(************** Content-type: application/mathematica **************
                     CreatedBy='Mathematica 5.0'

                    Mathematica-Compatible Notebook

This notebook can be used with any Mathematica-compatible
application, such as Mathematica, MathReader or Publicon. The data
for the notebook starts with the line containing 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[    231271,       9539]*)
(*NotebookOutlinePosition[    232502,       9576]*)
(*  CellTagsIndexPosition[    232458,       9572]*)
(*WindowFrame->Normal*)



Notebook[{

Cell[CellGroupData[{
Cell["Nonlinear Differential Equations", "Subtitle",
  TextAlignment->Center,
  TextJustification->0],

Cell["\<\
In this notebook, we solve nonlinear differential equations, \
looking at the time dependence, phase space plots, Poincare sections, and the \
power spectrum.

The notebook starts with the Duffing equation.  Your job is to modify it to \
the damped, driven pendulum, then to reproduce and extend the results from \
session 9 (which used diffeq_pendulum.cpp).\
\>", "Text"],

Cell[CellGroupData[{

Cell["Define the Differential Equation", "Section"],

Cell["\<\
Name the equation \"diffeq\".  Note the \"==\" in defining the \
equation.  \
\>", "Text"],

Cell[BoxData[
    \(diffeq\  := \ \(x''\)[t] + 
          2\ \[Gamma]\ \(x'\)[t] + \[Alpha]\ \ x[
              t] + \[Beta]\ x[
                t]^3 \[Equal] \(\(fext\)\(\ \)\(Cos[\[Omega]ext\ t]\)\(\ \)\)\
\)], "Input",
  CellLabel->"In[1]:="],

Cell["Choose among the parameters:", "Text"],

Cell[BoxData[
    \(\(p1\  := \ {\[Alpha]\  = \(-1\), \[Beta] = 1, \[Omega]ext = 
            1, \ \[Gamma] = 0.25, fext = 0.34875};\)\)], "Input",
  CellLabel->"In[2]:="],

Cell[CellGroupData[{

Cell[BoxData[
    \(p1\)], "Input",
  CellLabel->"In[3]:="],

Cell[BoxData[
    \({\(-1\), 1, 1, 0.25`, 0.34875`}\)], "Output",
  CellLabel->"Out[3]="]
}, Open  ]],

Cell["Choose among the initial conditions:", "Text"],

Cell[BoxData[
    \(\(ic1\  := \ {x0 = 1, v0 = 0. };\)\)], "Input",
  CellLabel->"In[4]:="],

Cell[CellGroupData[{

Cell[BoxData[
    \(ic1\)], "Input",
  CellLabel->"In[5]:="],

Cell[BoxData[
    \({1, 0.`}\)], "Output",
  CellLabel->"Out[5]="]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Solve the Differential Equation", "Section"],

Cell["\<\
Specify the range in time over which we will solve the differential \
equation.  We won't be able to use the solution outside of this range. (I.e., \
we'll have to extend this range if we get an \"outside of range\" error \
later.)\
\>", "Text"],

Cell[BoxData[
    \(tmin = 0; \ tmax = 1000;\)], "Input",
  CellLabel->"In[6]:="],

Cell["\<\
Numerically solve the differential equaiton using NDSolve, \
specifying the initial conditions.  Setting MaxSteps to a large number is \
needed if tmax is large.\
\>", "Text"],

Cell[BoxData[
    \(\(solution\  = \ 
        NDSolve[{diffeq, x[0] \[Equal] x0, \ \(x'\)[0] \[Equal] v0}, 
          x, {t, tmin, tmax}, MaxSteps \[Rule] 20000];\)\)], "Input",
  CellLabel->"In[7]:="],

Cell["\<\
NDSolve returns an \"interpolating function\", which can be \
evaluated later at any time t in tmin < t < tmax.\
\>", "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Plot the Time Dependence and Phase Space", "Section"],

Cell["\<\
We can just use \"Plot\" with Evaluate and the \"interpolating \
function\" defined by \"solution\".\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Plot[Evaluate[x[t] /. solution], {t, 0, 100}]\)], "Input",
  CellLabel->"In[8]:="],

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 0.418578 [
[.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 .09843 -18 -4.5 ]
[.01131 .09843 0 4.5 ]
[.01131 .18215 -18 -4.5 ]
[.01131 .18215 0 4.5 ]
[.01131 .26586 -18 -4.5 ]
[.01131 .26586 0 4.5 ]
[.01131 .34958 -18 -4.5 ]
[.01131 .34958 0 4.5 ]
[.01131 .43329 -6 -4.5 ]
[.01131 .43329 0 4.5 ]
[.01131 .51701 -18 -4.5 ]
[.01131 .51701 0 4.5 ]
[.01131 .60072 -18 -4.5 ]
[.01131 .60072 0 4.5 ]
[ 0 0 0 0 ]
[ 1 .61803 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.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 .09843 m
.03006 .09843 L
s
[(0.2)] .01131 .09843 1 0 Mshowa
.02381 .18215 m
.03006 .18215 L
s
[(0.4)] .01131 .18215 1 0 Mshowa
.02381 .26586 m
.03006 .26586 L
s
[(0.6)] .01131 .26586 1 0 Mshowa
.02381 .34958 m
.03006 .34958 L
s
[(0.8)] .01131 .34958 1 0 Mshowa
.02381 .43329 m
.03006 .43329 L
s
[(1)] .01131 .43329 1 0 Mshowa
.02381 .51701 m
.03006 .51701 L
s
[(1.2)] .01131 .51701 1 0 Mshowa
.02381 .60072 m
.03006 .60072 L
s
[(1.4)] .01131 .60072 1 0 Mshowa
.125 Mabswid
.02381 .03564 m
.02756 .03564 L
s
.02381 .05657 m
.02756 .05657 L
s
.02381 .0775 m
.02756 .0775 L
s
.02381 .11936 m
.02756 .11936 L
s
.02381 .14029 m
.02756 .14029 L
s
.02381 .16122 m
.02756 .16122 L
s
.02381 .20308 m
.02756 .20308 L
s
.02381 .224 m
.02756 .224 L
s
.02381 .24493 m
.02756 .24493 L
s
.02381 .28679 m
.02756 .28679 L
s
.02381 .30772 m
.02756 .30772 L
s
.02381 .32865 m
.02756 .32865 L
s
.02381 .37051 m
.02756 .37051 L
s
.02381 .39144 m
.02756 .39144 L
s
.02381 .41236 m
.02756 .41236 L
s
.02381 .45422 m
.02756 .45422 L
s
.02381 .47515 m
.02756 .47515 L
s
.02381 .49608 m
.02756 .49608 L
s
.02381 .53794 m
.02756 .53794 L
s
.02381 .55887 m
.02756 .55887 L
s
.02381 .5798 m
.02756 .5798 L
s
.25 Mabswid
.02381 0 m
.02381 .61803 L
s
0 0 m
1 0 L
1 .61803 L
0 .61803 L
closepath
clip
newpath
.5 Mabswid
.02381 .43329 m
.02499 .43438 L
.02605 .43714 L
.02729 .44217 L
.02846 .44839 L
.03279 .47698 L
.03398 .4842 L
.03524 .49053 L
.03631 .49447 L
.0375 .49693 L
.03877 .49709 L
.03949 .49599 L
.04014 .49421 L
.04141 .48869 L
.04262 .48101 L
.045 .4598 L
.04753 .43058 L
.0521 .37073 L
.05472 .33718 L
.05749 .30538 L
.06005 .28086 L
.06244 .26343 L
.0637 .25675 L
.06441 .25383 L
.06505 .25172 L
.06575 .25004 L
.06652 .249 L
.06724 .24879 L
.06791 .2493 L
.06861 .2506 L
.06927 .25256 L
.07 .25555 L
.07078 .2598 L
.07237 .27188 L
.07382 .28714 L
.07632 .32275 L
.07905 .37453 L
.08193 .43959 L
.08454 .50015 L
.08578 .52617 L
.08712 .55044 L
.08839 .56826 L
.08956 .57935 L
.0908 .58492 L
.09151 .58515 L
.09217 .58347 L
.09286 .57977 L
.09349 .57476 L
.09423 .5672 L
.09492 .55844 L
Mistroke
.09954 .47563 L
.10458 .37862 L
.10991 .29949 L
.11252 .26984 L
.11492 .24694 L
.11707 .2296 L
.11943 .21398 L
.12179 .20217 L
.12309 .19761 L
.12429 .19474 L
.1256 .1933 L
.12634 .19334 L
.12702 .19396 L
.12827 .19669 L
.1289 .1989 L
.1296 .20203 L
.1308 .20922 L
.13209 .2197 L
.13443 .24649 L
.13575 .26634 L
.13719 .29203 L
.14009 .35581 L
.14528 .49282 L
.14782 .55205 L
.14852 .56495 L
.14926 .57651 L
.15058 .59114 L
.15181 .5971 L
.15296 .59576 L
.15422 .58696 L
.15493 .57898 L
.15558 .57001 L
.15788 .52808 L
.16038 .47258 L
.16493 .37301 L
.1702 .28326 L
.17287 .24864 L
.17581 .21692 L
.17831 .19458 L
.18101 .17503 L
.18225 .16776 L
.18355 .1614 L
.18467 .15713 L
.18589 .15382 L
.18721 .15204 L
.18842 .1522 L
.18905 .15305 L
.18975 .15463 L
.19048 .15703 L
.19117 .16002 L
Mistroke
.19242 .16751 L
.19357 .17677 L
.19489 .19053 L
.19615 .20685 L
.19846 .24559 L
.20061 .29182 L
.20548 .42651 L
.20822 .50681 L
.20956 .5415 L
.2108 .56811 L
.21192 .58654 L
.21311 .5989 L
.21431 .60332 L
.21562 .59888 L
.21634 .59247 L
.21703 .58404 L
.21831 .56287 L
.2212 .49795 L
.22642 .36812 L
.2314 .2678 L
.23608 .19806 L
.24096 .14372 L
.24355 .12149 L
.245 .11123 L
.24634 .10322 L
.24752 .09756 L
.24858 .09359 L
.24977 .0906 L
.25103 .08923 L
.25225 .08984 L
.25356 .09283 L
.25481 .09808 L
.25596 .10517 L
.25701 .11369 L
.258 .1235 L
.26024 .15291 L
.26242 .1916 L
.26477 .2445 L
.26968 .38798 L
.27238 .47357 L
.27491 .54279 L
.27636 .57149 L
.27717 .58294 L
.27792 .59011 L
.27855 .59356 L
.27925 .59455 L
.27997 .59251 L
.28064 .58786 L
.28134 .58052 L
.28199 .57136 L
Mistroke
.28321 .54921 L
.28596 .48308 L
.291 .34792 L
.29572 .24236 L
.30064 .16098 L
.30325 .12813 L
.30607 .10028 L
.3073 .09055 L
.30862 .08197 L
.30938 .07791 L
.31007 .0748 L
.31076 .07223 L
.31141 .0704 L
.31266 .06837 L
.31333 .06817 L
.31402 .06863 L
.3152 .07103 L
.31649 .07614 L
.31773 .08367 L
.31887 .09288 L
.32142 .12226 L
.32379 .16084 L
.32603 .20786 L
.33479 .46341 L
.33719 .52762 L
.33785 .5418 L
.33854 .55465 L
.33978 .57162 L
.34094 .5798 L
.34202 .58044 L
.3432 .57358 L
.34447 .55828 L
.34571 .53641 L
.34707 .50694 L
.34952 .44466 L
.35411 .32637 L
.3567 .26891 L
.35945 .2179 L
.36182 .18196 L
.36437 .15153 L
.36558 .14002 L
.36673 .13089 L
.36786 .12375 L
.3689 .11871 L
.36988 .1154 L
.37092 .1135 L
.37208 .11341 L
.37314 .11527 L
.37438 .11998 L
.37552 .12682 L
Mistroke
.37678 .13724 L
.37811 .15172 L
.38034 .18454 L
.38278 .23316 L
.3876 .36421 L
.39013 .44419 L
.39282 .52316 L
.39395 .55042 L
.39517 .57365 L
.39587 .58355 L
.39651 .59023 L
.39776 .59631 L
.39882 .59411 L
.39998 .58433 L
.4012 .56681 L
.40232 .54504 L
.40762 .40865 L
.41327 .27202 L
.4185 .17926 L
.42325 .11904 L
.42556 .09711 L
.42811 .07893 L
.42939 .07234 L
.4301 .06949 L
.43077 .06734 L
.43206 .06474 L
.43325 .0643 L
.43436 .06566 L
.43554 .06911 L
.43655 .07378 L
.43766 .08087 L
.43885 .09081 L
.44014 .1044 L
.44246 .13698 L
.44498 .18439 L
.44774 .25076 L
.45331 .41821 L
.4558 .49229 L
.45717 .52671 L
.45847 .55256 L
.45967 .56933 L
.46098 .57847 L
.46217 .57825 L
.46327 .57104 L
.47306 .35073 L
.47564 .29049 L
.47846 .23473 L
.48115 .19163 L
.48359 .16099 L
.48609 .13792 L
Mistroke
.48746 .12891 L
.48875 .1229 L
.48995 .11956 L
.49105 .11848 L
.49226 .11962 L
.49353 .12358 L
.49462 .12929 L
.49578 .13791 L
.49687 .14852 L
.49787 .16038 L
.50031 .19855 L
.50263 .24696 L
.50716 .37265 L
.51142 .50384 L
.51356 .55688 L
.51476 .57829 L
.51586 .59117 L
.517 .59704 L
.51824 .59457 L
.51955 .5826 L
.52076 .56395 L
.52209 .53673 L
.52335 .50647 L
.52571 .44391 L
.531 .30895 L
.53554 .21813 L
.53792 .17998 L
.54047 .14511 L
.54303 .11597 L
.54536 .09439 L
.54649 .0858 L
.54771 .07785 L
.54886 .07181 L
.54994 .06746 L
.5506 .06547 L
.55131 .06391 L
.55256 .06276 L
.55326 .06303 L
.55401 .06408 L
.55465 .06562 L
.55534 .06801 L
.5566 .07422 L
.5573 .07882 L
.55794 .08374 L
.56035 .10893 L
.56166 .12713 L
.56305 .15008 L
.56554 .20092 L
.57117 .357 L
.57391 .44274 L
Mistroke
.57525 .48247 L
.57651 .5155 L
.57773 .54244 L
.57885 .56108 L
.58008 .57421 L
.5814 .57871 L
.58261 .57415 L
.58372 .56308 L
.58494 .54432 L
.58624 .51848 L
.5908 .40327 L
.59603 .27787 L
.59858 .22909 L
.60091 .19244 L
.60293 .16672 L
.60512 .14496 L
.60632 .13583 L
.60744 .12921 L
.6085 .12459 L
.60963 .12157 L
.61076 .12059 L
.61198 .12193 L
.61313 .12558 L
.61418 .13107 L
.61535 .13966 L
.61663 .15223 L
.61921 .18817 L
.62174 .23781 L
.62449 .30725 L
.62947 .45974 L
.63183 .52741 L
.63312 .55745 L
.63432 .57886 L
.63535 .59099 L
.63645 .59716 L
.63768 .59548 L
.6388 .58642 L
.64009 .56807 L
.64147 .54099 L
.64394 .47993 L
.64954 .3331 L
.65489 .22236 L
.65974 .14937 L
.66227 .11987 L
.66463 .09733 L
.66709 .07925 L
.66839 .07212 L
.66911 .06895 L
.66978 .06654 L
.67097 .0636 L
Mistroke
.67226 .06242 L
.6734 .06325 L
.67461 .06617 L
.67569 .07067 L
.6767 .07658 L
.67781 .08506 L
.67901 .09661 L
.68154 .1298 L
.68431 .18042 L
.6872 .2494 L
.68988 .32644 L
.6924 .40518 L
.69506 .48545 L
.69616 .51425 L
.69734 .54048 L
.69863 .56216 L
.69984 .57452 L
.70049 .57777 L
.7012 .57854 L
.70248 .57272 L
.70374 .55876 L
.7049 .53959 L
.70755 .4801 L
.71038 .40638 L
.7155 .28264 L
.71801 .23386 L
.72032 .19674 L
.72256 .16762 L
.72501 .14353 L
.72629 .13428 L
.72748 .12778 L
.72873 .1232 L
.72944 .1217 L
.73008 .12103 L
.73121 .12151 L
.73226 .12391 L
.7334 .12883 L
.73462 .13676 L
.73567 .14602 L
.73666 .15678 L
.73891 .18912 L
.74387 .29988 L
.74929 .46475 L
.75177 .53454 L
.75315 .56493 L
.7544 .58463 L
.75558 .59514 L
.75685 .59727 L
.75805 .59056 L
.75915 .57753 L
Mistroke
.76023 .55949 L
.76138 .53543 L
.76345 .48391 L
.76816 .35869 L
.77278 .25538 L
.77768 .17286 L
.78019 .13972 L
.78296 .10951 L
.78548 .08789 L
.78661 .08014 L
.78785 .07313 L
.7892 .06736 L
.78994 .0651 L
.79063 .06359 L
.79186 .06238 L
.79317 .06335 L
.79392 .06499 L
.79472 .0677 L
.79548 .07119 L
.79618 .07523 L
.79751 .08514 L
.79891 .09902 L
.8013 .13099 L
.80386 .17779 L
.8085 .29459 L
.81114 .37563 L
.81396 .46304 L
.81533 .50139 L
.81663 .53231 L
.81778 .55428 L
.81903 .57052 L
.82026 .57802 L
.82096 .57844 L
.8216 .57637 L
.82291 .56529 L
.82365 .55542 L
.82431 .54442 L
.82681 .4907 L
.82916 .42998 L
.8349 .28859 L
.83742 .23864 L
.84021 .19377 L
.84262 .16337 L
.84488 .14204 L
.84613 .13332 L
.84727 .12731 L
.84852 .12295 L
.84984 .12103 L
.85109 .12186 L
.8518 .12351 L
Mistroke
.85243 .12578 L
.85367 .13236 L
.85484 .14129 L
.85621 .15525 L
.85747 .1716 L
.86031 .2214 L
.86937 .47715 L
.87062 .5132 L
.87199 .54741 L
.87327 .57284 L
.87446 .5889 L
.87553 .59642 L
.87671 .59678 L
.87795 .5885 L
.8791 .57343 L
.88041 .54947 L
.88178 .51824 L
.88424 .45406 L
.88978 .31206 L
.89454 .21708 L
.89976 .14107 L
.90229 .113 L
.90503 .08887 L
.90629 .08016 L
.90762 .07267 L
.90876 .0678 L
.91001 .06416 L
.91123 .0625 L
.91233 .06268 L
.91361 .06504 L
.91483 .06956 L
.91595 .07579 L
.91699 .08344 L
.91934 .10785 L
.92066 .12601 L
.92208 .14944 L
.92466 .20223 L
.92948 .33367 L
.93218 .41822 L
.93507 .50273 L
.93647 .53576 L
.93716 .54908 L
.93779 .55938 L
.93899 .57291 L
.94028 .57857 L
.94127 .57642 L
.9422 .56951 L
.94322 .55696 L
.94432 .53841 L
.94861 .43616 L
Mistroke
.95297 .3249 L
.95545 .27049 L
.95775 .22734 L
.9602 .18931 L
.96244 .16187 L
.96482 .14003 L
.96613 .13141 L
.96737 .12557 L
.96844 .1224 L
.96957 .12101 L
.97054 .1215 L
.9716 .12391 L
.97275 .12878 L
.97397 .13677 L
.97513 .14705 L
.97619 .15888 L
Mfstroke
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  CellLabel->"From In[8]:=",
  ImageSize->{288, 177.938},
  ImageMargins->{{0, 0}, {0, 0}},
  ImageRegion->{{0, 1}, {0, 1}},
  ImageCacheValid->False,
  ImageRangeCache->{{{109, 396}, {285.938, 109}} -> {-50.8007, 0.847879, \
0.389667, 0.008866}}],

Cell[BoxData[
    TagBox[\(\[SkeletonIndicator]  Graphics  \[SkeletonIndicator]\),
      False,
      Editable->False]], "Output",
  CellLabel->"Out[8]="]
}, Open  ]],

Cell["\<\
Or we can do a parametric plot (\"ParametricPlot\") with the same \
solution.  We've added various options here to (try to) make a nicer \
plot.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(ParametricPlot[
      Evaluate[{t, x[t]} /. solution], {t, 0, 
        100}, \[IndentingNewLine]PlotStyle \[Rule] 
        Hue[ .6], \[IndentingNewLine]TextStyle \[Rule] {FontFamily -> \
"\<Times\>", FontSize \[Rule] 14}, ImageSize \[Rule] {350, 200}, 
      PlotLabel \[Rule] StyleForm["\<Time Dependence\>"], 
      AxesLabel \[Rule] {"\<t\>", "\<x\>"}]\)], "Input",
  CellLabel->"In[9]:="],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .61803 
%%ImageSize: 350 200 
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 0.418578 [
[.21429 .00222 -9 -14.5 ]
[.21429 .00222 9 0 ]
[.40476 .00222 -9 -14.5 ]
[.40476 .00222 9 0 ]
[.59524 .00222 -9 -14.5625 ]
[.59524 .00222 9 0 ]
[.78571 .00222 -9 -14.5 ]
[.78571 .00222 9 0 ]
[.97619 .00222 -12.5 -14.5 ]
[.97619 .00222 12.5 0 ]
[1.025 .01472 0 -7.25 ]
[1.025 .01472 7.875 7.25 ]
[.01131 .09843 -21.5 -7.25 ]
[.01131 .09843 0 7.25 ]
[.01131 .18215 -21.5 -7.25 ]
[.01131 .18215 0 7.25 ]
[.01131 .26586 -21.5 -7.28125 ]
[.01131 .26586 0 7.28125 ]
[.01131 .34958 -21.5 -7.25 ]
[.01131 .34958 0 7.25 ]
[.01131 .43329 -11 -7.25 ]
[.01131 .43329 0 7.25 ]
[.01131 .51701 -21.5 -7.25 ]
[.01131 .51701 0 7.25 ]
[.01131 .60072 -21.5 -7.25 ]
[.01131 .60072 0 7.25 ]
[.02381 .64303 -5.5 0 ]
[.02381 .64303 5.5 14.5 ]
[.5 .63053 -52.9688 0 ]
[.5 .63053 52.9688 14.5 ]
[ 0 0 0 0 ]
[ 1 .61803 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.21429 .01472 m
.21429 .02097 L
s
gsave
.21429 .00222 -70 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(20) show
1.000 setlinewidth
grestore
.40476 .01472 m
.40476 .02097 L
s
gsave
.40476 .00222 -70 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(40) show
1.000 setlinewidth
grestore
.59524 .01472 m
.59524 .02097 L
s
gsave
.59524 .00222 -70 -18.5625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.562 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(60) show
1.000 setlinewidth
grestore
.78571 .01472 m
.78571 .02097 L
s
gsave
.78571 .00222 -70 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(80) show
1.000 setlinewidth
grestore
.97619 .01472 m
.97619 .02097 L
s
gsave
.97619 .00222 -73.5 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(100) show
1.000 setlinewidth
grestore
.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
gsave
1.025 .01472 -61 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(t) show
66.875 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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
.02381 .09843 m
.03006 .09843 L
s
gsave
.01131 .09843 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.2) show
1.000 setlinewidth
grestore
.02381 .18215 m
.03006 .18215 L
s
gsave
.01131 .18215 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.4) show
1.000 setlinewidth
grestore
.02381 .26586 m
.03006 .26586 L
s
gsave
.01131 .26586 -82.5 -11.2812 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.562 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.6) show
1.000 setlinewidth
grestore
.02381 .34958 m
.03006 .34958 L
s
gsave
.01131 .34958 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.8) show
1.000 setlinewidth
grestore
.02381 .43329 m
.03006 .43329 L
s
gsave
.01131 .43329 -72 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1) show
1.000 setlinewidth
grestore
.02381 .51701 m
.03006 .51701 L
s
gsave
.01131 .51701 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1.2) show
1.000 setlinewidth
grestore
.02381 .60072 m
.03006 .60072 L
s
gsave
.01131 .60072 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1.4) show
1.000 setlinewidth
grestore
.125 Mabswid
.02381 .03564 m
.02756 .03564 L
s
.02381 .05657 m
.02756 .05657 L
s
.02381 .0775 m
.02756 .0775 L
s
.02381 .11936 m
.02756 .11936 L
s
.02381 .14029 m
.02756 .14029 L
s
.02381 .16122 m
.02756 .16122 L
s
.02381 .20308 m
.02756 .20308 L
s
.02381 .224 m
.02756 .224 L
s
.02381 .24493 m
.02756 .24493 L
s
.02381 .28679 m
.02756 .28679 L
s
.02381 .30772 m
.02756 .30772 L
s
.02381 .32865 m
.02756 .32865 L
s
.02381 .37051 m
.02756 .37051 L
s
.02381 .39144 m
.02756 .39144 L
s
.02381 .41236 m
.02756 .41236 L
s
.02381 .45422 m
.02756 .45422 L
s
.02381 .47515 m
.02756 .47515 L
s
.02381 .49608 m
.02756 .49608 L
s
.02381 .53794 m
.02756 .53794 L
s
.02381 .55887 m
.02756 .55887 L
s
.02381 .5798 m
.02756 .5798 L
s
.25 Mabswid
.02381 0 m
.02381 .61803 L
s
gsave
.02381 .64303 -66.5 -4 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(x) show
70.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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
.5 .63053 -113.969 -4 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(Time) show
95.938 14.500 moveto
(Dependence) show
164.938 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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
0 .4 1 r
.5 Mabswid
.02381 .43329 m
.02499 .43438 L
.02605 .43714 L
.02729 .44217 L
.02846 .44839 L
.03279 .47698 L
.03398 .4842 L
.03524 .49053 L
.03631 .49447 L
.0375 .49693 L
.03877 .49709 L
.03949 .49599 L
.04014 .49421 L
.04141 .48869 L
.04262 .48101 L
.045 .4598 L
.04753 .43058 L
.0521 .37073 L
.05472 .33718 L
.05749 .30538 L
.06005 .28086 L
.06244 .26343 L
.0637 .25675 L
.06441 .25383 L
.06505 .25172 L
.06575 .25004 L
.06652 .249 L
.06724 .24879 L
.06791 .2493 L
.06861 .2506 L
.06927 .25256 L
.07 .25555 L
.07078 .2598 L
.07237 .27188 L
.07382 .28714 L
.07632 .32275 L
.07905 .37453 L
.08193 .43959 L
.08454 .50015 L
.08578 .52617 L
.08712 .55044 L
.08839 .56826 L
.08956 .57935 L
.0908 .58492 L
.09151 .58515 L
.09217 .58347 L
.09286 .57977 L
.09349 .57476 L
.09423 .5672 L
.09492 .55844 L
Mistroke
.09954 .47563 L
.10458 .37862 L
.10991 .29949 L
.11252 .26984 L
.11492 .24694 L
.11707 .2296 L
.11943 .21398 L
.12179 .20217 L
.12309 .19761 L
.12429 .19474 L
.1256 .1933 L
.12634 .19334 L
.12702 .19396 L
.12827 .19669 L
.1289 .1989 L
.1296 .20203 L
.1308 .20922 L
.13209 .2197 L
.13443 .24649 L
.13575 .26634 L
.13719 .29203 L
.14009 .35581 L
.14528 .49282 L
.14782 .55205 L
.14852 .56495 L
.14926 .57651 L
.15058 .59114 L
.15181 .5971 L
.15296 .59576 L
.15422 .58696 L
.15493 .57898 L
.15558 .57001 L
.15788 .52808 L
.16038 .47258 L
.16493 .37301 L
.1702 .28326 L
.17287 .24864 L
.17581 .21692 L
.17831 .19458 L
.18101 .17503 L
.18225 .16776 L
.18355 .1614 L
.18467 .15713 L
.18589 .15382 L
.18721 .15204 L
.18842 .1522 L
.18905 .15305 L
.18975 .15463 L
.19048 .15703 L
.19117 .16002 L
Mistroke
.19242 .16751 L
.19357 .17677 L
.19489 .19053 L
.19615 .20685 L
.19846 .24559 L
.20061 .29182 L
.20548 .42651 L
.20822 .50681 L
.20956 .5415 L
.2108 .56811 L
.21192 .58654 L
.21311 .5989 L
.21431 .60332 L
.21562 .59888 L
.21634 .59247 L
.21703 .58404 L
.21831 .56287 L
.2212 .49795 L
.22642 .36812 L
.2314 .2678 L
.23608 .19806 L
.24096 .14372 L
.24355 .12149 L
.245 .11123 L
.24634 .10322 L
.24752 .09756 L
.24858 .09359 L
.24977 .0906 L
.25103 .08923 L
.25225 .08984 L
.25356 .09283 L
.25481 .09808 L
.25596 .10517 L
.25701 .11369 L
.258 .1235 L
.26024 .15291 L
.26242 .1916 L
.26477 .2445 L
.26968 .38798 L
.27238 .47357 L
.27491 .54279 L
.27636 .57149 L
.27717 .58294 L
.27792 .59011 L
.27855 .59356 L
.27925 .59455 L
.27997 .59251 L
.28064 .58786 L
.28134 .58052 L
.28199 .57136 L
Mistroke
.28321 .54921 L
.28596 .48308 L
.291 .34792 L
.29572 .24236 L
.30064 .16098 L
.30325 .12813 L
.30607 .10028 L
.3073 .09055 L
.30862 .08197 L
.30938 .07791 L
.31007 .0748 L
.31076 .07223 L
.31141 .0704 L
.31266 .06837 L
.31333 .06817 L
.31402 .06863 L
.3152 .07103 L
.31649 .07614 L
.31773 .08367 L
.31887 .09288 L
.32142 .12226 L
.32379 .16084 L
.32603 .20786 L
.33479 .46341 L
.33719 .52762 L
.33785 .5418 L
.33854 .55465 L
.33978 .57162 L
.34094 .5798 L
.34202 .58044 L
.3432 .57358 L
.34447 .55828 L
.34571 .53641 L
.34707 .50694 L
.34952 .44466 L
.35411 .32637 L
.3567 .26891 L
.35945 .2179 L
.36182 .18196 L
.36437 .15153 L
.36558 .14002 L
.36673 .13089 L
.36786 .12375 L
.3689 .11871 L
.36988 .1154 L
.37092 .1135 L
.37208 .11341 L
.37314 .11527 L
.37438 .11998 L
.37552 .12682 L
Mistroke
.37678 .13724 L
.37811 .15172 L
.38034 .18454 L
.38278 .23316 L
.3876 .36421 L
.39013 .44419 L
.39282 .52316 L
.39395 .55042 L
.39517 .57365 L
.39587 .58355 L
.39651 .59023 L
.39776 .59631 L
.39882 .59411 L
.39998 .58433 L
.4012 .56681 L
.40232 .54504 L
.40762 .40865 L
.41327 .27202 L
.4185 .17926 L
.42325 .11904 L
.42556 .09711 L
.42811 .07893 L
.42939 .07234 L
.4301 .06949 L
.43077 .06734 L
.43206 .06474 L
.43325 .0643 L
.43436 .06566 L
.43554 .06911 L
.43655 .07378 L
.43766 .08087 L
.43885 .09081 L
.44014 .1044 L
.44246 .13698 L
.44498 .18439 L
.44774 .25076 L
.45331 .41821 L
.4558 .49229 L
.45717 .52671 L
.45847 .55256 L
.45967 .56933 L
.46098 .57847 L
.46217 .57825 L
.46327 .57104 L
.47306 .35073 L
.47564 .29049 L
.47846 .23473 L
.48115 .19163 L
.48359 .16099 L
.48609 .13792 L
Mistroke
.48746 .12891 L
.48875 .1229 L
.48995 .11956 L
.49105 .11848 L
.49226 .11962 L
.49353 .12358 L
.49462 .12929 L
.49578 .13791 L
.49687 .14852 L
.49787 .16038 L
.50031 .19855 L
.50263 .24696 L
.50716 .37265 L
.51142 .50384 L
.51356 .55688 L
.51476 .57829 L
.51586 .59117 L
.517 .59704 L
.51824 .59457 L
.51955 .5826 L
.52076 .56395 L
.52209 .53673 L
.52335 .50647 L
.52571 .44391 L
.531 .30895 L
.53554 .21813 L
.53792 .17998 L
.54047 .14511 L
.54303 .11597 L
.54536 .09439 L
.54649 .0858 L
.54771 .07785 L
.54886 .07181 L
.54994 .06746 L
.5506 .06547 L
.55131 .06391 L
.55256 .06276 L
.55326 .06303 L
.55401 .06408 L
.55465 .06562 L
.55534 .06801 L
.5566 .07422 L
.5573 .07882 L
.55794 .08374 L
.56035 .10893 L
.56166 .12713 L
.56305 .15008 L
.56554 .20092 L
.57117 .357 L
.57391 .44274 L
Mistroke
.57525 .48247 L
.57651 .5155 L
.57773 .54244 L
.57885 .56108 L
.58008 .57421 L
.5814 .57871 L
.58261 .57415 L
.58372 .56308 L
.58494 .54432 L
.58624 .51848 L
.5908 .40327 L
.59603 .27787 L
.59858 .22909 L
.60091 .19244 L
.60293 .16672 L
.60512 .14496 L
.60632 .13583 L
.60744 .12921 L
.6085 .12459 L
.60963 .12157 L
.61076 .12059 L
.61198 .12193 L
.61313 .12558 L
.61418 .13107 L
.61535 .13966 L
.61663 .15223 L
.61921 .18817 L
.62174 .23781 L
.62449 .30725 L
.62947 .45974 L
.63183 .52741 L
.63312 .55745 L
.63432 .57886 L
.63535 .59099 L
.63645 .59716 L
.63768 .59548 L
.6388 .58642 L
.64009 .56807 L
.64147 .54099 L
.64394 .47993 L
.64954 .3331 L
.65489 .22236 L
.65974 .14937 L
.66227 .11987 L
.66463 .09733 L
.66709 .07925 L
.66839 .07212 L
.66911 .06895 L
.66978 .06654 L
.67097 .0636 L
Mistroke
.67226 .06242 L
.6734 .06325 L
.67461 .06617 L
.67569 .07067 L
.6767 .07658 L
.67781 .08506 L
.67901 .09661 L
.68154 .1298 L
.68431 .18042 L
.6872 .2494 L
.68988 .32644 L
.6924 .40518 L
.69506 .48545 L
.69616 .51425 L
.69734 .54048 L
.69863 .56216 L
.69984 .57452 L
.70049 .57777 L
.7012 .57854 L
.70248 .57272 L
.70374 .55876 L
.7049 .53959 L
.70755 .4801 L
.71038 .40638 L
.7155 .28264 L
.71801 .23386 L
.72032 .19674 L
.72256 .16762 L
.72501 .14353 L
.72629 .13428 L
.72748 .12778 L
.72873 .1232 L
.72944 .1217 L
.73008 .12103 L
.73121 .12151 L
.73226 .12391 L
.7334 .12883 L
.73462 .13676 L
.73567 .14602 L
.73666 .15678 L
.73891 .18912 L
.74387 .29988 L
.74929 .46475 L
.75177 .53454 L
.75315 .56493 L
.7544 .58463 L
.75558 .59514 L
.75685 .59727 L
.75805 .59056 L
.75915 .57753 L
Mistroke
.76023 .55949 L
.76138 .53543 L
.76345 .48391 L
.76816 .35869 L
.77278 .25538 L
.77768 .17286 L
.78019 .13972 L
.78296 .10951 L
.78548 .08789 L
.78661 .08014 L
.78785 .07313 L
.7892 .06736 L
.78994 .0651 L
.79063 .06359 L
.79186 .06238 L
.79317 .06335 L
.79392 .06499 L
.79472 .0677 L
.79548 .07119 L
.79618 .07523 L
.79751 .08514 L
.79891 .09902 L
.8013 .13099 L
.80386 .17779 L
.8085 .29459 L
.81114 .37563 L
.81396 .46304 L
.81533 .50139 L
.81663 .53231 L
.81778 .55428 L
.81903 .57052 L
.82026 .57802 L
.82096 .57844 L
.8216 .57637 L
.82291 .56529 L
.82365 .55542 L
.82431 .54442 L
.82681 .4907 L
.82916 .42998 L
.8349 .28859 L
.83742 .23864 L
.84021 .19377 L
.84262 .16337 L
.84488 .14204 L
.84613 .13332 L
.84727 .12731 L
.84852 .12295 L
.84984 .12103 L
.85109 .12186 L
.8518 .12351 L
Mistroke
.85243 .12578 L
.85367 .13236 L
.85484 .14129 L
.85621 .15525 L
.85747 .1716 L
.86031 .2214 L
.86937 .47715 L
.87062 .5132 L
.87199 .54741 L
.87327 .57284 L
.87446 .5889 L
.87553 .59642 L
.87671 .59678 L
.87795 .5885 L
.8791 .57343 L
.88041 .54947 L
.88178 .51824 L
.88424 .45406 L
.88978 .31206 L
.89454 .21708 L
.89976 .14107 L
.90229 .113 L
.90503 .08887 L
.90629 .08016 L
.90762 .07267 L
.90876 .0678 L
.91001 .06416 L
.91123 .0625 L
.91233 .06268 L
.91361 .06504 L
.91483 .06956 L
.91595 .07579 L
.91699 .08344 L
.91934 .10785 L
.92066 .12601 L
.92208 .14944 L
.92466 .20223 L
.92948 .33367 L
.93218 .41822 L
.93507 .50273 L
.93647 .53576 L
.93716 .54908 L
.93779 .55938 L
.93899 .57291 L
.94028 .57857 L
.94127 .57642 L
.9422 .56951 L
.94322 .55696 L
.94432 .53841 L
.94861 .43616 L
Mistroke
.95297 .3249 L
.95545 .27049 L
.95775 .22734 L
.9602 .18931 L
.96244 .16187 L
.96482 .14003 L
.96613 .13141 L
.96737 .12557 L
.96844 .1224 L
.96957 .12101 L
.97054 .1215 L
.9716 .12391 L
.97275 .12878 L
.97397 .13677 L
.97513 .14705 L
.97619 .15888 L
Mfstroke
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  CellLabel->"From In[9]:=",
  ImageSize->{350, 200},
  ImageCacheValid->False,
  ImageRangeCache->{{{144, 493}, {624.375, 425.375}} -> {-76.8992, 3.67108, \
0.395944, 0.00900882}}],

Cell[BoxData[
    TagBox[\(\[SkeletonIndicator]  Graphics  \[SkeletonIndicator]\),
      False,
      Editable->False]], "Output",
  CellLabel->"Out[9]="]
}, Open  ]],

Cell["\<\
Now do the phase space plot.  You may need to change AxesOrigin to \
get the axes in a reasonable place.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(ParametricPlot[Evaluate[{x[t], \(x'\)[t]} /. solution], {t, tmin, 100}, 
      PlotStyle \[Rule] Hue[ .6], AspectRatio \[Rule] 1, 
      TextStyle \[Rule] {FontFamily \[Rule] "\<Times\>", 
          FontSize \[Rule] 14}, ImageSize \[Rule] {250, 200}, 
      PlotLabel \[Rule] StyleForm["\<Phase Space\>"], 
      AxesOrigin \[Rule] {Automatic, Automatic}, 
      AxesLabel \[Rule] {"\<x\>", "\<v\>"}]\)], "Input",
  CellLabel->"In[10]:="],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: 1 
%%ImageSize: 250 200 
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 0.677366 0.462487 0.703299 [
[.15928 .44999 -10.75 -14.5 ]
[.15928 .44999 10.75 0 ]
[.29476 .44999 -10.75 -14.5 ]
[.29476 .44999 10.75 0 ]
[.43023 .44999 -10.75 -14.5625 ]
[.43023 .44999 10.75 0 ]
[.5657 .44999 -10.75 -14.5 ]
[.5657 .44999 10.75 0 ]
[.70118 .44999 -5.5 -14.5 ]
[.70118 .44999 5.5 0 ]
[.83665 .44999 -10.75 -14.5 ]
[.83665 .44999 10.75 0 ]
[.97212 .44999 -10.75 -14.5 ]
[.97212 .44999 10.75 0 ]
[1.025 .46249 0 -7.25 ]
[1.025 .46249 11 7.25 ]
[.01131 .04051 -31.1875 -7.28125 ]
[.01131 .04051 0 7.28125 ]
[.01131 .18117 -31.1875 -7.25 ]
[.01131 .18117 0 7.25 ]
[.01131 .32183 -31.1875 -7.25 ]
[.01131 .32183 0 7.25 ]
[.01131 .60315 -21.5 -7.25 ]
[.01131 .60315 0 7.25 ]
[.01131 .74381 -21.5 -7.25 ]
[.01131 .74381 0 7.25 ]
[.01131 .88447 -21.5 -7.28125 ]
[.01131 .88447 0 7.28125 ]
[.02381 1.025 -5.5 0 ]
[.02381 1.025 5.5 14.5 ]
[.5 1.0125 -36.6875 0 ]
[.5 1.0125 36.6875 14.5 ]
[ 0 0 0 0 ]
[ 1 1 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.15928 .46249 m
.15928 .46874 L
s
gsave
.15928 .44999 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.2) show
1.000 setlinewidth
grestore
.29476 .46249 m
.29476 .46874 L
s
gsave
.29476 .44999 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.4) show
1.000 setlinewidth
grestore
.43023 .46249 m
.43023 .46874 L
s
gsave
.43023 .44999 -71.75 -18.5625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.562 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.6) show
1.000 setlinewidth
grestore
.5657 .46249 m
.5657 .46874 L
s
gsave
.5657 .44999 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.8) show
1.000 setlinewidth
grestore
.70118 .46249 m
.70118 .46874 L
s
gsave
.70118 .44999 -66.5 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1) show
1.000 setlinewidth
grestore
.83665 .46249 m
.83665 .46874 L
s
gsave
.83665 .44999 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1.2) show
1.000 setlinewidth
grestore
.97212 .46249 m
.97212 .46874 L
s
gsave
.97212 .44999 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1.4) show
1.000 setlinewidth
grestore
.125 Mabswid
.05768 .46249 m
.05768 .46624 L
s
.09155 .46249 m
.09155 .46624 L
s
.12541 .46249 m
.12541 .46624 L
s
.19315 .46249 m
.19315 .46624 L
s
.22702 .46249 m
.22702 .46624 L
s
.26089 .46249 m
.26089 .46624 L
s
.32862 .46249 m
.32862 .46624 L
s
.36249 .46249 m
.36249 .46624 L
s
.39636 .46249 m
.39636 .46624 L
s
.4641 .46249 m
.4641 .46624 L
s
.49797 .46249 m
.49797 .46624 L
s
.53183 .46249 m
.53183 .46624 L
s
.59957 .46249 m
.59957 .46624 L
s
.63344 .46249 m
.63344 .46624 L
s
.66731 .46249 m
.66731 .46624 L
s
.73504 .46249 m
.73504 .46624 L
s
.76891 .46249 m
.76891 .46624 L
s
.80278 .46249 m
.80278 .46624 L
s
.87052 .46249 m
.87052 .46624 L
s
.90439 .46249 m
.90439 .46624 L
s
.93825 .46249 m
.93825 .46624 L
s
.25 Mabswid
0 .46249 m
1 .46249 L
s
gsave
1.025 .46249 -61 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(x) show
70.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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
.02381 .04051 m
.03006 .04051 L
s
gsave
.01131 .04051 -92.1875 -11.2812 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.562 moveto
%%IncludeResource: font Mathematica1
%%IncludeFont: Mathematica1
/Mathematica1 findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(-) show
72.688 14.562 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.6) show
1.000 setlinewidth
grestore
.02381 .18117 m
.03006 .18117 L
s
gsave
.01131 .18117 -92.1875 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Mathematica1
%%IncludeFont: Mathematica1
/Mathematica1 findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(-) show
72.688 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.4) show
1.000 setlinewidth
grestore
.02381 .32183 m
.03006 .32183 L
s
gsave
.01131 .32183 -92.1875 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Mathematica1
%%IncludeFont: Mathematica1
/Mathematica1 findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(-) show
72.688 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.2) show
1.000 setlinewidth
grestore
.02381 .60315 m
.03006 .60315 L
s
gsave
.01131 .60315 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.2) show
1.000 setlinewidth
grestore
.02381 .74381 m
.03006 .74381 L
s
gsave
.01131 .74381 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.4) show
1.000 setlinewidth
grestore
.02381 .88447 m
.03006 .88447 L
s
gsave
.01131 .88447 -82.5 -11.2812 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.562 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.6) show
1.000 setlinewidth
grestore
.125 Mabswid
.02381 .07567 m
.02756 .07567 L
s
.02381 .11084 m
.02756 .11084 L
s
.02381 .146 m
.02756 .146 L
s
.02381 .21633 m
.02756 .21633 L
s
.02381 .2515 m
.02756 .2515 L
s
.02381 .28666 m
.02756 .28666 L
s
.02381 .35699 m
.02756 .35699 L
s
.02381 .39216 m
.02756 .39216 L
s
.02381 .42732 m
.02756 .42732 L
s
.02381 .49765 m
.02756 .49765 L
s
.02381 .53282 m
.02756 .53282 L
s
.02381 .56798 m
.02756 .56798 L
s
.02381 .63831 m
.02756 .63831 L
s
.02381 .67348 m
.02756 .67348 L
s
.02381 .70864 m
.02756 .70864 L
s
.02381 .77897 m
.02756 .77897 L
s
.02381 .81414 m
.02756 .81414 L
s
.02381 .8493 m
.02756 .8493 L
s
.02381 .00534 m
.02756 .00534 L
s
.02381 .91963 m
.02756 .91963 L
s
.02381 .9548 m
.02756 .9548 L
s
.02381 .98996 m
.02756 .98996 L
s
.25 Mabswid
.02381 0 m
.02381 1 L
s
gsave
.02381 1.025 -66.5 -4 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(v) show
70.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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
.5 1.0125 -97.6875 -4 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(Phase) show
99.062 14.500 moveto
(Space) show
132.375 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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 1 L
0 1 L
closepath
clip
newpath
0 .4 1 r
.5 Mabswid
.70118 .46249 m
.70293 .49162 L
.7074 .5155 L
.71553 .53886 L
.7256 .55588 L
.73643 .56655 L
.74721 .57168 L
.75935 .57182 L
.77187 .56558 L
.78331 .55288 L
.79354 .5326 L
.8005 .50807 L
.80409 .48204 L
.80449 .44877 L
.80279 .42924 L
.79995 .41102 L
.79159 .37831 L
.7784 .34576 L
.77021 .33074 L
.76052 .31608 L
.7408 .29327 L
.72868 .28263 L
.71675 .27407 L
.70307 .2662 L
.68785 .2595 L
.67438 .25514 L
.65945 .2518 L
.63189 .24925 L
.605 .2507 L
.58046 .25506 L
.55731 .2617 L
.53636 .26984 L
.51448 .28066 L
.49244 .29435 L
.4724 .30984 L
.45353 .32816 L
.43941 .34541 L
.42629 .36603 L
.42022 .37808 L
.4147 .39145 L
.40977 .40688 L
.40631 .42182 L
.40288 .4505 L
.40263 .46781 L
.40357 .48468 L
.40851 .51778 L
.41683 .54984 L
.42306 .56823 L
.43123 .58875 L
.44986 .62713 L
Mistroke
.50955 .71425 L
.55357 .7599 L
.57679 .77948 L
.59938 .79583 L
.62143 .80934 L
.64653 .82177 L
.67255 .83131 L
.7006 .83761 L
.72561 .83952 L
.75239 .83731 L
.79961 .821 L
.82306 .80577 L
.84665 .78438 L
.88447 .73274 L
.90233 .69722 L
.91665 .66005 L
.92941 .61571 L
.93942 .56488 L
.94707 .47493 L
.9464 .42997 L
.94228 .38244 L
.9268 .30536 L
.90416 .24537 L
.87312 .1964 L
.83902 .16472 L
.80579 .14761 L
.76835 .13972 L
.72709 .1414 L
.70653 .14547 L
.68431 .15188 L
.64632 .16691 L
.61271 .18368 L
.49142 .25973 L
.39834 .3234 L
.36648 .34851 L
.35173 .36275 L
.33971 .37703 L
.33102 .39013 L
.32334 .40558 L
.31708 .42464 L
.31367 .44415 L
.31271 .46363 L
.31416 .48655 L
.3181 .51025 L
.32403 .53359 L
.33412 .56319 L
.34917 .59787 L
.38842 .66673 L
.44738 .74372 L
.48757 .78543 L
Mistroke
.5301 .82209 L
.57316 .85201 L
.61529 .87435 L
.6644 .8913 L
.71871 .89736 L
.77492 .88692 L
.82549 .85882 L
.86703 .81732 L
.90579 .7554 L
.93857 .66999 L
.9506 .62157 L
.96006 .56569 L
.96673 .46386 L
.96134 .37154 L
.94526 .28724 L
.92139 .21989 L
.8941 .1718 L
.85961 .13348 L
.81824 .1077 L
.77194 .09625 L
.73188 .09707 L
.68832 .10649 L
.64229 .12393 L
.5967 .14693 L
.5237 .19158 L
.39699 .2762 L
.35033 .30694 L
.31359 .3333 L
.28644 .35781 L
.27374 .37297 L
.26386 .38825 L
.2562 .40437 L
.2508 .42093 L
.24704 .44098 L
.2458 .46487 L
.24793 .49271 L
.25357 .52192 L
.26192 .55052 L
.27486 .58422 L
.31643 .66294 L
.3844 .75544 L
.42681 .80126 L
.47223 .84285 L
.51697 .87699 L
.5701 .90893 L
.62389 .93136 L
.67586 .94261 L
.73137 .94147 L
.78958 .9223 L
.84055 .88544 L
Mistroke
.88387 .83289 L
.91717 .77159 L
.94584 .69191 L
.96679 .59345 L
.97619 .47845 L
.9704 .36096 L
.9514 .26206 L
.92342 .18519 L
.8908 .13038 L
.84702 .08626 L
.80143 .06215 L
.75039 .05281 L
.7214 .05373 L
.69488 .05774 L
.64712 .07125 L
.5988 .09142 L
.44783 .17822 L
.31857 .25759 L
.26904 .28713 L
.23032 .31243 L
.20001 .33681 L
.17649 .36258 L
.16598 .37832 L
.15792 .39412 L
.15107 .41297 L
.14631 .43489 L
.1444 .45718 L
.14534 .48333 L
.14932 .51008 L
.15581 .53639 L
.16642 .56755 L
.18241 .604 L
.2298 .68432 L
.29748 .76965 L
.34202 .81557 L
.3959 .86306 L
.44839 .90175 L
.47812 .92042 L
.51139 .93848 L
.57254 .9634 L
.63201 .97619 L
.69427 .97522 L
.76075 .95368 L
.81952 .9106 L
.86798 .8497 L
.90795 .77034 L
.93554 .68466 L
.95564 .57454 L
.96219 .46642 L
.95553 .3516 L
Mistroke
.94564 .29109 L
.93276 .2391 L
.89728 .15028 L
.87277 .11099 L
.84815 .08198 L
.80009 .04561 L
.74424 .02631 L
.69021 .02381 L
.64062 .03173 L
.58527 .04925 L
.53579 .07076 L
.43388 .12667 L
.27423 .23074 L
.2251 .26726 L
.18179 .30529 L
.16115 .32769 L
.1452 .34885 L
.13197 .3712 L
.12221 .3935 L
.11499 .41828 L
.11258 .43138 L
.11091 .44627 L
.11059 .47394 L
.11351 .50137 L
.11686 .51871 L
.12118 .53568 L
.13242 .56886 L
.1493 .60652 L
.17362 .64966 L
.22319 .71895 L
.2964 .79839 L
.34058 .83788 L
.39366 .87854 L
.44375 .91049 L
.50253 .93991 L
.56027 .9596 L
.61566 .96871 L
.67455 .96591 L
.73616 .9457 L
.79024 .90846 L
.83641 .85592 L
.87222 .79467 L
.90356 .71484 L
.92841 .60891 L
.93919 .50541 L
.93697 .38667 L
.92094 .28284 L
.89552 .20086 L
.86431 .13932 L
.8235 .08916 L
Mistroke
.77476 .05514 L
.74537 .04388 L
.71779 .03818 L
.68725 .03643 L
.65502 .03898 L
.60168 .0513 L
.57228 .0617 L
.54556 .07302 L
.45718 .12095 L
.37601 .17662 L
.30572 .23442 L
.27495 .26421 L
.24697 .29575 L
.22654 .32355 L
.20835 .35503 L
.20187 .3692 L
.19592 .38479 L
.18796 .41401 L
.18382 .44401 L
.18315 .46171 L
.18364 .47865 L
.18809 .51442 L
.19267 .53533 L
.19818 .55491 L
.21141 .5914 L
.23082 .63287 L
.28023 .71248 L
.34983 .79623 L
.3967 .8416 L
.44657 .88224 L
.49714 .91599 L
.55631 .94586 L
.61287 .96398 L
.66661 .97049 L
.70026 .96843 L
.73625 .96014 L
.79895 .92716 L
.85436 .87103 L
.89775 .79859 L
.9341 .7 L
.94886 .637 L
.95845 .57524 L
.96404 .50831 L
.96502 .44731 L
.96133 .37853 L
.95326 .31664 L
.92932 .21988 L
.91075 .17294 L
.89058 .13497 L
.84343 .0768 L
Mistroke
.81407 .05459 L
.78598 .04038 L
.73442 .02788 L
.6774 .02935 L
.62443 .04129 L
.57694 .05847 L
.47066 .1118 L
.38763 .16156 L
.2435 .25526 L
.19541 .29167 L
.15888 .32624 L
.14367 .34456 L
.12986 .36527 L
.1232 .37765 L
.11774 .38982 L
.10984 .41387 L
.10561 .43606 L
.10394 .46116 L
.10495 .48386 L
.10883 .51031 L
.11638 .54023 L
.12868 .57435 L
.1627 .64073 L
.21801 .71848 L
.30189 .80722 L
.3536 .85115 L
.41552 .89492 L
.44785 .91406 L
.47962 .93032 L
.54177 .95438 L
.60266 .9668 L
.66794 .96541 L
.7227 .94955 L
.7799 .91397 L
.83507 .85301 L
.86209 .80857 L
.88374 .762 L
.91607 .65812 L
.93353 .54848 L
.93711 .43364 L
.93282 .37096 L
.92504 .31619 L
.90188 .22574 L
.86675 .14868 L
.82795 .09752 L
.78733 .06505 L
.73969 .0449 L
.687 .03853 L
.63085 .04524 L
.59976 .05365 L
Mistroke
.57166 .06365 L
.47294 .11337 L
.39559 .16507 L
.32708 .22005 L
.27895 .26665 L
.25776 .29101 L
.23852 .31686 L
.22421 .34 L
.21142 .36595 L
.20247 .39032 L
.1965 .41379 L
.1923 .44542 L
.19212 .47681 L
.19524 .50639 L
.20232 .54 L
.21463 .57856 L
.23314 .62146 L
.2813 .70312 L
.35455 .79356 L
.39913 .83742 L
.44526 .87597 L
.49465 .91012 L
.54247 .93623 L
.59838 .95761 L
.65988 .9684 L
.72675 .96202 L
.78619 .93603 L
.84618 .88246 L
.87321 .84531 L
.89968 .79712 L
.93544 .70008 L
.95922 .58044 L
.96656 .46135 L
.96035 .35588 L
.94237 .25919 L
.91207 .17305 L
.87875 .11548 L
.83608 .06986 L
.78567 .04048 L
.72868 .02829 L
.67438 .03122 L
.62556 .04277 L
.57848 .05996 L
.53671 .07901 L
.44999 .12631 L
.32055 .20602 L
.20876 .28116 L
.18463 .30057 L
.16213 .32156 L
.14524 .3405 L
Mistroke
.12991 .36197 L
.11825 .38361 L
.11015 .40469 L
.1046 .42731 L
.10191 .45015 L
.10213 .4785 L
.10576 .50649 L
.11376 .53915 L
.11949 .55642 L
.12719 .57606 L
.16309 .64467 L
.21127 .71238 L
.28202 .78985 L
.37698 .86957 L
.42304 .90013 L
.4757 .92871 L
.52816 .95004 L
.57755 .9629 L
.63674 .96766 L
.7006 .95695 L
.75856 .9287 L
.80802 .88532 L
.85734 .815 L
.89475 .72943 L
.91884 .64031 L
.93363 .53517 L
.93549 .41951 L
.9302 .35737 L
.92168 .30416 L
.89578 .21214 L
.86186 .14291 L
.82328 .09451 L
.77773 .06091 L
.73641 .04512 L
.68992 .03942 L
.63975 .04419 L
.58728 .05857 L
.53983 .07816 L
.49886 .0992 L
.34042 .21023 L
.27626 .27244 L
.252 .30204 L
.233 .3302 L
.21949 .35523 L
.20815 .38304 L
.20344 .39854 L
.19959 .41524 L
.19566 .44619 L
.19574 .48036 L
.19988 .51382 L
Mistroke
.20919 .55254 L
.21666 .57512 L
.22491 .59618 L
.26522 .67377 L
.33117 .76411 L
.37327 .80994 L
.42495 .85744 L
.47477 .89527 L
.53383 .93046 L
.59636 .95582 L
.6565 .96732 L
.71448 .96425 L
.77468 .94262 L
.8251 .90528 L
.86792 .85387 L
.90787 .77994 L
.94058 .68255 L
.96181 .56226 L
.96691 .44563 L
.96339 .38016 L
.95625 .32329 L
.94363 .26225 L
.92773 .21022 L
.90897 .16566 L
.88603 .12545 L
.83862 .07183 L
.80973 .05193 L
.78158 .03918 L
.74992 .03109 L
.71545 .02839 L
.65974 .03462 L
.62878 .0426 L
.60065 .05211 L
.50117 .09845 L
.34849 .18943 L
.22884 .26695 L
.18099 .30386 L
.15909 .3246 L
.14148 .34491 L
.12841 .36377 L
.11701 .3853 L
.1118 .39827 L
.10775 .41105 L
.10266 .43637 L
.101 .46127 L
.10221 .48576 L
.10677 .51428 L
.11554 .54645 L
.12702 .57686 L
.14071 .60602 L
Mistroke
.18333 .67588 L
.23522 .74125 L
.30495 .81159 L
.34838 .84822 L
.39943 .88526 L
.44715 .91418 L
.50215 .94045 L
.5372 .95296 L
.5702 .96146 L
.63624 .96761 L
.69608 .95821 L
.75704 .92952 L
.81153 .88109 L
.8626 .80477 L
.90014 .7124 L
.92367 .6136 L
.93516 .50897 L
.93504 .41414 L
.92284 .31113 L
.90062 .22604 L
.86609 .15019 L
.82083 .0924 L
.77721 .06084 L
.72637 .04309 L
.67018 .04024 L
.63882 .04449 L
.61066 .05124 L
.55755 .07032 L
.50998 .09328 L
.43245 .14035 L
.3621 .19244 L
.31122 .23691 L
.26659 .28418 L
.24618 .31077 L
.2304 .33549 L
.21726 .36124 L
.20775 .3859 L
.20009 .41561 L
.19756 .43187 L
.19604 .44968 L
.19658 .48403 L
.20101 .51685 L
.20976 .55256 L
.22194 .58753 L
.23996 .62764 L
.26496 .67249 L
.33504 .76805 L
.37738 .81356 L
.42173 .85432 L
.46633 .88904 L
Mistroke
.51972 .92273 L
.57706 .94914 L
.6408 .96548 L
.69761 .96663 L
.75803 .95073 L
.81222 .91684 L
.85758 .86843 L
.90283 .79137 L
.93932 .68771 L
.96035 .57586 L
.96711 .46933 L
.95988 .34759 L
.94892 .28427 L
.9348 .23095 L
.90011 .14852 L
.87902 .11533 L
.85359 .08546 L
.82554 .06186 L
.79754 .04573 L
.74284 .03013 L
.71176 .02852 L
.68295 .03074 L
.65164 .03656 L
.61887 .04587 L
.5616 .06843 L
.5109 .09343 L
.4254 .14226 L
.2849 .22976 L
.18994 .29634 L
.154 .33004 L
.1375 .35017 L
.12489 .36965 L
.11393 .39247 L
.10912 .40612 L
.10563 .41926 L
.10168 .44477 L
.10097 .45834 L
.10123 .47387 L
.10414 .50074 L
.11074 .53074 L
.1194 .55776 L
.13222 .58872 L
.17442 .66301 L
.23158 .73716 L
.3029 .80977 L
.38191 .87328 L
.43118 .90513 L
.4884 .93463 L
.54541 .95539 L
.59966 .9661 L
Mistroke
.66377 .96527 L
.72351 .94804 L
.7745 .91676 L
.82514 .86436 L
.87176 .78614 L
.89118 .73897 L
.90891 .68187 L
.92973 .572 L
.93633 .46429 L
.93092 .36508 L
.91366 .26969 L
.89058 .19955 L
.85795 .13723 L
.81606 .08804 L
.76603 .05544 L
.71605 .04142 L
.66981 .04028 L
.61546 .04992 L
.58868 .05821 L
.55989 .06933 L
.46842 .11716 L
.37781 .18001 L
.30943 .23865 L
.25925 .29327 L
.24034 .31944 L
.22564 .34419 L
.21226 .37339 L
.20673 .38927 L
.20204 .40661 L
.19876 .42357 L
.19676 .43997 L
.19594 .47182 L
.19891 .5041 L
.20643 .54053 L
.21784 .57668 L
.23207 .61111 L
.28324 .70065 L
.35426 .78954 L
.3982 .83347 L
.45079 .8776 L
.50078 .91173 L
.5587 .9418 L
.62411 .96261 L
.68715 .96747 L
.72359 .9622 L
.76127 .94928 L
.79244 .93176 L
.82498 .9054 L
.87697 .83992 L
.91717 .75724 L
Mistroke
.94405 .6687 L
.96186 .56258 L
.96694 .44282 L
.95609 .32179 L
.93468 .23056 L
.90019 .14865 L
.8599 .09202 L
.81822 .05701 L
.76654 .03466 L
.71586 .02849 L
.66913 .03291 L
.62658 .04342 L
.58138 .05987 L
.53546 .08085 L
.36683 .1782 L
.23769 .26092 L
.18659 .29913 L
.16388 .31974 L
.14304 .3429 L
.12721 .36567 L
.11579 .38795 L
.10741 .41204 L
.10256 .43656 L
.10093 .46087 L
.10255 .48949 L
.1048 .50462 L
.10833 .52145 L
.1178 .55332 L
.13054 .58505 L
.14813 .62008 L
.19089 .68646 L
.26063 .7688 L
.34501 .84558 L
.40079 .88618 L
.45825 .92012 L
.49184 .93613 L
.52939 .95048 L
.56437 .9602 L
.59707 .96581 L
.66131 .96561 L
.7212 .94906 L
.7724 .91842 L
.82332 .86673 L
.87034 .78915 L
.88998 .74225 L
.90797 .6854 L
.92927 .57575 L
.93631 .46803 L
.9313 .3685 L
.9144 .27263 L
Mistroke
.89158 .20199 L
.85918 .1391 L
.81744 .08928 L
.76752 .05611 L
.71758 .04164 L
.67135 .04017 L
.61691 .04954 L
.59007 .05773 L
.56122 .06877 L
.46954 .11646 L
.37869 .17933 L
.31012 .23799 L
.25976 .29264 L
.24076 .3188 L
.22599 .34353 L
.21253 .37271 L
.20695 .38858 L
.20221 .40589 L
.19888 .42283 L
.19683 .43921 L
.19591 .47099 L
.1973 .49133 L
.20061 .51439 L
.20612 .53933 L
.21322 .5634 L
.23086 .60843 L
.2571 .65924 L
Mfstroke
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  CellLabel->"From In[10]:=",
  ImageSize->{250, 200},
  ImageCacheValid->False,
  ImageRangeCache->{{{144, 393}, {346, 147}} -> {-1.55516, 0.503602, \
0.00820179, 0.00789936}}],

Cell[BoxData[
    TagBox[\(\[SkeletonIndicator]  Graphics  \[SkeletonIndicator]\),
      False,
      Editable->False]], "Output",
  CellLabel->"Out[10]="]
}, Open  ]],

Cell["\<\
Here is the same plot, with the starting time t set to skip the \
transient region.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(ParametricPlot[Evaluate[{x[t], \(x'\)[t]} /. solution], {t, 100, 300}, 
      PlotStyle \[Rule] Hue[ .6], AspectRatio \[Rule] 1, 
      TextStyle \[Rule] {FontFamily -> "\<Times\>", FontSize \[Rule] 14}, 
      ImageSize \[Rule] {250, 200}, 
      PlotLabel \[Rule] StyleForm["\<Phase Space\>"], 
      AxesOrigin \[Rule] {Automatic, Automatic}, 
      AxesLabel \[Rule] {"\<x\>", "\<v\>"}]\)], "Input",
  CellLabel->"In[11]:="],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: 1 
%%ImageSize: 250 200 
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 0.68393 0.463778 0.713134 [
[.1606 .45128 -10.75 -14.5 ]
[.1606 .45128 10.75 0 ]
[.29738 .45128 -10.75 -14.5 ]
[.29738 .45128 10.75 0 ]
[.43417 .45128 -10.75 -14.5625 ]
[.43417 .45128 10.75 0 ]
[.57095 .45128 -10.75 -14.5 ]
[.57095 .45128 10.75 0 ]
[.70774 .45128 -5.5 -14.5 ]
[.70774 .45128 5.5 0 ]
[.84453 .45128 -10.75 -14.5 ]
[.84453 .45128 10.75 0 ]
[.98131 .45128 -10.75 -14.5 ]
[.98131 .45128 10.75 0 ]
[1.025 .46378 0 -7.25 ]
[1.025 .46378 11 7.25 ]
[.01131 .0359 -31.1875 -7.28125 ]
[.01131 .0359 0 7.28125 ]
[.01131 .17852 -31.1875 -7.25 ]
[.01131 .17852 0 7.25 ]
[.01131 .32115 -31.1875 -7.25 ]
[.01131 .32115 0 7.25 ]
[.01131 .60641 -21.5 -7.25 ]
[.01131 .60641 0 7.25 ]
[.01131 .74903 -21.5 -7.25 ]
[.01131 .74903 0 7.25 ]
[.01131 .89166 -21.5 -7.28125 ]
[.01131 .89166 0 7.28125 ]
[.02381 1.025 -5.5 0 ]
[.02381 1.025 5.5 14.5 ]
[.5 1.0125 -36.6875 0 ]
[.5 1.0125 36.6875 14.5 ]
[ 0 0 0 0 ]
[ 1 1 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.1606 .46378 m
.1606 .47003 L
s
gsave
.1606 .45128 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.2) show
1.000 setlinewidth
grestore
.29738 .46378 m
.29738 .47003 L
s
gsave
.29738 .45128 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.4) show
1.000 setlinewidth
grestore
.43417 .46378 m
.43417 .47003 L
s
gsave
.43417 .45128 -71.75 -18.5625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.562 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.6) show
1.000 setlinewidth
grestore
.57095 .46378 m
.57095 .47003 L
s
gsave
.57095 .45128 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.8) show
1.000 setlinewidth
grestore
.70774 .46378 m
.70774 .47003 L
s
gsave
.70774 .45128 -66.5 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1) show
1.000 setlinewidth
grestore
.84453 .46378 m
.84453 .47003 L
s
gsave
.84453 .45128 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1.2) show
1.000 setlinewidth
grestore
.98131 .46378 m
.98131 .47003 L
s
gsave
.98131 .45128 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1.4) show
1.000 setlinewidth
grestore
.125 Mabswid
.05801 .46378 m
.05801 .46753 L
s
.0922 .46378 m
.0922 .46753 L
s
.1264 .46378 m
.1264 .46753 L
s
.19479 .46378 m
.19479 .46753 L
s
.22899 .46378 m
.22899 .46753 L
s
.26319 .46378 m
.26319 .46753 L
s
.33158 .46378 m
.33158 .46753 L
s
.36577 .46378 m
.36577 .46753 L
s
.39997 .46378 m
.39997 .46753 L
s
.46836 .46378 m
.46836 .46753 L
s
.50256 .46378 m
.50256 .46753 L
s
.53676 .46378 m
.53676 .46753 L
s
.60515 .46378 m
.60515 .46753 L
s
.63935 .46378 m
.63935 .46753 L
s
.67354 .46378 m
.67354 .46753 L
s
.74194 .46378 m
.74194 .46753 L
s
.77613 .46378 m
.77613 .46753 L
s
.81033 .46378 m
.81033 .46753 L
s
.87872 .46378 m
.87872 .46753 L
s
.91292 .46378 m
.91292 .46753 L
s
.94712 .46378 m
.94712 .46753 L
s
.25 Mabswid
0 .46378 m
1 .46378 L
s
gsave
1.025 .46378 -61 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(x) show
70.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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
.02381 .0359 m
.03006 .0359 L
s
gsave
.01131 .0359 -92.1875 -11.2812 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.562 moveto
%%IncludeResource: font Mathematica1
%%IncludeFont: Mathematica1
/Mathematica1 findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(-) show
72.688 14.562 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.6) show
1.000 setlinewidth
grestore
.02381 .17852 m
.03006 .17852 L
s
gsave
.01131 .17852 -92.1875 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Mathematica1
%%IncludeFont: Mathematica1
/Mathematica1 findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(-) show
72.688 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.4) show
1.000 setlinewidth
grestore
.02381 .32115 m
.03006 .32115 L
s
gsave
.01131 .32115 -92.1875 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Mathematica1
%%IncludeFont: Mathematica1
/Mathematica1 findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(-) show
72.688 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.2) show
1.000 setlinewidth
grestore
.02381 .60641 m
.03006 .60641 L
s
gsave
.01131 .60641 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.2) show
1.000 setlinewidth
grestore
.02381 .74903 m
.03006 .74903 L
s
gsave
.01131 .74903 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.4) show
1.000 setlinewidth
grestore
.02381 .89166 m
.03006 .89166 L
s
gsave
.01131 .89166 -82.5 -11.2812 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.562 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.6) show
1.000 setlinewidth
grestore
.125 Mabswid
.02381 .07155 m
.02756 .07155 L
s
.02381 .10721 m
.02756 .10721 L
s
.02381 .14287 m
.02756 .14287 L
s
.02381 .21418 m
.02756 .21418 L
s
.02381 .24984 m
.02756 .24984 L
s
.02381 .28549 m
.02756 .28549 L
s
.02381 .35681 m
.02756 .35681 L
s
.02381 .39246 m
.02756 .39246 L
s
.02381 .42812 m
.02756 .42812 L
s
.02381 .49944 m
.02756 .49944 L
s
.02381 .53509 m
.02756 .53509 L
s
.02381 .57075 m
.02756 .57075 L
s
.02381 .64206 m
.02756 .64206 L
s
.02381 .67772 m
.02756 .67772 L
s
.02381 .71338 m
.02756 .71338 L
s
.02381 .78469 m
.02756 .78469 L
s
.02381 .82035 m
.02756 .82035 L
s
.02381 .856 m
.02756 .856 L
s
.02381 .00024 m
.02756 .00024 L
s
.02381 .92732 m
.02756 .92732 L
s
.02381 .96297 m
.02756 .96297 L
s
.02381 .99863 m
.02756 .99863 L
s
.25 Mabswid
.02381 0 m
.02381 1 L
s
gsave
.02381 1.025 -66.5 -4 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(v) show
70.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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
.5 1.0125 -97.6875 -4 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(Phase) show
99.062 14.500 moveto
(Space) show
132.375 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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 1 L
0 1 L
closepath
clip
newpath
0 .4 1 r
.5 Mabswid
.25937 .66328 m
.31647 .74724 L
.38591 .82477 L
.48619 .90703 L
.59752 .96241 L
.7081 .9745 L
.80751 .93423 L
.89998 .82047 L
.96202 .62869 L
.97443 .40438 L
.93171 .19503 L
.85147 .0719 L
.76019 .02699 L
.64894 .03411 L
.58847 .05483 L
.5354 .07932 L
.3663 .17792 L
.23932 .2597 L
.19161 .29526 L
.15583 .32886 L
.13037 .36208 L
.11166 .40131 L
.10242 .446 L
.1048 .50187 L
.11239 .53591 L
.12405 .57022 L
.15854 .63965 L
.21558 .72082 L
.30265 .81321 L
.40006 .89047 L
.52281 .95461 L
.63758 .97605 L
.76294 .93813 L
.87005 .81212 L
.91289 .70293 L
.93727 .58458 L
.94511 .45257 L
.93607 .33727 L
.90816 .2213 L
.86757 .13632 L
.77273 .05083 L
.67424 .03581 L
.56817 .06383 L
.51831 .08749 L
.46725 .11702 L
.37596 .1815 L
.30661 .24225 L
.27548 .27531 L
.24726 .31155 L
.22687 .34521 L
Mistroke
.21256 .3775 L
.20264 .41229 L
.19799 .44677 L
.20235 .51655 L
.21282 .55909 L
.2279 .60036 L
.25081 .64798 L
.28254 .70049 L
.35503 .79276 L
.4415 .8742 L
.49716 .91417 L
.56296 .9494 L
.69145 .97593 L
.80999 .93238 L
.91304 .79353 L
.96522 .60943 L
.9727 .38165 L
.95332 .26353 L
.91712 .16178 L
.82396 .0514 L
.76324 .02757 L
.70513 .02437 L
.642 .03601 L
.57743 .05951 L
.47149 .11411 L
.38591 .16571 L
.25923 .24624 L
.21233 .27903 L
.17043 .31397 L
.13913 .34916 L
.11819 .38477 L
.10408 .43218 L
.10168 .46208 L
.1034 .49189 L
.11735 .5519 L
.14908 .6231 L
.19696 .6969 L
.26953 .78117 L
.35855 .86044 L
.45685 .92484 L
.58021 .97067 L
.65356 .97538 L
.72115 .95999 L
.78875 .91861 L
.84353 .85655 L
.89481 .75694 L
.928 .64069 L
.94496 .44397 L
.916 .24555 L
.84309 .10372 L
Mistroke
.75174 .04308 L
.65976 .03744 L
.57766 .05998 L
.49049 .10296 L
.41758 .15026 L
.35075 .2021 L
.2927 .25639 L
.25018 .30738 L
.22206 .35488 L
.20219 .41451 L
.19777 .45056 L
.19831 .48559 L
.21166 .55528 L
.24472 .6364 L
.29764 .72223 L
.37967 .81858 L
.48025 .903 L
.59009 .95995 L
.69674 .97562 L
.81167 .93109 L
.91058 .79893 L
.96574 .60598 L
.97126 .36687 L
.91684 .1612 L
.83589 .05939 L
.73058 .02384 L
.61531 .04453 L
.5547 .06986 L
.5032 .09628 L
.34088 .19386 L
.23674 .26148 L
.1918 .29511 L
.1572 .32737 L
.12835 .36537 L
.11699 .38748 L
.10811 .41305 L
.10167 .46367 L
.10747 .51613 L
.12607 .57523 L
.15594 .63523 L
.20394 .7061 L
.27362 .78531 L
.3585 .86039 L
.45379 .92319 L
.54977 .96337 L
.65933 .97488 L
.78311 .92333 L
.87569 .80094 L
.9374 .58362 L
.9386 .3557 L
Mistroke
.89248 .1822 L
.82056 .0813 L
.7246 .03709 L
.61885 .04609 L
.51948 .08687 L
.46875 .11608 L
.42602 .14431 L
.35281 .20037 L
.29734 .25157 L
.24792 .31059 L
.22831 .3425 L
.21249 .37771 L
.20252 .41287 L
.19793 .44781 L
.20274 .51864 L
.22539 .59429 L
.24683 .64049 L
.27281 .68552 L
.34356 .77992 L
.3896 .82836 L
.44698 .87855 L
.56599 .9507 L
.69142 .97594 L
.81165 .93111 L
.90442 .81175 L
.96803 .58983 L
.96996 .3553 L
.94611 .23711 L
.91093 .14969 L
.86115 .081 L
.80047 .03914 L
.74152 .0245 L
.67775 .02778 L
.56777 .06379 L
.50618 .09465 L
.45269 .12509 L
.36467 .17894 L
.25335 .25016 L
.20478 .28476 L
.16656 .31773 L
.14851 .33722 L
.13185 .35974 L
.11094 .40346 L
.10186 .45467 L
.10603 .50897 L
.11402 .54149 L
.12758 .57886 L
.16616 .65211 L
.22244 .72918 L
.29145 .80275 L
Mistroke
.38526 .88024 L
.44667 .91926 L
.50849 .94912 L
.64188 .97597 L
.71719 .96152 L
.78226 .92402 L
.87565 .80103 L
.93488 .60145 L
.94353 .40909 L
.90846 .22217 L
.83087 .09079 L
.72265 .03681 L
.61577 .04696 L
.52388 .08458 L
.44611 .13064 L
.38316 .17586 L
.32022 .22921 L
.27412 .27689 L
.23685 .32758 L
.2126 .37741 L
.19916 .43385 L
.19993 .50104 L
.21834 .57573 L
.25216 .65047 L
.31316 .74299 L
.39378 .83238 L
.48719 .90769 L
.58737 .959 L
.70571 .97479 L
.8272 .91807 L
.92304 .76984 L
.95762 .65168 L
.97397 .5308 L
.96336 .31074 L
.90185 .13372 L
.85424 .07439 L
.79655 .0375 L
.68577 .0265 L
.61911 .04321 L
.5592 .06773 L
.45791 .12202 L
.30735 .21507 L
.24346 .25686 L
.19384 .29344 L
.15924 .32519 L
.13026 .36225 L
.11792 .38537 L
.10923 .40901 L
.10174 .45833 L
.10823 .51959 L
Mistroke
.11926 .55744 L
.13426 .59392 L
.17817 .67052 L
.23856 .74796 L
.33384 .84055 L
.44429 .91791 L
.50959 .94957 L
.58543 .97163 L
.66668 .97404 L
.74102 .95096 L
.85292 .84218 L
.89602 .75378 L
.92894 .63589 L
.94338 .40668 L
.90678 .21742 L
.86806 .13709 L
.81747 .07869 L
.71331 .03577 L
.65306 .03847 L
.59817 .05247 L
.54067 .07619 L
.48349 .10709 L
.39875 .16399 L
.32363 .22604 L
.26847 .2836 L
.23112 .33736 L
.20889 .38831 L
.19786 .44886 L
.20276 .51877 L
.22414 .59116 L
.26241 .6685 L
.32522 .75818 L
.40547 .8433 L
.49727 .91424 L
.60174 .96373 L
.70253 .97512 L
.81545 .92812 L
.9041 .8124 L
.96427 .61544 L
.97233 .37758 L
.93456 .2025 L
.85762 .07756 L
.75246 .02574 L
.69061 .02583 L
.63516 .03802 L
.53397 .08005 L
.44906 .12725 L
.31754 .2086 L
.21222 .27911 L
.16662 .31767 L
Mistroke
.13448 .35575 L
.11245 .39902 L
.1024 .4462 L
.10476 .50165 L
.12348 .56877 L
.15837 .63936 L
.2059 .70864 L
.28265 .79426 L
.33224 .83922 L
.3914 .88455 L
.44849 .92027 L
.51607 .9521 L
.64279 .97595 L
.7667 .93561 L
.86582 .82007 L
.9247 .65636 L
.945 .44576 L
.91332 .2368 L
.83159 .0915 L
.74011 .04 L
.63317 .04243 L
.53904 .07698 L
.46126 .12079 L
.38851 .17174 L
.32227 .22729 L
.27849 .27187 L
.24177 .31976 L
.21454 .37228 L
.20042 .42455 L
.19873 .49049 L
.20533 .53115 L
.21684 .57143 L
.25689 .65896 L
.28989 .71128 L
.32699 .76035 L
.40949 .84695 L
.52221 .92914 L
.64499 .97353 L
.76284 .95983 L
.82979 .91568 L
.89267 .83388 L
.93837 .72645 L
.96537 .60841 L
.97154 .36955 L
.91757 .16269 L
.87102 .09147 L
.81247 .04486 L
.69713 .02508 L
.62708 .04055 L
.56397 .06553 L
Mistroke
.45751 .12226 L
.3129 .21154 L
.25072 .25192 L
.20183 .28706 L
.16462 .31965 L
.13736 .35161 L
.11547 .3911 L
.10304 .43978 L
.10392 .49595 L
.11842 .55505 L
.1514 .62728 L
.17834 .67076 L
.20839 .71182 L
.28622 .79773 L
.33645 .84272 L
.39634 .88795 L
.45401 .92331 L
.52223 .9544 L
.64977 .97563 L
.77899 .92661 L
.87712 .79801 L
.93807 .57841 L
.9449 .44121 L
.93381 .32305 L
.87617 .15043 L
.82791 .08794 L
.77743 .05298 L
.67765 .03555 L
.57393 .06146 L
.48863 .10405 L
.40888 .15653 L
.29716 .25176 L
.24888 .30922 L
.21734 .36539 L
.2013 .41929 L
.19813 .48325 L
.21301 .5597 L
.24599 .63888 L
.27388 .68721 L
.30543 .73284 L
.34973 .78689 L
.39808 .83646 L
.45561 .88521 L
.51356 .92419 L
.5833 .95754 L
.66174 .97543 L
.7311 .9703 L
.80344 .93716 L
.91281 .79404 L
.96883 .58368 L
Mistroke
.97619 .45012 L
.96657 .33027 L
.90492 .1389 L
.85215 .0725 L
.79737 .03783 L
.69339 .02549 L
.58325 .05701 L
.48932 .10397 L
.41299 .14901 L
.28845 .22716 L
.19176 .29514 L
.15395 .33093 L
.13662 .35266 L
.12335 .37425 L
.1073 .4162 L
.1017 .46746 L
.10893 .52263 L
.13235 .58976 L
.171 .6597 L
.22214 .72881 L
.28735 .79882 L
.36212 .86318 L
.45342 .92299 L
.56643 .96772 L
.69711 .96799 L
.76817 .93459 L
.82797 .87762 L
.91085 .70986 L
.94511 .4742 L
.91828 .25341 L
.84815 .10967 L
.76296 .04685 L
.66256 .03707 L
.55518 .06945 L
.49908 .09802 L
.4508 .12755 L
.35971 .19462 L
.29422 .2548 L
.24796 .31055 L
.21747 .36509 L
.20007 .42693 L
.19744 .46458 L
.19998 .50143 L
.2173 .57275 L
.25475 .65515 L
.30365 .73044 L
.37578 .81465 L
.47545 .89968 L
.53992 .93858 L
.60258 .96398 L
Mistroke
.72976 .97062 L
.84277 .90274 L
.92578 .76279 L
.97211 .55361 L
.97085 .36305 L
.9284 .18681 L
.84739 .06838 L
.73998 .02437 L
.63568 .03786 L
.54636 .07388 L
.45278 .12505 L
.36755 .17714 L
.24671 .25464 L
.19812 .28999 L
.15579 .3289 L
.1365 .35283 L
.12222 .37642 L
.11185 .40074 L
.1047 .42848 L
.10225 .47991 L
.11432 .54246 L
.1414 .60858 L
.18065 .67416 L
.24605 .75631 L
.34158 .84695 L
.3938 .8862 L
.45442 .92353 L
.57401 .96942 L
.69787 .96778 L
.82253 .88426 L
.90856 .71734 L
.94399 .51062 L
.93071 .30596 L
.88172 .16042 L
.79538 .06277 L
.70031 .03503 L
.59535 .05343 L
.49363 .10114 L
.41786 .15006 L
.34754 .20483 L
.28671 .26277 L
.25974 .2945 L
.23849 .32492 L
.22253 .35388 L
.20947 .3865 L
.19794 .4475 L
.20126 .51017 L
.21797 .57468 L
.2529 .65182 L
.31159 .74095 L
Mistroke
.39244 .8311 L
.50106 .91663 L
.60925 .96592 L
.73477 .96938 L
.84579 .89948 L
.9248 .76533 L
.97267 .54738 L
.96655 .33014 L
.91972 .16718 L
.85115 .07162 L
.76075 .02709 L
.66077 .0312 L
.55922 .06772 L
.46079 .12033 L
.31684 .20904 L
.21252 .27888 L
.17716 .30773 L
.14583 .34047 L
.11876 .38351 L
.10444 .43 L
.10173 .45883 L
.10337 .49167 L
.119 .55671 L
.14959 .62403 L
.19344 .69216 L
.25985 .77116 L
.35282 .85596 L
.4588 .92588 L
.56981 .9685 L
.69761 .96785 L
.82269 .88408 L
.90347 .733 L
.94172 .54383 L
.93493 .32986 L
.87629 .15063 L
.79468 .06234 L
.69148 .03497 L
.59362 .05404 L
.50925 .09236 L
.43489 .13818 L
.37611 .18138 L
.32189 .22765 L
.27441 .27655 L
.23556 .32972 L
.2111 .38163 L
.20207 .41516 L
.19788 .44857 L
.2023 .51629 L
.22586 .59545 L
.26673 .67571 L
Mistroke
.33439 .76925 L
.38253 .82143 L
.43324 .86748 L
.5291 .93293 L
.64549 .97361 L
.75153 .96423 L
.85439 .88964 L
.93879 .7251 L
.97475 .51827 L
.95947 .29048 L
.88859 .11354 L
.83668 .05997 L
.7757 .03048 L
.66191 .03094 L
.60063 .04996 L
.54624 .07393 L
.43563 .13527 L
.28083 .23207 L
.2287 .26712 L
.18134 .30401 L
.14514 .34132 L
.12054 .37977 L
.1061 .42139 L
.10182 .4719 L
.10497 .5029 L
.11322 .53881 L
.14217 .61008 L
.18927 .68642 L
.25041 .76108 L
.3367 .84293 L
.43698 .91371 L
.53994 .96042 L
.65954 .97486 L
.78538 .92146 L
.84085 .86041 L
.89101 .76656 L
.94107 .55106 L
.93605 .33716 L
.88818 .17308 L
.80591 .06978 L
.72243 .03678 L
.62849 .04355 L
.53237 .08026 L
.44151 .13371 L
.31377 .2353 L
.28464 .26502 L
.25823 .29646 L
.22238 .35418 L
.20903 .38786 L
.20103 .42085 L
Mistroke
.19748 .45905 L
.20016 .50274 L
.20815 .5427 L
.22322 .58883 L
.24391 .63483 L
.26895 .67934 L
.33242 .7669 L
.42357 .85933 L
.52451 .93042 L
.64851 .97402 L
.76919 .95702 L
.86879 .87115 L
.94748 .69491 L
.97611 .44522 L
.96528 .32208 L
.93664 .20818 L
.85124 .07169 L
.74705 .02505 L
.68529 .02657 L
.62851 .04009 L
.52189 .08628 L
.42234 .14331 L
.29117 .22541 L
.2363 .26179 L
.18749 .29871 L
.1625 .3218 L
.14317 .34382 L
.12712 .36746 L
.11532 .39146 L
.10689 .41788 L
.10258 .44412 L
.10196 .47518 L
.10635 .51063 L
.12743 .57851 L
.16412 .64883 L
.22512 .73238 L
.31614 .82536 L
.3664 .86643 L
.42551 .90683 L
.54415 .96172 L
.61458 .9753 L
.68138 .97165 L
.75256 .9446 L
.82262 .88416 L
.91159 .70739 L
.93624 .59214 L
.94516 .45879 L
.91521 .24292 L
.84487 .10576 L
.74483 .04115 L
Mistroke
.64323 .04025 L
.5555 .0693 L
.46933 .11572 L
.38848 .17176 L
.31835 .23096 L
.27089 .28069 L
.23184 .33608 L
.20637 .39684 L
.1975 .45828 L
.20578 .53312 L
.2194 .57867 L
.23772 .62224 L
.28724 .70745 L
.36502 .80351 L
.46166 .88975 L
.56786 .95148 L
.68108 .97619 L
.78649 .94802 L
.8873 .84309 L
.95818 .64891 L
.97431 .40254 L
.93327 .19907 L
.86098 .08083 L
.76195 .02731 L
.64803 .03435 L
.54752 .07331 L
.44999 .1267 L
.3608 .18136 L
.23003 .26618 L
.17713 .30776 L
.15591 .32877 L
.13938 .34883 L
.11618 .38939 L
.10313 .43907 L
.10171 .46806 L
.1048 .50189 L
.11247 .53619 L
.12387 .56977 L
.15454 .6328 L
.20517 .7077 L
.27827 .78995 L
.36566 .86587 L
.47664 .93496 L
.53863 .96001 L
.60999 .97491 L
.73628 .95333 L
.84152 .85945 L
.88886 .77179 L
.92445 .65748 L
.94443 .42694 L
Mistroke
.93053 .30501 L
.90318 .20772 L
.86017 .1254 L
.80342 .06803 L
.6958 .03495 L
.63388 .04226 L
.57847 .05966 L
.48449 .1065 L
.39874 .164 L
.33877 .21243 L
.28595 .26359 L
.24173 .31981 L
.21364 .37461 L
.19896 .43561 L
.19952 .49781 L
.21751 .57335 L
.23618 .61899 L
.25881 .66232 L
.31527 .7457 L
.39865 .83699 L
.49793 .91466 L
.60354 .96427 L
.7126 .97389 L
.81121 .93144 L
.90239 .81579 L
.96333 .62109 L
.97305 .38562 L
.93139 .19423 L
.86211 .08196 L
.76789 .02855 L
.66033 .0313 L
.56638 .06442 L
.47359 .1129 L
.38906 .16375 L
.27288 .23724 L
.22194 .27196 L
.18149 .30387 L
.16187 .32245 L
.14341 .34351 L
.11864 .38378 L
.10433 .43062 L
.10225 .47993 L
.11391 .5411 L
.12771 .57918 L
.14572 .61688 L
.19804 .69835 L
.27966 .79132 L
.3274 .83512 L
.38466 .87981 L
.50264 .94672 L
Mistroke
.58215 .97103 L
.65908 .9749 L
.72725 .95746 L
.79635 .91184 L
.85072 .84567 L
.89854 .74702 L
.93163 .6213 L
.9447 .49349 L
.92425 .2762 L
.89103 .17905 L
.85042 .11246 L
.7486 .04217 L
.64658 .03961 L
.53957 .07672 L
.49006 .10322 L
.43977 .13487 L
.36612 .18937 L
.30166 .24718 L
.25464 .30123 L
.22347 .35194 L
.20238 .41359 L
.19778 .47734 L
.20755 .54039 L
.23445 .61526 L
.28506 .70424 L
.36431 .80276 L
.45308 .88328 L
.57022 .95246 L
.6915 .97593 L
.80085 .93897 L
.90645 .80764 L
.96578 .60571 L
.9737 .39388 L
.94101 .22086 L
.87054 .09093 L
.77283 .02973 L
.66045 .03127 L
.56235 .06627 L
.46609 .11724 L
.37905 .16997 L
.26079 .2452 L
.20962 .28106 L
.16963 .31475 L
.15068 .33466 L
.13329 .35753 L
.11147 .40186 L
.1019 .45391 L
.10602 .50892 L
.12679 .57698 L
.14696 .6192 L
Mistroke
.17173 .66082 L
.2401 .74969 L
.34221 .84746 L
.39829 .88928 L
.45611 .92444 L
.57449 .96952 L
.70805 .96472 L
.77955 .92617 L
.83838 .86388 L
.91251 .70425 L
.94504 .47973 L
.91901 .25599 L
.84931 .11109 L
.79694 .06375 L
.7346 .03881 L
.67384 .03585 L
.61825 .04625 L
.51921 .08701 L
.42723 .14347 L
.35063 .20221 L
.28529 .26431 L
.25576 .29973 L
.2338 .33268 L
.21745 .36513 L
.20533 .40073 L
.19745 .46592 L
.20537 .53133 L
.23431 .61494 L
.28298 .70115 L
.34798 .78493 L
.42507 .86061 L
.52727 .93194 L
.65009 .97423 L
.77728 .95306 L
.84301 .90249 L
.89501 .8297 L
.96242 .62642 L
.97413 .39981 L
.95756 .28154 L
.92398 .17649 L
.83371 .05784 L
.77411 .03006 L
.71593 .02381 L
.65236 .03322 L
.58634 .05571 L
.49377 .10148 L
.41949 .14504 L
.28489 .22945 L
.2363 .26179 L
.19245 .29457 L
Mistroke
.15879 .32566 L
.13365 .357 L
.11314 .39711 L
.10227 .44777 L
.10548 .50595 L
.1142 .54208 L
.12691 .57728 L
.16205 .64547 L
.21979 .72598 L
.29408 .80524 L
.38039 .87675 L
.49418 .94309 L
.56465 .9673 L
.63166 .97605 L
.75328 .94418 L
.86292 .8253 L
.92656 .6477 L
.94509 .45144 L
.91797 .25229 L
.84443 .10526 L
.79099 .06013 L
.73738 .03939 L
.67681 .03561 L
.61316 .04772 L
.51312 .09026 L
.46162 .12057 L
.41735 .15042 L
.35034 .20245 L
.29281 .25627 L
.26792 .28426 L
.24484 .3151 L
.215 .3711 L
Mfstroke
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  CellLabel->"From In[11]:=",
  ImageSize->{250, 200},
  ImageCacheValid->False,
  ImageRangeCache->{{{144, 393}, {673, 474}} -> {-1.5507, 3.05274, \
0.00816062, 0.00782643}}],

Cell[BoxData[
    TagBox[\(\[SkeletonIndicator]  Graphics  \[SkeletonIndicator]\),
      False,
      Editable->False]], "Output",
  CellLabel->"Out[11]="]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Poincare Sections", "Section"],

Cell["\<\
The idea of a Poincare section is to plot a point in phase space \
once every period of the external force, 2\[Pi]/(external frequency).  The \
resulting pattern gives information about the periodicity of the signal (or \
indicates chaos).  Start the plot at a large enough time t (\"tstart\") so \
that the transients have died out.\
\>", "Text"],

Cell["\<\
Set the external period and how many periods we'll consider.  \
Define a function timeperiod[i] giving the corresponding time as a function \
of the period number.\
\>", "Text"],

Cell[BoxData[
    \(\(Texternal\  := \ 2\ Pi/\[Omega]ext;\)\)], "Input",
  CellLabel->"In[12]:="],

Cell[BoxData[
    \(\(tstart\  = \ 40  Texternal;\)\)], "Input",
  CellLabel->"In[13]:="],

Cell[BoxData[
    \(\(numperiods\  = \ 20;\)\)], "Input",
  CellLabel->"In[14]:="],

Cell[BoxData[
    \(timeperiod[i_]\  := \ tstart\  + \ i*Texternal\)], "Input",
  CellLabel->"In[15]:="],

Cell["\<\
Just evaluate at the relevant points.  Flatten[expr,1] strips off a \
layer of {}'s.\
\>", "Text"],

Cell[BoxData[
    \(\(PoincarePts\  = \ 
        Flatten[Table[
            Evaluate[{x[timeperiod[i]], \(x'\)[timeperiod[i]]} /. 
                solution], {i, 0, numperiods}], 1];\)\)], "Input",
  CellLabel->"In[16]:="],

Cell["ListPlot plots pairs of numbers in the PlotRange.", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(ListPlot[PoincarePts, AspectRatio \[Rule] 1, 
      TextStyle \[Rule] {FontFamily \[Rule] "\<Times\>", 
          FontSize \[Rule] 14}, 
      ImageSize \[Rule] {250, 
          200}, \[IndentingNewLine]PlotRange \[Rule] {{0,  .6}, {0, 1}}, 
      PlotLabel \[Rule] StyleForm["\<Poincare Section\>"], 
      AxesOrigin \[Rule] Automatic, AxesLabel \[Rule] {"\<x\>", "\<v\>"}, 
      PlotStyle \[Rule] {PointSize[0.015], RGBColor[1, 0, 0]}]\)], "Input",
  CellLabel->"In[17]:="],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: 1 
%%ImageSize: 250 200 
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
-3.68629e-18 1.66667 0 1 [
[.16667 -0.0125 -10.75 -14.5 ]
[.16667 -0.0125 10.75 0 ]
[.33333 -0.0125 -10.75 -14.5 ]
[.33333 -0.0125 10.75 0 ]
[.5 -0.0125 -10.75 -14.5 ]
[.5 -0.0125 10.75 0 ]
[.66667 -0.0125 -10.75 -14.5 ]
[.66667 -0.0125 10.75 0 ]
[.83333 -0.0125 -10.75 -14.625 ]
[.83333 -0.0125 10.75 0 ]
[1.025 0 0 -7.25 ]
[1.025 0 11 7.25 ]
[-0.0125 .2 -21.5 -7.25 ]
[-0.0125 .2 0 7.25 ]
[-0.0125 .4 -21.5 -7.25 ]
[-0.0125 .4 0 7.25 ]
[-0.0125 .6 -21.5 -7.28125 ]
[-0.0125 .6 0 7.28125 ]
[-0.0125 .8 -21.5 -7.25 ]
[-0.0125 .8 0 7.25 ]
[-0.0125 1 -11 -7.25 ]
[-0.0125 1 0 7.25 ]
[0 1.025 -5.5 0 ]
[0 1.025 5.5 14.5 ]
[.5 1.0125 -49.0938 0 ]
[.5 1.0125 49.0938 14.5 ]
[ 0 0 0 0 ]
[ 1 1 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.16667 0 m
.16667 .00625 L
s
gsave
.16667 -0.0125 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.1) show
1.000 setlinewidth
grestore
.33333 0 m
.33333 .00625 L
s
gsave
.33333 -0.0125 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.2) show
1.000 setlinewidth
grestore
.5 0 m
.5 .00625 L
s
gsave
.5 -0.0125 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.3) show
1.000 setlinewidth
grestore
.66667 0 m
.66667 .00625 L
s
gsave
.66667 -0.0125 -71.75 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.4) show
1.000 setlinewidth
grestore
.83333 0 m
.83333 .00625 L
s
gsave
.83333 -0.0125 -71.75 -18.625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.5) show
1.000 setlinewidth
grestore
.125 Mabswid
.03333 0 m
.03333 .00375 L
s
.06667 0 m
.06667 .00375 L
s
.1 0 m
.1 .00375 L
s
.13333 0 m
.13333 .00375 L
s
.2 0 m
.2 .00375 L
s
.23333 0 m
.23333 .00375 L
s
.26667 0 m
.26667 .00375 L
s
.3 0 m
.3 .00375 L
s
.36667 0 m
.36667 .00375 L
s
.4 0 m
.4 .00375 L
s
.43333 0 m
.43333 .00375 L
s
.46667 0 m
.46667 .00375 L
s
.53333 0 m
.53333 .00375 L
s
.56667 0 m
.56667 .00375 L
s
.6 0 m
.6 .00375 L
s
.63333 0 m
.63333 .00375 L
s
.7 0 m
.7 .00375 L
s
.73333 0 m
.73333 .00375 L
s
.76667 0 m
.76667 .00375 L
s
.8 0 m
.8 .00375 L
s
.86667 0 m
.86667 .00375 L
s
.9 0 m
.9 .00375 L
s
.93333 0 m
.93333 .00375 L
s
.96667 0 m
.96667 .00375 L
s
.25 Mabswid
0 0 m
1 0 L
s
gsave
1.025 0 -61 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(x) show
70.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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 .2 m
.00625 .2 L
s
gsave
-0.0125 .2 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.2) show
1.000 setlinewidth
grestore
0 .4 m
.00625 .4 L
s
gsave
-0.0125 .4 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.4) show
1.000 setlinewidth
grestore
0 .6 m
.00625 .6 L
s
gsave
-0.0125 .6 -82.5 -11.2812 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.562 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.6) show
1.000 setlinewidth
grestore
0 .8 m
.00625 .8 L
s
gsave
-0.0125 .8 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.8) show
1.000 setlinewidth
grestore
0 1 m
.00625 1 L
s
gsave
-0.0125 1 -72 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1) show
1.000 setlinewidth
grestore
.125 Mabswid
0 .05 m
.00375 .05 L
s
0 .1 m
.00375 .1 L
s
0 .15 m
.00375 .15 L
s
0 .25 m
.00375 .25 L
s
0 .3 m
.00375 .3 L
s
0 .35 m
.00375 .35 L
s
0 .45 m
.00375 .45 L
s
0 .5 m
.00375 .5 L
s
0 .55 m
.00375 .55 L
s
0 .65 m
.00375 .65 L
s
0 .7 m
.00375 .7 L
s
0 .75 m
.00375 .75 L
s
0 .85 m
.00375 .85 L
s
0 .9 m
.00375 .9 L
s
0 .95 m
.00375 .95 L
s
.25 Mabswid
0 0 m
0 1 L
s
gsave
0 1.025 -66.5 -4 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(v) show
70.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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
.5 1.0125 -110.094 -4 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(Poincare) show
115.312 14.500 moveto
(Section) show
157.188 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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 1 L
0 1 L
closepath
clip
newpath
1 0 0 r
.015 w
.93395 .53423 Mdot
.4904 .37653 Mdot
.93395 .53423 Mdot
.4904 .37653 Mdot
.93395 .53423 Mdot
.4904 .37653 Mdot
.93395 .53423 Mdot
.4904 .37653 Mdot
.93395 .53423 Mdot
.4904 .37653 Mdot
.93395 .53423 Mdot
.4904 .37653 Mdot
.93395 .53423 Mdot
.4904 .37653 Mdot
.93395 .53423 Mdot
.4904 .37653 Mdot
.93395 .53423 Mdot
.4904 .37653 Mdot
.93395 .53423 Mdot
.4904 .37653 Mdot
.93395 .53423 Mdot
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  CellLabel->"From In[17]:=",
  ImageSize->{250, 200},
  ImageCacheValid->False,
  ImageRangeCache->{{{144, 393}, {656.5, 457.5}} -> {-0.699404, 2.69235, \
0.00366449, 0.00610749}}],

Cell[BoxData[
    TagBox[\(\[SkeletonIndicator]  Graphics  \[SkeletonIndicator]\),
      False,
      Editable->False]], "Output",
  CellLabel->"Out[17]="]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Power Spectrum", "Section"],

Cell["\<\
The power spectrum is found by taking a Fourier transform (FFT) of \
the signal.  We generate points at the same time intervals as in \
diffeq_pendulum.cpp.\
\>", "Text"],

Cell[BoxData[
    \(\(Tskip\  = \ 100;\)\)], "Input",
  CellLabel->"In[18]:="],

Cell[BoxData[
    \(time[i_] := tstart + i*Texternal/Tskip\)], "Input",
  CellLabel->"In[19]:="],

Cell[BoxData[
    \(\(numpoints\  = \ 5000;\)\)], "Input",
  CellLabel->"In[20]:="],

Cell[BoxData[
    \(SampleTime\  := \ numpoints\ *\ Texternal/Tskip\)], "Input",
  CellLabel->"In[21]:="],

Cell[BoxData[
    \(\(SamplePts = 
        Flatten[Table[Evaluate[x[time[i]] /. solution], {i, 0, numpoints}], 
          1];\)\)], "Input",
  CellLabel->"In[22]:="],

Cell["Check first that the plot still looks ok.", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(ListPlot[SamplePts, 
      PlotRange \[Rule] {{0, 1000}, Automatic}]\)], "Input",
  CellLabel->"In[23]:="],

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
-1.04083e-17 0.001 0.0147151 0.422776 [
[.2 .00222 -9 -9 ]
[.2 .00222 9 0 ]
[.4 .00222 -9 -9 ]
[.4 .00222 9 0 ]
[.6 .00222 -9 -9 ]
[.6 .00222 9 0 ]
[.8 .00222 -9 -9 ]
[.8 .00222 9 0 ]
[1 .00222 -12 -9 ]
[1 .00222 12 0 ]
[-0.0125 .09927 -18 -4.5 ]
[-0.0125 .09927 0 4.5 ]
[-0.0125 .18383 -18 -4.5 ]
[-0.0125 .18383 0 4.5 ]
[-0.0125 .26838 -18 -4.5 ]
[-0.0125 .26838 0 4.5 ]
[-0.0125 .35294 -18 -4.5 ]
[-0.0125 .35294 0 4.5 ]
[-0.0125 .43749 -6 -4.5 ]
[-0.0125 .43749 0 4.5 ]
[-0.0125 .52205 -18 -4.5 ]
[-0.0125 .52205 0 4.5 ]
[-0.0125 .6066 -18 -4.5 ]
[-0.0125 .6066 0 4.5 ]
[ 0 0 0 0 ]
[ 1 .61803 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.2 .01472 m
.2 .02097 L
s
[(200)] .2 .00222 0 1 Mshowa
.4 .01472 m
.4 .02097 L
s
[(400)] .4 .00222 0 1 Mshowa
.6 .01472 m
.6 .02097 L
s
[(600)] .6 .00222 0 1 Mshowa
.8 .01472 m
.8 .02097 L
s
[(800)] .8 .00222 0 1 Mshowa
1 .01472 m
1 .02097 L
s
[(1000)] 1 .00222 0 1 Mshowa
.125 Mabswid
.05 .01472 m
.05 .01847 L
s
.1 .01472 m
.1 .01847 L
s
.15 .01472 m
.15 .01847 L
s
.25 .01472 m
.25 .01847 L
s
.3 .01472 m
.3 .01847 L
s
.35 .01472 m
.35 .01847 L
s
.45 .01472 m
.45 .01847 L
s
.5 .01472 m
.5 .01847 L
s
.55 .01472 m
.55 .01847 L
s
.65 .01472 m
.65 .01847 L
s
.7 .01472 m
.7 .01847 L
s
.75 .01472 m
.75 .01847 L
s
.85 .01472 m
.85 .01847 L
s
.9 .01472 m
.9 .01847 L
s
.95 .01472 m
.95 .01847 L
s
.25 Mabswid
0 .01472 m
1 .01472 L
s
0 .09927 m
.00625 .09927 L
s
[(0.2)] -0.0125 .09927 1 0 Mshowa
0 .18383 m
.00625 .18383 L
s
[(0.4)] -0.0125 .18383 1 0 Mshowa
0 .26838 m
.00625 .26838 L
s
[(0.6)] -0.0125 .26838 1 0 Mshowa
0 .35294 m
.00625 .35294 L
s
[(0.8)] -0.0125 .35294 1 0 Mshowa
0 .43749 m
.00625 .43749 L
s
[(1)] -0.0125 .43749 1 0 Mshowa
0 .52205 m
.00625 .52205 L
s
[(1.2)] -0.0125 .52205 1 0 Mshowa
0 .6066 m
.00625 .6066 L
s
[(1.4)] -0.0125 .6066 1 0 Mshowa
.125 Mabswid
0 .03585 m
.00375 .03585 L
s
0 .05699 m
.00375 .05699 L
s
0 .07813 m
.00375 .07813 L
s
0 .12041 m
.00375 .12041 L
s
0 .14155 m
.00375 .14155 L
s
0 .16269 m
.00375 .16269 L
s
0 .20496 m
.00375 .20496 L
s
0 .2261 m
.00375 .2261 L
s
0 .24724 m
.00375 .24724 L
s
0 .28952 m
.00375 .28952 L
s
0 .31066 m
.00375 .31066 L
s
0 .3318 m
.00375 .3318 L
s
0 .37408 m
.00375 .37408 L
s
0 .39521 m
.00375 .39521 L
s
0 .41635 m
.00375 .41635 L
s
0 .45863 m
.00375 .45863 L
s
0 .47977 m
.00375 .47977 L
s
0 .50091 m
.00375 .50091 L
s
0 .54319 m
.00375 .54319 L
s
0 .56432 m
.00375 .56432 L
s
0 .58546 m
.00375 .58546 L
s
.25 Mabswid
0 0 m
0 .61803 L
s
0 0 m
1 0 L
1 .61803 L
0 .61803 L
closepath
clip
newpath
.008 w
.001 .25163 Mdot
.002 .2662 Mdot
.003 .28153 Mdot
.004 .29758 Mdot
.005 .31429 Mdot
.006 .33163 Mdot
.007 .34951 Mdot
.008 .36786 Mdot
.009 .38656 Mdot
.01 .40552 Mdot
.011 .4246 Mdot
.012 .44364 Mdot
.013 .46248 Mdot
.014 .48094 Mdot
.015 .49884 Mdot
.016 .51595 Mdot
.017 .53208 Mdot
.018 .54702 Mdot
.019 .56057 Mdot
.02 .57252 Mdot
.021 .58271 Mdot
.022 .59099 Mdot
.023 .59723 Mdot
.024 .60136 Mdot
.025 .60332 Mdot
.026 .60311 Mdot
.027 .60078 Mdot
.028 .59638 Mdot
.029 .59003 Mdot
.03 .58187 Mdot
.031 .57206 Mdot
.032 .56078 Mdot
.033 .54822 Mdot
.034 .53457 Mdot
.035 .52004 Mdot
.036 .50481 Mdot
.037 .48906 Mdot
.038 .47295 Mdot
.039 .45663 Mdot
.04 .44025 Mdot
.041 .4239 Mdot
.042 .4077 Mdot
.043 .39172 Mdot
.044 .37604 Mdot
.045 .36069 Mdot
.046 .34573 Mdot
.047 .33119 Mdot
.048 .31708 Mdot
.049 .30342 Mdot
.05 .29022 Mdot
.051 .27746 Mdot
.052 .26515 Mdot
.053 .25328 Mdot
.054 .24185 Mdot
.055 .23083 Mdot
.056 .22021 Mdot
.057 .21 Mdot
.058 .20016 Mdot
.059 .19069 Mdot
.06 .18157 Mdot
.061 .1728 Mdot
.062 .16437 Mdot
.063 .15626 Mdot
.064 .14848 Mdot
.065 .14101 Mdot
.066 .13386 Mdot
.067 .12701 Mdot
.068 .12048 Mdot
.069 .11426 Mdot
.07 .10835 Mdot
.071 .10276 Mdot
.072 .0975 Mdot
.073 .09256 Mdot
.074 .08796 Mdot
.075 .08371 Mdot
.076 .07982 Mdot
.077 .07629 Mdot
.078 .07314 Mdot
.079 .07038 Mdot
.08 .06803 Mdot
.081 .0661 Mdot
.082 .0646 Mdot
.083 .06356 Mdot
.084 .06297 Mdot
.085 .06286 Mdot
.086 .06325 Mdot
.087 .06415 Mdot
.088 .06558 Mdot
.089 .06755 Mdot
.09 .07008 Mdot
.091 .07319 Mdot
.092 .07688 Mdot
.093 .08118 Mdot
.094 .08611 Mdot
.095 .09166 Mdot
.096 .09787 Mdot
.097 .10474 Mdot
.098 .11229 Mdot
.099 .12053 Mdot
.1 .12947 Mdot
.101 .13911 Mdot
.102 .14947 Mdot
.103 .16056 Mdot
.104 .17236 Mdot
.105 .1849 Mdot
.106 .19815 Mdot
.107 .21212 Mdot
.108 .22679 Mdot
.109 .24214 Mdot
.11 .25814 Mdot
.111 .27476 Mdot
.112 .29197 Mdot
.113 .30969 Mdot
.114 .32787 Mdot
.115 .34643 Mdot
.116 .36527 Mdot
.117 .38429 Mdot
.118 .40337 Mdot
.119 .42236 Mdot
.12 .44112 Mdot
.121 .45948 Mdot
.122 .47726 Mdot
.123 .49429 Mdot
.124 .51035 Mdot
.125 .52527 Mdot
.126 .53885 Mdot
.127 .55092 Mdot
.128 .56132 Mdot
.129 .56989 Mdot
.13 .57653 Mdot
.131 .58116 Mdot
.132 .58371 Mdot
.133 .58419 Mdot
.134 .5826 Mdot
.135 .57902 Mdot
.136 .57353 Mdot
.137 .56625 Mdot
.138 .55733 Mdot
.139 .54693 Mdot
.14 .53523 Mdot
.141 .5224 Mdot
.142 .50864 Mdot
.143 .49411 Mdot
.144 .47901 Mdot
.145 .46347 Mdot
.146 .44767 Mdot
.147 .43172 Mdot
.148 .41576 Mdot
.149 .39988 Mdot
.15 .38418 Mdot
.151 .36874 Mdot
.152 .3536 Mdot
.153 .33884 Mdot
.154 .32448 Mdot
.155 .31056 Mdot
.156 .2971 Mdot
.157 .28412 Mdot
.158 .27162 Mdot
.159 .25963 Mdot
.16 .24814 Mdot
.161 .23715 Mdot
.162 .22666 Mdot
.163 .21667 Mdot
.164 .20718 Mdot
.165 .19818 Mdot
.166 .18968 Mdot
.167 .18166 Mdot
.168 .17414 Mdot
.169 .1671 Mdot
.17 .16055 Mdot
.171 .15449 Mdot
.172 .14892 Mdot
.173 .14386 Mdot
.174 .1393 Mdot
.175 .13525 Mdot
.176 .13172 Mdot
.177 .12872 Mdot
.178 .12626 Mdot
.179 .12435 Mdot
.18 .123 Mdot
.181 .12224 Mdot
.182 .12206 Mdot
.183 .12249 Mdot
.184 .12355 Mdot
.185 .12524 Mdot
.186 .12759 Mdot
.187 .1306 Mdot
.188 .13431 Mdot
.189 .13872 Mdot
.19 .14386 Mdot
.191 .14973 Mdot
.192 .15636 Mdot
.193 .16375 Mdot
.194 .17193 Mdot
.195 .18089 Mdot
.196 .19066 Mdot
.197 .20124 Mdot
.198 .21262 Mdot
.199 .22482 Mdot
.2 .23783 Mdot
.201 .25163 Mdot
.202 .2662 Mdot
.203 .28153 Mdot
.204 .29758 Mdot
.205 .31429 Mdot
.206 .33163 Mdot
.207 .34951 Mdot
.208 .36785 Mdot
.209 .38656 Mdot
.21 .40552 Mdot
.211 .4246 Mdot
.212 .44364 Mdot
.213 .46248 Mdot
.214 .48094 Mdot
.215 .49884 Mdot
.216 .51595 Mdot
.217 .53208 Mdot
.218 .54702 Mdot
.219 .56057 Mdot
.22 .57252 Mdot
.221 .58271 Mdot
.222 .59099 Mdot
.223 .59723 Mdot
.224 .60136 Mdot
.225 .60332 Mdot
.226 .60311 Mdot
.227 .60078 Mdot
.228 .59638 Mdot
.229 .59003 Mdot
.23 .58187 Mdot
.231 .57206 Mdot
.232 .56078 Mdot
.233 .54822 Mdot
.234 .53457 Mdot
.235 .52004 Mdot
.236 .50481 Mdot
.237 .48906 Mdot
.238 .47295 Mdot
.239 .45663 Mdot
.24 .44025 Mdot
.241 .4239 Mdot
.242 .4077 Mdot
.243 .39172 Mdot
.244 .37604 Mdot
.245 .36069 Mdot
.246 .34573 Mdot
.247 .33119 Mdot
.248 .31708 Mdot
.249 .30342 Mdot
.25 .29022 Mdot
.251 .27746 Mdot
.252 .26515 Mdot
.253 .25328 Mdot
.254 .24185 Mdot
.255 .23083 Mdot
.256 .22021 Mdot
.257 .21 Mdot
.258 .20016 Mdot
.259 .19069 Mdot
.26 .18157 Mdot
.261 .1728 Mdot
.262 .16437 Mdot
.263 .15626 Mdot
.264 .14848 Mdot
.265 .14101 Mdot
.266 .13386 Mdot
.267 .12701 Mdot
.268 .12048 Mdot
.269 .11426 Mdot
.27 .10835 Mdot
.271 .10276 Mdot
.272 .0975 Mdot
.273 .09256 Mdot
.274 .08796 Mdot
.275 .08371 Mdot
.276 .07982 Mdot
.277 .07629 Mdot
.278 .07314 Mdot
.279 .07038 Mdot
.28 .06803 Mdot
.281 .0661 Mdot
.282 .0646 Mdot
.283 .06356 Mdot
.284 .06297 Mdot
.285 .06286 Mdot
.286 .06325 Mdot
.287 .06415 Mdot
.288 .06558 Mdot
.289 .06755 Mdot
.29 .07008 Mdot
.291 .07319 Mdot
.292 .07688 Mdot
.293 .08118 Mdot
.294 .08611 Mdot
.295 .09166 Mdot
.296 .09787 Mdot
.297 .10474 Mdot
.298 .11229 Mdot
.299 .12053 Mdot
.3 .12947 Mdot
.301 .13911 Mdot
.302 .14947 Mdot
.303 .16056 Mdot
.304 .17236 Mdot
.305 .1849 Mdot
.306 .19815 Mdot
.307 .21212 Mdot
.308 .22679 Mdot
.309 .24214 Mdot
.31 .25814 Mdot
.311 .27476 Mdot
.312 .29197 Mdot
.313 .30969 Mdot
.314 .32787 Mdot
.315 .34643 Mdot
.316 .36527 Mdot
.317 .38429 Mdot
.318 .40337 Mdot
.319 .42236 Mdot
.32 .44112 Mdot
.321 .45948 Mdot
.322 .47726 Mdot
.323 .49429 Mdot
.324 .51035 Mdot
.325 .52527 Mdot
.326 .53885 Mdot
.327 .55092 Mdot
.328 .56132 Mdot
.329 .56989 Mdot
.33 .57653 Mdot
.331 .58116 Mdot
.332 .58371 Mdot
.333 .58419 Mdot
.334 .5826 Mdot
.335 .57902 Mdot
.336 .57353 Mdot
.337 .56625 Mdot
.338 .55733 Mdot
.339 .54693 Mdot
.34 .53523 Mdot
.341 .5224 Mdot
.342 .50864 Mdot
.343 .49411 Mdot
.344 .47901 Mdot
.345 .46347 Mdot
.346 .44767 Mdot
.347 .43172 Mdot
.348 .41576 Mdot
.349 .39988 Mdot
.35 .38418 Mdot
.351 .36874 Mdot
.352 .3536 Mdot
.353 .33884 Mdot
.354 .32448 Mdot
.355 .31056 Mdot
.356 .2971 Mdot
.357 .28412 Mdot
.358 .27162 Mdot
.359 .25963 Mdot
.36 .24814 Mdot
.361 .23715 Mdot
.362 .22666 Mdot
.363 .21667 Mdot
.364 .20718 Mdot
.365 .19818 Mdot
.366 .18968 Mdot
.367 .18166 Mdot
.368 .17414 Mdot
.369 .1671 Mdot
.37 .16055 Mdot
.371 .15449 Mdot
.372 .14892 Mdot
.373 .14386 Mdot
.374 .1393 Mdot
.375 .13525 Mdot
.376 .13172 Mdot
.377 .12872 Mdot
.378 .12626 Mdot
.379 .12435 Mdot
.38 .123 Mdot
.381 .12224 Mdot
.382 .12206 Mdot
.383 .12249 Mdot
.384 .12355 Mdot
.385 .12524 Mdot
.386 .12759 Mdot
.387 .1306 Mdot
.388 .13431 Mdot
.389 .13872 Mdot
.39 .14386 Mdot
.391 .14973 Mdot
.392 .15636 Mdot
.393 .16375 Mdot
.394 .17193 Mdot
.395 .18089 Mdot
.396 .19066 Mdot
.397 .20124 Mdot
.398 .21262 Mdot
.399 .22482 Mdot
.4 .23783 Mdot
.401 .25163 Mdot
.402 .2662 Mdot
.403 .28153 Mdot
.404 .29758 Mdot
.405 .31429 Mdot
.406 .33163 Mdot
.407 .34951 Mdot
.408 .36785 Mdot
.409 .38656 Mdot
.41 .40552 Mdot
.411 .4246 Mdot
.412 .44364 Mdot
.413 .46248 Mdot
.414 .48094 Mdot
.415 .49884 Mdot
.416 .51595 Mdot
.417 .53208 Mdot
.418 .54702 Mdot
.419 .56057 Mdot
.42 .57252 Mdot
.421 .58271 Mdot
.422 .59099 Mdot
.423 .59723 Mdot
.424 .60136 Mdot
.425 .60332 Mdot
.426 .60311 Mdot
.427 .60078 Mdot
.428 .59638 Mdot
.429 .59003 Mdot
.43 .58187 Mdot
.431 .57206 Mdot
.432 .56078 Mdot
.433 .54822 Mdot
.434 .53457 Mdot
.435 .52004 Mdot
.436 .50481 Mdot
.437 .48906 Mdot
.438 .47295 Mdot
.439 .45663 Mdot
.44 .44025 Mdot
.441 .4239 Mdot
.442 .4077 Mdot
.443 .39172 Mdot
.444 .37604 Mdot
.445 .36069 Mdot
.446 .34573 Mdot
.447 .33119 Mdot
.448 .31708 Mdot
.449 .30342 Mdot
.45 .29022 Mdot
.451 .27746 Mdot
.452 .26515 Mdot
.453 .25328 Mdot
.454 .24185 Mdot
.455 .23083 Mdot
.456 .22021 Mdot
.457 .21 Mdot
.458 .20016 Mdot
.459 .19069 Mdot
.46 .18157 Mdot
.461 .1728 Mdot
.462 .16437 Mdot
.463 .15626 Mdot
.464 .14848 Mdot
.465 .14101 Mdot
.466 .13386 Mdot
.467 .12701 Mdot
.468 .12048 Mdot
.469 .11426 Mdot
.47 .10835 Mdot
.471 .10276 Mdot
.472 .0975 Mdot
.473 .09256 Mdot
.474 .08796 Mdot
.475 .08371 Mdot
.476 .07982 Mdot
.477 .07629 Mdot
.478 .07314 Mdot
.479 .07038 Mdot
.48 .06803 Mdot
.481 .0661 Mdot
.482 .0646 Mdot
.483 .06356 Mdot
.484 .06297 Mdot
.485 .06286 Mdot
.486 .06325 Mdot
.487 .06415 Mdot
.488 .06558 Mdot
.489 .06755 Mdot
.49 .07008 Mdot
.491 .07319 Mdot
.492 .07688 Mdot
.493 .08118 Mdot
.494 .08611 Mdot
.495 .09166 Mdot
.496 .09787 Mdot
.497 .10474 Mdot
.498 .11229 Mdot
.499 .12053 Mdot
.5 .12947 Mdot
.501 .13911 Mdot
.502 .14947 Mdot
.503 .16056 Mdot
.504 .17236 Mdot
.505 .1849 Mdot
.506 .19815 Mdot
.507 .21212 Mdot
.508 .22679 Mdot
.509 .24214 Mdot
.51 .25814 Mdot
.511 .27476 Mdot
.512 .29197 Mdot
.513 .30969 Mdot
.514 .32787 Mdot
.515 .34643 Mdot
.516 .36527 Mdot
.517 .38429 Mdot
.518 .40337 Mdot
.519 .42236 Mdot
.52 .44112 Mdot
.521 .45948 Mdot
.522 .47726 Mdot
.523 .49429 Mdot
.524 .51035 Mdot
.525 .52527 Mdot
.526 .53885 Mdot
.527 .55092 Mdot
.528 .56132 Mdot
.529 .56989 Mdot
.53 .57653 Mdot
.531 .58116 Mdot
.532 .58371 Mdot
.533 .58419 Mdot
.534 .5826 Mdot
.535 .57902 Mdot
.536 .57353 Mdot
.537 .56625 Mdot
.538 .55733 Mdot
.539 .54693 Mdot
.54 .53523 Mdot
.541 .5224 Mdot
.542 .50864 Mdot
.543 .49411 Mdot
.544 .47901 Mdot
.545 .46347 Mdot
.546 .44767 Mdot
.547 .43172 Mdot
.548 .41576 Mdot
.549 .39988 Mdot
.55 .38418 Mdot
.551 .36874 Mdot
.552 .3536 Mdot
.553 .33884 Mdot
.554 .32448 Mdot
.555 .31056 Mdot
.556 .2971 Mdot
.557 .28412 Mdot
.558 .27162 Mdot
.559 .25963 Mdot
.56 .24814 Mdot
.561 .23715 Mdot
.562 .22666 Mdot
.563 .21667 Mdot
.564 .20718 Mdot
.565 .19818 Mdot
.566 .18968 Mdot
.567 .18166 Mdot
.568 .17414 Mdot
.569 .1671 Mdot
.57 .16055 Mdot
.571 .15449 Mdot
.572 .14892 Mdot
.573 .14386 Mdot
.574 .1393 Mdot
.575 .13525 Mdot
.576 .13172 Mdot
.577 .12872 Mdot
.578 .12626 Mdot
.579 .12435 Mdot
.58 .123 Mdot
.581 .12224 Mdot
.582 .12206 Mdot
.583 .12249 Mdot
.584 .12355 Mdot
.585 .12524 Mdot
.586 .12759 Mdot
.587 .1306 Mdot
.588 .13431 Mdot
.589 .13872 Mdot
.59 .14386 Mdot
.591 .14973 Mdot
.592 .15636 Mdot
.593 .16375 Mdot
.594 .17193 Mdot
.595 .18089 Mdot
.596 .19066 Mdot
.597 .20124 Mdot
.598 .21262 Mdot
.599 .22482 Mdot
.6 .23783 Mdot
.601 .25163 Mdot
.602 .2662 Mdot
.603 .28153 Mdot
.604 .29758 Mdot
.605 .31429 Mdot
.606 .33163 Mdot
.607 .34951 Mdot
.608 .36785 Mdot
.609 .38656 Mdot
.61 .40552 Mdot
.611 .4246 Mdot
.612 .44364 Mdot
.613 .46248 Mdot
.614 .48094 Mdot
.615 .49884 Mdot
.616 .51595 Mdot
.617 .53208 Mdot
.618 .54702 Mdot
.619 .56057 Mdot
.62 .57252 Mdot
.621 .58271 Mdot
.622 .59099 Mdot
.623 .59723 Mdot
.624 .60136 Mdot
.625 .60332 Mdot
.626 .60311 Mdot
.627 .60078 Mdot
.628 .59638 Mdot
.629 .59003 Mdot
.63 .58187 Mdot
.631 .57206 Mdot
.632 .56078 Mdot
.633 .54822 Mdot
.634 .53457 Mdot
.635 .52004 Mdot
.636 .50481 Mdot
.637 .48906 Mdot
.638 .47295 Mdot
.639 .45663 Mdot
.64 .44025 Mdot
.641 .4239 Mdot
.642 .4077 Mdot
.643 .39172 Mdot
.644 .37604 Mdot
.645 .36069 Mdot
.646 .34573 Mdot
.647 .33119 Mdot
.648 .31708 Mdot
.649 .30342 Mdot
.65 .29022 Mdot
.651 .27746 Mdot
.652 .26515 Mdot
.653 .25328 Mdot
.654 .24185 Mdot
.655 .23083 Mdot
.656 .22021 Mdot
.657 .21 Mdot
.658 .20016 Mdot
.659 .19069 Mdot
.66 .18157 Mdot
.661 .1728 Mdot
.662 .16437 Mdot
.663 .15626 Mdot
.664 .14848 Mdot
.665 .14101 Mdot
.666 .13386 Mdot
.667 .12701 Mdot
.668 .12048 Mdot
.669 .11426 Mdot
.67 .10835 Mdot
.671 .10276 Mdot
.672 .0975 Mdot
.673 .09256 Mdot
.674 .08796 Mdot
.675 .08371 Mdot
.676 .07982 Mdot
.677 .07629 Mdot
.678 .07314 Mdot
.679 .07038 Mdot
.68 .06803 Mdot
.681 .0661 Mdot
.682 .0646 Mdot
.683 .06356 Mdot
.684 .06297 Mdot
.685 .06286 Mdot
.686 .06325 Mdot
.687 .06415 Mdot
.688 .06558 Mdot
.689 .06755 Mdot
.69 .07008 Mdot
.691 .07319 Mdot
.692 .07688 Mdot
.693 .08118 Mdot
.694 .08611 Mdot
.695 .09166 Mdot
.696 .09787 Mdot
.697 .10474 Mdot
.698 .11229 Mdot
.699 .12053 Mdot
.7 .12947 Mdot
.701 .13911 Mdot
.702 .14947 Mdot
.703 .16056 Mdot
.704 .17236 Mdot
.705 .1849 Mdot
.706 .19815 Mdot
.707 .21212 Mdot
.708 .22679 Mdot
.709 .24214 Mdot
.71 .25814 Mdot
.711 .27476 Mdot
.712 .29197 Mdot
.713 .30969 Mdot
.714 .32787 Mdot
.715 .34643 Mdot
.716 .36527 Mdot
.717 .38429 Mdot
.718 .40337 Mdot
.719 .42236 Mdot
.72 .44112 Mdot
.721 .45948 Mdot
.722 .47727 Mdot
.723 .49429 Mdot
.724 .51035 Mdot
.725 .52527 Mdot
.726 .53885 Mdot
.727 .55092 Mdot
.728 .56132 Mdot
.729 .56989 Mdot
.73 .57653 Mdot
.731 .58116 Mdot
.732 .58371 Mdot
.733 .58419 Mdot
.734 .5826 Mdot
.735 .57902 Mdot
.736 .57353 Mdot
.737 .56625 Mdot
.738 .55733 Mdot
.739 .54693 Mdot
.74 .53523 Mdot
.741 .5224 Mdot
.742 .50864 Mdot
.743 .49411 Mdot
.744 .47901 Mdot
.745 .46347 Mdot
.746 .44767 Mdot
.747 .43172 Mdot
.748 .41576 Mdot
.749 .39988 Mdot
.75 .38418 Mdot
.751 .36874 Mdot
.752 .3536 Mdot
.753 .33884 Mdot
.754 .32448 Mdot
.755 .31056 Mdot
.756 .2971 Mdot
.757 .28412 Mdot
.758 .27162 Mdot
.759 .25963 Mdot
.76 .24814 Mdot
.761 .23715 Mdot
.762 .22666 Mdot
.763 .21667 Mdot
.764 .20718 Mdot
.765 .19818 Mdot
.766 .18968 Mdot
.767 .18166 Mdot
.768 .17413 Mdot
.769 .1671 Mdot
.77 .16055 Mdot
.771 .15449 Mdot
.772 .14892 Mdot
.773 .14386 Mdot
.774 .1393 Mdot
.775 .13525 Mdot
.776 .13172 Mdot
.777 .12872 Mdot
.778 .12626 Mdot
.779 .12435 Mdot
.78 .123 Mdot
.781 .12224 Mdot
.782 .12206 Mdot
.783 .12249 Mdot
.784 .12355 Mdot
.785 .12524 Mdot
.786 .12758 Mdot
.787 .1306 Mdot
.788 .13431 Mdot
.789 .13872 Mdot
.79 .14386 Mdot
.791 .14973 Mdot
.792 .15636 Mdot
.793 .16375 Mdot
.794 .17193 Mdot
.795 .18089 Mdot
.796 .19066 Mdot
.797 .20124 Mdot
.798 .21262 Mdot
.799 .22482 Mdot
.8 .23783 Mdot
.801 .25163 Mdot
.802 .2662 Mdot
.803 .28153 Mdot
.804 .29758 Mdot
.805 .31429 Mdot
.806 .33163 Mdot
.807 .34951 Mdot
.808 .36785 Mdot
.809 .38656 Mdot
.81 .40552 Mdot
.811 .4246 Mdot
.812 .44364 Mdot
.813 .46248 Mdot
.814 .48094 Mdot
.815 .49884 Mdot
.816 .51595 Mdot
.817 .53208 Mdot
.818 .54702 Mdot
.819 .56057 Mdot
.82 .57252 Mdot
.821 .58271 Mdot
.822 .59099 Mdot
.823 .59723 Mdot
.824 .60136 Mdot
.825 .60332 Mdot
.826 .60311 Mdot
.827 .60078 Mdot
.828 .59638 Mdot
.829 .59003 Mdot
.83 .58187 Mdot
.831 .57206 Mdot
.832 .56078 Mdot
.833 .54822 Mdot
.834 .53457 Mdot
.835 .52004 Mdot
.836 .50481 Mdot
.837 .48906 Mdot
.838 .47295 Mdot
.839 .45663 Mdot
.84 .44025 Mdot
.841 .4239 Mdot
.842 .4077 Mdot
.843 .39172 Mdot
.844 .37604 Mdot
.845 .36069 Mdot
.846 .34574 Mdot
.847 .33119 Mdot
.848 .31708 Mdot
.849 .30342 Mdot
.85 .29022 Mdot
.851 .27746 Mdot
.852 .26515 Mdot
.853 .25328 Mdot
.854 .24185 Mdot
.855 .23083 Mdot
.856 .22021 Mdot
.857 .21 Mdot
.858 .20016 Mdot
.859 .19069 Mdot
.86 .18157 Mdot
.861 .1728 Mdot
.862 .16437 Mdot
.863 .15626 Mdot
.864 .14848 Mdot
.865 .14101 Mdot
.866 .13386 Mdot
.867 .12701 Mdot
.868 .12048 Mdot
.869 .11426 Mdot
.87 .10835 Mdot
.871 .10276 Mdot
.872 .0975 Mdot
.873 .09256 Mdot
.874 .08796 Mdot
.875 .08371 Mdot
.876 .07982 Mdot
.877 .07629 Mdot
.878 .07314 Mdot
.879 .07038 Mdot
.88 .06803 Mdot
.881 .0661 Mdot
.882 .0646 Mdot
.883 .06356 Mdot
.884 .06297 Mdot
.885 .06286 Mdot
.886 .06325 Mdot
.887 .06415 Mdot
.888 .06558 Mdot
.889 .06755 Mdot
.89 .07008 Mdot
.891 .07319 Mdot
.892 .07688 Mdot
.893 .08118 Mdot
.894 .08611 Mdot
.895 .09166 Mdot
.896 .09787 Mdot
.897 .10474 Mdot
.898 .11229 Mdot
.899 .12053 Mdot
.9 .12947 Mdot
.901 .13911 Mdot
.902 .14947 Mdot
.903 .16056 Mdot
.904 .17236 Mdot
.905 .1849 Mdot
.906 .19815 Mdot
.907 .21212 Mdot
.908 .22679 Mdot
.909 .24214 Mdot
.91 .25814 Mdot
.911 .27476 Mdot
.912 .29196 Mdot
.913 .30969 Mdot
.914 .32787 Mdot
.915 .34643 Mdot
.916 .36527 Mdot
.917 .38429 Mdot
.918 .40337 Mdot
.919 .42236 Mdot
.92 .44112 Mdot
.921 .45948 Mdot
.922 .47726 Mdot
.923 .49429 Mdot
.924 .51035 Mdot
.925 .52527 Mdot
.926 .53885 Mdot
.927 .55092 Mdot
.928 .56132 Mdot
.929 .56989 Mdot
.93 .57653 Mdot
.931 .58116 Mdot
.932 .58371 Mdot
.933 .58419 Mdot
.934 .5826 Mdot
.935 .57902 Mdot
.936 .57353 Mdot
.937 .56625 Mdot
.938 .55733 Mdot
.939 .54693 Mdot
.94 .53523 Mdot
.941 .5224 Mdot
.942 .50864 Mdot
.943 .49411 Mdot
.944 .47901 Mdot
.945 .46347 Mdot
.946 .44767 Mdot
.947 .43172 Mdot
.948 .41576 Mdot
.949 .39988 Mdot
.95 .38418 Mdot
.951 .36874 Mdot
.952 .3536 Mdot
.953 .33884 Mdot
.954 .32448 Mdot
.955 .31056 Mdot
.956 .2971 Mdot
.957 .28412 Mdot
.958 .27163 Mdot
.959 .25963 Mdot
.96 .24814 Mdot
.961 .23715 Mdot
.962 .22666 Mdot
.963 .21667 Mdot
.964 .20718 Mdot
.965 .19818 Mdot
.966 .18968 Mdot
.967 .18166 Mdot
.968 .17414 Mdot
.969 .1671 Mdot
.97 .16055 Mdot
.971 .15449 Mdot
.972 .14892 Mdot
.973 .14386 Mdot
.974 .1393 Mdot
.975 .13525 Mdot
.976 .13172 Mdot
.977 .12872 Mdot
.978 .12626 Mdot
.979 .12435 Mdot
.98 .123 Mdot
.981 .12224 Mdot
.982 .12206 Mdot
.983 .12249 Mdot
.984 .12355 Mdot
.985 .12524 Mdot
.986 .12759 Mdot
.987 .1306 Mdot
.988 .13431 Mdot
.989 .13873 Mdot
.99 .14386 Mdot
.991 .14973 Mdot
.992 .15636 Mdot
.993 .16375 Mdot
.994 .17193 Mdot
.995 .18089 Mdot
.996 .19066 Mdot
.997 .20124 Mdot
.998 .21262 Mdot
.999 .22482 Mdot
1 .23783 Mdot
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  CellLabel->"From In[23]:=",
  ImageSize->{288, 177.938},
  ImageMargins->{{0, 0}, {0, 0}},
  ImageRegion->{{0, 1}, {0, 1}},
  ImageCache->GraphicsData["Bitmap", "\<\
CF5dJ6E]HGAYHf4PAg9QL6QYHg<PAVmbKF5d0`40006`00012Q000`40n007h00Ooooo/Ooo003ooona
ool00?oook7oo`00oooo/Ooo003ooonaool00?oook7oo`00oooo/Ooo003ooonaool00?oook7oo`00
G_oo1`001Ooo10001_oo1000=?oo10001_oo10001_oo1000=Ooo0`001_oo10001_oo1000=?oo1000
1_oo10001_oo1000;_oo1`001Ooo10001_oo10001_oo10000_oo001Oool00`00ooooo`02ool00`00
ooooo`03ool01000ooooo`001_oo00@00?ooool003Koo`03003ooooo00Goo`04003ooooo0006ool0
1000ooooo`00=?oo00<00?ooool00P001Ooo00@00?ooool000Koo`04003ooooo000cool20003ool0
0`00ooooo`03ool01000ooooo`001_oo00@00?ooool0037oo`03003ooooo00Koo`04003ooooo0006
ool01000ooooo`001_oo00@00?ooool000;oo`00H?oo00D00?ooooooo`0000Coo`03003ooooo00;o
o`03003ooooo00;oo`03003ooooo00;oo`03003ooooo02ooo`H000Goo`03003ooooo00;oo`03003o
oooo00;oo`03003ooooo00;oo`03003ooooo033oo`03003ooooo00;oo`03003ooooo00;oo`03003o
oooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo033oo`03003ooooo00;oo`03003o
oooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo02koo`03003o
oooo00Goo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03003o
oooo00;oo`40007oo`00HOoo00<00?ooool01Ooo00<00?ooool00_oo00<00?ooool00_oo00<00?oo
ool00_oo00<00?ooool0;ooo00D00?ooooooo`0000Koo`03003ooooo00;oo`03003ooooo00;oo`03
003ooooo00;oo`03003ooooo033oo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03
003ooooo00;oo`03003ooooo00;oo`03003ooooo033oo`8000;oo`8000Coo`03003ooooo00;oo`03
003ooooo00;oo`03003ooooo00;oo`03003ooooo02koo`03003ooooo00Goo`03003ooooo00;oo`03
003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`40007oo`00H_oo0P00
1Ooo00<00?ooool00_oo00<00?ooool00_oo00<00?ooool00_oo00<00?ooool0<?oo00@00?ooool0
00Koo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo033oo`8000;oo`80
00Coo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo03;oo`8000Koo`03
003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo02koo`03003ooooo00Goo`03
003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`40
007oo`00Hooo00<00?ooool00ooo00<00?ooool00_oo00<00?ooool00_oo00<00?ooool00_oo00<0
0?ooool0<?oo00@00?ooool000Koo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;oo`03
003ooooo033oo`03003oo`00008000Goo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;o
o`03003ooooo033oo`8000;oo`8000Coo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;o
o`03003ooooo02koo`03003ooooo00Goo`03003ooooo00;oo`03003ooooo00;oo`03003ooooo00;o
o`03003ooooo00;oo`03003ooooo00;oo`40007oo`00I?oo00<00?ooool00_oo00<00?ooool00_oo
00<00?ooool00_oo00<00?ooool00_oo00<00?ooool0<Ooo00<00?oo00001_oo00<00?ooool00_oo
00<00?ooool00_oo00<00?ooool00_oo00<00?ooool0<?oo00<00?ooool01ooo00<00?ooool00_oo
00<00?ooool00_oo00<00?ooool00_oo00<00?ooool0<?oo00<00?ooool00_oo00<00?ooool00_oo
00<00?ooool00_oo00<00?ooool00_oo00<00?ooool00_oo00<00?ooool0;_oo00<00?ooool01Ooo
00<00?ooool00_oo00<00?ooool00_oo00<00?ooool00_oo00<00?ooool00_oo00<00?ooool00_oo
0@000Ooo001Nool00`00ooooo`03ool00`00ooooo`02ool00`00ooooo`02ool00`00ooooo`02ool0
0`00ooooo`02ool00`00ooooo`0aool00`00ool00006ool00`00ooooo`02ool00`00ooooo`02ool0
0`00ooooo`02ool00`00ooooo`0aool00`00ooooo`06ool00`00ooooo`02ool00`00ooooo`02ool0
0`00ooooo`02ool00`00ooooo`0`ool00`00ooooo`02ool00`00ooooo`02ool00`00ooooo`02ool0
0`00ooooo`02ool00`00ooooo`02ool00`00ooooo`0^ool00`00ooooo`05ool00`00ooooo`02ool0
0`00ooooo`02ool00`00ooooo`02ool00`00ooooo`02ool00`00ooooo`02ool10001ool005koo`80
00?oo`8000Goo`04003ooooo0006ool01000ooooo`00=Ooo0P001ooo00@00?ooool000Koo`04003o
oooo000dool20008ool01000ooooo`001_oo00@00?ooool003?oo`8000;oo`8000Goo`04003ooooo
0006ool01000ooooo`00;_oo0P0000?oo`00ool01ooo00@00?ooool000Koo`04003ooooo0006ool0
1000ooooo`000_oo001Pool30007ool40006ool4000eool20007ool40006ool4000fool30005ool4
0006ool4000dool40006ool40006ool4000`ool20008ool40006ool40006ool40002ool00?oook7o
o`007ooo00<00?ooool0ooooSooo000Oool00`00ooooo`3ooon?ool001ooo`03003ooooo0?ooohoo
o`007ooo00<00?ooool0ooooSooo000Oool00`00ooooo`3ooon?ool001ooool0080001;oo`007ooo
00<00?ooool04?oo00<00?ooool04?oo00<00?ooool04?oo00<00?ooool04Ooo00<00?ooool04?oo
00<00?ooool04?oo00<00?ooool04?oo00<00?ooool04?oo00<00?ooool04?oo00<00?ooool04?oo
00<00?ooool04?oo00<00?ooool04?oo00<00?ooool04?oo00<00?ooool04?oo00<00?ooool04?oo
00<00?ooool04?oo00<00?ooool04?oo00<00?ooool04?oo00<00?ooool04?oo00<00?ooool04Ooo
00<00?ooool04?oo000Oool00`00ooooo`0@ool00`00ooooo`0@ool00`00ooooo`0@ool00`00oooo
o`0Aool00`00ooooo`0@ool00`00ooooo`0@ool00`00ooooo`0@ool00`00ooooo`0@ool00`00oooo
o`0@ool00`00ooooo`0@ool00`00ooooo`0@ool00`00ooooo`0@ool00`00ooooo`0@ool00`00oooo
o`0@ool00`00ooooo`0@ool00`00ooooo`0@ool00`00ooooo`0@ool00`00ooooo`0@ool00`00oooo
o`0@ool00`00ooooo`0Aool00`00ooooo`0@ool001ooo`03003ooooo04[oo`03003ooooo04Woo`03
003ooooo04Woo`03003ooooo04Woo`03003ooooo04[oo`03003ooooo013oo`007ooo00<00?ooool0
ooooSooo000Oool00`00ooooo`3ooon?ool001ooo`03003ooooo0?ooohooo`007ooo00<00?ooool0
ooooSooo000Oool00`00ooooo`3ooon?ool001ooo`<00?ooohooo`007ooo00<00?ooool0ooooSooo
000Oool00`00ooooo`3ooon?ool001ooo`03003ooooo0?ooohooo`007ooo00<00?ooool0ooooSooo
000Oool00`00ooooo`3ooon?ool001ooo`03003ooooo0?ooohooo`007ooo00<00?ooool0ooooSooo
000Oool3003ooon?ool001ooo`03003ooooo01goo`<004Woo`@004Soo`@004Woo`<004Woo`<003go
o`007ooo00<00?ooool07?oo1@00Aooo1@00B?oo1000B?oo1@00Aooo1@00??oo000Oool00`00oooo
o`0Lool50017ool50017ool60017ool200000ooo00000017ool5000lool001ooo`03003ooooo01_o
o`<00004ool000000016ool200001?oo00000000A_oo0P000_oo0P00A_oo0`0000?oo`000000A_oo
0`0000Coo`00000003_oo`007ooo00<00?ooool06ooo0P000ooo0P00AOoo0`000_oo0P00AOoo0`00
0_oo0P00A_oo0P000_oo0`00AOoo0P000ooo0P00>ooo000Oool00`00ooooo`0Kool20003ool20015
ool20003ool30014ool20003ool30014ool30003ool20015ool20003ool2000kool001ooo`03003o
oooo01[oo`<000?oo`8004Coo`<000Coo`8004Coo`8000Coo`8004Coo`8000Coo`8004Coo`<000?o
o`8003_oo`007ooo0`006_oo0P001Ooo0P00@ooo0P001Ooo0P00A?oo0P001?oo0P00A?oo0P001?oo
0P00A?oo0P001Ooo0P00>_oo000Oool00`00ooooo`0Jool20005ool20013ool20005ool20013ool2
0005ool20014ool20004ool20014ool20005ool2000jool001ooo`03003ooooo01Woo`<000Goo`80
04?oo`8000Goo`8004?oo`8000Koo`8004;oo`<000Goo`8004;oo`<000Goo`8003[oo`007ooo00<0
0?ooool06Ooo0P001_oo0P00@ooo0P001Ooo0P00@ooo0P001_oo0P00@_oo0P001_oo0P00@_oo0P00
1_oo0P00>_oo000Oool00`00ooooo`0Iool20006ool20012ool20007ool20012ool20006ool20012
ool20006ool20012ool20006ool2000jool000@000Ooo`8000Goo`L000Koo`03003ooooo01Woo`80
00Koo`8004;oo`8000Ooo`8004;oo`8000Koo`8004;oo`8000Koo`8004;oo`8000Koo`8003[oo`00
00@00?ooool000Ooo`8000Koo`03003ooooo00;oo`03003ooooo00Coo`03003ooooo01Woo`8000Oo
o`80047oo`8000Ooo`80047oo`8000Ooo`80047oo`8000Soo`80047oo`8000Ooo`8003Woo`001?oo
00<00?ooool03Ooo00D00?ooooooo`0000Koo`03003ooooo01Woo`8000Ooo`80047oo`8000Ooo`80
047oo`8000Ooo`80047oo`8000Soo`80047oo`8000Ooo`8003Woo`001?oo00<00?ooool03_oo00<0
0?ooool01ooo10005ooo0P00Booo0P00B_oo0P00B_oo0P00B_oo0P00@ooo0004ool00`00ooooo`0?
ool20007ool00`00ooooo`0Hool20008ool20011ool20007ool20011ool20008ool20010ool20008
ool20010ool20008ool2000iool000Coo`03003ooooo013oo`03003ooooo00Goo`03003ooooo01So
o`8000Soo`80043oo`8000Soo`80043oo`8000Woo`80043oo`8000Soo`80043oo`8000Soo`8003Wo
o`001?oo00<00?ooool04Ooo00<00?ooool01?oo00<00?ooool06?oo0P00B_oo0P00B_oo0P00Booo
0P00B_oo0P00@ooo0004ool00`00ooooo`0;ool00`00ooooo`03ool00`00ooooo`04ool00`00oooo
o`0Hool20009ool2000oool20009ool2000oool20009ool2000oool20009ool20010ool20009ool2
000hool00004003ooooo000>ool20003ool20006ool00`00ooooo`0Hool20009ool2000oool20009
ool2000oool20009ool2000oool20009ool20010ool20009ool2000hool000@0013oo`<000Soo`03
003ooooo0?ooohooo`007ooo00<00?ooool05ooo0P002_oo0P007Ooo0`007_oo0P002_oo0P007_oo
0P007ooo0P002_oo0P007Ooo0P007ooo0P002_oo0P007Ooo0P007ooo0P002_oo0P007Ooo0`006?oo
000Oool3000Gool2000:ool2000Mool3000Nool2000:ool2000Mool4000Nool2000:ool2000Lool4
000Nool2000:ool2000Lool4000Nool2000:ool2000Lool4000Hool001ooo`03003ooooo01Ooo`80
02Soo`D001goo`8002Soo`D001goo`8002Woo`@001koo`8002Soo`D001goo`8002Soo`D001Ooo`00
7ooo00<00?ooool05ooo0P002_oo0P007?oo0P0000?oo`0000007Ooo0P002ooo0P006ooo0P0000?o
o`0000007Ooo0P002ooo0P006ooo1P007Ooo0P002_oo0P006ooo0`0000?oo`0000007Ooo0P002_oo
0P007?oo0P0000?oo`0000005ooo000Oool00`00ooooo`0Sool2000Kool300001?oo00000000:Ooo
0P006ooo0P0000Coo`00000002Woo`8001_oo`8000;oo`8002Woo`8001_oo`8000;oo`8002Woo`80
01_oo`<00004ool00000000Fool001ooo`03003ooooo01Koo`8002Soo`8000?oo`8001coo`8002Oo
o`<000;oo`8001coo`8002Ooo`<000;oo`8001coo`8002Soo`8000;oo`<001_oo`8002Soo`8000?o
o`8001Koo`007ooo00<00?ooool05_oo0P00:?oo0P000ooo0P007?oo0P009ooo0P000ooo0P007?oo
0P009ooo0P000ooo0P007?oo0P00:?oo0P000ooo0P006ooo0P00:?oo0P000ooo0P005_oo000Oool0
0`00ooooo`0Tool2000Jool20003ool2000Yool2000Jool20004ool2000Xool2000Jool20004ool2
000Yool2000Iool20004ool2000Yool2000Jool20003ool2000Fool001ooo`03003ooooo01Koo`80
00coo`8001[oo`8000?oo`8001_oo`8000coo`8001[oo`8000Coo`8001_oo`8000_oo`8001[oo`80
00Coo`8001_oo`8000coo`8001Woo`8000Coo`8001_oo`8000coo`8001[oo`8000?oo`8001Koo`00
7ooo0`005_oo0P009ooo0P001Ooo0P006_oo0P009ooo0P001Ooo0P006ooo0P009ooo0P001?oo0P00
6ooo0P009ooo0P001?oo0P006ooo0P009ooo0P001Ooo0P005Ooo000Oool00`00ooooo`0Fool2000W
ool20005ool2000Jool2000Wool20005ool2000Jool2000Xool20004ool2000Jool2000Xool20004
ool2000Kool2000Wool20005ool2000Eool001ooo`03003ooooo01Koo`8000coo`8001Woo`8000Go
o`8001[oo`8000coo`8001Woo`8000Goo`8001[oo`8000goo`8001Soo`8000Koo`8001Woo`8000go
o`8001Woo`8000Goo`8001[oo`8000coo`8001Woo`8000Goo`8001Goo`007ooo00<00?ooool09?oo
0P006Ooo0P001Ooo0P00:?oo0P006Ooo0P001Ooo0P00:Ooo0P006?oo0P001_oo0P00:?oo0P006Ooo
0P001Ooo0P00:?oo0P006Ooo0P001Ooo0P005Ooo000Oool00`00ooooo`0Eool2000Wool20006ool2
000Jool2000Wool20006ool2000Iool2000Wool20006ool2000Iool2000Wool20006ool2000Iool2
000Wool20006ool2000Eool001ooo`03003ooooo01Goo`8002Ooo`8000Koo`8001[oo`8002Ooo`80
00Koo`8001Woo`8002Ooo`8000Koo`8001Woo`8002Ooo`8000Koo`8001Woo`8002Ooo`8000Koo`80
01Goo`007ooo00<00?ooool09Ooo0P005ooo0P00<Ooo0P005ooo0P00<Ooo0P006?oo0P00<?oo0P00
6?oo0P00<Ooo0P005ooo0P007Ooo000Oool00`00ooooo`0Uool2000Gool20007ool2000Xool2000G
ool20007ool2000Xool2000Hool20006ool2000Xool2000Hool20007ool2000Xool2000Gool20007
ool2000Dool001ooo`<001Goo`80033oo`8001Soo`80033oo`8001Soo`80033oo`8001Woo`80033o
o`8001Soo`80033oo`8001Coo`007ooo00<00?ooool05Ooo0P009ooo0P008Ooo0P009ooo0P008Ooo
0P009ooo0P008_oo0P009_oo0P008_oo0P009ooo0P007Ooo000Oool00`00ooooo`0nool20007ool2
0011ool20007ool20011ool20008ool20010ool20008ool20011ool20007ool2000Dool001ooo`03
003ooooo01Goo`8000koo`8001Koo`8000Soo`8001Soo`8000koo`8001Ooo`8000Ooo`8001Soo`80
00koo`8001Ooo`8000Soo`8001Ooo`8000ooo`8001Koo`8000Soo`8001Soo`8000koo`8001Koo`80
00Soo`8001Coo`007ooo00<00?ooool05Ooo0P003_oo0P005_oo0P008_oo0P003_oo0P005ooo0P00
8Ooo0P003_oo0P005ooo0P008Ooo0P003ooo0P005_oo0P008_oo0P003_oo0P005_oo0P007_oo0004
0007ool20007ool40007ool00`00ooooo`3ooon?ool00004003ooooo0007ool20009ool00`00oooo
o`06ool00`00ooooo`0Dool2000Wool20009ool2000Fool2000Wool20009ool2000Gool2000Vool2
0009ool2000Gool2000Wool20008ool2000Gool2000Wool20009ool2000Cool000Coo`03003ooooo
00_oo`H000Ooo`03003ooooo01Coo`8000ooo`8001Koo`8000Woo`8001Koo`80013oo`8001Goo`80
00Woo`8001Ooo`8000ooo`8001Goo`8000Woo`8001Ooo`8000ooo`8001Koo`8000Soo`8001Ooo`80
00ooo`8001Koo`8000Woo`8001?oo`001?oo00<00?ooool02ooo00D00?ooooooo`0000Soo`@002Co
o`8004_oo`8004[oo`8004[oo`8004[oo`8003Koo`001?oo00<00?ooool03?oo00@00?ooool000So
o`03003ooooo03goo`8004[oo`8004[oo`8004[oo`8004_oo`8001koo`001?oo00<00?ooool03?oo
00@00?ooool000Soo`03003ooooo01Coo`8002Ooo`8000Woo`8001Koo`8002Ooo`8000Woo`8001Ko
o`8002Ooo`8000Woo`8001Ooo`8002Koo`8000[oo`8001Koo`8002Ooo`8000Woo`8001?oo`001?oo
00<00?ooool03Ooo00<00?oo00002?oo00<00?ooool05?oo0P00<_oo0P005_oo0P00<_oo0P005_oo
0P00<_oo0P005ooo0P00<_oo0P005_oo0P00<_oo0P004ooo0004ool00`00ooooo`0=ool00`00ool0
0008ool00`00ooooo`0Vool2000Dool2000dool2000Dool2000dool2000Eool2000cool2000Eool2
000dool2000Dool2000Oool00004003ooooo000Aool20008ool00`00ooooo`0Cool2000Aool2000D
ool2000Rool2000@ool2000Dool2000Rool2000@ool2000Eool2000Qool2000@ool2000Eool2000Q
ool2000Aool2000Dool2000Oool000@0017oo`8000Soo`03003ooooo01?oo`8003?oo`8001Koo`80
03?oo`8001Goo`8003?oo`8001Goo`8003?oo`8001Goo`8003?oo`8001?oo`007ooo00<00?ooool0
B?oo0P00Booo0P00B_oo0P00B_oo0P00B_oo0P004ooo000Oool3000lool2001:ool2001:ool2001;
ool2001:ool2000Oool001ooo`03003ooooo01?oo`8002Ooo`80027oo`8002Ooo`80027oo`8002Oo
o`8002;oo`8002Ooo`80027oo`8002Ooo`8001ooo`007ooo00<00?ooool04ooo0P004Ooo0P008Ooo
0P005?oo0P004Ooo0P008Ooo0P005?oo0P004_oo0P008?oo0P005Ooo0P004Ooo0P008?oo0P005Ooo
0P004Ooo0P008Ooo00<00?ooool04Ooo000Oool00`00ooooo`0Vool2000Cool2000<ool2000Wool2
000Dool2000;ool2000Xool2000Cool2000;ool2000Xool2000Cool2000;ool2000Xool2000Cool2
000<ool00`00ooooo`0Aool001ooo`03003ooooo03_oo`8004_oo`8004[oo`8004[oo`8004[oo`80
023oo`007ooo00<00?ooool04ooo0P00B_oo0P00B_oo0P00B_oo0P00Booo0P00B?oo000Oool00`00
ooooo`0Cool2001:ool2001:ool2001:ool2001;ool20018ool001ooo`03003ooooo02Koo`8001?o
o`8000coo`8002Soo`8001;oo`8000coo`8002Soo`8001?oo`8000coo`8002Ooo`8001?oo`8000co
o`8002Ooo`8001?oo`8000coo`03003ooooo017oo`007ooo0`009_oo0P004ooo0P003?oo0P00:?oo
0P004_oo0P003?oo0P00:?oo0P004ooo0P003?oo0P009ooo0P004ooo0P003?oo0P009ooo0P004ooo
0P003?oo00<00?ooool04Ooo000Oool00`00ooooo`0Bool2001:ool2001;ool2001:ool2001:ool2
0019ool001ooo`03003ooooo01;oo`8004[oo`8004_oo`8004[oo`8004[oo`8004Woo`007ooo00<0
0?ooool0>ooo0P00B_oo0P00B_oo0P00B_oo0P00Booo0P008?oo000Oool00`00ooooo`0kool2000=
ool2000kool2000=ool2000kool2000=ool2000kool2000=ool2000lool2000Pool001ooo`03003o
oooo01;oo`8001?oo`80027oo`8001;oo`8001?oo`80027oo`8001;oo`8001?oo`80027oo`8001?o
o`8001?oo`80023oo`8001?oo`8001?oo`8003Coo`007ooo00<00?ooool04_oo0P004ooo0P00=Ooo
0P004ooo0P00=Ooo0P004ooo0P00=_oo0P004ooo0P00=Ooo0P004ooo0P00=?oo000Oool00`00oooo
o`0jool2001;ool2001:ool2001:ool2001:ool2000Qool001ooo`<003[oo`8004_oo`8004[oo`80
04[oo`8004[oo`80027oo`007ooo0`004Ooo0P00=ooo0P004_oo0P00=_oo0P004_oo0P00=_oo0P00
4_oo0P00=ooo0P004Ooo0P00B_oo000Oool3000Aool2000gool2000Bool2000fool2000Bool2000f
ool2000Bool2000gool2000Aool2001:ool001ooo`03003ooooo02Ooo`8004[oo`8004_oo`8004[o
o`8004[oo`8003Coo`007ooo00<00?ooool09ooo0P004Ooo0P00=ooo0P004Ooo0P00>?oo0P004?oo
0P00>?oo0P004Ooo0P00=ooo0P004Ooo0P008Ooo00040007ool20008ool30007ool00`00ooooo`0j
ool2001:ool2001:ool2001;ool2001:ool2000Qool00004003ooooo0007ool20007ool00`00oooo
o`020006ool3000Aool2000gool2000Aool2000hool2000Aool2000gool2000Aool2000gool2000A
ool2001:ool000Coo`03003ooooo00coo`03003ooooo00;oo`03003ooooo00Coo`<0017oo`8003Oo
o`80017oo`8003Soo`80017oo`8003Ooo`80017oo`8003Ooo`80017oo`8004[oo`001?oo00<00?oo
ool03?oo00<00?ooool00_oo00<00?ooool01?oo1000>Ooo0P00B_oo0P00B_oo0P00B_oo0P00B_oo
0P008_oo0004ool00`00ooooo`0<ool20002ool20006ool00`00ooooo`0jool2001:ool2001:ool2
001:ool2001:ool2000Rool000Coo`03003ooooo00coo`03003oo`00008000Ooo`03003ooooo02So
o`8004[oo`8004[oo`8004[oo`8004_oo`8003?oo`001?oo00<00?ooool03?oo00<00?ooool02Ooo
00<00?ooool04Ooo0P005Ooo0P00<ooo0P005Ooo0P00<ooo0P005Ooo0P00<ooo0P005Ooo0P00=?oo
0P005Ooo0P00<ooo0004ool00`00ooooo`0=ool00`00ooooo`08ool3000Aool2000hool2000@ool2
000hool2000@ool2000hool2000@ool2000hool2000Aool2001:ool00004003ooooo000@ool20009
ool3000iool2000@ool2000hool2000@ool2000iool2000?ool2000iool2000?ool2000iool2000R
ool000@001;oo`<000Koo`03003ooooo03Woo`8004[oo`8004_oo`8004[oo`8004[oo`8002;oo`00
7ooo00<00?ooool0ooooSooo000Oool3000@ool2000Fool2000cool2000Eool2000cool2000Eool2
000cool2000Fool2000bool2000Fool2000cool001ooo`03003ooooo013oo`8001Koo`8003?oo`80
01Goo`8003?oo`8001Goo`8003?oo`8001Koo`8003;oo`8001Koo`8003?oo`007ooo00@00?oo0000
03Soo`80013oo`8003Soo`80013oo`8003Soo`80017oo`8003Ooo`80017oo`8003Soo`8002;oo`00
7ooo00@00?oo000003Soo`80013oo`8003Soo`80013oo`8003Soo`80017oo`8003Ooo`80017oo`80
03Soo`8002;oo`007ooo00<00?ooool0ooooSooo000Oool00`00ooooo`0@ool2001:ool2001:ool2
001;ool2001:ool2001;ool001ooo`03003ooooo013oo`8004[oo`8004[oo`8004_oo`8004[oo`80
04_oo`007ooo00<00?ooool0:?oo0P003_oo0P00>ooo0P003_oo0P00>_oo0P003_oo0P00>_oo0P00
3_oo0P00>_oo0P003_oo0P008ooo000Oool3000Xool2000>ool2000kool2000>ool2000jool2000>
ool2000jool2000>ool2000jool2000>ool2000Sool001ooo`04003oo`00001:ool2001;ool2001:
ool2001:ool2001Lool001ooo`04003oo`00000?ool2000iool2000?ool2000jool2000>ool2000j
ool2000>ool2000jool2000?ool2001;ool001ooo`03003ooooo013oo`8004[oo`8004[oo`8004[o
o`8004_oo`8004_oo`007ooo00<00?ooool0ooooSooo000Oool00`00ooooo`0hool2001:ool2001:
ool2001;ool2001:ool2000Sool001ooo`03003ooooo02Woo`8000goo`8003_oo`8000goo`8003_o
o`8000goo`8003_oo`8000koo`8003_oo`8000goo`8002?oo`007ooo00<00?ooool00P003Ooo0P00
6?oo0P008Ooo0P003Ooo0P006?oo0P008Ooo0P003_oo0P005ooo0P008Ooo0P003_oo0P005ooo0P00
8_oo0P003Ooo0P006?oo0P00<_oo000Oool5000=ool2000kool2000=ool2000kool2000>ool2000j
ool2000>ool2000kool2000=ool2001<ool001ooo`03003ooooo0?ooohooo`007ooo00<00?ooool0
>?oo0P00B_oo0P00B_oo0P00B_oo0P00Booo0P008ooo000Oool00`00ooooo`0hool2001:ool2001:
ool2001:ool2001;ool2000Sool001ooo`03003ooooo0?ooohooo`0010001ooo0P001ooo10001ooo
00<00?ooool03ooo0P006?oo0P00<?oo0P006?oo0P00<?oo0P006Ooo0P00<?oo0P006?oo0P00<?oo
0P006?oo0P00<_oo00001000ooooo`001ooo0P001_oo0P000ooo00<00?ooool01?oo00<00?ooool0
0P003Ooo0P006?oo0P008Ooo0P003Ooo0P006?oo0P008Ooo0P003Ooo0P006Ooo0P008Ooo0P003Ooo
0P006?oo0P008Ooo0P003Ooo0P006?oo0P00<_oo0004ool00`00ooooo`0<ool00`00ooooo`02ool0
0`00ooooo`04ool00`00ooooo`02001:ool2001:ool2001;ool2001:ool2001Kool000Coo`03003o
oooo00coo`8000;oo`8000Koo`@003Koo`8004[oo`8004_oo`8004[oo`8004[oo`8002Coo`001?oo
00<00?ooool03_oo0P002?oo00<00?ooool0=ooo0P00B_oo0P00Booo0P00B_oo0P00B_oo0P009?oo
0004ool00`00ooooo`0<ool20002ool20006ool00`00ooooo`0>ool2001;ool2001:ool2001:ool2
001:ool2001=ool000Coo`03003ooooo00coo`03003ooooo00;oo`03003ooooo00Coo`03003ooooo
00koo`8004_oo`8004[oo`8004[oo`8004[oo`8004goo`001?oo00<00?ooool03?oo00<00?ooool0
0_oo00<00?ooool01?oo00<00?ooool0:Ooo0P00Booo0P00B_oo0P00B_oo0P00B_oo0P00<_oo0000
1000ooooo`003ooo0P000_oo0P001_oo00<00?ooool00P009ooo0P003?oo0P005?oo0P009ooo0P00
2ooo0P005?oo0P009ooo0P002ooo0P005?oo0P009ooo0P003?oo0P004ooo0P009ooo0P003?oo0P00
9?oo0004000@ool40007ool00`00ooooo`02000eool2000Dool2000dool2000Dool2000dool2000D
ool2000eool2000Cool2000eool2000Tool001ooo`03003ooooo0?ooohooo`007ooo0`003_oo0P00
B_oo0P00Booo0P00B_oo0P00B_oo0P00COoo000Oool00`00ooooo`0>ool2001:ool2001;ool2001:
ool2001:ool2001=ool001ooo`03003ooooo0?ooohooo`007ooo00<00?ooool0:_oo0P002_oo0P00
?_oo0P002ooo0P00?Ooo0P002ooo0P00?_oo0P002_oo0P00?_oo0P002_oo0P009Ooo000Oool01000
oooooooo0P009ooo0P002_oo0P005Ooo0P009ooo0P002ooo0P005?oo0P009ooo0P002ooo0P005?oo
0P00:?oo0P002_oo0P005Ooo0P009ooo0P002_oo0P009Ooo000Oool01000oooooooo0P00B_oo0P00
B_oo0P00B_oo0P00Booo0P00F_oo000Oool00`00ooooo`0>ool2001:ool2001:ool2001:ool2001;
ool2001=ool001ooo`03003ooooo00koo`8004[oo`8004[oo`8004[oo`8004_oo`8004goo`007ooo
00<00?ooool0ooooSooo000Oool3000fool2001:ool2001;ool2001:ool2001:ool2000Uool001oo
o`03003ooooo03Koo`8004[oo`8004_oo`8004[oo`8004[oo`8002Goo`007ooo00@00?ooooooo`80
02Ooo`80027oo`8002Soo`80027oo`8002Ooo`80027oo`8002Ooo`80027oo`8002Ooo`80037oo`00
7ooo00@00?ooooooo`8000[oo`8001_oo`80027oo`8000_oo`8001_oo`80027oo`8000[oo`8001_o
o`80027oo`8000[oo`8001_oo`80027oo`8000[oo`8001_oo`80037oo`007ooo00<00?ooool03Ooo
0P00Booo0P00B_oo0P00B_oo0P00B_oo0P00C_oo000Oool00`00ooooo`3ooon?ool001ooo`03003o
oooo03Koo`8004[oo`8004[oo`8004[oo`8004_oo`8002Goo`007ooo00<00?ooool0=_oo0P00B_oo
0P00B_oo0P00B_oo0P00Booo0P009Ooo000Oool3003ooon?ool001ooo`03003ooooo00goo`8001co
o`8002coo`8001coo`8002coo`8001coo`8002goo`8001_oo`8002goo`8001coo`80033oo`007ooo
00@00?ooooooo`8000[oo`8001coo`80027oo`8000Woo`8001coo`80027oo`8000Woo`8001coo`80
027oo`8000[oo`8001_oo`80027oo`8000[oo`8001coo`80033oo`007ooo00@00?ooooooo`8004_o
o`8004[oo`8004[oo`8004[oo`8005[oo`007ooo00<00?ooool0=Ooo0P00Booo0P00B_oo0P00B_oo
0P00B_oo0P009_oo000Bool70006ool00`00ooooo`0eool2001;ool2001:ool2001:ool2001:ool2
000Vool001Goo`03003ooooo00Ooo`03003ooooo0?ooohooo`005Ooo00<00?ooool01ooo00<00?oo
ool0ooooSooo000Eool00`00ooooo`07ool4000<ool2000Lool2000/ool2000Lool2000/ool2000M
ool2000[ool2000Mool2000/ool2000Lool2000`ool001Goo`03003ooooo00Ooo`03003ooooo00;o
o`8000Woo`8001coo`80027oo`8000Woo`8001coo`80027oo`8000Woo`8001goo`80027oo`8000So
o`8001goo`80027oo`8000Woo`8001coo`80033oo`005Ooo00<00?ooool01ooo00<00?ooool00_oo
0P00B_oo0P00B_oo0P00Booo0P00B_oo0P00FOoo000Eool00`00ooooo`07ool00`00ooooo`0eool2
001:ool2001:ool2001;ool2001:ool2000Vool001Goo`03003ooooo00Ooo`03003ooooo03Goo`80
04[oo`8004[oo`8004_oo`8004[oo`8002Koo`004_oo0P0000?oo`00ool02?oo00<00?ooool0oooo
Sooo000Dool20009ool00`00ooooo`0<ool2001:ool2001;ool2001:ool2001:ool2001?ool001oo
o`03003ooooo00coo`8001goo`8002_oo`8001koo`8002_oo`8001goo`8002_oo`8001goo`8002_o
o`8001goo`80033oo`007ooo0`000_oo0P009ooo0P008Ooo0P00:?oo0P008Ooo0P009ooo0P008Ooo
0P009ooo0P008Ooo0P009ooo0P00<?oo000Oool00`00ooooo`02ool2000aool2000Gool2000aool2
000Hool2000`ool2000Hool2000`ool2000Hool2000aool2000Vool001ooo`03003ooooo03Goo`80
04[oo`8004[oo`8004[oo`8004_oo`8002Koo`007ooo00<00?ooool0ooooSooo000Oool00`00oooo
o`0<ool2001:ool2001:ool2001:ool2001;ool2001?ool001ooo`03003ooooo00coo`8004[oo`80
04[oo`8004[oo`8004_oo`8004ooo`007ooo00<00?ooool0;?oo0P001_oo0P00@_oo0P001_oo0P00
@_oo0P001ooo0P00@_oo0P001_oo0P00@_oo0P001_oo0P009ooo000Oool00`00ooooo`03ool2000W
ool20006ool2000Iool2000Wool20006ool2000Iool2000Wool20007ool2000Hool2000Xool20006
ool2000Iool2000Wool20006ool2000Wool001ooo`<000?oo`8004[oo`8004[oo`8004[oo`8004_o
o`8005Soo`007ooo00<00?ooool0ooooSooo000Oool00`00ooooo`0;ool2001;ool2001:ool2001:
ool2001:ool2001@ool001ooo`03003ooooo00_oo`8004_oo`8004[oo`8004[oo`8004[oo`80053o
o`007ooo00<00?ooool0;?oo0P001_oo0P00@_oo0P001_oo0P00@ooo0P001Ooo0P00@ooo0P001_oo
0P00@_oo0P001_oo0P009ooo000Oool00`00ooooo`0/ool20006ool20012ool20006ool20013ool2
0005ool20013ool20006ool20012ool20006ool2000Wool001ooo`03003ooooo00?oo`8004[oo`80
04[oo`8004_oo`8004[oo`8005Soo`007ooo00<00?ooool00ooo0P00B_oo0P00B_oo0P00Booo0P00
B_oo0P00F?oo000Oool3000;ool2001:ool2001:ool2001;ool2001:ool2001@ool001ooo`03003o
oooo00_oo`8004[oo`8004[oo`8004_oo`8004[oo`80053oo`007ooo00<00?ooool0;Ooo0P001?oo
0P00A?oo0P001Ooo0P00@ooo0P001Ooo0P00@ooo0P001Ooo0P00A?oo0P001?oo0P00:?oo000Oool0
0`00ooooo`0]ool20004ool20014ool20005ool20013ool20005ool20013ool20005ool20014ool2
0004ool2000Xool001ooo`03003ooooo0?ooohooo`001@001_oo0P001Ooo1`001_oo00<00?ooool0
0ooo0P00Booo0P00B_oo0P00B_oo0P00B_oo0P00F?oo00000ooo003oo`08ool20006ool00`00oooo
o`02ool00`00ooooo`04ool00`00ooooo`03ool20006ool20013ool20005ool20013ool20005ool2
0013ool20005ool20013ool20006ool2001@ool00003ool00?oo017oo`05003oooooool00006ool0
0`00ooooo`0;ool2000Vool2000Rool2000Vool2000Rool2000Wool2000Qool2000Wool2000Rool2
000Vool2000Xool00003ool00?oo01;oo`03003ooooo00Ooo`@002coo`8000Coo`8004Coo`8000Co
o`8004Coo`8000Goo`8004Coo`8000Coo`8004Coo`8000Coo`8002Soo`0000?oo`00ool04ooo0P00
1ooo00<00?ooool0;Ooo0P00B_oo0P00B_oo0P00Booo0P00B_oo0P00;_oo00000ooo003oo`0Dool0
0`00ooooo`05ool00`00ooooo`3ooon?ool00003ool00?oo01Goo`03003ooooo00Coo`03003ooooo
00Coo`8004[oo`8004[oo`8004[oo`8004_oo`8005Ooo`0000?oo`00ool03ooo00<00?ooool00ooo
00<00?ooool01?oo00<00?ooool01?oo0P001?oo0P009ooo0P006ooo0P001?oo0P009ooo0P006ooo
0P001Ooo0P009_oo0P006ooo0P001Ooo0P009_oo0P007?oo0P001?oo0P009ooo0P00:?oo00000ooo
003oo`0?ool20003ool20006ool00`00ooooo`0:ool2000Qool20004ool2000Qool2000Rool20003
ool2000Rool2000Qool20003ool2000Rool2000Qool20003ool2000Rool2000Qool20004ool2000X
ool0008001;oo`<000Soo`03003ooooo02goo`8004_oo`8004[oo`8004[oo`8004[oo`8002koo`00
7ooo00<00?ooool0ooooSooo000Oool30004ool2000/ool2000Lool2000]ool2000Lool2000/ool2
000Lool2000/ool2000Lool2000/ool2000Yool001ooo`03003ooooo00Coo`8000Coo`8002Koo`80
01coo`8000Coo`8002Ooo`8001coo`8000?oo`8002Ooo`8001coo`8000Coo`8002Koo`8001coo`80
00Coo`8002Koo`8002Woo`007ooo00<00?ooool02_oo0P008_oo0P009_oo0P008_oo0P009_oo0P00
8_oo0P009ooo0P008Ooo0P009ooo0P008_oo0P00;Ooo000Oool00`00ooooo`0^ool2001:ool2001:
ool2001:ool2001;ool2000]ool001ooo`03003ooooo03;oo`8004[oo`8004[oo`8004_oo`8004[o
o`8002Woo`007ooo00<00?ooool0<_oo0P00B_oo0P00B_oo0P00Booo0P00B_oo0P00:Ooo000Oool0
0`00ooooo`05ool20002ool2000Sool2000Qool20003ool2000Rool2000Qool20003ool2000Sool2
000Pool20003ool2000Sool2000Pool20003ool2000Sool2000]ool001ooo`03003ooooo00Goo`80
00;oo`8002?oo`80027oo`8000?oo`8002;oo`80027oo`8000?oo`8002?oo`80023oo`8000?oo`80
02?oo`80023oo`8000?oo`8002?oo`8002goo`007ooo0`00<Ooo0P00Booo0P00B_oo0P00B_oo0P00
B_oo0P00:_oo000Oool00`00ooooo`0^ool200000ooo00000018ool200000ooo00000017ool20000
0ooo00000017ool200000ooo00000017ool200000ooo0000000Zool001ooo`03003ooooo00Goo`80
00;oo`8002?oo`80027oo`8000;oo`8002Coo`80023oo`8000?oo`8002?oo`80027oo`8000;oo`80
02?oo`80027oo`8000;oo`8002?oo`8002goo`007ooo00<00?ooool01Ooo0P000_oo0P009_oo0P00
7_oo0P000_oo0P009_oo0P007_oo0P000ooo0P009_oo0P007_oo0P000_oo0P009_oo0P007_oo0P00
0_oo0P009_oo0P00:_oo000Oool00`00ooooo`0_ool40018ool40018ool200000ooo00000018ool4
0018ool4000Zool001ooo`03003ooooo02ooo`@004Soo`@004Soo`@004Woo`<004Woo`@002[oo`00
7ooo00<00?ooool01Ooo0P000_oo0P009?oo10007ooo0P0000?oo`0000009?oo10007ooo0P0000?o
o`0000009Ooo0`007ooo0P0000?oo`0000009Ooo0`007ooo0P000_oo0P009?oo1000:_oo000Oool0
0`00ooooo`05ool20002ool2000Uool2000Pool200000ooo0000000Uool3000Oool200000ooo0000
000Uool3000Oool200000ooo0000000Uool3000Oool20002ool2000Uool2000[ool001ooo`<0033o
o`8004[oo`8004[oo`8004_oo`8004[oo`8002_oo`007ooo00<00?ooool01_oo1000B?oo0P0000?o
o`000000Aooo0P0000?oo`000000Aooo0P0000?oo`000000B?oo1000Dooo000Oool00`00ooooo`06
ool40018ool200000ooo00000017ool200000ooo00000017ool200000ooo00000018ool4001Cool0
01ooo`03003ooooo00Soo`8004[oo`8004[oo`8004_oo`8004[oo`8005?oo`007ooo00<00?ooool0
1_oo1000B?oo1000BOoo0`00BOoo1000B?oo1000Dooo00050006ool20007ool40007ool00`00oooo
o`06ool40018ool40019ool30019ool30019ool4001Cool00003ool00?oo00Soo`8000Woo`03003o
oooo00Koo`03003ooooo00Koo`@004Woo`<004Woo`<004Woo`<004Woo`@005?oo`0000?oo`00ool0
3ooo1P001ooo00<00?ooool01ooo0P00B_oo0P00B_oo0`00B_oo0P00B_oo0P00E?oo00000ooo003o
o`0?ool01@00oooooooo00002?oo1000ooooS_oo00000ooo003oo`0@ool01000ooooo`002?oo00<0
0?ooool0ooooSooo00000ooo003oo`0@ool01000ooooo`002?oo00<00?ooool0ooooSooo00000ooo
003oo`0Aool00`00ool00008ool00`00ooooo`3ooon?ool00003ool00?oo017oo`03003oo`0000So
o`03003ooooo0?ooohooo`0000?oo`00ool04_oo0P00ooooV_oo0002000Cool2003ooonJool00?oo
ok7oo`00oooo/Ooo003ooonaool00?oook7oo`00oooo/Ooo003ooonaool00?oook7oo`00oooo/Ooo
0000\
\>"],
  ImageRangeCache->{{{109, 396}, {502.688, 325.75}} -> {-512.851, 2.87541, \
3.93973, 0.00931871}}],

Cell[BoxData[
    TagBox[\(\[SkeletonIndicator]  Graphics  \[SkeletonIndicator]\),
      False,
      Editable->False]], "Output",
  CellLabel->"Out[23]="]
}, Open  ]],

Cell["\<\
The basic command is Fourier.  FourierParameters chooses a \
particular conention for defining the transform.  Abs takes the magnitude of \
the resulting complex number (which we then square).  \
\>", "Text"],

Cell[BoxData[
    \(\(transform\  = \ 
        Abs[Fourier[SamplePts, 
              FourierParameters \[Rule] {\(-1\), 1}]]^2;\)\)], "Input",
  CellLabel->"In[24]:="],

Cell[BoxData[
    \(\(frequencies = 
        Table[\((2  Pi/SampleTime)\)*i, {i, 0, numpoints}];\)\)], "Input",
  CellLabel->"In[25]:="],

Cell["\<\
Transpose to make pairs of points from two separate lists of \
points.\
\>", "Text"],

Cell[BoxData[
    \(\(PlotPts\  = \ Transpose[{frequencies, transform}];\)\)], "Input",
  CellLabel->"In[26]:="],

Cell["\<\
We load Graphics in case we want to do a LogListPlot (try \
it).\
\>", "Text"],

Cell[BoxData[
    \(<< Graphics`Graphics`\)], "Input",
  CellLabel->"In[27]:="],

Cell[CellGroupData[{

Cell[BoxData[
    \(LogListPlot[PlotPts, PlotJoined \[Rule] True, 
      PlotRange \[Rule] {{0, 2}, {0.001,  .1}}, 
      TextStyle \[Rule] {FontFamily \[Rule] "\<Times\>", 
          FontSize \[Rule] 14}, 
      ImageSize \[Rule] {400, 300}, \[IndentingNewLine]PlotLabel \[Rule] 
        StyleForm["\<Power Spectrum\>"], AxesOrigin \[Rule] Automatic, 
      AxesLabel \[Rule] {"\<freq.\>", "\<power\>"}]\)], "Input",
  CellLabel->"In[28]:="],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .61803 
%%ImageSize: 400 300 
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 0.5 0.927051 0.309017 [
[.125 -0.0125 -14.25 -14.625 ]
[.125 -0.0125 14.25 0 ]
[.25 -0.0125 -10.75 -14.625 ]
[.25 -0.0125 10.75 0 ]
[.375 -0.0125 -14.25 -14.625 ]
[.375 -0.0125 14.25 0 ]
[.5 -0.0125 -5.5 -14.5 ]
[.5 -0.0125 5.5 0 ]
[.625 -0.0125 -14.25 -14.625 ]
[.625 -0.0125 14.25 0 ]
[.75 -0.0125 -10.75 -14.625 ]
[.75 -0.0125 10.75 0 ]
[.875 -0.0125 -14.25 -14.625 ]
[.875 -0.0125 14.25 0 ]
[1 -0.0125 -5.5 -14.5 ]
[1 -0.0125 5.5 0 ]
[1.025 0 0 -7.25 ]
[1.025 0 29.9375 7.25 ]
[-0.0125 .09302 -35.5 -7.25 ]
[-0.0125 .09302 0 7.25 ]
[-0.0125 .21599 -35.5 -7.3125 ]
[-0.0125 .21599 0 7.3125 ]
[-0.0125 .30902 -28.5 -7.25 ]
[-0.0125 .30902 0 7.25 ]
[-0.0125 .40204 -28.5 -7.25 ]
[-0.0125 .40204 0 7.25 ]
[-0.0125 .52501 -28.5 -7.3125 ]
[-0.0125 .52501 0 7.3125 ]
[-0.0125 .61803 -21.5 -7.25 ]
[-0.0125 .61803 0 7.25 ]
[0 .64303 -19.4688 0 ]
[0 .64303 19.4688 14.5 ]
[.5 .63053 -48.3438 0 ]
[.5 .63053 48.3438 14.5 ]
[ -0.0005 0 0 0 ]
[ 1 .61803 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.125 0 m
.125 .00625 L
s
gsave
.125 -0.0125 -75.25 -18.625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.25) show
1.000 setlinewidth
grestore
.25 0 m
.25 .00625 L
s
gsave
.25 -0.0125 -71.75 -18.625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.5) show
1.000 setlinewidth
grestore
.375 0 m
.375 .00625 L
s
gsave
.375 -0.0125 -75.25 -18.625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.75) show
1.000 setlinewidth
grestore
.5 0 m
.5 .00625 L
s
gsave
.5 -0.0125 -66.5 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1) show
1.000 setlinewidth
grestore
.625 0 m
.625 .00625 L
s
gsave
.625 -0.0125 -75.25 -18.625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1.25) show
1.000 setlinewidth
grestore
.75 0 m
.75 .00625 L
s
gsave
.75 -0.0125 -71.75 -18.625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1.5) show
1.000 setlinewidth
grestore
.875 0 m
.875 .00625 L
s
gsave
.875 -0.0125 -75.25 -18.625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1.75) show
1.000 setlinewidth
grestore
1 0 m
1 .00625 L
s
gsave
1 -0.0125 -66.5 -18.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(2) show
1.000 setlinewidth
grestore
.125 Mabswid
.025 0 m
.025 .00375 L
s
.05 0 m
.05 .00375 L
s
.075 0 m
.075 .00375 L
s
.1 0 m
.1 .00375 L
s
.15 0 m
.15 .00375 L
s
.175 0 m
.175 .00375 L
s
.2 0 m
.2 .00375 L
s
.225 0 m
.225 .00375 L
s
.275 0 m
.275 .00375 L
s
.3 0 m
.3 .00375 L
s
.325 0 m
.325 .00375 L
s
.35 0 m
.35 .00375 L
s
.4 0 m
.4 .00375 L
s
.425 0 m
.425 .00375 L
s
.45 0 m
.45 .00375 L
s
.475 0 m
.475 .00375 L
s
.525 0 m
.525 .00375 L
s
.55 0 m
.55 .00375 L
s
.575 0 m
.575 .00375 L
s
.6 0 m
.6 .00375 L
s
.65 0 m
.65 .00375 L
s
.675 0 m
.675 .00375 L
s
.7 0 m
.7 .00375 L
s
.725 0 m
.725 .00375 L
s
.775 0 m
.775 .00375 L
s
.8 0 m
.8 .00375 L
s
.825 0 m
.825 .00375 L
s
.85 0 m
.85 .00375 L
s
.9 0 m
.9 .00375 L
s
.925 0 m
.925 .00375 L
s
.95 0 m
.95 .00375 L
s
.975 0 m
.975 .00375 L
s
.25 Mabswid
0 0 m
1 0 L
s
gsave
1.025 0 -61 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(freq) show
85.438 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(.) show
88.938 14.500 moveto
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 .09302 m
.00625 .09302 L
s
gsave
-0.0125 .09302 -96.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.002) show
94.500 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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 .21599 m
.00625 .21599 L
s
gsave
-0.0125 .21599 -96.5 -11.3125 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.005) show
94.500 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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 .30902 m
.00625 .30902 L
s
gsave
-0.0125 .30902 -89.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.01) show
87.500 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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 .40204 m
.00625 .40204 L
s
gsave
-0.0125 .40204 -89.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.02) show
87.500 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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 .52501 m
.00625 .52501 L
s
gsave
-0.0125 .52501 -89.5 -11.3125 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.625 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.05) show
87.500 14.625 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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 .61803 m
.00625 .61803 L
s
gsave
-0.0125 .61803 -82.5 -11.25 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.1) show
80.500 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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
.001 w
0 .14744 m
.00375 .14744 L
s
0 .18605 m
.00375 .18605 L
s
0 .24046 m
.00375 .24046 L
s
0 .26115 m
.00375 .26115 L
s
0 .27907 m
.00375 .27907 L
s
0 .29488 m
.00375 .29488 L
s
0 .45646 m
.00375 .45646 L
s
0 .49506 m
.00375 .49506 L
s
0 .54948 m
.00375 .54948 L
s
0 .57017 m
.00375 .57017 L
s
0 .58809 m
.00375 .58809 L
s
0 .60389 m
.00375 .60389 L
s
.25 Mabswid
0 0 m
0 .61803 L
s
gsave
0 .64303 -80.4688 -4 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(power) show
97.938 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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
.5 .63053 -109.344 -4 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 22.5 translate 1 -1 scale
/g { setgray} bind def
/k { setcmykcolor} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/rL { rlineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/S { show} bind def
/N {currentpoint 3 -1 roll show moveto} bind def
/Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def
/m { moveto} bind def
/Mr { rmoveto} bind def
/Mx {currentpoint exch pop moveto} bind def
/My {currentpoint pop exch moveto} bind def
/X {0 rmoveto} bind def
/Y {0 exch rmoveto} bind def
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(Power) show
102.188 14.500 moveto
(Spectrum) show
155.688 14.500 moveto
%%IncludeResource: font Times-Roman
%%IncludeFont: Times-Roman
/Times-Roman findfont 14.000 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
.5 Mabswid
.00073 .61803 m
.00296 0 L
s
.24874 0 m
.25 .1885 L
s
.25 .1885 m
.25139 0 L
s
.49529 0 m
.5 .58385 L
s
.5 .58385 m
.50473 0 L
s
.74946 0 m
.75 .0643 L
s
.75 .0643 m
.7506 0 L
s
.99894 0 m
1 .11075 L
s
1 .11075 m
1 .11075 L
s
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  CellLabel->"From In[28]:=",
  ImageSize->{400, 300},
  ImageCache->GraphicsData["Bitmap", "\<\
CF5dJ6E]HGAYHf4PAg9QL6QYHg<PAVmbKF5d0`40009H0001`Q000`40n007h00OooooooooF_oo003o
oooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00oooooooo
F_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00
ooooooooF_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooo
oe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool0
0?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooo
oomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo
003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00oooo
ooooF_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[o
o`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oo
oooooe[oo`00ooooooooF_oo001Yool40005ool30003ool90004ool6000Oool40005ool30004ool6
000Qool40005ool30006ool20008ool6000Vool8000Wool80003ool30003ool90004ool6000Nool8
0003ool30004ool6000Oool80003ool30006ool20008ool6000Tool9000fool006Soo`8000;oo`80
00Coo`<000?oo`T000?oo`<000?oo`8001goo`8000;oo`8000Coo`<000?oo`<000?oo`8001ooo`80
00;oo`8000Coo`<000Koo`8000Ooo`<000?oo`8002Soo`8002goo`8000Koo`<000?oo`T000?oo`<0
00?oo`80023oo`8000Koo`<000?oo`<000?oo`80027oo`8000Koo`<000Koo`8000Ooo`<000?oo`80
02?oo`T003Koo`00Iooo0P001?oo0P002_oo00<00?ooool02?oo0P001Ooo0P006ooo0P001?oo0P00
2Ooo0P001Ooo0P007Ooo0P001?oo0P003?oo0P001ooo0P001Ooo0P009ooo0P00;Ooo0P003Ooo00<0
0?ooool02?oo0P001Ooo0P007ooo0P003?oo0P001Ooo0P008?oo0P003ooo0P001ooo0P001Ooo0P00
8ooo00<00?ooool0>ooo001Wool00`00ooooo`04ool00`00ooooo`09ool00`00ooooo`07ool00`00
ooooo`04ool2000Kool00`00ooooo`04ool00`00ooooo`07ool00`00ooooo`04ool2000Mool00`00
ooooo`04ool00`00ooooo`0:ool20007ool00`00ooooo`04ool2000Wool2000]ool2000>ool00`00
ooooo`07ool00`00ooooo`04ool2000Oool2000<ool00`00ooooo`04ool2000Pool2000?ool20007
ool00`00ooooo`04ool2000Tool00`00ooooo`0jool006Koo`8000Koo`8000_oo`03003ooooo00go
o`8001[oo`8000Koo`8000ooo`8001coo`8000Koo`8000coo`03003ooooo00coo`8002Ooo`8002go
o`8000ooo`03003ooooo00goo`8001ooo`8001?oo`80023oo`80013oo`03003ooooo00coo`8002Go
o`03003ooooo03Woo`00I_oo0P001_oo0P003?oo00<00?ooool03?oo0P006_oo0P001_oo0P003ooo
0P007?oo0P001_oo0P003?oo0P003Ooo0P009ooo0P00;Ooo0P004?oo00<00?ooool03?oo0P007ooo
0P004ooo0P008?oo0P004?oo0P003Ooo0P009_oo00<00?ooool0>?oo001Vool20006ool2000=ool0
0`00ooooo`0;ool2000Jool20006ool2000?ool2000Lool20006ool2000=ool00`00ooooo`0;ool2
000Wool2000]ool2000Aool00`00ooooo`0;ool2000Oool2000Cool2000Pool2000Aool00`00oooo
o`0;ool2000Wool00`00ooooo`0gool006Koo`8000Koo`8000koo`03003ooooo00Coo`8000?oo`80
01_oo`8000Koo`8000Woo`8000?oo`8001goo`8000Koo`8000goo`03003ooooo00Goo`8000?oo`80
02Soo`8002goo`8001;oo`03003ooooo00Coo`8000?oo`80023oo`8000goo`8000?oo`80027oo`80
017oo`03003ooooo00Goo`8000?oo`8002Woo`03003ooooo03Koo`00I_oo0P001_oo0P003_oo0P00
1Ooo00<00?oo00000`007?oo0P001_oo0P002Ooo00<00?oo00000`007_oo0P001_oo0P003_oo00<0
0?ooool01?oo00<00?oo00000`00:Ooo0P00;Ooo0P004_oo0P001Ooo00<00?oo00000`008Ooo0P00
3Ooo00<00?oo00000`008_oo0P004_oo00<00?ooool01?oo00<00?oo00000`00:_oo0P00=ooo001V
ool20006ool2000?ool20004ool00`00ooooo`0Oool20006ool20009ool00`00ooooo`0Qool20006
ool2000>ool00`00ooooo`04ool00`00ooooo`0/ool2000]ool2000Cool20004ool00`00ooooo`0T
ool2000=ool00`00ooooo`0Uool2000Bool00`00ooooo`04ool00`00ooooo`0^ool2000fool006Ko
o`8000Koo`8000ooo`8000Coo`03003ooooo01ooo`8000Koo`8000Woo`03003ooooo027oo`8000Ko
o`8000ooo`03003ooooo00?oo`03003ooooo02coo`8002goo`8001?oo`8000Coo`03003ooooo02Co
o`8000goo`03003ooooo02Goo`8001?oo`03003ooooo00?oo`03003ooooo02koo`8003Koo`00Iooo
00<00?ooool01?oo00<00?ooool01ooo0P001Ooo0P001?oo00<00?ooool08?oo00<00?ooool01?oo
00<00?ooool02?oo00<00?ooool08_oo00<00?ooool01?oo00<00?ooool03ooo00<00?ooool00_oo
00<00?ooool0;?oo0P00;Ooo0P003?oo0P001Ooo0P001?oo00<00?ooool09?oo0P003Ooo00<00?oo
ool09Ooo0P005?oo00<00?ooool00_oo00<00?ooool09ooo0P001Ooo0P00=_oo001Wool20004ool2
000:ool20004ool20004ool00`00ooooo`0Pool20004ool2000:ool00`00ooooo`0Rool20004ool2
0009ool00`00ooooo`05ool00`00ooooo`02ool00`00ooooo`0/ool2000]ool2000=ool20004ool2
0004ool00`00ooooo`0Tool2000=ool00`00ooooo`0Uool2000<ool00`00ooooo`05ool00`00oooo
o`02ool00`00ooooo`0Xool20004ool2000]ool60003ool006Soo`8000;oo`8000_oo`8000?oo`80
00Goo`L001goo`8000;oo`8000_oo`L001ooo`8000;oo`8000[oo`X000?oo`L002Koo`@002_oo`@0
00goo`8000?oo`8000Goo`L001koo`@000goo`L001ooo`@000coo`X000?oo`L002Coo`8000?oo`80
033oo`8000Goo`00JOoo10003Ooo1@001_oo1`007_oo10003?oo1`008?oo10003?oo2@000ooo1`00
9ooo0`00;?oo0`003_oo1@001_oo1`007ooo0`003Ooo1`008?oo0`003Ooo2@000ooo1`009Ooo1@00
<Ooo0P001Ooo003ooooooomCool20005ool00?oooooooe?oo`8000Goo`00oooooooo;ooo1P0000?o
o`00000010001_oo1@001_oo20001Ooo003ooooooolaool20005ool20007ool70004ool90005ool0
0?oooooooc7oo`8000Goo`8000Koo`<000Coo`03003ooooo00;oo`8000Coo`<000Goo`00oooooooo
<Ooo0P001Ooo0P001_oo0P001_oo00<00?ooool00`001Ooo0P001Ooo000koooo003U000@ool20005
ool20006ool20009ool20006ool20005ool003_oo`8000[oo`03003ooooo00Woo`03003ooooo00Wo
o`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Wo
o`03003ooooo00Woo`03003ooooo00Woo`8000_oo`03003ooooo00Woo`03003ooooo00Woo`03003o
oooo00Woo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Woo`03003o
oooo00Woo`03003ooooo00Ooo`05003oo`00ool00009ool00`00ooooo`09ool00`00ooooo`09ool0
0`00ooooo`09ool00`00ooooo`09ool00`00ooooo`0:ool00`00ooooo`09ool00`00ooooo`09ool0
0`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool0
0`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool0
0`00ooooo`09ool00`00ooooo`09ool2000@ool20005ool20006ool20009ool20006ool20005ool0
03_oo`8000[oo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Woo`03
003ooooo00Woo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Woo`80
00_oo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo
00Woo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo00Ooo`05003oo`00
ool00009ool00`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00
ooooo`0:ool00`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00
ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00
ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool00`00ooooo`09ool2000@
ool20005ool20006ool90002ool20006ool20005ool003_oo`8003[oo`03003ooooo03Woo`8003_o
o`03003ooooo03Ooo`05003oo`00ool0000iool00`00ooooo`0jool00`00ooooo`0iool00`00oooo
o`0iool2000@ool20005ool20006ool20005ool20002ool20006ool20005ool003_oo`8007Koo`80
07Goo`05003oooooool0001fool00`00ooooo`1eool00`00ooooo`0?ool20005ool20007ool00`00
ooooo`03ool20003ool20005ool20005ool003_oo`8007Koo`8007Goo`05003oooooool0001fool0
0`00ooooo`1eool00`00ooooo`0?ool20005ool60003ool20003ool20005ool20003ool30005ool0
03_oo`8007Koo`8007Goo`05003oooooool0001fool00`00ooooo`1eool00`00ooooo`0=ool;0000
1?oo000000001Ooo10001ooo1@0000?oo`00ool01?oo000kool2001fool2001eool01@00oooooooo
0000M_oo00<00?ooool0MOoo00<00?ooool03ooo0P009ooo000kool2001fool2001eool01@00oooo
oooo0000M_oo00<00?ooool0MOoo00<00?ooool03ooo0P009ooo000kool2001fool2001eool01@00
oooooooo0000M_oo00<00?ooool0MOoo00<00?ooool03ooo0P009ooo000kool2001fool2001eool0
1@00oooooooo0000M_oo00<00?ooool0MOoo00<00?ooool04?oo00<00?ooool00P008ooo000kool2
001fool2001eool01@00oooooooo0000M_oo00<00?ooool0MOoo00<00?ooool04Ooo0`009?oo000k
ool2001fool2001eool01@00oooooooo0000M_oo00<00?ooool0MOoo00<00?ooool0>?oo000kool2
001fool2001eool01@00oooooooo0000M_oo00<00?ooool0MOoo00<00?ooool0>?oo000kool2001f
ool2001eool01@00oooooooo0000M_oo00<00?ooool0MOoo00<00?ooool0>?oo000kool2001fool2
001eool01@00oooooooo0000M_oo00<00?ooool0MOoo00<00?ooool0>?oo000kool2001fool2001e
ool01@00oooooooo0000M_oo00<00?ooool0MOoo00<00?ooool0>?oo000kool2001fool2001eool0
1@00oooooooo0000M_oo00<00?ooool0MOoo00<00?ooool0>?oo000kool2001fool2001eool01@00
oooooooo0000M_oo00<00?ooool0MOoo00<00?ooool0>?oo000kool2001fool2001eool01@00oooo
oooo0000M_oo00<00?ooool0MOoo00<00?ooool0>?oo000kool2001fool2001eool01@00oooooooo
0000M_oo00<00?ooool0MOoo00<00?ooool0>?oo000kool2001fool2001eool01@00oooooooo0000
M_oo00<00?ooool0MOoo00<00?ooool0>?oo000kool2001fool2001eool01@00oooooooo0000M_oo
00<00?ooool0MOoo00<00?ooool0>?oo000kool2001fool2001eool01@00oooooooo0000M_oo00<0
0?ooool0MOoo00<00?ooool0>?oo000kool2001fool2001eool01@00oooooooo0000M_oo00<00?oo
ool0MOoo00<00?ooool0>?oo000kool2001fool2001eool01@00oooooooo0000M_oo00<00?ooool0
MOoo00<00?ooool0>?oo000kool2001fool2001eool01@00oooooooo0000M_oo00<00?ooool0MOoo
00<00?ooool0>?oo000kool2001fool2001eool01@00oooooooo0000M_oo00<00?ooool0/?oo000k
ool2001fool2001eool01@00oooooooo0000M_oo00<00?ooool0/?oo000kool2001fool2001eool0
1@00oooooooo0000M_oo00<00?ooool0/?oo000kool2001fool2001eool01@00oooooooo0000M_oo
00<00?ooool0/?oo000kool2001fool2001eool01@00oooooooo0000M_oo00<00?ooool0/?oo000k
ool2001fool2001eool01@00oooooooo0000oooo:_oo000kool2001fool2001eool01@00oooooooo
0000oooo:_oo000kool2001fool2001eool01@00oooooooo0000oooo:_oo000kool2001fool2001e
ool01@00oooooooo0000oooo:_oo000kool2001fool2001eool01@00oooooooo0000oooo:_oo000k
ool2001fool2001eool01@00oooooooo0000oooo:_oo000kool2001fool2001eool01@00oooooooo
0000oooo:_oo000kool2001fool2001eool01@00oooooooo0000oooo:_oo000kool2001fool2001e
ool01@00oooooooo0000oooo:_oo0007ool40005ool30006ool40008ool40005ool90004ool2001f
ool2001eool01@00oooooooo0000oooo:_oo0006ool20002ool20004ool30005ool20002ool20006
ool20002ool20004ool90004ool2001fool2001eool01@00oooooooo0000oooo:_oo0005ool20004
ool2000:ool20004ool20004ool20004ool20004ool00`00ooooo`09ool2001fool2001eool01@00
oooooooo0000oooo:_oo0005ool00`00ooooo`04ool00`00ooooo`08ool00`00ooooo`04ool00`00
ooooo`02ool00`00ooooo`04ool00`00ooooo`03ool00`00ooooo`08ool2001fool2001eool01@00
oooooooo0000oooo:_oo0004ool20006ool20008ool20006ool20002ool20006ool20005ool00`00
ooooo`07ool4001dool2001eool01@00oooooooo0000oooo:_oo0004ool20006ool20008ool20006
ool20002ool20006ool20006ool00`00ooooo`06ool2001fool00`00ooooo`1dool01@00oooooooo
0000oooo:_oo0004ool20006ool20008ool20006ool20002ool20006ool20007ool00`00ooooo`05
ool2001fool00`00ooooo`1dool01@00oooooooo0000oooo:_oo0004ool20006ool20008ool20006
ool20002ool20006ool20008ool00`00ooooo`04ool2001fool00`00ooooo`1dool01@00oooooooo
0000oooo:_oo0004ool20006ool20008ool20006ool20002ool20006ool20008ool20005ool2001f
ool00`00ooooo`1dool01@00oooooooo0000oooo:_oo0004ool20006ool20008ool20006ool20002
ool20006ool20009ool20004ool2001fool00`00ooooo`1dool01@00oooooooo0000oooo:_oo0004
ool20006ool20008ool20006ool20002ool20006ool20009ool20004ool2001fool00`00ooooo`1d
ool01@00oooooooo0000oooo:_oo0005ool00`00ooooo`04ool00`00ooooo`08ool00`00ooooo`04
ool00`00ooooo`02ool00`00ooooo`04ool01000oooooooo0P001Ooo0P001?oo0P00M_oo00<00?oo
ool0M?oo00D00?ooooooo`000?ooob[oo`001Ooo0P001?oo0P002_oo0P001?oo0P001?oo0P001?oo
0P001?oo0P001?oo0P001?oo0P00M_oo00<00?ooool0M?oo00D00?ooooooo`000?ooob[oo`001_oo
0P000_oo0P003?oo0P000_oo0P001_oo0P000_oo0P001Ooo0P000ooo0P001Ooo0P00M_oo00<00?oo
ool0M?oo00D00?ooooooo`000?ooob[oo`001ooo10003_oo10002?oo10001ooo1@001_oo0P00M_oo
00<00?ooool0M?oo00D00?ooooooo`000?ooob[oo`00>ooo0P00M_oo00<00?ooool0M?oo00D00?oo
ooooo`000?ooob[oo`00>ooo0P00M_oo00<00?ooool0M?oo00D00?ooooooo`000?ooob[oo`00>ooo
0P00M_oo00<00?ooool0M?oo00D00?ooooooo`000?ooob[oo`00>ooo0P00M_oo00<00?ooool0M?oo
00D00?ooooooo`000?ooob[oo`00>ooo0P00M_oo00<00?ooool0M?oo00D00?ooooooo`000?ooob[o
o`00>ooo0P00M_oo00<00?ooool0M?oo00D00?ooooooo`000?ooob[oo`00>ooo0P00M_oo00<00?oo
ool0M?oo00D00?ooooooo`000?ooob[oo`00>ooo0P00M_oo00<00?ooool0M?oo00D00?ooooooo`00
0?ooob[oo`00>ooo0P00M_oo00<00?ooool0M?oo00D00?ooooooo`000?ooob[oo`00>ooo0P00M_oo
00<00?ooool0M?oo00D00?ooooooo`000?ooob[oo`00>ooo0P00M_oo00<00?ooool0M?oo00D00?oo
ooooo`000?ooob[oo`00>ooo0P00M_oo00<00?ooool0M?oo00D00?ooooooo`000?ooob[oo`00>ooo
0P00M_oo00<00?ooool0M?oo00D00?ooooooo`000?ooob[oo`00>ooo0P00M_oo00<00?ooool0M?oo
00D00?ooooooo`000?ooob[oo`00>ooo0P00M_oo00<00?ooool0M?oo00D00?ooooooo`000?ooob[o
o`00>ooo0`00MOoo00<00?ooool0MOoo00<00?oo0000oooo:ooo000kool2001fool00`00ooooo`1e
ool00`00ool0003oool[ool003_oo`8007Koo`03003ooooo07Goo`03003oo`000?ooob_oo`00>ooo
0P00M_oo00<00?ooool0MOoo00<00?oo0000oooo:ooo000kool2001fool00`00ooooo`1eool00`00
ool0003oool[ool003_oo`8007Koo`03003ooooo07Goo`03003oo`000?ooob_oo`00>ooo0P00M_oo
00<00?ooool0MOoo00<00?oo0000oooo:ooo000kool2001fool00`00ooooo`1eool00`00ool0003o
ool[ool003_oo`8007Koo`03003ooooo07Goo`03003oo`000?ooob_oo`00>ooo0P00M_oo00<00?oo
ool0MOoo00<00?oo0000oooo:ooo000kool2001fool00`00ooooo`1eool00`00ool0003oool[ool0
03_oo`8007Koo`03003ooooo07Goo`03003oo`000?ooob_oo`00>ooo0P00M_oo00<00?ooool0MOoo
00<00?oo0000oooo:ooo000kool2001fool00`00ooooo`1eool00`00ool0003oool[ool003_oo`80
07Koo`03003ooooo07Goo`03003oo`000?ooob_oo`00>ooo0P00M_oo00<00?ooool0MOoo00<00?oo
0000oooo:ooo000kool2001fool00`00ooooo`1eool00`00ool0003oool[ool003_oo`8007Koo`03
003ooooo07Goo`03003oo`000?ooob_oo`00>ooo0P00M_oo00<00?ooool0MOoo00<00?oo0000oooo
:ooo000kool3001eool00`00ooooo`1eool00`00ool0003oool[ool003_oo`8007Koo`03003ooooo
07Goo`03003oo`000?ooob_oo`00>ooo0P00k_oo00<00?oo0000oooo:ooo000kool2003^ool00`00
ool0003oool[ool003_oo`800>koo`03003oo`000?ooob_oo`00>ooo0P00k_oo00<00?oo0000oooo
:ooo000kool2003^ool00`00ool0003oool[ool003_oo`800>koo`03003oo`000?ooob_oo`00>ooo
0P00k_oo00<00?oo0000oooo:ooo000kool2003^ool00`00ool0003oool[ool000Ooo`@000Goo`<0
00Koo`@000Soo`@000Koo`H000Koo`800>koo`03003oo`000?ooob_oo`001_oo0P000_oo0P001?oo
0`001Ooo0P000_oo0P001_oo0P000_oo0P001?oo0`000ooo0P001Ooo0P00k_oo00<00?oo0000oooo
:ooo0005ool20004ool2000:ool20004ool20004ool20004ool20003ool20005ool20004ool2003^
ool00`00ool0003oool[ool000Goo`03003ooooo00Coo`03003ooooo00Soo`03003ooooo00Coo`03
003ooooo00;oo`03003ooooo00Coo`05003oooooool00006ool20004ool2003^ool00`00ool0003o
ool[ool000Coo`8000Koo`8000Soo`8000Koo`8000;oo`8000Koo`8000Woo`8000Coo`@00>coo`03
003oo`000?ooob_oo`001?oo0P001_oo0P002?oo0P001_oo0P000_oo0P001_oo0P002Ooo0P001?oo
0P00k_oo00<00?oo0000oooo:ooo0004ool20006ool20008ool20006ool20002ool20006ool20009
ool20004ool2003^ool00`00ool0003oool[ool000Coo`8000Koo`8000Soo`8000Koo`8000;oo`80
00Koo`8000?oo`8000?oo`8000Goo`800>koo`03003oo`000?ooob_oo`001?oo0P001_oo0P002?oo
0P001_oo0P000_oo0P001_oo0P000ooo00<00?oo00000`001_oo0P00k_oo00<00?oo0000oooo:ooo
0004ool20006ool20008ool20006ool20002ool20006ool20003ool00`00ooooo`09ool2003^ool0
0`00ool0003oool[ool000Coo`8000Koo`8000Soo`8000Koo`8000;oo`8000Koo`8000?oo`03003o
oooo00Woo`800>koo`03003oo`000?ooob_oo`001Ooo00<00?ooool01?oo00<00?ooool02?oo00<0
0?ooool01?oo00<00?ooool00_oo00<00?ooool01?oo00<00?ooool00_oo00<00?ooool02Ooo0P00
k_oo00<00?oo0000oooo:ooo0005ool20004ool2000:ool20004ool20004ool20004ool20004ool0
0`00ooooo`09ool2003^ool00`00ool0003oool[ool000Koo`8000;oo`8000coo`8000;oo`8000Ko
o`8000;oo`8000Goo`L000Goo`800>koo`03003oo`000?ooob_oo`001ooo10003_oo10002?oo1000
1_oo1`001Ooo0P00k_oo00<00?oo0000oooo:ooo000kool2003^ool00`00ool0003oool[ool003_o
o`<00>goo`03003oo`000?ooob_oo`00>ooo0P00k_oo00<00?oo0000oooo:ooo000kool2003^ool0
0`00ool0003oool[ool003_oo`800>koo`03003oo`000?ooob_oo`00>ooo0P00k_oo00<00?oo0000
oooo:ooo000kool2003^ool00`00ool0003oool[ool003_oo`800>koo`03003oo`000?ooob_oo`00
>ooo0P00k_oo00<00?oo0000oooo:ooo000kool2003^ool00`00ool0003oool[ool003_oo`800>ko
o`03003oo`000?ooob_oo`00>ooo0`00kOoo00<00?oo0000oooo:ooo000kool2003^ool00`00ool0
003oool[ool003_oo`800>koo`03003oo`000?ooob_oo`00>ooo0P00k_oo00<00?oo0000oooo:ooo
000kool2003^ool00`00ool0003oool[ool003_oo`800>koo`03003oo`000?ooob_oo`00>ooo0P00
k_oo00<00?oo0000oooo:ooo000kool2003^ool00`00ool0003oool[ool003_oo`800>koo`03003o
o`000?ooob_oo`00>ooo0`00kOoo00<00?oo0000oooo:ooo000kool2003^ool00`00ool0003oool[
ool003_oo`800>koo`03003oo`000?ooob_oo`00>ooo0P00k_oo00<00?oo0000oooo:ooo000kool2
003^ool00`00ool0003oool[ool003_oo`800>koo`03003oo`000?ooob_oo`00>ooo0P00k_oo00<0
0?oo0000oooo:ooo000kool3003]ool00`00ool0003oool[ool003_oo`800>koo`03003oo`000?oo
ob_oo`00>ooo0P00k_oo00<00?oo0000oooo:ooo000Aool40005ool30006ool40006ool80006ool2
003^ool00`00ool0003oool[ool0013oo`8000;oo`8000Coo`<000Goo`8000;oo`8000Soo`8000Wo
o`800>koo`03003oo`000?ooob_oo`003ooo0P001?oo0P002_oo0P001?oo0P001ooo0P002Ooo0P00
k_oo00<00?oo0000oooo:ooo000?ool00`00ooooo`04ool00`00ooooo`08ool00`00ooooo`04ool0
0`00ooooo`05ool20009ool2003^ool00`00ool0003oool[ool000koo`8000Koo`8000Soo`8000Ko
o`8000Koo`8000Woo`@00>coo`03003oo`000?ooob_oo`003_oo0P001_oo0P002?oo0P001_oo0P00
1_oo0P002Ooo00<00?ooool0kOoo00<00?oo0000oooo:ooo000>ool20006ool20008ool20006ool2
0006ool20009ool00`00ooooo`3]ool00`00ool0003oool[ool000koo`8000Koo`8000Soo`8000Ko
o`8000Koo`8000Woo`03003ooooo0>goo`03003oo`000?ooob_oo`003_oo0P001_oo0P002?oo0P00
1_oo0P001_oo0P002Ooo00<00?ooool0kOoo00<00?oo0000oooo:ooo000>ool20006ool20008ool2
0006ool20006ool20009ool00`00ooooo`3]ool00`00ool0003oool[ool000koo`8000Koo`8000So
o`8000Koo`8000Koo`8000Woo`03003ooooo0>goo`03003oo`000?ooob_oo`003ooo00<00?ooool0
1?oo00<00?ooool02?oo00<00?ooool01?oo00<00?ooool01Ooo0P002Ooo00<00?ooool0kOoo00<0
0?oo0000oooo:ooo000?ool20004ool2000:ool20004ool20007ool20009ool00`00ooooo`3]ool0
0`00ool0003oool[ool0013oo`8000;oo`8000coo`8000;oo`8000Koo`@000Woo`03003ooooo0>go
o`03003oo`000?ooob_oo`004Ooo10003_oo10002?oo0`002Ooo00<00?ooool0kOoo00<00?oo0000
oooo:ooo000kool00`00ooooo`3]ool00`00ool0003oool[ool003_oo`03003ooooo0>goo`03003o
o`000?ooob_oo`00>ooo00<00?ooool0kOoo00<00?oo0000oooo:ooo000kool00`00ooooo`3]ool0
0`00ool0003oool[ool003_oo`03003ooooo0>goo`03003oo`000?ooob_oo`00>ooo00<00?ooool0
kOoo00<00?oo0000oooo:ooo000kool00`00ooooo`3]ool00`00ool0003oool[ool003_oo`03003o
oooo0>goo`03003oo`000?ooob_oo`00>ooo00<00?ooool0kOoo00<00?oo0000oooo:ooo000kool0
0`00ooooo`3]ool00`00ool0003oool[ool003_oo`03003ooooo0>goo`03003oo`000?ooob_oo`00
>ooo00<00?ooool0kOoo00<00?oo0000oooo:ooo000kool00`00ooooo`3]ool00`00ool0003oool[
ool003_oo`03003ooooo0>goo`03003oo`000?ooob_oo`00>ooo00<00?ooool0kOoo00<00?oo0000
oooo:ooo000kool00`00ooooo`3]ool00`00ool0003oool[ool003_oo`03003ooooo0>goo`03003o
o`000?ooob_oo`00>ooo00<00?ooool0kOoo00<00?oo0000oooo:ooo000kool00`00ooooo`3]ool0
0`00ool0003oool[ool003_oo`03003ooooo0>goo`03003oo`000?ooob_oo`00>ooo00<00?ooool0
kOoo00<00?oo0000oooo:ooo000kool00`00ooooo`3]ool00`00ool0003oool[ool003_oo`03003o
oooo0>goo`03003oo`000?ooob_oo`00>ooo00<00?ooool0kOoo00<00?oo0000oooo:ooo000kool0
0`00ooooo`3]ool00`00ool0003oool[ool003_oo`03003ooooo0>goo`03003oo`000?ooob_oo`00
>ooo00<00?ooool0kOoo00<00?oo0000oooo:ooo000kool00`00ooooo`3]ool00`00ool0003oool[
ool003_oo`03003ooooo0>goo`03003oo`000?ooob_oo`00>ooo00<00?ooool0kOoo00<00?oo0000
oooo:ooo000Aool40005ool30006ool40005ool90006ool00`00ooooo`3]ool00`00ool0003oool[
ool0013oo`8000;oo`8000Coo`<000Goo`8000;oo`8000Coo`T000Koo`03003ooooo0>goo`03003o
o`000?ooob_oo`003ooo0P001?oo0P002_oo0P001?oo0P001?oo00<00?ooool02ooo00<00?ooool0
kOoo00<00?oo0000oooo:ooo000?ool00`00ooooo`04ool00`00ooooo`08ool00`00ooooo`04ool0
0`00ooooo`03ool00`00ooooo`0:ool00`00ooooo`3]ool00`00ool0003oool[ool000koo`8000Ko
o`8000Soo`8000Koo`8000Goo`03003ooooo00Woo`@00>coo`03003oo`000?ooob_oo`003_oo0P00
1_oo0P002?oo0P001_oo0P001_oo00<00?ooool02?oo00<00?ooool0kOoo00<00?oo0000oooo:ooo
000>ool20006ool20008ool20006ool20007ool00`00ooooo`07ool00`00ooooo`3]ool00`00ool0
003oool[ool000koo`8000Koo`8000Soo`8000Koo`8000Soo`03003ooooo00Koo`03003ooooo0>go
o`03003oo`000?ooob_oo`003_oo0P001_oo0P002?oo0P001_oo0P002?oo0P001ooo00<00?ooool0
kOoo00<00?oo0000oooo:ooo000>ool20006ool20008ool20006ool20009ool20006ool00`00oooo
o`3]ool00`00ool0003oool[ool000koo`8000Koo`8000Soo`8000Koo`8000Woo`8000Koo`03003o
oooo0>goo`03003oo`000?ooob_oo`003ooo00<00?ooool01?oo00<00?ooool02?oo00<00?ooool0
1?oo00@00?ooooooo`8000Goo`8000Koo`03003ooooo0>goo`03003oo`000?ooob_oo`003ooo0P00
1?oo0P002_oo0P001?oo0P001?oo0P001?oo0P001_oo00<00?ooool0kOoo00<00?oo0000oooo:ooo
000@ool20002ool2000<ool20002ool20005ool20003ool20007ool00`00ooooo`3]ool00`00ool0
003oool[ool0017oo`@000koo`@000Ooo`D000Soo`03003ooooo0>goo`03003oo`000?ooob_oo`00
>ooo00<00?ooool0kOoo00<00?oo0000oooo:ooo000kool00`00ooooo`3]ool00`00ool0003oool[
ool003_oo`03003ooooo0>goo`03003oo`000?ooob_oo`00>ooo00<00?ooool0kOoo00<00?oo0000
oooo:ooo000kool00`00ooooo`3]ool00`00ool0003oool[ool003_oo`03003ooooo0>goo`03003o
o`000?ooob_oo`00>ooo00<00?ooool0kOoo00<00?oo0000oooo:ooo000kool00`00ooooo`3^ool0
0`00ooooo`3ooolZool003_oo`03003ooooo0>koo`03003ooooo0?ooob[oo`00>ooo00<00?ooool0
k_oo00<00?ooool0oooo:_oo000kool00`00ooooo`3^ool00`00ooooo`3ooolZool003_oo`03003o
oooo0>koo`03003ooooo0?ooob[oo`00>ooo00<00?ooool0k_oo00<00?ooool0oooo:_oo000kool0
0`00ooooo`3^ool00`00ooooo`3ooolZool003_oo`03003ooooo0>koo`03003ooooo0?ooob[oo`00
>ooo0`00k_oo00<00?ooool0oooo:_oo000kool00`00ooooo`3^ool00`00ooooo`3ooolZool003_o
o`03003ooooo0>koo`03003ooooo0?ooob[oo`00>ooo00<00?ooool0k_oo00<00?ooool0oooo:_oo
000kool00`00ooooo`3^ool00`00ooooo`3ooolZool003_oo`03003ooooo0>koo`03003ooooo0?oo
ob[oo`00>ooo00<00?ooool0k_oo00<00?ooool0oooo:_oo000kool00`00ooooo`3^ool00`00oooo
o`3ooolZool003_oo`03003ooooo0>koo`03003ooooo0?ooob[oo`00>ooo00<00?ooool0k_oo00<0
0?ooool0oooo:_oo000kool00`00ooooo`3^ool00`00ooooo`3ooolZool003_oo`03003ooooo0>ko
o`03003ooooo0?ooob[oo`00>ooo00<00?ooool0k_oo00<00?ooool0oooo:_oo000kool00`00oooo
o`3^ool00`00ooooo`3ooolZool003_oo`03003ooooo0>koo`03003ooooo0?ooob[oo`00>ooo00<0
0?ooool0k_oo00<00?ooool0oooo:_oo000kool00`00ooooo`3^ool00`00ooooo`3ooolZool003_o
o`03003ooooo0>koo`03003ooooo0?ooob[oo`00>ooo00<00?ooool0k_oo00<00?ooool0oooo:_oo
000kool3003^ool00`00ooooo`3ooolZool003_oo`03003ooooo0>koo`03003ooooo0?ooob[oo`00
>ooo00<00?ooool0k_oo00<00?ooool0oooo:_oo000kool00`00ooooo`3^ool00`00ooooo`3ooolZ
ool003_oo`03003ooooo0>koo`03003ooooo0?ooob[oo`00>ooo00<00?ooool0k_oo00<00?ooool0
oooo:_oo000kool00`00ooooo`3^ool00`00ooooo`3ooolZool003_oo`03003ooooo0>koo`03003o
oooo0?ooob[oo`00>ooo00<00?ooool0k_oo00<00?ooool0oooo:_oo000kool00`00ooooo`3^ool0
0`00ooooo`3ooolZool0017oo`@000Goo`<000Koo`@000Koo`H000Soo`03003ooooo0>koo`03003o
oooo0?ooob[oo`004?oo0P000_oo0P001?oo0`001Ooo0P000_oo0P001?oo0`000ooo0P001ooo00<0
0?ooool0k_oo00<00?ooool0oooo:_oo000?ool20004ool2000:ool20004ool20003ool20005ool2
0006ool00`00ooooo`3^ool00`00ooooo`3ooolZool000ooo`03003ooooo00Coo`03003ooooo00So
o`03003ooooo00Coo`05003oooooool00006ool20006ool00`00ooooo`3^ool00`00ooooo`3ooolZ
ool000koo`8000Koo`8000Soo`8000Koo`8000Woo`8000Koo`@00>goo`03003ooooo0?ooob[oo`00
3_oo0P001_oo0P002?oo0P001_oo0P002Ooo0P001_oo00<00?ooool0k_oo00<00?ooool0oooo:_oo
000>ool20006ool20008ool20006ool20009ool20006ool00`00ooooo`3^ool00`00ooooo`3ooolZ
ool000koo`8000Koo`8000Soo`8000Koo`8000?oo`8000?oo`8000Ooo`03003ooooo0>koo`03003o
oooo0?ooob[oo`003_oo0P001_oo0P002?oo0P001_oo0P000ooo00<00?oo00000`002?oo00<00?oo
ool0k_oo00<00?ooool0oooo:_oo000>ool20006ool20008ool20006ool20003ool00`00ooooo`0;
ool00`00ooooo`3^ool00`00ooooo`3ooolZool000koo`8000Koo`8000Soo`8000Koo`8000?oo`03
003ooooo00_oo`03003ooooo0>koo`03003ooooo0?ooob[oo`003ooo00<00?ooool01?oo00<00?oo
ool02?oo00<00?ooool01?oo00<00?ooool00_oo00<00?ooool02ooo00<00?ooool0k_oo00<00?oo
ool0oooo:_oo000?ool20004ool2000:ool20004ool20004ool00`00ooooo`0;ool00`00ooooo`3^
ool00`00ooooo`3ooolZool0013oo`8000;oo`8000coo`8000;oo`8000Goo`L000Ooo`03003ooooo
0>koo`03003ooooo0?ooob[oo`004Ooo10003_oo10001_oo1`001ooo00<00?ooool0k_oo00<00?oo
ool0oooo:_oo000kool00`00ooooo`3^ool00`00ooooo`3ooolZool003_oo`<00>koo`03003ooooo
0?ooob[oo`00>ooo00<00?ooool0k_oo00<00?ooool0oooo:_oo000kool00`00ooooo`3^ool00`00
ooooo`3ooolZool003_oo`03003ooooo0>koo`03003ooooo0?ooob[oo`00>ooo00<00?ooool0k_oo
00<00?ooool0oooo:_oo000kool00`00ooooo`3^ool00`00ooooo`3ooolZool003_oo`03003ooooo
0>koo`03003ooooo0?ooob[oo`00>ooo00<00?ooool0k_oo00<00?ooool0oooo:_oo000kool00`00
ooooo`3^ool00`00ooooo`3ooolZool003_oo`03003ooooo0>koo`03003ooooo0?ooob[oo`00>ooo
0`00k_oo00<00?ooool0oooo:_oo000kool00`00ooooo`3^ool00`00ooooo`3ooolZool003_oo`03
003ooooo0>koo`03003ooooo0?ooob[oo`00>ooo00<00?ooool0k_oo00<00?ooool0oooo:_oo000k
ool00`00ooooo`3^ool00`00ooooo`3ooolZool003_oo`03003ooooo0>koo`03003ooooo0?ooob[o
o`00>ooo00<00?ooool0k_oo00<00?ooool0oooo:_oo000kool00`00ooooo`3^ool00`00ooooo`3o
oolZool003_oo`03003ooooo0?oooooooacoo`00>ooo0`00oooooooo7?oo000kool00`00ooooo`3o
oooooolLool003_oo`03003ooooo0?oooooooacoo`00>ooo00<00?ooool0oooooooo7?oo000kool0
0`00ooooo`3ooooooolLool003_oo`03003ooooo0?oooooooacoo`00>ooo00<00?ooool0oooooooo
7?oo000kool3003ooooooolLool003_oo`03003ooooo0?oooooooacoo`00>ooo00<00?ooool0oooo
oooo7?oo000Lool40005ool30004ool80007ool00`00ooooo`3ooooooolLool001_oo`8000;oo`80
00Coo`<000Ooo`8000[oo`03003ooooo0?oooooooacoo`006_oo0P001?oo0P003Ooo0P002_oo00<0
0?ooool0oooooooo7?oo000Jool00`00ooooo`04ool00`00ooooo`0;ool2000:ool00`00ooooo`3o
oooooolLool001Woo`8000Koo`8000coo`8000[oo`@00?oooooooa_oo`006Ooo0P001_oo0P003?oo
0P00oooooooo:Ooo000Iool20006ool2000<ool2003ooooooolYool001Woo`8000Koo`8000coo`80
0?ooooooobWoo`006Ooo0P001_oo0P003?oo0P00oooooooo:Ooo000Iool20006ool2000<ool2003o
oooooolYool001Woo`8000Koo`8000coo`800?ooooooobWoo`006_oo00<00?ooool01?oo00<00?oo
ool02ooo0P00oooooooo:Ooo000Jool20004ool2000=ool2003lool6003ooolVool001_oo`8000;o
o`8000coo`@00?koo`800?ooobSoo`007?oo10003_oo0`00o_oo0P00oooo:?oo003oool`ool2003o
oolXool00?oooc3oo`800?ooobSoo`00j?oo1P002_oo10002Ooo0P001Ooo0P001ooo1@000ooo1P00
00?oo`0000000`001_oo1`001ooo1@001_oo1@001_oo0`000_oo1P001_oo10000_oo2P0000?oo`00
0000100000?oo`0000001000e_oo000Qool60033ool2000:ool20004ool20007ool30004ool20006
ool70004ool200001?oo000000001?oo0P001?oo0`001?oo0P001?oo1`001?oo1`001?oo1@000ooo
0P001ooo1P0000Coo`00000000?oo`8000Goo`8000Goo`800=Soo`008ooo0P00aOoo0P002_oo0P00
1?oo0P001ooo0`000ooo0`001Ooo0`001?oo00<00?ooool00_oo0P0000?oo`0000001_oo0P000ooo
0P001Ooo0P000ooo0`001?oo00<00?ooool00_oo0P001?oo0P000ooo0P001_oo0P001ooo0`000ooo
0`001?oo0P001Ooo0P001Ooo0P00f?oo000Sool20035ool20009ool20006ool20005ool200000ooo
003oo`02ool200000ooo003oo`03ool20006ool01000oooooooo0P0000?oo`00ool01_oo0P000ooo
0P001_oo0P000_oo0P001_oo00<00?ooool00`001Ooo00@00?ooooooo`8000Koo`8000Ooo`8000Go
o`8000Coo`8000Goo`8000Goo`800=Soo`008ooo0P00aOoo0P002Ooo0P001_oo0P001Ooo0P000_oo
00<00?ooool00P0000?oo`00ool00ooo0P002_oo0P0000?oo`00ool01_oo0P000ooo0P001_oo0P00
0_oo0P002Ooo0P002_oo0P001_oo0P001ooo0P001Ooo0P001?oo0P001Ooo0P001Ooo0P00f?oo000S
ool20035ool20009ool20006ool20005ool20002ool01000ool000000_oo00<00?ooool00_oo0P00
2_oo0P002?oo0`000ooo0P001_oo0P000_oo0P002Ooo0P002_oo0P001_oo0P001ooo0P001Ooo0P00
1?oo0P001Ooo0P001Ooo0P00f?oo000Sool70008ool40009ool20005ool20007ool50003ool6002=
ool60005ool20006ool20004ool20003ool01000ool000000ooo00@00?ooooooo`T000?oo`8000Oo
o`<000Coo`8000Koo`8000;oo`T000;oo`8000[oo`8000Koo`8000Ooo`8000Goo`8000Coo`8000Go
o`8000Goo`800=Soo`008ooo0`001?oo0P001?oo0P001?oo0P001ooo0`001?oo0P001_oo1`001?oo
0P00Sooo0P001?oo0P000ooo0P001_oo0P001?oo0P000ooo00@00?oo000000?oo`04003oooooool2
0005ool20003ool20004ool50005ool20006ool20002ool20005ool20002ool2000:ool20006ool2
0007ool20005ool20004ool20005ool20005ool2003Hool002?oo`8000Goo`8000Coo`8000Coo`80
00Ooo`<000?oo`<000Goo`<000Coo`03003ooooo00;oo`8008ooo`8000Goo`8000?oo`8000Coo`80
00Goo`8000Coo`8000Coo`03003ooooo00;oo`03003ooooo00?oo`8000?oo`8000;oo`D000Ooo`<0
00Coo`<000?oo`03003ooooo00?oo`8000?oo`03003ooooo00?oo`8000?oo`8000Koo`8000Ooo`80
00Goo`8000Coo`<000?oo`@000?oo`<00=Soo`008ooo0P001_oo0P000_oo0P001_oo0P001Ooo0P00
00?oo`00ool00_oo0P0000?oo`00ool00ooo0P001_oo00@00?ooooooo`8008ooo`8000Goo`8000?o
o`8000Coo`8000Coo`8000Goo`8000Coo`8000?oo`8000?oo`8000Coo`H000Soo`@00003ool00000
00@000Coo`8000?oo`8000Coo`8000?oo`<000?oo`8000Koo`H000?oo`8000Goo`8000;oo`@00003
ool0000000<000;oo`H00=Soo`008ooo0P001_oo0P000_oo0P001_oo0P001Ooo0P000_oo00<00?oo
ool00P0000?oo`00ool00ooo0P002_oo0P00Sooo0P001Ooo0P001Ooo1@001?oo1@002?oo10001?oo
10000ooo100000Coo`00000000[oo`8000;oo`@000Ooo`@000Ooo`D000;oo`L00003ool000000080
0005ool00000003oo`040003ool40004ool20002ool40003ool4003Iool002?oo`8000Koo`8000;o
o`8000Koo`8000Goo`8000;oo`04003oo`000002ool00`00ooooo`02ool2000:ool2002?ool20005
ool2000_ool20006ool00`00ooooo`0Uool2003oool5ool002?oo`8000Koo`8000;oo`8000Koo`80
00Coo`8000?oo`04003oo`000003ool01000oooooooo2@000ooo0P00Sooo0P001Ooo0P00;ooo0P00
1_oo00<00?ooool09_oo00<00?ooool0oooo0ooo000Sool20006ool20002ool20006ool20004ool2
0003ool01000ool000000ooo00@00?ooooooo`8000Goo`8000?oo`8008ooo`8000Coo`80037oo`80
00Coo`8002Soo`03003ooooo0?ooo`?oo`008ooo0`001?oo0`000ooo0P001?oo0P001Ooo0P001?oo
0P001?oo00<00?ooool00_oo00<00?ooool00ooo0P000ooo0P00SOoo2@00<ooo1P00oooo;ooo000Q
ool400000ooo000000040004ool20004ool20004ool20005ool20004ool20003ool20003ool20004
ool6003oooojool002?oo`8000;oo`@000Ooo`D000Coo`D000Soo`@000Coo`@000?oo`@00004ool0
0000003oooojool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00oooo
ooooF_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[o
o`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oo
oooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJ
ool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003o
oooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00oooooooo
F_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00
ooooooooF_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool00?oooooo
oe[oo`00ooooooooF_oo003ooooooomJool00?oooooooe[oo`00ooooooooF_oo003ooooooomJool0
0?oooooooe[oo`00\
\>"],
  ImageRangeCache->{{{144, 543}, {455.125, 156.125}} -> {-1.14164, -1.91373, \
0.00622079, 0.0100654}}],

Cell[BoxData[
    TagBox[\(\[SkeletonIndicator]  Graphics  \[SkeletonIndicator]\),
      False,
      Editable->False]], "Output",
  CellLabel->"Out[28]="]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
FrontEndVersion->"5.0 for X",
ScreenRectangle->{{0, 1280}, {0, 1024}},
WindowToolbars->"EditBar",
WindowSize->{995, 1024},
WindowMargins->{{Automatic, 69}, {Automatic, 29}},
PrintingPageRange->{Automatic, Automatic},
PrintingOptions->{"PrintingMargins"->{{54, 54}, {72, 72}},
"PaperSize"->{612, 792},
"PaperOrientation"->"Portrait",
"PrintCellBrackets"->False,
"PrintRegistrationMarks"->True,
"PrintMultipleHorizontalPages"->False,
"PostScriptOutputFile":>FrontEnd`FileName[{$RootDirectory, "home", \
"furnstah", "Teaching", "Computational_Physics", "class", "2004", \
"session_9", "pipe", "power_spectrum"}, "nonlinear.nb.ps", CharacterEncoding \
-> "iso8859-1"],
"Magnification"->1},
Magnification->1.5,
StyleDefinitions -> "ArticleClassic.nb"
]

(*******************************************************************
Cached data follows.  If you edit this Notebook file directly, not
using Mathematica, you must remove the line containing CacheID at
the top of  the file.  The cache data will then be recreated when
you save this file from within Mathematica.
*******************************************************************)

(*CellTagsOutline
CellTagsIndex->{}
*)

(*CellTagsIndex
CellTagsIndex->{}
*)

(*NotebookFileOutline
Notebook[{

Cell[CellGroupData[{
Cell[1776, 53, 101, 2, 58, "Subtitle"],
Cell[1880, 57, 382, 8, 130, "Text"],

Cell[CellGroupData[{
Cell[2287, 69, 51, 0, 86, "Section"],
Cell[2341, 71, 100, 3, 38, "Text"],
Cell[2444, 76, 245, 6, 40, "Input"],
Cell[2692, 84, 44, 0, 38, "Text"],
Cell[2739, 86, 171, 3, 40, "Input"],

Cell[CellGroupData[{
Cell[2935, 93, 59, 2, 40, "Input"],
Cell[2997, 97, 89, 2, 40, "Output"]
}, Open  ]],
Cell[3101, 102, 52, 0, 38, "Text"],
Cell[3156, 104, 91, 2, 40, "Input"],

Cell[CellGroupData[{
Cell[3272, 110, 60, 2, 40, "Input"],
Cell[3335, 114, 66, 2, 40, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[3450, 122, 50, 0, 86, "Section"],
Cell[3503, 124, 255, 5, 61, "Text"],
Cell[3761, 131, 81, 2, 40, "Input"],
Cell[3845, 135, 185, 4, 61, "Text"],
Cell[4033, 141, 201, 4, 63, "Input"],
Cell[4237, 147, 135, 3, 38, "Text"]
}, Open  ]],

Cell[CellGroupData[{
Cell[4409, 155, 59, 0, 86, "Section"],
Cell[4471, 157, 124, 3, 38, "Text"],

Cell[CellGroupData[{
Cell[4620, 164, 102, 2, 40, "Input"],
Cell[4725, 168, 11789, 764, 279, 11541, 757, "GraphicsData", "PostScript", \
"Graphics",
  ImageCacheValid->False],
Cell[16517, 934, 154, 4, 40, "Output"]
}, Open  ]],
Cell[16686, 941, 168, 4, 61, "Text"],

Cell[CellGroupData[{
Cell[16879, 949, 412, 8, 109, "Input"],
Cell[17294, 959, 26713, 1312, 312, 26531, 1307, "GraphicsData", "PostScript", \
"Graphics",
  ImageCacheValid->False],
Cell[44010, 2273, 154, 4, 40, "Output"]
}, Open  ]],
Cell[44179, 2280, 128, 3, 38, "Text"],

Cell[CellGroupData[{
Cell[44332, 2287, 458, 8, 132, "Input"],
Cell[44793, 2297, 31954, 1608, 312, 31776, 1603, "GraphicsData", \
"PostScript", "Graphics",
  ImageCacheValid->False],
Cell[76750, 3907, 155, 4, 40, "Output"]
}, Open  ]],
Cell[76920, 3914, 107, 3, 38, "Text"],

Cell[CellGroupData[{
Cell[77052, 3921, 448, 8, 132, "Input"],
Cell[77503, 3931, 34447, 1766, 312, 34271, 1761, "GraphicsData", \
"PostScript", "Graphics",
  ImageCacheValid->False],
Cell[111953, 5699, 155, 4, 40, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[112157, 5709, 36, 0, 86, "Section"],
Cell[112196, 5711, 357, 6, 84, "Text"],
Cell[112556, 5719, 187, 4, 61, "Text"],
Cell[112746, 5725, 97, 2, 40, "Input"],
Cell[112846, 5729, 89, 2, 40, "Input"],
Cell[112938, 5733, 82, 2, 40, "Input"],
Cell[113023, 5737, 104, 2, 40, "Input"],
Cell[113130, 5741, 108, 3, 38, "Text"],
Cell[113241, 5746, 222, 5, 86, "Input"],
Cell[113466, 5753, 65, 0, 38, "Text"],

Cell[CellGroupData[{
Cell[113556, 5757, 497, 9, 132, "Input"],
Cell[114056, 5768, 16410, 737, 312, 16228, 732, "GraphicsData", "PostScript", \
"Graphics",
  ImageCacheValid->False],
Cell[130469, 6507, 155, 4, 40, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[130673, 6517, 33, 0, 86, "Section"],
Cell[130709, 6519, 180, 4, 61, "Text"],
Cell[130892, 6525, 78, 2, 40, "Input"],
Cell[130973, 6529, 96, 2, 40, "Input"],
Cell[131072, 6533, 83, 2, 40, "Input"],
Cell[131158, 6537, 105, 2, 40, "Input"],
Cell[131266, 6541, 165, 4, 63, "Input"],
Cell[131434, 6547, 57, 0, 38, "Text"],

Cell[CellGroupData[{
Cell[131516, 6551, 126, 3, 40, "Input"],
Cell[131645, 6556, 45889, 1558, 279, 19770, 1230, "GraphicsData", \
"PostScript", "Graphics"],
Cell[177537, 8116, 155, 4, 40, "Output"]
}, Open  ]],
Cell[177707, 8123, 218, 4, 61, "Text"],
Cell[177928, 8129, 167, 4, 40, "Input"],
Cell[178098, 8135, 136, 3, 40, "Input"],
Cell[178237, 8140, 94, 3, 38, "Text"],
Cell[178334, 8145, 112, 2, 40, "Input"],
Cell[178449, 8149, 88, 3, 38, "Text"],
Cell[178540, 8154, 79, 2, 40, "Input"],

Cell[CellGroupData[{
Cell[178644, 8160, 442, 8, 109, "Input"],
Cell[179089, 8170, 51984, 1358, 462, 22842, 994, "GraphicsData", \
"PostScript", "Graphics"],
Cell[231076, 9530, 155, 4, 40, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}
]
*)



(*******************************************************************
End of Mathematica Notebook file.
*******************************************************************)