oomoo`0ROol00`0?Oomoo`0EOol^In04Ool00`0?Oomoo`0R Ool00`0?Oomoo`0NOol65n04Ool00`00Oomoo`14Ool00`00Oomoo`0YOol00`00Oomoo`04Ool20004 Ool00`00Oomoo`02Ool00`00Oomoo`0UOol8000>Ool0051oo`8002Uoo`0300moogoo029oo`0300mo ogoo00]oobiWh0ioo`0300moogoo029oo`0300moogoo01Eoo`lGh0=oo`8004Ioo`03001oogoo00Io oaT1W`Yoo`03001oogoo00Yoo`03001oogoo009oo`03001oogoo02Eoo`P000ioo`00D7oo00<007oo Ool0:7oo00<03gooOol07Woo;VOP87oo00<03gooOol08Woo00<03gooOol03Woo5QOP17oo00<007oo Ool0A7oo00<007ooOol01Woo6@6O2Woo00<007ooOol02Woo00<007ooOol00Woo00<007ooOol09Goo 20003Woo001@Ool00`00Oomoo`0XOol00`0?Oomoo`0DOolVIn0=Ool00`0?Oomoo`0ROol00`0?Oomo o`0ROol00`0?Oomoo`0:OolD5n02Ool40n`4Ool00`00Oomoo`14Ool00`00Oomoo`06OolI0Il:Ool0 0`00Oomoo`0;Ool4000XOol8000>Ool0051oo`03001oogoo02Qoo`0300moogoo00]oobEWh1Moo`03 00moogoo029oo`0300moogoo029oo`0300moogoo00=ooa8Gh0Moo`P3k0Aoo`03001oogoo04Aoo`03 001oogoo02Uoo`03001oogoo00Yoo`03001oogoo009oo`03001oogoo02Eoo`P000ioo`00D7oo00<0 07ooOol0:7oo00<03gooOol00Woo76OP17oo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol0 7Woo5AOP2Woo30?/17oo00<007ooOol0A7oo00<007ooOol09goo0`0037oo00<007ooOol00Woo00<0 07ooOol09Goo20003Woo001@Ool2000UOolKIn0>Ool00`0?Oomoo`0ROol00`0?Oomoo`0ROol00`0? Oomoo`0EOolJ5n09Ool=0n`7Ool20016Ool00`00Oomoo`0YOol00`00Oomoo`0;Ool4000XOol8000> Ool004Eoo`<000Qoo`03001oogoo01eooaUWh1Moo`0300moogoo029oo`0300moogoo029oo`0300mo ogoo00iooaXGh0Uooa03k0aoo`03001oogoo04Aoo`03001oogoo06=oo`P000ioo`00AWoo00<007oo Ool01goo00<007ooOol067oo5FOP87oo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol02Goo 5AOP17oo00<03gooOol01Goo4`?/47oo00<007ooOol0A7oo00<007ooOol0Hgoo20003Woo0016Ool0 0`00Oomoo`07Ool00`00Oomoo`0AOolCIn04Ool00`0?Oomoo`0ROol00`0?Oomoo`0ROol00`0?Oomo o`0ROol00`0?Oomoo`02OolC5n0=Ool0100?Oomoogoo4P?/5Goo00<007ooOol0A7oo00<007ooOol0 Hgoo20003Woo0016Ool00`00Oomoo`07Ool00`00Oomoo`0:OolCIn0;Ool00`0?Oomoo`0ROol00`0? Oomoo`0ROol00`0?Oomoo`0NOolE5n0COol@0n`EOol30ol4Ool00`00Oomoo`14Ool00`00Oomoo`1S Ool8000>Ool004Ioo`03001oogoo00Moo`8000H03a=Wh7403aXGh1<03`h3k1T03`H3o`803`<004Io o`03001oogoo06=oo`P000ioo`00=7oo1@003Goo00<007ooOol01goo00@007ooOomooa1Wh1Moo`03 00moogoo029oo`0300moogoo029oo`0300moogoo00]ooa`Gh1=ooa43k1Yoo`T3o`Aoo`03001oogoo 04Aoo`03001oogoo06=oo`P000ioo`000ol?Ool20016Ool00`00Oomoo`0VOol00`00Oomoo`02Ool00`00Oomoo`02Ool20007Ool00`00 Oomoo`06Ool00`00Oomoo`0NOol8000>Ool0051oo`03001oogoo02Qoo`0300moogoo029oo`0300mo ogoo00iooaLGh1aooa83k1Uoo`0300moogoo00Eoo`h3oaEoo`03001oogoo04Aoo`03001oogoo00Io oaT3o`Moo`03001oogoo009oo`03001oogoo00]oo`03001oogoo00Ioo`03001oogoo01ioo`P000io o`00Ool003Ioo`03001oogoo01Moo`03001oogoo02Qoo`0300moogoo 01MooaLGh1Uoo`0300moogoo01@3k0ioo`0300moogoo01aoo``3oaEoo`T1W`0olEOol90Il651l3Ool20016Ool00`00Oomoo`0WOol4000>Ool00`00Oomoo`05 Ool2000POol8000>Ool003=oo`8000=oo`8001Ioo`03001oogoo02Qoo`0300moogoo00eooa4Gh0Ao o`0300moogoo01aoo`d3k1ioo`0300moogoo01=oo`h3o`03Ool03goo01=oo`T1W`TD7`Aoo`03001o ogoo04Aoo`03001oogoo06=oo`P000ioo`005n0@Ool00`0?Oomoo`0>OolB0n`2Ool00`0?Oomoo`0ROol00`0? Oomoo`09Ool>0ol;Ool00`0?Oomoo`0;Ool;0Il951l9Ool00`00Oomoo`14Ool00`00Oomoo`1SOol8 000>Ool003Aoo`03001oogoo00Eoo`03001oogoo015oo`03001oogoo02Qoo`0300moogoo00dGh1Eo o`0300moogoo00Uooa<3k0Ioo`0300moogoo029oo`0300moogoo00Aoo`l3o`moo`0300moogoo00Qo o`/1W`03OolD7a@O00HD7`aoo`03001oogoo04Aoo`03001oogoo06=oo`P000ioo`005n0POol>0n`IOol00`0? Oomoo`0LOol=0olNOol00`0?Ool1W`090Il2Ool:51lCOol00`00Oomoo`14Ool00`00Oomoo`1SOol8 000>Ool003=oo`03001oogoo00=oo`03001oogoo01Aoo`03001oogoo01Yoo``Gh09oo`0300moogoo 01aoo`d3k1ioo`0300moogoo01Moo`h3ob5oo`X1W`9oo`XD7aIoo`03001oogoo04Aoo`03001oogoo 06=oo`P000ioo`00=7oo1@005goo00<007ooOol05goo2aOP1Woo00<03gooOol05goo3P?/8Woo00<0 3gooOol057oo30?o0Woo00<03gooOol07Woo2P6O0goo2A@O6Goo00<007ooOol0A7oo00<007ooOol0 Hgoo20003Woo001@Ool2000EOol:5n0:Ool00`0?Oomoo`0BOol>0n`2Ool00`0?Oomoo`0ROol00`0? Oomoo`0AOol;0ol6Ool00`0?Oomoo`0KOol:0Il4Ool851lKOol20016Ool00`00Oomoo`0WOol40005 Ool20005Ool5000WOol8000>Ool0051oo`03001oogoo019oo`TGh0eoo`0300moogoo00eoo`l3k0Io o`0300moogoo029oo`0300moogoo00eoo`/3o`Yoo`0300moogoo01Moo`/1W`0400moogooOol851lO Ool00`00Oomoo`14Ool00`00Oomoo`0VOol00`00Oomoo`02Ool00`00Oomoo`02Ool20007Ool00`00 Oomoo`0WOol8000>Ool004Aoo`D000Moo`03001oogoo00moo`TGh11oo`0300moogoo00Uoo`h3k0]o o`0300moogoo029oo`0300moogoo00Uoo``3o`eoo`0300moogoo01=oo``1W`=oo`0300mooa@O00LD 7b5oo`03001oogoo04Aoo`03001oogoo00IooaT3k0Moo`03001oogoo009oo`03001oogoo00]oo`03 001oogoo02Moo`P000ioo`00=7oo1@002goo00D007ooOomoo`0000Moo`03001oogoo00eoo`PGh1=o o`0300moogoo00Aoo`h3k11oo`0300moogoo029oo`0300moogoo00Aoo`h3oa1oo`0300moogoo00io o`h1W`Eoo`TD7b=oo`03001oogoo04Aoo`03001oogoo00IooaT3k0Moo`03001oogoo009oo`03001o ogoo00]oo`03001oogoo02Moo`P000ioo`00Ool003Ao o`80009oo`03001oogoo00aoo`03001oogoo00Ioo`03001oogoo00=oo`TGh1Moo`X3k21oo`0300mo ogoo01Moo`h3ob9oo`0400moogooOol;0Il8Ool;51l3Ool00`0?Oomoo`0XOol00`00Oomoo`14Ool0 0`00Oomoo`0WOol4000>Ool00`00Oomoo`0WOol8000>Ool004Qoo`03001oogoo00Eoo`04001oogoo Ool85n0GOol:0n`SOol00`0?Oomoo`0COol=0ol2Ool00`0?Oomoo`0ROol00`0?0Il1W`090Il8Ool; 51l6Ool00`0?Oomoo`0XOol00`00Oomoo`14Ool00`00Oomoo`1SOol8000>Ool004Qoo`03001oogoo 00Eoo`04001oogooOol65n0FOol:0n`00goo00moo`0SOol00`0?Oomoo`0>Ool>0ol6Ool00`0?Oomo o`0POol:0Il9Ool:51l:Ool00`0?Oomoo`0XOol00`00Oomoo`14Ool00`00Oomoo`1SOol8000>Ool0 03Aoo`D000]oo`05001oogooOol00007Ool01000Oomoogoo0aOP5Woo2P?/17oo00<03gooOol08Woo 00<03gooOol02goo30?o2goo00<03gooOol077oo2`6O2Goo2Q@O3Goo00<03gooOol0:7oo00<007oo Ool0A7oo00<007ooOol0Hgoo20003Woo000cOol00`00Oomoo`03Ool00`00Oomoo`09Ool30008Ool2 000HOol:0n`7Ool00`0?Oomoo`0ROol00`0?Oomoo`08Ool;0ol?Ool00`0?Oomoo`0GOol=0Il9Ool: 51l@Ool00`0?Oomoo`0WOol20016Ool00`00Oomoo`1SOol8000>Ool003=oo`03001oogoo00=oo`03 001oogoo01Aoo`03001oogoo01Aoo`X3k0Yoo`0300moogoo029oo`0300moogoo00Aoo`/3oa=oo`03 00moogoo01Aoo``1W`9oo`0300moogoo00Aoo`/D7a=oo`0300moogoo02Qoo`03001oogoo04Aoo`03 001oogoo06=oo`P000ioo`00Ool60n`EOol00`0?Oomoo`0JOol;0olROol00`0?Oomoo`07Ool;0Il;Ool:51lPOol00`0? Oomoo`0WOol20016Ool00`00Oomoo`0WOol40005Ool20005Ool40004Ool4000POol8000>Ool0035o o`T001Ioo`03001oogoo00]oo`H3k1Moo`0300moogoo01Moo`X3o`03Ool03goo02=oo`0300moogoo 00Aoo`X1W`aoo`XD7b=oo`0300moogoo02Qoo`03001oogoo04Aoo`03001oogoo02Ioo`03001oogoo 009oo`03001oogoo009oo`8000Aoo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`0MOol8 000>Ool003=oo`03001oogoo00=oo`03001oogoo01Aoo`03001oogoo00Qoo`P3k1Qoo`0300moogoo 01Aoo`X3o`Aoo`0300moogoo029oo`0400moogooOol:0IlOol:0Il: Ool0100?Oomoogoo2Q@O5goo00<03gooOol08Woo00<03gooOol0:7oo00<007ooOol0A7oo00<007oo Ool0Hgoo20003Woo001@Ool00`00Oomoo`0XOol00`0?0ol3o`060olLOol00`0?Oomoo`0;Ool:0Il= Ool00`0?51lD7`0851lJOol00`0?Oomoo`0ROol00`0?Oomoo`0XOol00`00Oomoo`14Ool00`00Oomo o`1SOol8000>Ool0051oo`8002Qoo`P3oaioo`0300moogoo00Qoo`X1W`ioo`XD7aeoo`0300moogoo 029oo`0300moogoo02Moo`8004Ioo`03001oogoo06=oo`P000ioo`00=7oo1@002goo100027oo00<0 07ooOol09Goo1`?o8Goo00<03gooOol017oo2`6O3Woo2Q@O87oo00<03gooOol08Woo00<03gooOol0 :7oo00<007ooOol0A7oo00<007ooOol0Hgoo20003Woo000cOol00`00Oomoo`03Ool00`00Oomoo`0< Ool00`00Oomoo`05Ool00`00Oomoo`0ROol80olSOol0100?Oomoogoo2`6O3Woo2Q@O8goo00<03goo Ool08Woo00<03gooOol0:7oo00<007ooOol0A7oo00<007ooOol0Hgoo20003Woo000cOol00`00Oomo o`03Ool00`00Oomoo`0Ool:51l00goo00moo`0SOol00`0?Oomoo`0ROol00`0?Oomoo`0XOol00`00Oomoo`14 Ool00`00Oomoo`1SOol8000>Ool0031oo`04001oogoo0004Ool00`00Oomoo`0=Ool00`00Oomoo`05 Ool00`00Oomoo`0NOol80ol2Ool00`0?Oomoo`0QOol90Il?Ool:51l4Ool00`0?Oomoo`0ROol00`0? Oomoo`0ROol00`0?Oomoo`0XOol00`00Oomoo`14Ool00`00Oomoo`1SOol8000>Ool002moo`/000io o`03001oogoo00Eoo`8001d03`L3obL03`P1W`l03`XD7gX03`<004Ioo`03001oogoo06=oo`P000io o`00>7oo00<007ooOol02goo0P0027oo00<007ooOol06Woo1`?o1goo00<03gooOol077oo206O47oo 2A@O2Woo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol0:7oo00<007ooOol0A7oo00<007oo Ool09goo10001Goo0P001Goo10001Woo0`007goo20003Woo0017Ool00`00Oomoo`06Ool00`00Oomo o`0HOol70ol9Ool00`0?Oomoo`0JOol80Il00`0?Oomoo`0Ool003=o o`03001oogoo019oo`03001oogoo00Eoo`03001oogoo01Ioo`L3o`]oo`0300moogoo01Qoo`P1W`9o o`0300moogoo00Yoo`PD7a1oo`0300moogoo029oo`0300moogoo029oo`0300moogoo02Qoo`03001o ogoo04Aoo`03001oogoo00IooaUWh0Moo`03001oogoo009oo`03001oogoo00Qoo`03001oogoo009o o`03001oogoo00Aoo`03001oogoo01ioo`P000ioo`00Goo00<007ooOol057oo0P004Woo1P?o4Goo 00<03gooOol047oo2@6O2Goo00@03gooOomoo`XD7aMoo`0300moogoo029oo`0300moogoo029oo`03 00moogoo02Moo`8004Ioo`03001oogoo02Ioo`03001oogoo009oo`03001oogoo00Qoo`03001oogoo 009oo`05001oogooOol00002Ool00`00Oomoo`0NOol8000>Ool003=oo`03001oogoo00<001Moo`03 001oogoo011oo`D3oa=oo`0300moogoo00ioo`P1W`aoo`0300lD7a@O00PD7aYoo`0300moogoo029o o`0300moogoo029oo`0300moogoo02Qoo`03001oogoo04Aoo`03001oogoo02Ioo`03001oogoo009o o`03001oogoo00Qoo`03001oogoo009oo`03001oogoo009oo`03001oo`00021oo`P000ioo`00Ool851lPOol00`0?Oomoo`0ROol00`0?Oomoo`0ROol00`0?Oomoo`0XOol00`00Oomoo`14Ool0 0`00Oomoo`1SOol8000>Ool0051oo`03001oogoo00]oo`H3oaMoo`0300moogoo00Moo`P1W`eoo`PD 7b=oo`0300moogoo029oo`0300moogoo029oo`0300moogoo02Qoo`03001oogoo04Aoo`03001oogoo 06=oo`P000ioo`00D7oo0P002goo1@?o6Goo00<03gooOol01Goo206O3Goo21@O00<03gooOol08Woo 00<03gooOol08Woo00<03gooOol08Woo00<03gooOol09goo0P00AWoo00<007ooOol0Hgoo20003Woo 000dOol00`00Oomoo`02000GOol00`00Oomoo`08Ool60olJOol00`0?Oomoo`03Ool70Il>Ool851l2 Ool00`0?Oomoo`0ROol00`0?Oomoo`0ROol00`0?Oomoo`0ROol00`0?Oomoo`0XOol00`00Oomoo`14 Ool00`00Oomoo`1SOol8000>Ool003=oo`04001oogoo0002Ool00`00Oomoo`0DOol00`00Oomoo`07 Ool50olLOol0100?Oomoogoo1`6O3Goo21@O1Goo00<03gooOol08Woo00<03gooOol08Woo00<03goo Ool08Woo00<03gooOol0:7oo00<007ooOol0A7oo00<007ooOol0Hgoo20003Woo000cOol01000Oomo o`000Woo00<007ooOol057oo00<007ooOol01Woo1@?o7Goo00<03gooOol01P6O3Goo21@O1goo00<0 3gooOol08Woo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol0:7oo00<007ooOol0A7oo00<0 07ooOol0Hgoo20003Woo000cOol01P00Oomoo`00Ool001Moo`03001oogoo00Aoo`D3oamoo`0300l1 W`6O00@1W`aoo`TD7`Uoo`0300moogoo029oo`0300moogoo029oo`0300moogoo029oo`0300moogoo 02Qoo`03001oogoo04Aoo`03001oogoo06=oo`P000ioo`00=7oo1P005Woo0P0017oo1@?o7goo1P6O 37oo21@O37oo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol09goo0P00 AWoo00<007ooOol09goo00<007ooOol0>Goo20003Woo000hOol00`00Oomoo`0EOol01000Oomoogoo 1P?o7Woo1`6O2goo21@O3Woo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol08Woo00<03goo Ool0:7oo00<007ooOol0A7oo00<007ooOol09goo00<007ooOol0>Goo20003Woo000`Ool00`00Oomo o`06Ool00`00Oomoo`0DOol01000Oomoogoo10?o7Woo1`6O2goo1a@O4Goo00<03gooOol08Woo00<0 3gooOol08Woo00<03gooOol08Woo00<03gooOol0:7oo00<007ooOol0A7oo00<007ooOol0:7oo00<0 07oo00000P002goo10009goo20003Woo000_Ool;000FOol01000Oomoogoo0`?o7Woo1P6O00<03goo Ool02Goo1Q@O4goo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol08Woo00<03gooOol0:7oo 00<007ooOol0A7oo00<007ooOol0:7oo00<007ooOol00Woo00<007ooOol01P0000=oo`00Ool00goo 00<007ooOol097oo20003Woo000iOol00`00Oomoo`0DOol00`00Oomoo`0POol60Il2Ool00`0?Oomo o`07Ool651lEOol00`0?Oomoo`0ROol00`0?Oomoo`0ROol00`0?Oomoo`0ROol00`0?Oomoo`0XOol0 0`00Oomoo`14Ool00`00Oomoo`06OolIOT09Ool00`00Oomoo`02Ool00`00Oomoo`07Ool00`00Oomo o`02Ool00`00Oomoo`0TOol8000>Ool0051oo`03001oogoo01ioo`H1W`Aoo`0300moogoo00Eoo`HD 7aMoo`0300moogoo029oo`0300moogoo029oo`0300moogoo029oo`0300moogoo02Qoo`03001oogoo 04Aoo`03001oogoo00IooaUn@0Uoo`03001oogoo009oo`03001oogoo00H00003Ool007oo00=oo`03 001oogoo02Aoo`P000ioo`00"], ImageRangeCache->{{{98.625, 423.813}, {647.813, 507.438}} -> {-1.99019, 4.04276, 0.0073967, 0.0073967}, {{107.063, 323.375}, {644.438, 510.75}} -> { 0.439978, 30.6925, 0.00374942, 0.0523647}, {{345, 409.875}, {631.688, 545.125}} -> {-17.9684, 53.7426, 0.0414339, 0.0876772}, {{348.438, 367.75}, {630, 620.875}} -> {-24.9664, 111.631, 0.0568932, 0.18411}, {{ 348.438, 367.75}, {619.375, 610.25}} -> {-24.9664, 109.186, 0.0568932, 0.18411}, {{348.438, 367.75}, {608.813, 599.688}} -> {-24.9664, 106.755, 0.0568932, 0.18411}, {{348.438, 367.75}, {598.25, 589.125}} -> {-24.9664, 104.324, 0.0568932, 0.18411}, {{348.438, 367.75}, {587.625, 578.5}} -> {-24.9664, 101.879, 0.0568932, 0.18411}, {{348.438, 367.75}, { 577.063, 567.938}} -> {-24.9664, 99.4483, 0.0568932, 0.18411}, {{348.438, 367.75}, {566.5, 557.375}} -> {-24.9664, 97.0174, 0.0568932, 0.18411}, {{ 348.438, 367.75}, {555.875, 546.75}} -> {-24.9664, 94.5722, 0.0568932, 0.18411}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", PageWidth->PaperWidth], Cell[TextData[StyleBox["The importance of the above is that we can see \ expected value falling for all values of \[Beta] with the rise in \[Alpha]. \ Or, we can ask if, to some degree, at a constant expected value, an increase \ in \[Alpha] is offset by an increase in \[Beta]. We also see that expected \ value = \[Delta] when the distribution is symmetrical (\[Beta] = 0).\n\n\ Below, in a contour plot where ev is constant throughout each \"band\", we \ see expected value move upward in the direction of the northwest quadrant \ with rise in \[Beta] as \[Alpha] declines.", FontColor->GrayLevel[0]]], "Text", PageWidth->PaperWidth, FontSlant->"Plain"], Cell[CellGroupData[{ Cell[BoxData[ \(pucev1 = ShowLegend[ ContourPlot[ Evaluate[ tvf1[\[Alpha], \[Beta]], {\[Alpha], 1.2, 1.8}, {\[Beta], 0, .2}], Contours -> { .5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5}, ColorFunction -> Hue, DisplayFunction\ -> \ Identity, TextStyle -> {FontSize -> 12, FontFamily \[Rule] Times}, Epilog -> {{Text["\", {1.52315, \ 0.0348515}]}, {Text["\", {1.43655, \ 0.130151}]}, {Text["\", {1.27, \ 0.189055}]}}, FrameLabel -> {\[Alpha], \[Beta]}], {Hue[\((1 - #)\)] &\ , 10, "\<>4.5\>", "\<<.5\>", \n\ \ \ \ LegendPosition -> {1.2, \(- .5\ \)}, LegendSize -> { .6, 1.2}}]\)], "Input", PageWidth->PaperWidth], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .70175 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.357978 0.334169 0.350877 0.334169 [ [ 0 0 0 0 ] [ 1 .70175 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath % Start of sub-graphic p 0.0238095 0.0167084 0.692147 0.685046 MathSubStart %% ContourGraphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -1.90385 1.60256 0.0192308 4.80769 [ [.01923 -0.0125 -9.5625 -15.75 ] [.01923 -0.0125 9.5625 0 ] [.17949 -0.0125 -9.5625 -15.75 ] [.17949 -0.0125 9.5625 0 ] [.33974 -0.0125 -9.5625 -15.75 ] [.33974 -0.0125 9.5625 0 ] [.5 -0.0125 -9.5625 -15.75 ] [.5 -0.0125 9.5625 0 ] [.66026 -0.0125 -9.5625 -15.75 ] [.66026 -0.0125 9.5625 0 ] [.82051 -0.0125 -9.5625 -15.75 ] [.82051 -0.0125 9.5625 0 ] [.98077 -0.0125 -9.5625 -15.75 ] [.98077 -0.0125 9.5625 0 ] [ 0 0 -0.125 0 ] [.5 -0.0125 -5.625 -31.5 ] [.5 -0.0125 5.625 -15.75 ] [-0.0125 .01923 -10 -7.875 ] [-0.0125 .01923 0 7.875 ] [-0.0125 .25962 -25.125 -7.875 ] [-0.0125 .25962 0 7.875 ] [-0.0125 .5 -19.125 -7.875 ] [-0.0125 .5 0 7.875 ] [-0.0125 .74038 -25.125 -7.875 ] [-0.0125 .74038 0 7.875 ] [-0.0125 .98077 -19.125 -7.875 ] [-0.0125 .98077 0 7.875 ] [ 0 0 -0.125 0 ] [-0.01875 .5 -40.875 -5.625 ] [-0.01875 .5 -25.125 5.625 ] [ 0 1 .125 0 ] [ 1 0 .125 0 ] [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .01923 0 m .01923 .00625 L s gsave .01923 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.2) show 1.000 setlinewidth grestore .17949 0 m .17949 .00625 L s gsave .17949 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.3) show 1.000 setlinewidth grestore .33974 0 m .33974 .00625 L s gsave .33974 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.4) show 1.000 setlinewidth grestore .5 0 m .5 .00625 L s gsave .5 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.5) show 1.000 setlinewidth grestore .66026 0 m .66026 .00625 L s gsave .66026 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.6) show 1.000 setlinewidth grestore .82051 0 m .82051 .00625 L s gsave .82051 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.7) show 1.000 setlinewidth grestore .98077 0 m .98077 .00625 L s gsave .98077 -0.0125 -70.5625 -19.75 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.8) show 1.000 setlinewidth grestore .125 Mabswid .05128 0 m .05128 .00375 L s .08333 0 m .08333 .00375 L s .11538 0 m .11538 .00375 L s .14744 0 m .14744 .00375 L s .21154 0 m .21154 .00375 L s .24359 0 m .24359 .00375 L s .27564 0 m .27564 .00375 L s .30769 0 m .30769 .00375 L s .37179 0 m .37179 .00375 L s .40385 0 m .40385 .00375 L s .4359 0 m .4359 .00375 L s .46795 0 m .46795 .00375 L s .53205 0 m .53205 .00375 L s .5641 0 m .5641 .00375 L s .59615 0 m .59615 .00375 L s .62821 0 m .62821 .00375 L s .69231 0 m .69231 .00375 L s .72436 0 m .72436 .00375 L s .75641 0 m .75641 .00375 L s .78846 0 m .78846 .00375 L s .85256 0 m .85256 .00375 L s .88462 0 m .88462 .00375 L s .91667 0 m .91667 .00375 L s .94872 0 m .94872 .00375 L s .25 Mabswid 0 0 m 1 0 L s gsave .5 -0.0125 -66.625 -35.5 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Math1 %%IncludeFont: Math1 /Math1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (a) show 1.000 setlinewidth grestore 0 .01923 m .00625 .01923 L s gsave -0.0125 .01923 -71 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 1.000 setlinewidth grestore 0 .25962 m .00625 .25962 L s gsave -0.0125 .25962 -86.125 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0.05) show 1.000 setlinewidth grestore 0 .5 m .00625 .5 L s gsave -0.0125 .5 -80.125 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0.1) show 1.000 setlinewidth grestore 0 .74038 m .00625 .74038 L s gsave -0.0125 .74038 -86.125 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0.15) show 1.000 setlinewidth grestore 0 .98077 m .00625 .98077 L s gsave -0.0125 .98077 -80.125 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0.2) show 1.000 setlinewidth grestore .125 Mabswid 0 .06731 m .00375 .06731 L s 0 .11538 m .00375 .11538 L s 0 .16346 m .00375 .16346 L s 0 .21154 m .00375 .21154 L s 0 .30769 m .00375 .30769 L s 0 .35577 m .00375 .35577 L s 0 .40385 m .00375 .40385 L s 0 .45192 m .00375 .45192 L s 0 .54808 m .00375 .54808 L s 0 .59615 m .00375 .59615 L s 0 .64423 m .00375 .64423 L s 0 .69231 m .00375 .69231 L s 0 .78846 m .00375 .78846 L s 0 .83654 m .00375 .83654 L s 0 .88462 m .00375 .88462 L s 0 .93269 m .00375 .93269 L s .25 Mabswid 0 0 m 0 1 L s gsave -0.01875 .5 -99.625 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate 66.625 11.875 translate 90 rotate -66.625 -11.875 translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 64.188 15.875 moveto %%IncludeResource: font Math1 %%IncludeFont: Math1 /Math1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (b) show 1.000 setlinewidth grestore .01923 .99375 m .01923 1 L s .17949 .99375 m .17949 1 L s .33974 .99375 m .33974 1 L s .5 .99375 m .5 1 L s .66026 .99375 m .66026 1 L s .82051 .99375 m .82051 1 L s .98077 .99375 m .98077 1 L s .125 Mabswid .05128 .99625 m .05128 1 L s .08333 .99625 m .08333 1 L s .11538 .99625 m .11538 1 L s .14744 .99625 m .14744 1 L s .21154 .99625 m .21154 1 L s .24359 .99625 m .24359 1 L s .27564 .99625 m .27564 1 L s .30769 .99625 m .30769 1 L s .37179 .99625 m .37179 1 L s .40385 .99625 m .40385 1 L s .4359 .99625 m .4359 1 L s .46795 .99625 m .46795 1 L s .53205 .99625 m .53205 1 L s .5641 .99625 m .5641 1 L s .59615 .99625 m .59615 1 L s .62821 .99625 m .62821 1 L s .69231 .99625 m .69231 1 L s .72436 .99625 m .72436 1 L s .75641 .99625 m .75641 1 L s .78846 .99625 m .78846 1 L s .85256 .99625 m .85256 1 L s .88462 .99625 m .88462 1 L s .91667 .99625 m .91667 1 L s .94872 .99625 m .94872 1 L s .25 Mabswid 0 1 m 1 1 L s .99375 .01923 m 1 .01923 L s .99375 .25962 m 1 .25962 L s .99375 .5 m 1 .5 L s .99375 .74038 m 1 .74038 L s .99375 .98077 m 1 .98077 L s .125 Mabswid .99625 .06731 m 1 .06731 L s .99625 .11538 m 1 .11538 L s .99625 .16346 m 1 .16346 L s .99625 .21154 m 1 .21154 L s .99625 .30769 m 1 .30769 L s .99625 .35577 m 1 .35577 L s .99625 .40385 m 1 .40385 L s .99625 .45192 m 1 .45192 L s .99625 .54808 m 1 .54808 L s .99625 .59615 m 1 .59615 L s .99625 .64423 m 1 .64423 L s .99625 .69231 m 1 .69231 L s .99625 .78846 m 1 .78846 L s .99625 .83654 m 1 .83654 L s .99625 .88462 m 1 .88462 L s .99625 .93269 m 1 .93269 L s .25 Mabswid 1 0 m 1 1 L s 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath 1 0 0 r .01923 .98077 m .98077 .98077 L .98077 .01923 L .01923 .01923 L F 0 g .5 Mabswid 1 .718 0 r .01923 .10226 m .08791 .11335 L .15659 .12369 L .22527 .1334 L .29396 .14275 L .36264 .1521 L .39489 .15659 L .43132 .16181 L .5 .17221 L .56868 .18369 L .63736 .19676 L .70604 .21213 L .75559 .22527 L .77473 .23095 L .84341 .25503 L .91209 .28723 L .92404 .29396 L .98077 .33207 L .98077 .98077 L .01923 .98077 L F 0 g .01923 .10226 m .08791 .11335 L .15659 .12369 L .22527 .1334 L .29396 .14275 L .36264 .1521 L .39489 .15659 L .43132 .16181 L .5 .17221 L .56868 .18369 L .63736 .19676 L .70604 .21213 L .75559 .22527 L .77473 .23095 L .84341 .25503 L .91209 .28723 L .92404 .29396 L .98077 .33207 L s .646 1 0 r .01923 .19559 m .08791 .21927 L .10604 .22527 L .15659 .24138 L .22527 .26215 L .29396 .28217 L .33456 .29396 L .36264 .3022 L .43132 .32298 L .5 .34526 L .54934 .36264 L .56868 .36985 L .63736 .39782 L .70604 .43072 L .70718 .43132 L .77473 .47098 L .81565 .5 L .84341 .52247 L .89178 .56868 L .91209 .59131 L .94812 .63736 L .98077 .68716 L .98077 .98077 L .01923 .98077 L F 0 g .01923 .19559 m .08791 .21927 L .10604 .22527 L .15659 .24138 L .22527 .26215 L .29396 .28217 L .33456 .29396 L .36264 .3022 L .43132 .32298 L .5 .34526 L .54934 .36264 L .56868 .36985 L .63736 .39782 L .70604 .43072 L .70718 .43132 L .77473 .47098 L .81565 .5 L .84341 .52247 L .89178 .56868 L .91209 .59131 L .94812 .63736 L .98077 .68716 L s .01 1 0 r .01923 .28899 m .02854 .29396 L .08791 .32526 L .15659 .35914 L .16397 .36264 L .22527 .39097 L .29396 .42166 L .3157 .43132 L .36264 .45237 L .43132 .48423 L .46376 .5 L .5 .51839 L .56868 .55609 L .58989 .56868 L .63736 .59896 L .69077 .63736 L .70604 .64939 L .76965 .70604 L .77473 .7111 L .83148 .77473 L .84341 .78999 L .88083 .84341 L .91209 .89546 L .92118 .91209 L .95489 .98077 L .01923 .98077 L F 0 g .01923 .28899 m .02854 .29396 L .08791 .32526 L .15659 .35914 L .16397 .36264 L .22527 .39097 L .29396 .42166 L .3157 .43132 L .36264 .45237 L .43132 .48423 L .46376 .5 L .5 .51839 L .56868 .55609 L .58989 .56868 L .63736 .59896 L .69077 .63736 L .70604 .64939 L .76965 .70604 L .77473 .7111 L .83148 .77473 L .84341 .78999 L .88083 .84341 L .91209 .89546 L .92118 .91209 L .95489 .98077 L s 0 1 .625 r .01923 .38246 m .08788 .43132 L .08791 .43134 L .15659 .47699 L .19301 .5 L .22527 .51989 L .29396 .56127 L .30636 .56868 L .36264 .60265 L .41846 .63736 L .43132 .6456 L .5 .69163 L .52027 .70604 L .56868 .74244 L .60828 .77473 L .63736 .80022 L .68243 .84341 L .70604 .86818 L .7442 .91209 L .77473 .95133 L .79561 .98077 L .01923 .98077 L F 0 g .01923 .38246 m .08788 .43132 L .08791 .43134 L .15659 .47699 L .19301 .5 L .22527 .51989 L .29396 .56127 L .30636 .56868 L .36264 .60265 L .41846 .63736 L .43132 .6456 L .5 .69163 L .52027 .70604 L .56868 .74244 L .60828 .77473 L .63736 .80022 L .68243 .84341 L .70604 .86818 L .7442 .91209 L .77473 .95133 L .79561 .98077 L s 0 .739 1 r .01923 .47605 m .04566 .5 L .08791 .53755 L .12449 .56868 L .15659 .59499 L .21024 .63736 L .22527 .64896 L .29396 .70102 L .30064 .70604 L .36264 .75309 L .39059 .77473 L .43132 .80712 L .47504 .84341 L .5 .86503 L .55132 .91209 L .56868 .92895 L .61866 .98077 L .01923 .98077 L F 0 g .01923 .47605 m .04566 .5 L .08791 .53755 L .12449 .56868 L .15659 .59499 L .21024 .63736 L .22527 .64896 L .29396 .70102 L .30064 .70604 L .36264 .75309 L .39059 .77473 L .43132 .80712 L .47504 .84341 L .5 .86503 L .55132 .91209 L .56868 .92895 L .61866 .98077 L s 0 .103 1 r .01923 .56979 m .08167 .63736 L .08791 .64392 L .1493 .70604 L .15659 .71316 L .22151 .77473 L .22527 .77821 L .29396 .84096 L .29665 .84341 L .36264 .90372 L .37166 .91209 L .43132 .96884 L .44346 .98077 L .01923 .98077 L F 0 g .01923 .56979 m .08167 .63736 L .08791 .64392 L .1493 .70604 L .15659 .71316 L .22151 .77473 L .22527 .77821 L .29396 .84096 L .29665 .84341 L .36264 .90372 L .37166 .91209 L .43132 .96884 L .44346 .98077 L s .532 0 1 r .01923 .6637 m .05237 .70604 L .08791 .75049 L .1079 .77473 L .15659 .83154 L .16706 .84341 L .22527 .90769 L .22935 .91209 L .29361 .98077 L .01923 .98077 L F 0 g .01923 .6637 m .05237 .70604 L .08791 .75049 L .1079 .77473 L .15659 .83154 L .16706 .84341 L .22527 .90769 L .22935 .91209 L .29361 .98077 L s 1 0 .832 r .01923 .75782 m .03077 .77473 L .07808 .84341 L .08791 .8573 L .1278 .91209 L .15659 .95018 L .18028 .98077 L .01923 .98077 L F 0 g .01923 .75782 m .03077 .77473 L .07808 .84341 L .08791 .8573 L .1278 .91209 L .15659 .95018 L .18028 .98077 L s 1 0 0 r .01923 .85218 m .05551 .91209 L .08791 .96439 L .09831 .98077 L .01923 .98077 L F 0 g .01923 .85218 m .05551 .91209 L .08791 .96439 L .09831 .98077 L s gsave .5371 .18679 -77 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (ev) show 74.125 15.875 moveto %%IncludeResource: font Math1 %%IncludeFont: Math1 /Math1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (=) show 81.875 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (.5) show 91.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .39832 .64496 -75.4375 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (ev) show 74.125 15.875 moveto %%IncludeResource: font Math1 %%IncludeFont: Math1 /Math1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (=) show 81.875 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 87.875 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .13141 .92815 -80 -11.875 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 23.75 translate 1 -1 scale 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (ev) show 74.125 15.875 moveto %%IncludeResource: font Math1 %%IncludeFont: Math1 /Math1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (=) show 81.875 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (4.5) show 97.000 15.875 moveto %%IncludeResource: font Times-Roman %%IncludeFont: Times-Roman /Times-Roman findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore MathSubEnd P % End of sub-graphic 0 g .77569 .16708 m .77569 .56809 L .97619 .56809 L .97619 .16708 L F 1 g .75898 .18379 m .75898 .5848 L .95948 .5848 L .95948 .18379 L F 0 g .001 w [ ] 0 setdash .75898 .18379 m .95948 .18379 L .95948 .5848 L .75898 .5848 L .75898 .18379 L s % Start of sub-graphic p 0.758981 0.183793 0.959482 0.584795 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.03125 0.3125 0.0196078 0.196078 [ [ 0 0 0 0 ] [ 1 2 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 2 L 0 2 L closepath clip newpath 1 0 0 r .03125 .01961 m .03125 .21569 L .34375 .21569 L .34375 .01961 L F 0 g gsave .35938 .11765 -61 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (<) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (.5) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 1 .667 0 r .03125 .21569 m .03125 .41176 L .34375 .41176 L .34375 .21569 L F .667 1 0 r .03125 .41176 m .03125 .60784 L .34375 .60784 L .34375 .41176 L F 0 1 0 r .03125 .60784 m .03125 .80392 L .34375 .80392 L .34375 .60784 L F 0 1 .667 r .03125 .80392 m .03125 1 L .34375 1 L .34375 .80392 L F 0 .667 1 r .03125 1 m .03125 1.19608 L .34375 1.19608 L .34375 1 L F 0 0 1 r .03125 1.19608 m .03125 1.39216 L .34375 1.39216 L .34375 1.19608 L F .667 0 1 r .03125 1.39216 m .03125 1.58824 L .34375 1.58824 L .34375 1.39216 L F 1 0 .667 r .03125 1.58824 m .03125 1.78431 L .34375 1.78431 L .34375 1.58824 L F 1 0 0 r .03125 1.78431 m .03125 1.98039 L .34375 1.98039 L .34375 1.78431 L F 0 g gsave .35938 1.88235 -61 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.875 translate 1 -1 scale 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (>) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (4.5) show 87.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore MathSubEnd P % End of sub-graphic 0 0 m 1 0 L 1 .70175 L 0 .70175 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{288, 202.063}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggoo0`000goo00@007oo Oomoo`D000eoo`<000=oo`04001oogooOol4000>Ool30003Ool00`00Oomoo`04Ool00`00Oomoo`0= Ool30003Ool01000Oomoogoo0`003goo0`000goo00<007ooOol00Woo0`003Woo0`000goo00<007oo Ool00goo00<007ooOol03Goo0`000goo00<007ooOol00Woo0`00MWoo000lOol00`00Oomoo`06Ool0 1@00Oomoogoo00003Woo00<007ooOol02Woo00<007ooOol037oo00<007ooOol02Goo00<007ooOol0 3Woo00<007ooOol02Goo00<007ooOol03Goo00<007ooOol01Woo00D007ooOomoo`0000ioo`03001o ogoo00Qoo`03001oogoo00ioo`03001oogoo00Ioo`05001oogooOol0001eOol003aoo`03001oogoo 00Moo`03001oogoo00moo`03001oogoo00Yoo`03001oogoo00aoo`03001oogoo00Uoo`03001oogoo 00ioo`03001oogoo00Yoo`03001oogoo00aoo`03001oogoo00Ioo`05001oogooOol0000>Ool00`00 Oomoo`09Ool00`00Oomoo`0=Ool00`00Oomoo`06Ool01@00Oomoogoo0000MGoo000lOol00`00Oomo o`08Ool00`00Oomoo`0>Ool00`00Oomoo`0:Ool00`00Oomoo`0Ool00`00 Oomoo`09Ool00`00Oomoo`0=Ool00`00Oomoo`07Ool00`00Ool0001fOol003aoo`03001oogoo00Uo o`03001oogoo00eoo`03001oogoo00Qoo`8000moo`03001oogoo00Ioo`04001oogoo000@Ool00`00 Oomoo`09Ool00`00Oomoo`0=Ool00`00Oomoo`06Ool20002Ool00`00Oomoo`0Ool2000IOol30009 Ool00`00Oomoo`07Ool01000Oomoo`9O0P