(***********************************************************************

                    Mathematica-Compatible Notebook

This notebook can be used on any computer system with Mathematica 3.0,
MathReader 3.0, or any compatible application. The data for the notebook 
starts with the line of stars above.

To get the notebook into a Mathematica-compatible application, do one of 
the following:

* Save the data starting with the line of stars above into a file
  with a name ending in .nb, then open the file inside the application;

* Copy the data starting with the line of stars above to the
  clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be
sent directly in email or through ftp in text mode.  Newlines can be
CR, LF or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing the 
word CacheID, otherwise Mathematica-compatible applications may try to 
use invalid cache data.

For more information on notebooks and Mathematica-compatible 
applications, contact Wolfram Research:
  web: http://www.wolfram.com
  email: info@wolfram.com
  phone: +1-217-398-0700 (U.S.)

Notebook reader applications are available free of charge from 
Wolfram Research.
***********************************************************************)

(*CacheID: 232*)


(*NotebookFileLineBreakTest
NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[     33004,       1237]*)
(*NotebookOutlinePosition[     33875,       1265]*)
(*  CellTagsIndexPosition[     33831,       1261]*)
(*WindowFrame->Normal*)



Notebook[{

Cell[CellGroupData[{
Cell["Geostrophic Adjustment", "Title",
  TextAlignment->Center],

Cell[TextData[{
  "Consider an initial displacement \[Eta](x,0) in a layer of shallow water.  \
The displacement is shaped like a \"tophat\" , with value of 1 for -L <x< L \
and a value 0 elsewhere.  The initial displacent is the superposition of a \
steady geostrophic solution ",
  Cell[BoxData[
      \(TraditionalForm\`\[Eta]\_g\)]],
  "(x,0) and gravity waves that will propagate away.  We find the  ",
  Cell[BoxData[
      \(TraditionalForm\`\[Eta]\_g\)]],
  "(x,0)."
}], "Text"],

Cell[TextData["First find the Fourier transform of \[Eta](x,0):"], "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(tran = Integrate[Cos[k\ x], {x, \(-L\), L}]\)], "Input"],

Cell[BoxData[
    \(\(2\ Sin[k\ L]\)\/k\)], "Output"]
}, Open  ]],

Cell[TextData[{
  "Check to see if the inverse transform gives back the tophat function.  (Is \
",
  Cell[BoxData[
      \(1\/\(2\ \)\)]],
  "(Sign[L-x]+Sign[L+x]) the tophat function?)."
}], "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(invtran = 
      Integrate[tran*Cos[k\ x], {k, \(-Infinity\), Infinity}]/\((2\ Pi)\)\)], 
  "Input"],

Cell[BoxData[
    RowBox[{\(1\/\(2\ \[Pi]\)\), 
      RowBox[{"(", 
        RowBox[{"If", "[", 
          RowBox[{
          \(Im[L - x] == 0 && Im[L + x] == 0\), ",", 
            \(\[Pi]\ \((Sign[L - x] + Sign[L + x])\)\), ",", 
            RowBox[{
              SubsuperscriptBox["\[Integral]", 
                InterpretationBox[\(-\[Infinity]\),
                  DirectedInfinity[ -1]], 
                InterpretationBox["\[Infinity]",
                  DirectedInfinity[ 1]]], 
              \(\(\(2\ Cos[k\ x]\ Sin[k\ L]\)\/k\) \[DifferentialD]k\)}]}], 
          "]"}], ")"}]}]], "Output"]
}, Open  ]],

Cell[TextData[
"Recall the amplitude of geostrophic part of a sine wave disturbance in \
\[Eta] is: "], "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(geopart = 1/\((1 + \((LR*k)\)^2)\)\)], "Input"],

Cell[BoxData[
    \(1\/\(1 + k\^2\ LR\^2\)\)], "Output"]
}, Open  ]],

Cell[TextData[{
  "We now find ",
  Cell[BoxData[
      \(TraditionalForm\`\[Eta]\_g\)]],
  "(x,0) using an inverse Fourier transform method: "
}], "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(geotran = 
      Integrate[tran*geopart*Cos[k\ x], {k, \(-Infinity\), Infinity}]/
        \((2\ Pi)\)\)], "Input"],

Cell[BoxData[
    RowBox[{\(1\/\(2\ \[Pi]\)\), 
      RowBox[{"(", 
        RowBox[{"If", "[", 
          RowBox[{
          \(Im[L - x] == 0 && Im[L + x] == 0 && 
              Arg[LR\^2] \[NotEqual] \[Pi]\), ",", 
            \(\[Pi]\ \((
                Sign[L - x]\ 
                    \((1 - Cosh[\@\(\((L - x)\)\^2\/LR\^2\)] + 
                        Sinh[\@\(\((L - x)\)\^2\/LR\^2\)])\) + 
                  Sign[L + x]\ 
                    \((1 - Cosh[\@\(\((L + x)\)\^2\/LR\^2\)] + 
                        Sinh[\@\(\((L + x)\)\^2\/LR\^2\)])\))\)\), ",", 
            RowBox[{
              SubsuperscriptBox["\[Integral]", 
                InterpretationBox[\(-\[Infinity]\),
                  DirectedInfinity[ -1]], 
                InterpretationBox["\[Infinity]",
                  DirectedInfinity[ 1]]], 
              \(\(\(2\ Cos[k\ x]\ Sin[k\ L]\)\/\(k\ \((1 + k\^2\ LR\^2)\)\)\) 
                \[DifferentialD]k\)}]}], "]"}], ")"}]}]], "Output"]
}, Open  ]],

Cell[TextData[{
  "All that stuff in the middle of the ",
  StyleBox["If",
    FontFamily->"Courier",
    FontWeight->"Bold"],
  " statement is what we are looking for.  We grab it with the mouse and \
clean it up with ",
  StyleBox["TrigToExp",
    FontFamily->"Courier",
    FontWeight->"Bold"],
  ":"
}], "Text"],

Cell[CellGroupData[{

Cell["\<\
trythis =TrigToExp[ 
  1/2*(Sign[L - x]*(-Cosh[Sqrt[(L - x)^2/LR^2]] + 
        Sinh[Sqrt[(L - x)^2/LR^2]] + 1) + 
     Sign[L + x]*(-Cosh[Sqrt[(L + x)^2/LR^2]] + 
        Sinh[Sqrt[(L + x)^2/LR^2]] + 1))]\
\>", "Input"],

Cell[BoxData[
    \(1\/2\ Sign[L - x] - 
      1\/2\ E\^\(-\@\(\((L - x)\)\^2\/LR\^2\)\)\ Sign[L - x] + 
      1\/2\ Sign[L + x] - 
      1\/2\ E\^\(-\@\(\((L + x)\)\^2\/LR\^2\)\)\ Sign[L + x]\)], "Output"]
}, Open  ]],

Cell["\<\
Make a function so that we can plot it out.  Notice I used = and \
not := to define the function.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(h[x_, \ LR_, \ L_] = trythis\)], "Input"],

Cell[BoxData[
    \(1\/2\ Sign[L - x] - 
      1\/2\ E\^\(-\@\(\((L - x)\)\^2\/LR\^2\)\)\ Sign[L - x] + 
      1\/2\ Sign[L + x] - 
      1\/2\ E\^\(-\@\(\((L + x)\)\^2\/LR\^2\)\)\ Sign[L + x]\)], "Output"]
}, Open  ]],

Cell["\<\
Let's see if the function works...well it does give back a \
number...that's nice...\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(h[1.9,  .1, 1. ]\)], "Input"],

Cell[BoxData[
    \(0.0000617049019161413969`\)], "Output"]
}, Open  ]],

Cell[TextData[
"For comparison, we need to be able to plot \[Eta](x,0):"], "Text"],

Cell[BoxData[
    \(h0[x_, L_] := 1/2*\((Sign[L - \ x] + \ \n\ \ \ \ \ Sign[L + \ x])\)\)], 
  "Input"],

Cell[TextData[{
  "We can nondimensionalize distance in terms of L, so L=1 in the argument \
list.  We plot the case for ",
  Cell[BoxData[
      \(TraditionalForm\`L\_R\)]],
  "=0, which is the same as the initial condition, and the solution for three \
other values of ",
  Cell[BoxData[
      \(TraditionalForm\`L\_R\)]],
  "."
}], "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(fourplots = 
      Plot[\n\t{h0[x, 1], h[x,  .25, 1], h[x, 1, 1], h[x, 4, 1]}, \n
        \t{x, \(-10\), 10}, PlotRange -> {\(- .2\), 1}, 
        AxesOrigin -> {\(-10\), 0}, \n
        PlotStyle -> {{RGBColor[1, 0, 0]}, \n\t\t\t{RGBColor[0, 0, 0]}, 
            \t{RGBColor[0, 0, 0]}, \n\t{RGBColor[0, 0, 0]}, 
            \t{RGBColor[0, 0, 0]}}, AxesLabel -> {x, h}\n]; \)\)], "Input"],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .61803 
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10  scalefont  setfont
% Scaling calculations
0.5 0.0476191 0.103006 0.515028 [
[.2619 .09051 -6 -9 ]
[.2619 .09051 6 0 ]
[.5 .09051 -3 -9 ]
[.5 .09051 3 0 ]
[.7381 .09051 -3 -9 ]
[.7381 .09051 3 0 ]
[.97619 .09051 -6 -9 ]
[.97619 .09051 6 0 ]
[1.025 .10301 0 -6 ]
[1.025 .10301 10 6 ]
[.01131 0 -24 -4.5 ]
[.01131 0 0 4.5 ]
[.01131 .20601 -18 -4.5 ]
[.01131 .20601 0 4.5 ]
[.01131 .30902 -18 -4.5 ]
[.01131 .30902 0 4.5 ]
[.01131 .41202 -18 -4.5 ]
[.01131 .41202 0 4.5 ]
[.01131 .51503 -18 -4.5 ]
[.01131 .51503 0 4.5 ]
[.01131 .61803 -6 -4.5 ]
[.01131 .61803 0 4.5 ]
[.02381 .64303 -5 0 ]
[.02381 .64303 5 12 ]
[ 0 0 0 0 ]
[ 1 .61803 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.2619 .10301 m
.2619 .10926 L
s
[(-5)] .2619 .09051 0 1 Mshowa
.5 .10301 m
.5 .10926 L
s
[(0)] .5 .09051 0 1 Mshowa
.7381 .10301 m
.7381 .10926 L
s
[(5)] .7381 .09051 0 1 Mshowa
.97619 .10301 m
.97619 .10926 L
s
[(10)] .97619 .09051 0 1 Mshowa
.125 Mabswid
.07143 .10301 m
.07143 .10676 L
s
.11905 .10301 m
.11905 .10676 L
s
.16667 .10301 m
.16667 .10676 L
s
.21429 .10301 m
.21429 .10676 L
s
.30952 .10301 m
.30952 .10676 L
s
.35714 .10301 m
.35714 .10676 L
s
.40476 .10301 m
.40476 .10676 L
s
.45238 .10301 m
.45238 .10676 L
s
.54762 .10301 m
.54762 .10676 L
s
.59524 .10301 m
.59524 .10676 L
s
.64286 .10301 m
.64286 .10676 L
s
.69048 .10301 m
.69048 .10676 L
s
.78571 .10301 m
.78571 .10676 L
s
.83333 .10301 m
.83333 .10676 L
s
.88095 .10301 m
.88095 .10676 L
s
.92857 .10301 m
.92857 .10676 L
s
.25 Mabswid
0 .10301 m
1 .10301 L
s
gsave
1.025 .10301 -61 -10 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 20 translate 1 -1 scale
gsave
0.000000 0.000000 0.000000 setrgbcolor
1.000000 setlinewidth
gsave
newpath
 61.000000 16.000000 moveto
 558.000000 16.000000 lineto
 558.000000 4.000000 lineto
 61.000000 4.000000 lineto
 61.000000 16.000000 lineto
closepath
clip newpath
63.000000 13.000000 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000000 0.000000 0.000000 setrgbcolor
(x) show
1.000000 setlinewidth
grestore
grestore
%%DocumentNeededResources: font Courier
%%DocumentSuppliedResources:
%%DocumentNeededFonts: Courier
%%DocumentSuppliedFonts:
%%DocumentFonts: font Courier
grestore
.02381 0 m
.03006 0 L
s
[(-0.2)] .01131 0 1 0 Mshowa
.02381 .20601 m
.03006 .20601 L
s
[(0.2)] .01131 .20601 1 0 Mshowa
.02381 .30902 m
.03006 .30902 L
s
[(0.4)] .01131 .30902 1 0 Mshowa
.02381 .41202 m
.03006 .41202 L
s
[(0.6)] .01131 .41202 1 0 Mshowa
.02381 .51503 m
.03006 .51503 L
s
[(0.8)] .01131 .51503 1 0 Mshowa
.02381 .61803 m
.03006 .61803 L
s
[(1)] .01131 .61803 1 0 Mshowa
.125 Mabswid
.02381 .02575 m
.02756 .02575 L
s
.02381 .0515 m
.02756 .0515 L
s
.02381 .07725 m
.02756 .07725 L
s
.02381 .12876 m
.02756 .12876 L
s
.02381 .15451 m
.02756 .15451 L
s
.02381 .18026 m
.02756 .18026 L
s
.02381 .23176 m
.02756 .23176 L
s
.02381 .25751 m
.02756 .25751 L
s
.02381 .28327 m
.02756 .28327 L
s
.02381 .33477 m
.02756 .33477 L
s
.02381 .36052 m
.02756 .36052 L
s
.02381 .38627 m
.02756 .38627 L
s
.02381 .43777 m
.02756 .43777 L
s
.02381 .46353 m
.02756 .46353 L
s
.02381 .48928 m
.02756 .48928 L
s
.02381 .54078 m
.02756 .54078 L
s
.02381 .56653 m
.02756 .56653 L
s
.02381 .59228 m
.02756 .59228 L
s
.25 Mabswid
.02381 0 m
.02381 .61803 L
s
gsave
.02381 .64303 -66 -4 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 20 translate 1 -1 scale
gsave
0.000000 0.000000 0.000000 setrgbcolor
1.000000 setlinewidth
gsave
newpath
 61.000000 16.000000 moveto
 558.000000 16.000000 lineto
 558.000000 4.000000 lineto
 61.000000 4.000000 lineto
 61.000000 16.000000 lineto
closepath
clip newpath
63.000000 13.000000 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000000 0.000000 0.000000 setrgbcolor
(h) show
1.000000 setlinewidth
grestore
grestore
%%DocumentNeededResources: font Courier
%%DocumentSuppliedResources:
%%DocumentNeededFonts: Courier
%%DocumentSuppliedFonts:
%%DocumentFonts: font Courier
grestore
0 0 m
1 0 L
1 .61803 L
0 .61803 L
closepath
clip
newpath
1 0 0 r
.5 Mabswid
.02381 .10301 m
.06244 .10301 L
.10458 .10301 L
.14415 .10301 L
.18221 .10301 L
.22272 .10301 L
.26171 .10301 L
.30316 .10301 L
.34309 .10301 L
.3815 .10301 L
.40095 .10301 L
.42237 .10301 L
.43215 .10301 L
.43755 .10301 L
.44268 .10301 L
.44744 .10301 L
.44874 .10301 L
.45013 .10301 L
.45143 .10301 L
.45262 .61803 L
.45379 .61803 L
.45487 .61803 L
.45731 .61803 L
.46172 .61803 L
.5012 .61803 L
.52107 .61803 L
.52974 .61803 L
.53918 .61803 L
.5417 .61803 L
.54438 .61803 L
.54548 .61803 L
.54667 .61803 L
.54797 .10301 L
.54919 .10301 L
.55869 .10301 L
.5796 .10301 L
.62074 .10301 L
.66036 .10301 L
.69847 .10301 L
.73903 .10301 L
.77808 .10301 L
.81958 .10301 L
.85956 .10301 L
.89802 .10301 L
.93894 .10301 L
.97619 .10301 L
s
0 0 0 r
.02381 .10301 m
.02605 .10301 L
.02846 .10301 L
.03279 .10301 L
.03543 .10301 L
.03793 .10301 L
.04262 .10301 L
.04502 .10301 L
.04756 .10301 L
.05212 .10301 L
.05466 .10301 L
.05704 .10301 L
.06244 .10301 L
.06504 .10301 L
.06788 .10301 L
.07038 .10301 L
.07305 .10301 L
.07568 .10301 L
.07807 .10301 L
.08274 .10301 L
.08556 .10301 L
.08814 .10301 L
.09099 .10301 L
.09399 .10301 L
.09904 .10301 L
.1019 .10301 L
.10458 .10301 L
.10959 .10301 L
.11241 .10301 L
.11503 .10301 L
.11983 .10301 L
.12226 .10301 L
.12493 .10301 L
.12954 .10301 L
.13213 .10301 L
.1345 .10301 L
.13888 .10301 L
.14108 .10301 L
.14349 .10301 L
.14602 .10301 L
.14877 .10301 L
.1512 .10301 L
.15376 .10301 L
.15608 .10301 L
.15862 .10301 L
.1631 .10301 L
.16583 .10301 L
.16832 .10301 L
.171 .10301 L
.17392 .10301 L
Mistroke
.17662 .10301 L
.17912 .10301 L
.18405 .10301 L
.1867 .10301 L
.18914 .10301 L
.19177 .10301 L
.19464 .10301 L
.19949 .10301 L
.20214 .10301 L
.20461 .10301 L
.20703 .10301 L
.20932 .10301 L
.2136 .10301 L
.216 .10301 L
.21822 .10301 L
.22084 .10301 L
.22323 .10301 L
.22788 .10301 L
.23032 .10301 L
.23288 .10301 L
.23721 .10301 L
.23966 .10301 L
.24193 .10301 L
.24462 .10301 L
.24716 .10301 L
.25191 .10301 L
.25457 .10301 L
.25702 .10301 L
.25991 .10301 L
.26255 .10301 L
.26724 .10301 L
.26982 .10301 L
.27227 .10301 L
.27662 .10301 L
.27908 .10301 L
.28135 .10301 L
.28611 .10301 L
.28882 .10301 L
.29136 .10301 L
.29648 .10301 L
.29936 .10301 L
.302 .10301 L
.30673 .10301 L
.30938 .10301 L
.31179 .10301 L
.31404 .10301 L
.31648 .10301 L
.32091 .10301 L
.32339 .10301 L
.32613 .10301 L
Mistroke
.32899 .10301 L
.33167 .10302 L
.33645 .10302 L
.33914 .10302 L
.3416 .10303 L
.34637 .10304 L
.34904 .10305 L
.35145 .10306 L
.35372 .10307 L
.35616 .10309 L
.3606 .10312 L
.3631 .10315 L
.36585 .10319 L
.36872 .10323 L
.3714 .10329 L
.37619 .10343 L
.37888 .10354 L
.38133 .10366 L
.38614 .10399 L
.38857 .10422 L
.39125 .10452 L
.39353 .10484 L
.39598 .10526 L
.40042 .10628 L
.40295 .10705 L
.4057 .10811 L
.40858 .10951 L
.41126 .11114 L
.41606 .11519 L
.41875 .11827 L
.42119 .12175 L
.42605 .13118 L
.42849 .13761 L
.43118 .14639 L
.43348 .15561 L
.43594 .16771 L
.44039 .19703 L
.44306 .22066 L
.44597 .25323 L
.45126 .33736 L
.45604 .4285 L
.45872 .46675 L
.46119 .49501 L
.46379 .51905 L
.46653 .53929 L
.46913 .5546 L
.47155 .56613 L
.47602 .58205 L
.47839 .58829 L
.48092 .59366 L
Mistroke
.48363 .59818 L
.48657 .60193 L
.48934 .60456 L
.49191 .60634 L
.49422 .60747 L
.49553 .60793 L
.49676 .60825 L
.49806 .60848 L
.49924 .60858 L
.4999 .6086 L
.50061 .60859 L
.50191 .60848 L
.50256 .60838 L
.50324 .60825 L
.50446 .60793 L
.50578 .60747 L
.50722 .60681 L
.50981 .60522 L
.51222 .60318 L
.51458 .60059 L
.51673 .59764 L
.52157 .58838 L
.52425 .58125 L
.52673 .57299 L
.52945 .56166 L
.53234 .54637 L
.53719 .51059 L
.53995 .48265 L
.54254 .44978 L
.54763 .36014 L
.55237 .27574 L
.55476 .24434 L
.55731 .21706 L
.5599 .19473 L
.56272 .17543 L
.56531 .16126 L
.5677 .15065 L
.56994 .14248 L
.57241 .13509 L
.57669 .1254 L
.57903 .12141 L
.58122 .11831 L
.58619 .11308 L
.58901 .11096 L
.59162 .1094 L
.5964 .10728 L
.59908 .10642 L
.6015 .10579 L
.60609 .1049 L
.60867 .10453 L
Mistroke
.61104 .10426 L
.61542 .10387 L
.61762 .10373 L
.62003 .10359 L
.62255 .10348 L
.62528 .10338 L
.6277 .10331 L
.63026 .10325 L
.63256 .10321 L
.6351 .10317 L
.63957 .10312 L
.64228 .1031 L
.64477 .10308 L
.64744 .10306 L
.65037 .10305 L
.6553 .10304 L
.65799 .10303 L
.66049 .10303 L
.66556 .10302 L
.66841 .10302 L
.67104 .10301 L
.67587 .10301 L
.67831 .10301 L
.68098 .10301 L
.68562 .10301 L
.68822 .10301 L
.69059 .10301 L
.6928 .10301 L
.69521 .10301 L
.69958 .10301 L
.7019 .10301 L
.70441 .10301 L
.70896 .10301 L
.71159 .10301 L
.71436 .10301 L
.71932 .10301 L
.72183 .10301 L
.72451 .10301 L
.72934 .10301 L
.7323 .10301 L
.73509 .10301 L
.73779 .10301 L
.74032 .10301 L
.74493 .10301 L
.74738 .10301 L
.75002 .10301 L
.75277 .10301 L
.75539 .10301 L
.75776 .10301 L
.7603 .10301 L
Mistroke
.7627 .10301 L
.76487 .10301 L
.76911 .10301 L
.7715 .10301 L
.77407 .10301 L
.77874 .10301 L
.78111 .10301 L
.78366 .10301 L
.78825 .10301 L
.79105 .10301 L
.79371 .10301 L
.79868 .10301 L
.80123 .10301 L
.80393 .10301 L
.80877 .10301 L
.81147 .10301 L
.81399 .10301 L
.81697 .10301 L
.81975 .10301 L
.82445 .10301 L
.82693 .10301 L
.82958 .10301 L
.83238 .10301 L
.83501 .10301 L
.8374 .10301 L
.83994 .10301 L
.84214 .10301 L
.84456 .10301 L
.84882 .10301 L
.85122 .10301 L
.85379 .10301 L
.85844 .10301 L
.86099 .10301 L
.8637 .10301 L
.86858 .10301 L
.87157 .10301 L
.87438 .10301 L
.87693 .10301 L
.87962 .10301 L
.88203 .10301 L
.88466 .10301 L
.88929 .10301 L
.8919 .10301 L
.89469 .10301 L
.89973 .10301 L
.9023 .10301 L
.90503 .10301 L
.90993 .10301 L
.91265 .10301 L
.9152 .10301 L
Mistroke
.91818 .10301 L
.92101 .10301 L
.92343 .10301 L
.92608 .10301 L
.93071 .10301 L
.93333 .10301 L
.93612 .10301 L
.93876 .10301 L
.94115 .10301 L
.94541 .10301 L
.94774 .10301 L
.94991 .10301 L
.95375 .10301 L
.95798 .10301 L
.95911 .10301 L
.96034 .10301 L
.9615 .10301 L
.96257 .10301 L
.96354 .10301 L
.9646 .10301 L
.96572 .10301 L
.96676 .10301 L
.96792 .10301 L
.96913 .10301 L
.97017 .10301 L
.9713 .10301 L
.97252 .10301 L
.97383 .10301 L
.97507 .10301 L
.97619 .10301 L
Mfstroke
.02381 .10303 m
.03279 .10304 L
.04262 .10305 L
.06244 .10307 L
.07298 .10308 L
.08426 .1031 L
.10458 .10316 L
.1148 .10319 L
.12589 .10324 L
.13547 .10329 L
.14603 .10336 L
.16586 .10355 L
.17672 .10369 L
.18689 .10385 L
.19727 .10406 L
.20714 .1043 L
.22566 .10491 L
.23525 .10534 L
.24547 .10589 L
.26386 .10725 L
.27414 .10828 L
.28527 .10967 L
.29488 .11116 L
.30544 .11318 L
.32538 .11847 L
.33627 .12245 L
.34644 .12708 L
.35689 .13298 L
.36679 .13991 L
.38535 .1575 L
.395 .16974 L
.40526 .18578 L
.42368 .22487 L
.43305 .25138 L
.44315 .28644 L
.46143 .36295 L
.471 .39234 L
.47643 .40487 L
.48147 .41404 L
.48422 .41807 L
.48682 .42126 L
.48918 .42365 L
.49167 .42566 L
.49297 .4265 L
.49439 .42725 L
.49569 .42779 L
.4969 .42816 L
.49763 .42833 L
.49833 .42845 L
.49963 .42856 L
Mistroke
.50036 .42856 L
.50104 .42852 L
.50178 .42843 L
.50257 .42829 L
.50382 .42796 L
.50519 .42744 L
.50661 .42674 L
.50794 .42592 L
.51033 .42409 L
.51288 .42159 L
.51871 .41375 L
.52402 .40394 L
.53439 .37696 L
.54421 .34089 L
.56246 .26604 L
.57285 .23409 L
.58259 .20985 L
.6024 .17348 L
.61252 .15998 L
.62342 .14833 L
.6435 .13274 L
.65359 .12706 L
.66461 .12209 L
.68426 .11564 L
.69525 .11303 L
.70523 .11114 L
.72445 .10844 L
.73528 .10733 L
.74526 .10651 L
.76406 .10537 L
.77474 .10489 L
.78472 .10454 L
.79515 .10424 L
.80504 .10401 L
.82359 .10368 L
.83323 .10356 L
.84348 .10345 L
.86189 .10331 L
.87124 .10325 L
.88134 .10321 L
.89961 .10314 L
.90916 .10312 L
.91962 .1031 L
.93067 .10308 L
.94072 .10306 L
.95786 .10305 L
.96729 .10304 L
.97619 .10303 L
Mfstroke
.02381 .11369 m
.06244 .11609 L
.10458 .11933 L
.14415 .12309 L
.18221 .12754 L
.22272 .13335 L
.26171 .14024 L
.30316 .14929 L
.34309 .16009 L
.3815 .17284 L
.42237 .18956 L
.44268 .1993 L
.45262 .20446 L
.46172 .2088 L
.47106 .21229 L
.47994 .2147 L
.48481 .21565 L
.48932 .2163 L
.49192 .21657 L
.49427 .21675 L
.49558 .21682 L
.49626 .21685 L
.49699 .21688 L
.49763 .2169 L
.49832 .21691 L
.49955 .21693 L
.50086 .21693 L
.50206 .21691 L
.50269 .21689 L
.50339 .21687 L
.50479 .2168 L
.50602 .21673 L
.50735 .21663 L
.50976 .2164 L
.51212 .21612 L
.51461 .21575 L
.51906 .21492 L
.52424 .21368 L
.52905 .21226 L
.53998 .20806 L
.57902 .18893 L
.62052 .17211 L
.6605 .15902 L
.69897 .14878 L
.73989 .13993 L
.77929 .13303 L
.81718 .12762 L
.85752 .12292 L
.89634 .11925 L
.93762 .11608 L
Mistroke
.97619 .11369 L
Mfstroke
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  ImageSize->{288, 177.938},
  ImageMargins->{{43, 0}, {0, 0}},
  ImageRegion->{{0, 1}, {0, 1}},
  ImageCache->GraphicsData["Bitmap", "\<\
CF5dJ6E]HGAYHf4PAg9QL6QYHg<PAVmbKF5d0`40004P0000/A000`40O003h00Oogoo8Goo003oOolQ
Ool000Qoo`8000Aoo`8000=oo`@00?moo`Yoo`001goo00@007ooOol000=oo`8000Aoo`03001oogoo
0?moo`Yoo`0000=oo`0000000`0000Eoo`00Oomoo`0000Yoo`03001oogoo00=oo`800?moo`Aoo`00
1goo00@007ooOol000]oo`03001oogoo009oo`03001oogoo0?moo`=oo`001goo00@007ooOol000Qo
o`04001oogoo0004Ool00`00Oomoo`3oOol3Ool000Qoo`8000Yoo`8000Eoo`03001oogoo0?moo`=o
o`006goo00<007ooOol0ogoo0goo000KOol00`00Oomoo`3oOol3Ool001]oo`800?moo`Aoo`006goo
00<007ooOol0ogoo0goo000KOol00`00Oomoo`3oOol3Ool001]oo`03001oogoo0?moo`=oo`006goo
00<007ooOol0ogoo0goo000KOol00`00Oomoo`3oOol3Ool001]oo`03001oogoo0?moo`=oo`006goo
0P00ogoo17oo000KOol00`00Oomoo`3oOol3Ool001]oo`03001oogoo0?moo`=oo`006goo00<007oo
Ool0>Goo0`00=Woo0P00>Goo0`00=Goo0`0017oo0P0057oo000KOol00`00Oomoo`0lOol00`00Oomo
o`0bOol01000Oomoo`00>goo00<007ooOol0<goo00<007ooOol00Woo00@007ooOol001=oo`006goo
00<007ooOol0<goo1@0017oo00<007ooOol0<Woo00@007ooOol003]oo`03001oogoo03=oo`03001o
ogoo009oo`04001oogoo000COol001]oo`8003Yoo`<003Eoo`04001oogoo000hOol3000fOol00`00
Oomoo`02Ool01000Oomoo`004goo000KOol00`00Oomoo`0iOol00`00Oomoo`0eOol01000Oomoo`00
>7oo00<007ooOol0=Woo00<007ooOol00Woo00@007ooOol001=oo`006goo00<007ooOol0>Goo1000
=Goo0P00>Goo1000=7oo0P001Goo0P0057oo000KOol00`00Oomoo`3oOol3Ool001]oo`03001oogoo
0?moo`=oo`006goo00<007ooOol0n7oo0P0000=oo`0000001Goo000KOol00`00Oomoo`3iOol00`00
Ool00006Ool001Eoof@000el01L000il06@000Uoo`03001oogoo00Eoo`006goo00<007ooOol02Goo
00<007ooOol027oo00<007ooOol02Goo00<007ooOol02Goo00<007ooOol02Goo200017oo00<007oo
Ool02Goo00<007ooOol027oo0`002Goo00=l0000Ool02Goo00<007ooOol02Goo00=l07ooOol027oo
0`002Woo00<007ooOol02Goo00<007ooOol00goo2P0027oo00<007ooOol02Goo00<007ooOol02Goo
00<007ooOol027oo00<007ooOol02Goo00<007ooOol037oo00<007oo00001Woo000KOol6000mOol5
000HOol20008Ool00g`0Oomoo`0EOol00g`0Oomoo`07Ool2000HOol6000mOol5000=Ool200000goo
00000005Ool001]oo`03001oogoo00=oo`X003Qoo`<001Moo`03001oogoo00Eoo`03O01oogoo01Eo
o`03O01oogoo00Moo`03001oogoo01Aoo`<003Uoo`X001aoo`006goo00<007ooOol03Goo2P00<Goo
0`0057oo0P001Woo00=l07ooOol05Goo00=l07ooOol01Goo0P005Goo0P00<Woo2P009Woo000KOol0
0`00Oomoo`0GOol:000ZOol2000COol00`00Oomoo`04Ool00g`0Oomoo`0EOol00g`0Oomoo`05Ool0
0`00Oomoo`0BOol2000ZOol:000`Ool001]oo`80029oo`T002=oo`<0015oo`03001oogoo00=oo`03
O01oogoo01Eoo`03O01oogoo00Eoo`03001oogoo00moo`<0029oo`X003Yoo`006goo00<007ooOol0
:Woo20007Woo00<007ooOol03Woo00<007ooOol00goo00=l07ooOol05Goo00=l07ooOol017oo00<0
07ooOol03Goo0`007Woo1`00A7oo000KOol00`00Oomoo`0bOol5000JOol00`00Oomoo`0>Ool00`00
Oomoo`02Ool00g`0Oomoo`0EOol00g`0Oomoo`04Ool00`00Oomoo`0<Ool00`00Oomoo`0JOol5001;
Ool001]oo`03001oogoo03Moo`D001Ioo`8000ioo`03001oogoo009oo`03O01oogoo01Eoo`03O01o
ogoo00Aoo`03001oogoo00]oo`03001oogoo01Ioo`D0051oo`006goo00<007ooOol0?7oo1@004goo
00<007ooOol02goo00<007ooOol00Woo00=l07ooOol05Goo00=l07ooOol00goo00<007ooOol02goo
00<007ooOol04Woo1@00EGoo000KOol00`00Oomoo`11Ool4000@Ool00`00Oomoo`0:Ool00`00Oomo
o`02Ool00g`0Oomoo`0EOol00g`0Oomoo`03Ool00`00Oomoo`0:Ool00`00Oomoo`0?Ool4001JOol0
01]oo`03001oogoo04Eoo`<000ioo`03001oogoo00Uoo`03001oogoo009oo`03O01oogoo01Eoo`03
O01oogoo009oo`03001oogoo00]oo`03001oogoo00aoo`<005ioo`006goo0P00BGoo0`0037oo00<0
07ooOol02Goo00D007ooOomoog`001Moo`03O01oogoo009oo`03001oogoo00Yoo`03001oogoo00Yo
o`<0065oo`006goo00<007ooOol0Bgoo100027oo00<007ooOol02Goo00D007ooOomoog`001Moo`03
O01oogoo009oo`03001oogoo00Uoo`03001oogoo00Moo`@006Aoo`006goo00<007ooOol0Cgoo0`00
1Woo00<007ooOol027oo00D007ooOomoog`001Moo`03O01oogoo009oo`03001oogoo00Qoo`03001o
ogoo00Eoo`<006Qoo`006goo00<007ooOol0DWoo0`0017oo00<007ooOol01goo00D007ooOomoog`0
01Moo`03O01oogoo009oo`03001oogoo00Moo`03001oogoo00=oo`<006]oo`006goo00<007ooOol0
EGoo0`0000=oo`00Ool027oo00D007ooOomoog`001Moo`05O01oogooOol00009Ool01000Oomoogoo
0`00KWoo000KOol00`00Oomoo`1HOol30008Ool01@00OomoogooO0005goo00El07ooOomoo`0000Uo
o`@0075oo`006goo0P00G7oo0P001goo00@007ooOoml01Moo`05O01oogooOol00007Ool3001dOol0
01]oo`03001oogoo05aoo`@000Aoo`04001oogooO00GOol01G`0Oomoogoo000017oo0`0000=oo`00
Ool0M7oo000KOol00`00Oomoo`1LOol01000Oomoogoo0P000Woo00@007ooOoml01Moo`04O01oogoo
0003Ool20003Ool00`00Oomoo`1dOol001]oo`03001oogoo05eoo`03001oogoo009oo`800004Ool0
07ooO00GOol01G`0Oomoo`00Ool00P0017oo00<007ooOol0MGoo0008Ool20004Ool20003Ool40004
Ool00`00Oomoo`1MOol00`00Oomoo`04Ool200000gooO01oo`0FOol00g`0Oomoo`020006Ool00`00
Oomoo`1eOol000Moo`04001oogoo0003Ool20004Ool00`00Oomoo`04Ool00`00Oomoo`1MOol00`00
Oomoo`05Ool3000GOol017`0000000001Woo00<007ooOol0MWoo0007Ool01000Oomoo`002Woo00<0
07ooOol00goo0P00Ggoo00<007ooOol017oo00<007ooO0000P0057oo0P000Woo00<007ooOol017oo
00<007ooOol0MWoo0007Ool01000Oomoo`002goo00<007ooOol00Woo00<007ooOol0GWoo00<007oo
Ool017oo00<007ooO0000Woo0P0047oo0P0000Eoog`0Oomoo`0000Eoo`03001oogoo07Moo`001goo
00@007ooOol000Qoo`04001oogoo0004Ool00`00Oomoo`1OOol00`00Oomoo`03Ool00`00Ooml0004
Ool2000;Ool30003Ool017`0Oomoo`001Goo00<007ooOol0Mgoo0008Ool2000:Ool20005Ool00`00
Oomoo`1OOol00`00Oomoo`03Ool00`00Ooml0006Ool;0006Ool017`0Oomoo`0017oo00<007ooOol0
N7oo000KOol00`00Oomoo`1OOol00`00Oomoo`03Ool00`00Ooml000GOol017`0Oomoo`0017oo00<0
07ooOol0N7oo000KOol00`00Oomoo`1POol00`00Oomoo`02Ool00`00Ooml000GOol017`0Oomoo`00
17oo00<007ooOol0N7oo000KOol00`00Oomoo`1POol00`00Oomoo`02Ool00`00Ooml000GOol017`0
Oomoo`000goo00<007ooOol0NGoo000KOol2001ROol01`00Oomoogoo001oog`001Moo`03O01oo`00
00Aoo`03001oogoo07Uoo`006goo00<007ooOol0HGoo00L007ooOomoo`00Ooml000GOol00g`0Ool0
0004Ool00`00Oomoo`1iOol001]oo`03001oogoo069oo`06001oogooOol007`05goo00=l07oo0000
0goo00<007ooOol0NWoo000KOol00`00Oomoo`1ROol01P00Oomoogoo001l01Moo`03O01oo`0000=o
o`03001oogoo07Yoo`006goo00<007ooOol0HWoo00H007ooOomoo`00O00GOol00g`0Ool00003Ool0
0`00Oomoo`1jOol001]oo`03001oogoo06=oo`05001oogoo001l000GOol00g`0Ool00002Ool00`00
Oomoo`1kOol001]oo`8006Aoo`05001oogoo001l000GOol00g`0Ool00002Ool00`00Oomoo`1kOol0
01]oo`03001oogoo06=oo`05001oogoo001l000GOol00g`0Ool00002Ool00`00Oomoo`1kOol001]o
o`03001oogoo06Aoo`04001oo`00O00GOol01G`0Ool007oo0000OWoo000KOol00`00Oomoo`1TOol0
1000Ool007`05goo00El07oo001oo`0007ioo`006goo00<007ooOol0I7oo00@007oo001l01Moo`05
O01oo`00Ool0001nOol001]oo`03001oogoo06Aoo`04001oo`00O00GOol017`0Ool00000Ogoo000K
Ool00`00Oomoo`1TOol01000Ool007`05goo00Al07oo000007moo`006goo0P00IWoo0P0000=l07oo
Ool05Goo00Al07oo000007moo`006goo00<007ooOol0IGoo0P0000=l07ooOol05Goo00Al07oo0000
07moo`006goo00<007ooOol0IGoo0P0000=l07ooOol05Goo00Al07oo000007moo`006goo00<007oo
Ool0IGoo00<007oo00005goo00=l07oo0000P7oo0008Ool20004Ool20004Ool30004Ool00`00Oomo
o`1VOol2000GOol00g`000000020Ool000Moo`04001oogoo0003Ool20005Ool00`00Oomoo`03Ool0
0`00Oomoo`1VOol2000GOol00g`000000020Ool000Moo`04001oogoo0008Ool40004Ool2001WOol2
000GOol00g`000000020Ool000Moo`04001oogoo0008Ool00`00Ool00005Ool00`00Oomoo`1VOol2
000GOol00g`000000020Ool000Moo`04001oogoo0008Ool00`00Ool00005Ool00`00Oomoo`1WOol0
0`00Oomoo`0EOol00g`0001oo`20Ool000Qoo`8000Yoo`8000Eoo`03001oogoo06Moo`03001oogoo
01Eoo`03O00007oo081oo`006goo00<007ooOol0Igoo00<007ooOol05Goo00=l0000Ool0P7oo000K
Ool00`00Oomoo`1WOol2000FOol00g`0001oo`20Ool001]oo`03001oogoo06Moo`8001Ioo`03O000
07oo081oo`006goo0P00J7oo0P005Woo0P00PGoo000KOol00`00Oomoo`1WOol2000FOol20021Ool0
01]oo`03001oogoo06Moo`03001oo`0001Eoo`03001oogoo081oo`006goo00<007ooOol0Igoo00<0
07oo000057oo0P00PWoo000KOol00`00Oomoo`1WOol00`00Ool0000DOol20022Ool001]oo`03001o
ogoo06Moo`03001oo`0001Aoo`80089oo`006goo0P00J7oo00@007ooOol0019oo`03001oo`00089o
o`006goo00<007ooOol0J7oo00<007oo00004Woo00<007oo0000PWoo000KOol00`00Oomoo`1XOol0
0`00Ool0000BOol00`00Ool00022Ool001]oo`03001oogoo06Qoo`03001oo`00015oo`04001oogoo
0022Ool001]oo`03001oogoo06Qoo`04001oogoo000@Ool01000Oomoo`00PWoo000KOol00`00Oomo
o`1XOol01000Oomoo`0047oo00@007ooOol0089oo`006goo0P00JGoo00@007ooOol000moo`05001o
ogooOol00022Ool001]oo`03001oogoo06Qoo`05001oogooOol0000>Ool01@00Oomoogoo0000PWoo
000KOol00`00Oomoo`1XOol01@00Oomoogoo00003Goo00<007ooOol00Woo00<007ooOol0P7oo000K
Ool00`00Oomoo`1XOol01@00Oomoogoo00003Goo00<007ooOol00Woo00<007ooOol0P7oo000KOol0
0`00Oomoo`1XOol00`00Oomoo`02Ool00`00Oomoo`0:Ool00`00Oomoo`02Ool00`00Oomoo`20Ool0
00Qoo`8000Aoo`8000Aoo`8000Eoo`03001oogoo06Qoo`03001oogoo00=oo`03001oogoo00Qoo`03
001oogoo00=oo`03001oogoo081oo`001goo00@007ooOol000=oo`8000=oo`04001oogoo0004Ool0
0`00Oomoo`1XOol00g`0001oo`03Ool00`00Oomoo`08Ool00`00Oomoo`02Ool00`00O01oo`21Ool0
00Moo`04001oogoo0008Ool01000Oomoo`0017oo0P00JGoo00=l0000Ool017oo00<007ooOol01Woo
00<007ooOol00goo00<007`0Ool0PGoo0007Ool01000Oomoo`0027oo0`001Goo00<007ooOol0J7oo
00=l0000Ool01Goo00<007ooOol01Goo00<007ooOol00goo00<007`0Ool0PGoo0007Ool01000Oomo
o`0027oo00<007ooOol01Goo00<007ooOol0J7oo00=l0000Ool01Goo00<007ooOol017oo00<007oo
Ool017oo00<007`0Ool0PGoo0008Ool2000:Ool30004Ool00`00Oomoo`1XOol00g`0001oo`06Ool2
0002Ool20007Ool00`00O01oo`21Ool001]oo`03001oogoo06Qoo`03O00007oo00Moo`@000Qoo`03
001l07oo085oo`006goo00<007ooOol0J7oo00=l0000Ool04goo00<007`0Ool0PGoo000KOol2001Y
Ool00g`0001oo`0COol00`00O01oo`21Ool001]oo`03001oogoo06Qoo`03O00007oo01=oo`03001l
07oo085oo`006goo00<007ooOol0J7oo00=l0000Ool04goo00<007`0Ool0PGoo000KOol00`00Oomo
o`1XOol00g`0001oo`0COol00`00O01oo`21Ool001]oo`03001oogoo06Qoo`03O00007oo01=oo`03
001l07oo085oo`006goo00<007ooOol0J7oo00=l0000Ool04goo00<007`0Ool0PGoo000KOol00`00
Oomoo`1XOol00g`0001oo`0COol00`00O01oo`21Ool001]oo`8006Uoo`03O00007oo01=oo`03001l
07oo085oo`006goo00<007ooOol0J7oo00=l0000Ool04Woo00<007ooO000PWoo000KOol00`00Oomo
o`1XOol00g`0001oo`0BOol00`00Ooml0022Ool001]oo`03001oogoo06Qoo`03O00007oo019oo`03
001oog`0089oo`006goo00<007ooOol0J7oo00=l0000Ool04Woo00<007ooO000PWoo000KOol00`00
Oomoo`1XOol00g`0Ool0000BOol00`00Ooml0022Ool001]oo`8006Uoo`03O01oo`00019oo`03001o
og`0089oo`006goo00<007ooOol0J7oo00=l07oo00004Woo00<007ooO000PWoo000KOol00`00Oomo
o`1XOol00g`0Ool0000BOol00`00Ooml0022Ool001]oo`03001oogoo06Qoo`03O01oo`00019oo`03
001oog`0089oo`006goo00<007ooOol0J7oo00=l07oo00004Woo00<007ooO000PWoo0008Ool20004
Ool20004Ool20005Ool00`00Oomoo`1XOol00g`0Ool0000BOol00`00Ooml0022Ool000Moo`04001o
ogoo0003Ool20003Ool01000Oomoo`0017oo00<007ooOol0J7oo00=l07oo00004Woo00<007ooO000
PWoo0007Ool01000Oomoo`0027oo00@007ooOol000Aoo`8006Uoo`03O01oo`00019oo`03001oog`0
089oo`001goo00@007ooOol000Uoo`8000Eoo`03001oogoo06Qoo`03O01oo`00019oo`03001oog`0
089oo`001goo00@007ooOol000Qoo`04001oogoo0004Ool00`00Oomoo`1XOol00g`0Ool0000BOol0
0`00Ooml0022Ool000Qoo`8000Yoo`8000Eoo`03001oogoo06Qoo`03O01oo`00015oo`04001oogoo
O022Ool001]oo`03001oogoo06Qoo`04O01oogoo000@Ool01000Oomoog`0PWoo000KOol00`00Oomo
o`1XOol017`0Oomoo`0047oo00@007ooOoml089oo`006goo0P00JGoo00Al07ooOol0011oo`04001o
ogooO022Ool001]oo`03001oogoo06Qoo`04O01oogoo000@Ool01000Oomoog`0PWoo000KOol00`00
Oomoo`1XOol01G`0Oomoogoo00003goo00@007ooOoml089oo`006goo00<007ooOol0J7oo00El07oo
Oomoo`0000moo`04001oogooO022Ool001]oo`03001oogoo06Qoo`05O01oogooOol0000>Ool01@00
OomoogooO000PWoo000KOol00`00Oomoo`1XOol01G`0Oomoogoo00003Woo00D007ooOomoog`0089o
o`006goo0P00JGoo00El07ooOomoo`0000ioo`05001oogooOoml0022Ool001]oo`03001oogoo06Qo
o`05O01oogooOol0000=Ool00`00Oomoo`02Ool00g`0Oomoo`20Ool001]oo`03001oogoo06Qoo`05
O01oogooOol0000=Ool00`00Oomoo`02Ool00g`0Oomoo`20Ool001]oo`03001oogoo06Qoo`03O01o
ogoo009oo`03001oogoo00Yoo`03001oogoo009oo`03O01oogoo081oo`006goo00<007ooOol0J7oo
00=l07ooOol00Woo00<007ooOol02Woo00<007ooOol00Woo00=l07ooOol0P7oo000KOol00`00Oomo
o`1XOol00g`0Oomoo`02Ool00`00Oomoo`0:Ool00`00Oomoo`02Ool00g`0Oomoo`20Ool001]oo`03
001oogoo06Qoo`03O01oogoo00=oo`03001oogoo00Qoo`03001oogoo00=oo`03O01oogoo081oo`00
6goo0P00JGoo00=l07ooOol017oo00<007ooOol01goo00<007ooOol00goo00=l07ooOol0P7oo000K
Ool00`00Oomoo`1XOol00g`0Oomoo`04Ool00`00Oomoo`06Ool00`00Oomoo`04Ool00g`0Oomoo`20
Ool001]oo`03001oogoo06Qoo`03O01oogoo00Eoo`03001oogoo00Aoo`03001oogoo00Eoo`03O01o
ogoo081oo`006goo00<007ooOol0J7oo00=l07ooOol01Woo00@007ooOomoo`<000Moo`03O01oogoo
081oo`004goo0`001Goo00<007ooOol0J7oo00=l07ooOol01goo10002Goo00=l07ooOol0P7oo000D
Ool00`00Oomoo`04Ool00`00Oomoo`1XOol00g`0Oomoo`0DOol00g`0Oomoo`20Ool001Aoo`03001o
ogoo00Aoo`8006UooaQl089oo`0057oo00<007ooOol0ogoo2Woo000DOol00`00Oomoo`3oOol:Ool0
01=oo`800?moo`aoo`00ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol00?moob5o
o`006Goo0P0000=oo`000000ogoo0goo000IOol01000Oomoo`00ogoo17oo000IOol01000Oomoo`00
ogoo17oo000IOol01000Oomoo`00ogoo17oo000IOol4003oOol4Ool001Uoo`03001oogoo0?moo`Eo
o`0067oo0P00ogoo1goo003oOolQOol00?moob5oo`00\
\>"],
  ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-12.2861, -0.235027, 
  0.0841683, 0.00778214}}]
}, Open  ]],

Cell[BoxData[
    \(\(Display["\<fourplots.eps\>", fourplots, "\<EPS\>"]; \)\)], "Input"]
}, Open  ]]
},
FrontEndVersion->"Macintosh 3.0",
ScreenRectangle->{{0, 1024}, {0, 748}},
WindowSize->{490, 659},
WindowMargins->{{Automatic, 148}, {30, Automatic}},
StyleDefinitions -> "ok.nb",
MacintoshSystemPageSetup->"\<\
00<0001804P000000]P2:?oQon82n@960dL5:0?l0080001804P000000]P2:001
0000I00000400`<300000BL?00400@00000000000000060801T1T000000@0000
00000000004000000000000000000000\>"
]


(***********************************************************************
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[1731, 51, 64, 1, 49, "Title"],
Cell[1798, 54, 486, 11, 123, "Text"],
Cell[2287, 67, 74, 0, 53, "Text"],

Cell[CellGroupData[{
Cell[2386, 71, 76, 1, 47, "Input"],
Cell[2465, 74, 53, 1, 69, "Output"]
}, Open  ]],
Cell[2533, 78, 199, 6, 75, "Text"],

Cell[CellGroupData[{
Cell[2757, 88, 120, 3, 83, "Input"],
Cell[2880, 93, 600, 14, 126, "Output"]
}, Open  ]],
Cell[3495, 110, 111, 2, 70, "Text"],

Cell[CellGroupData[{
Cell[3631, 116, 67, 1, 47, "Input"],
Cell[3701, 119, 56, 1, 69, "Output"]
}, Open  ]],
Cell[3772, 123, 155, 5, 71, "Text"],

Cell[CellGroupData[{
Cell[3952, 132, 134, 3, 83, "Input"],
Cell[4089, 137, 970, 21, 395, "Output"]
}, Open  ]],
Cell[5074, 161, 315, 11, 87, "Text"],

Cell[CellGroupData[{
Cell[5414, 176, 230, 6, 143, "Input"],
Cell[5647, 184, 206, 4, 130, "Output"]
}, Open  ]],
Cell[5868, 191, 121, 3, 70, "Text"],

Cell[CellGroupData[{
Cell[6014, 198, 61, 1, 47, "Input"],
Cell[6078, 201, 206, 4, 130, "Output"]
}, Open  ]],
Cell[6299, 208, 108, 3, 70, "Text"],

Cell[CellGroupData[{
Cell[6432, 215, 49, 1, 47, "Input"],
Cell[6484, 218, 59, 1, 52, "Output"]
}, Open  ]],
Cell[6558, 222, 82, 1, 53, "Text"],
Cell[6643, 225, 103, 2, 65, "Input"],
Cell[6749, 229, 342, 10, 104, "Text"],

Cell[CellGroupData[{
Cell[7116, 243, 409, 7, 209, "Input"],
Cell[7528, 252, 25356, 978, 194, 12998, 821, "GraphicsData", 
"PostScript", "Graphics"]
}, Open  ]],
Cell[32899, 1233, 89, 1, 47, "Input"]
}, Open  ]]
}
]
*)




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