(************** 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[     35692,        910]*)
(*NotebookOutlinePosition[     36335,        932]*)
(*  CellTagsIndexPosition[     36291,        928]*)
(*WindowFrame->Normal*)



Notebook[{
Cell["Problem 6:", "Text"],

Cell["\<\
The function we'll be playing with is exp(cos(x)). The grid points are \
located at 2 pi j/N, where j is an integer and N is the number of grid \
points.\
\>", "Text"],

Cell[BoxData[
    \(\(f[j_, n_] := 1.  Exp[Cos[2  Pi\ j/n]];\)\)], "Input"],

Cell["The exact derivative:", "Text"],

Cell[BoxData[
    \(\(\(f'\)[j_, n_] := \(-1. \) Exp[Cos[2  Pi\ j/n]] 
          Sin[2  Pi\ j/n];\)\)], "Input"],

Cell["\<\
Here's the finite difference approximation to derivate. Note that the points \
are periodically identified on the interval [0, 2 Pi).\
\>", "Text"],

Cell[BoxData[
    \(\(finitediff[j_, n_] := 
        1/2 \((f[Mod[j + 1, n], n] - f[Mod[j - 1, n], n])\)/\((2 
                 Pi/n)\);\)\)], "Input"],

Cell["Pseudospectral approximation to derivative: ", "Text"],

Cell[BoxData[
    \(\(M[i_, j_, n_] := 
        Module[{d}, \[IndentingNewLine]If[i \[NotEqual] j, \ 
            d =  .5 \((\(-1\))\)^\((i + j)\) Cot[Pi \((i - j)\)/n], \ 
            d = 0]; \[IndentingNewLine]Return[
            d];\[IndentingNewLine]];\)\)], "Input"],

Cell[BoxData[
    \(\(pseudospec[j_, n_] := 
        Sum[M[j, k, n] f[k, n], {k, 0, n - 1}];\)\)], "Input"],

Cell["\<\
Let's represent the average error epsilon(N) using two arrays. We'll call \
epsilon(N) for the finite difference method \"error1\" and epsilon(N) for the \
pseudospectral method \"error2.\" Also let N=2,...,maxpoints=20.  \
\>", "Text"],

Cell[BoxData[{
    \(\(maxpoints = 20;\)\), "\[IndentingNewLine]", 
    \(\(error1 = Table[0, {i, 1, maxpoints/2}];\)\), "\[IndentingNewLine]", 
    \(\(error2 = error1;\)\)}], "Input"],

Cell["Compute epsilon(N) for each method. ", "Text"],

Cell[BoxData[
    \(\(For[n = 2, n \[LessEqual] maxpoints, 
        n += 2, \[IndentingNewLine]i = n/2; \[IndentingNewLine]For[j = 0, 
          j < n, \(j++\), \[IndentingNewLine]error1[\([i]\)] += 
            Abs[finitediff[j, n] - \(f'\)[j, 
                  n]]; \[IndentingNewLine]error2[\([i]\)] += 
            Abs[pseudospec[j, n] - \(f'\)[j, 
                  n]];\[IndentingNewLine]]; \
\[IndentingNewLine]error1[\([i]\)] = 
          error1[\([i]\)]/n; \[IndentingNewLine]error2[\([i]\)] = 
          error2[\([i]\)]/n;\[IndentingNewLine]];\)\)], "Input"],

Cell["\<\
Plot epsilon(N) for each method. Note that the error approaches 0 as 1/N^2 \
for the finite difference method and decays exponenetially for the \
pseudospectral method.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(Error1 = 
        Table[{2  i, error1[\([i]\)]}, {i, 1, 
            maxpoints/2}];\)\), "\[IndentingNewLine]", 
    \(\(Error2 = 
        Table[{2  i, error2[\([i]\)]}, {i, 1, 
            maxpoints/2}];\)\), "\[IndentingNewLine]", 
    \(ListPlot[Error1, PlotStyle \[Rule] PointSize[0.02], 
      PlotRange \[Rule] {{0, maxpoints + 1}, 
          Automatic}]\), "\[IndentingNewLine]", 
    \(ListPlot[Error2, PlotStyle \[Rule] PointSize[0.02], 
      PlotRange \[Rule] {{0, maxpoints + 1}, Automatic}]\)}], "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
2.77556e-017 0.047619 0.0147151 3.49089 [
[.2381 .00222 -3 -9 ]
[.2381 .00222 3 0 ]
[.47619 .00222 -6 -9 ]
[.47619 .00222 6 0 ]
[.71429 .00222 -6 -9 ]
[.71429 .00222 6 0 ]
[.95238 .00222 -6 -9 ]
[.95238 .00222 6 0 ]
[-0.0125 .10199 -30 -4.5 ]
[-0.0125 .10199 0 4.5 ]
[-0.0125 .18926 -24 -4.5 ]
[-0.0125 .18926 0 4.5 ]
[-0.0125 .27653 -30 -4.5 ]
[-0.0125 .27653 0 4.5 ]
[-0.0125 .3638 -18 -4.5 ]
[-0.0125 .3638 0 4.5 ]
[-0.0125 .45108 -30 -4.5 ]
[-0.0125 .45108 0 4.5 ]
[-0.0125 .53835 -24 -4.5 ]
[-0.0125 .53835 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
.2381 .01472 m
.2381 .02097 L
s
[(5)] .2381 .00222 0 1 Mshowa
.47619 .01472 m
.47619 .02097 L
s
[(10)] .47619 .00222 0 1 Mshowa
.71429 .01472 m
.71429 .02097 L
s
[(15)] .71429 .00222 0 1 Mshowa
.95238 .01472 m
.95238 .02097 L
s
[(20)] .95238 .00222 0 1 Mshowa
.125 Mabswid
.04762 .01472 m
.04762 .01847 L
s
.09524 .01472 m
.09524 .01847 L
s
.14286 .01472 m
.14286 .01847 L
s
.19048 .01472 m
.19048 .01847 L
s
.28571 .01472 m
.28571 .01847 L
s
.33333 .01472 m
.33333 .01847 L
s
.38095 .01472 m
.38095 .01847 L
s
.42857 .01472 m
.42857 .01847 L
s
.52381 .01472 m
.52381 .01847 L
s
.57143 .01472 m
.57143 .01847 L
s
.61905 .01472 m
.61905 .01847 L
s
.66667 .01472 m
.66667 .01847 L
s
.7619 .01472 m
.7619 .01847 L
s
.80952 .01472 m
.80952 .01847 L
s
.85714 .01472 m
.85714 .01847 L
s
.90476 .01472 m
.90476 .01847 L
s
.25 Mabswid
0 .01472 m
1 .01472 L
s
0 .10199 m
.00625 .10199 L
s
[(0.025)] -0.0125 .10199 1 0 Mshowa
0 .18926 m
.00625 .18926 L
s
[(0.05)] -0.0125 .18926 1 0 Mshowa
0 .27653 m
.00625 .27653 L
s
[(0.075)] -0.0125 .27653 1 0 Mshowa
0 .3638 m
.00625 .3638 L
s
[(0.1)] -0.0125 .3638 1 0 Mshowa
0 .45108 m
.00625 .45108 L
s
[(0.125)] -0.0125 .45108 1 0 Mshowa
0 .53835 m
.00625 .53835 L
s
[(0.15)] -0.0125 .53835 1 0 Mshowa
.125 Mabswid
0 .03217 m
.00375 .03217 L
s
0 .04962 m
.00375 .04962 L
s
0 .06708 m
.00375 .06708 L
s
0 .08453 m
.00375 .08453 L
s
0 .11944 m
.00375 .11944 L
s
0 .1369 m
.00375 .1369 L
s
0 .15435 m
.00375 .15435 L
s
0 .17181 m
.00375 .17181 L
s
0 .20671 m
.00375 .20671 L
s
0 .22417 m
.00375 .22417 L
s
0 .24162 m
.00375 .24162 L
s
0 .25908 m
.00375 .25908 L
s
0 .29399 m
.00375 .29399 L
s
0 .31144 m
.00375 .31144 L
s
0 .3289 m
.00375 .3289 L
s
0 .34635 m
.00375 .34635 L
s
0 .38126 m
.00375 .38126 L
s
0 .39871 m
.00375 .39871 L
s
0 .41617 m
.00375 .41617 L
s
0 .43362 m
.00375 .43362 L
s
0 .46853 m
.00375 .46853 L
s
0 .48599 m
.00375 .48599 L
s
0 .50344 m
.00375 .50344 L
s
0 .52089 m
.00375 .52089 L
s
0 .5558 m
.00375 .5558 L
s
0 .57326 m
.00375 .57326 L
s
0 .59071 m
.00375 .59071 L
s
0 .60817 m
.00375 .60817 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
.02 w
.09524 .01472 Mdot
.19048 .45429 Mdot
.28571 .60332 Mdot
.38095 .3784 Mdot
.47619 .29009 Mdot
.57143 .20683 Mdot
.66667 .16547 Mdot
.7619 .1295 Mdot
.85714 .1086 Mdot
.95238 .09027 Mdot
% 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/B000`400?l00000o`00003oo`3ooolQ
0?ooo`00o`3ooolQ0?ooo`00o`3ooolQ0?ooo`00o`3ooolQ0?ooo`00o`3ooolQ0?ooo`00o`3ooolQ
0?ooo`00F`3oool0103DP2/000000000000[P=@e0?ooo`080?ooZP1E000000000000000002/0P=Co
0?ooo`3DP2/20000000302^0e03oool0oooo02l0oooo00P0oonZ05D00000000000000000:`20e?l0
oooo0=B0:`80000000<0:h3D0?ooo`3oool0;`3oool0203oZUD00000000000000000001E0:[oo`3o
ool0e80[0P0000000`0[P=@0oooo0?ooo`070?ooo`00FP3oool01P3oe800:b^00?ooo`3oool0P2/[
083DocH0oooo00<0ojYE02^0e03oool00P3oool01@20EH00oooo0?ooo`20:eD0Z_oo0380oooo00H0
ojYE02^0e03oool0oooo0?oDP00[:h020?ooo`03080[:`20e?l0oooo0300oooo00<0P2/00000E@2Z
ool00`3oool01@20EH00oooo0?ooo`20:eD0Z_oo00P0oooo001N0?ooo`030:YE:`20e?l0oooo03D0
oooo00H0ojYE02^0e03oool0oooo0?ooZP1E:h020?ooo`030:YE:`20e?l0oooo0340oooo00<0ojYE
02^0e03oool01@3oool00`2ZEB/0P=Co0?ooo`0a0?ooo`060?nZE@000000EJ[o0?ooo`3oojX0EB^0
0P3oool00`2ZEB/0P=Co0?ooo`070?ooo`00F`3oool0102ZE@00000000000000EJXg0?ooo`060?nZ
E@0[P=@0oooo0?ooo`3oojX0EB^00P3oool00`2ZEB/0P=Co0?ooo`0a0?ooo`030?nZE@0[P=@0oooo
0080oooo00@0ZUD000000000000005FZ=03oool01@3oojX0ZZ[o0?ooo`3oojX0EB^00080oooo00<0
ZUD[083Do`3oool01`3oool005/0oooo00<0ZUD[083Do`3oool0=`3oool00`20:eD0ZZYE02^0e003
0?ooo`05080[:`20e?l0oonZ05D0E@2Zool0<@3oool00`20:eD0ZZYE02^0e0030?ooo`030:YE:`20
e?l0oooo0380oooo00`0omB002/[P03oool0oonZ05D0E@2Zool0oooo080[:`20e?l0oonZ05D0E@2Z
ool80?ooo`00F`3oool0102ZE@00000000000000EJXf0?ooo`030?nZE@000000:h3D00<0oooo00@0
omB002/000000000EJ[o<P3oool00`3oZUD0000002^0e0030?ooo`040:YE000000000000001EZS80
oooo00@0e80[000000000000:h3D0P3oool0103oe800:`000000001EZ_l90?ooo`00o`3ooolQ0?oo
o`00o`3ooolQ0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool00`000000oooo0?oo
o`3l0?ooo`008@3oool00`000000oooo0?ooo`0D0?ooo`<00000i@3oool00240oooo00<000000?oo
o`3oool04`3oool500000>@0oooo000Q0?ooool00000000Q0?ooo`030000003oool0oooo00T0oooo
00<000000?ooo`3oool01`3oool5000000T0oooo00<000000?ooo`3oool02@3oool00`000000oooo
0?ooo`090?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo
0?ooo`090?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool02P3oool00`000000oooo
0?ooo`090?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo
0?ooo`090?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo
0?ooo`090?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo
0?ooo`090?ooo`030000003oool0oooo00/0oooo000Q0?ooo`030000003oool0oooo01@0oooo0`00
003U0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool200000?d0oooo000Q0?ooo`03
0000003oool0oooo0?`0oooo000Q0?ooo`030000003oool0oooo0?`0oooo000Q0?ooo`030000003o
ool0oooo0?`0oooo000Q0?ooo`800000o@3oool00240oooo00<000000?ooo`3oool0o03oool00240
oooo00<000000?ooo`3oool0o03oool00240oooo00<000000?ooo`3oool0o03oool00240oooo00<0
00000?ooo`3oool0o03oool00240oooo0P00003m0?ooo`008@3oool00`000000oooo0?ooo`3l0?oo
o`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3o
ool200000>h0oooo0`00000<0?ooo`008@3oool00`000000oooo0?ooo`3/0?ooo`D000002`3oool0
0240oooo00<000000?ooo`3oool0k03oool5000000/0oooo00001@3oool0e80[000000000000:h3D
0080oooo00<0oonZ05D00000:h000`3oool01P3DP2/000000000000[P=@0oooo0?nZE@<0000000@0
001E0:[oo`3oool0e80[0P0000000`0[P=@0oooo0?ooo`020?ooo`030000003oool0oooo0>`0oooo
1@00000;0?ooo`0000H0oooo081EP03oool0oooo080[E@2Zool70?ooo`09081EP03oool0oooo080[
E@2Zool0oooo080[000005D0Z_oo0080oooo00H0omB002/[P03oool0oooo080[:`20e?l30?ooo`03
0000003oool0oooo0=D0oooo0`00000E0?ooo`<00000303oool000060?ooZP1E:h00oooo0?ooo`2Z
EB/0P=Co1P3oool01P3oojX0EB^00?ooo`3oool0ZUD[083Do`80oooo00<0ojYE0000001EZ_l01@3o
ool00`2ZEB/0P=Co0?ooo`020?ooo`800000e@3oool5000002<0oooo00001P3oojX0EB^00?ooo`3o
ool0ZUD[083Do`H0oooo00H0oonZ05D[P03oool0oooo0:YE:`20e?l30?ooo`050?ooZP2ZZ_l0oooo
0?ooo`2ZE@000P0000000`00EJX0oooo0?ooo`020?ooo`030000003oool0oooo0=@0oooo1@00000S
0?ooo`0000H0oooo080[:`20e?l0oonZ05D0E@2Zool70?ooo`0>080[:`20e?l0oonZ05D0E@2Zool0
omB002/[P03oool0oonZ05D0E@2Zool0oooo0:YE:`20e?l60?ooo`030000003oool0oooo0=@0oooo
1@00000S0?ooo`0000D0oooo0?oDP00[0000000005FZo`080?ooo`040?oDP00[0000000005FZo`80
oooo00@0e80[000000000000:h3D0P3oool0102ZE@00000000000000EJX40?ooo`030000003oool0
oooo0=D0oooo0`00000T0?ooo`008@3oool200000?d0oooo000Q0?ooo`030000003oool0oooo0;d0
oooo0`00000l0?ooo`008@3oool00`000000oooo0?ooo`2l0?ooo`D00000>`3oool00240oooo00<0
00000?ooo`3oool0_03oool5000003/0oooo000Q0?ooo`030000003oool0oooo0;`0oooo1@00000k
0?ooo`008@3oool200000;h0oooo0`00000l0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`00
8@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool2
00000?d0oooo000Q0?ooo`030000003oool0oooo0:D0oooo0`00001D0?ooo`008@3oool00`000000
oooo0?ooo`2T0?ooo`D00000D`3oool00240oooo00<000000?ooo`3oool0Y03oool5000005<0oooo
000Q0?ooo`800000Y@3oool5000005<0oooo000Q0?ooo`030000003oool0oooo0:D0oooo0`00001D
0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`001`3oool0103DP2/000000000000[P=@20?oo
o`030?ooZP1E000002^000<0oooo00@0e80[000000000000:h3D0P3oool0103DP2/000000000000[
P=@40?ooo`030000003oool0oooo0?`0oooo00070?ooo`05081EP03oool0oooo080[E@2Zool01`3o
ool01`20EH00oooo0?ooo`20:eD0Z_oo0?oDP00[:h000P3oool00`20:b/0P=Co0?ooo`020?ooo`03
0000003oool0oooo0?`0oooo00060?ooo`060?ooZP1E:h00oooo0?ooo`2ZEB/0P=Co1P3oool01P3o
ojX0EB^00?ooo`3oool0ZUD[083Do`@0oooo00<0ZUD[083Do`3oool00P3oool200000?d0oooo0006
0?ooo`060?ooZP1E:h00oooo0?ooo`2ZEB/0P=Co1P3oool0203oojX0EB^00?ooo`3oool0ZUD[083D
o`3oool0ZUD00P0000000`00EJX0oooo0?ooo`020?ooo`030000003oool0oooo0?`0oooo00070?oo
o`05080[:`20e?l0oonZ05D0E@2Zool01`3oool02020:b/0P=Co0?ooZP1E05D0Z_oo0?ooo`2ZEB/0
P=Co1P3oool00`000000oooo0?ooo`2=0?ooo`<00000K03oool000L0oooo00@0omB002/000000000
EJ[o203oool0103oe800:`000000001EZ_l20?ooo`040:YE000000000000001EZP@0oooo00<00000
0?ooo`3oool0S03oool5000006/0oooo000Q0?ooo`800000S@3oool5000006/0oooo000Q0?ooo`03
0000003oool0oooo08`0oooo1@00001[0?ooo`008@3oool00`000000oooo0?ooo`2=0?ooo`<00000
K03oool00240oooo00<000000?ooo`3oool0o03oool00240oooo00<000000?ooo`3oool0o03oool0
0240oooo0P00003m0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool00`000000oooo
0?ooo`3l0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool200000?d0oooo000Q0?oo
o`030000003oool0oooo0?`0oooo000Q0?ooo`030000003oool0oooo0?`0oooo000Q0?ooo`030000
003oool0oooo0?`0oooo000Q0?ooo`030000003oool0oooo0?`0oooo000Q0?ooo`800000o@3oool0
0240oooo00<000000?ooo`3oool0o03oool000050?ooo`3DP2/000000000000[P=@00P3oool00`3o
ojX0E@00000[P0030?ooo`040=B0:`000000000002^0e0<0oooo00<0e80[05FZo`3oool00P3oool0
103DP2/000000000000[P=@40?ooo`030000003oool0oooo0?`0oooo00001P3oool0P5F00?ooo`3o
ool0P2]E0:[oo`L0oooo00D0P5F00?ooo`3oool0P2]E0:[oo`020?ooo`060?ooZP1EEJX0oooo0?oo
o`3oe800:b^00P3oool00`20:b/0P=Co0?ooo`020?ooo`030000003oool0oooo0?`0oooo00001P3o
ojX0EB^00?ooo`3oool0ZUD[083Do`H0oooo00H0oonZ05D[P03oool0oooo0:YE:`20e?l30?ooo`03
0:YEE@2Zool0oooo00@0oooo00<0ZUD[083Do`3oool00P3oool200000?d0oooo00001P3oojX0EB^0
0?ooo`3oool0ZUD[083Do`H0oooo00H0oonZ05D[P03oool0oooo0:YE:`20e?l30?ooo`050?nZE@0[
P=@0oooo0?ooo`2ZE@000P0000000`00EJX0oooo0?ooo`020?ooo`030000003oool0oooo07D0oooo
0`0000240?ooo`0000H0oooo080[:`20e?l0oonZ05D0E@2Zool70?ooo`0:080[:`20e?l0oonZ05D0
E@2Zool0omB002]EZP3oool0oonZ05D[P080oooo00<0ZUD[083Do`3oool01@3oool00`000000oooo
0?ooo`1d0?ooo`D00000P`3oool000050?ooo`3oe800:`000000001EZ_l0203oool01`3oe800:`00
0000001EZ_l0oooo0?oDP00[00000P000000100005D0Z_oo0?ooo`2ZE@0200000003001EZP3oool0
oooo0080oooo00<000000?ooo`3oool0M03oool5000008<0oooo000Q0?ooo`800000M@3oool50000
08<0oooo000Q0?ooo`030000003oool0oooo07D0oooo0`0000240?ooo`008@3oool00`000000oooo
0?ooo`3l0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool00`000000oooo0?ooo`3l
0?ooo`008@3oool200000?d0oooo000Q0?ooo`030000003oool0oooo0?`0oooo000Q0?ooo`030000
003oool0oooo0?`0oooo000Q0?ooo`030000003oool0oooo0?`0oooo000Q0?ooo`800000o@3oool0
0240oooo00<000000?ooo`3oool0o03oool00240oooo00<000000?ooo`3oool0o03oool00240oooo
00<000000?ooo`3oool0o03oool00240oooo00<000000?ooo`3oool0o03oool00240oooo0P00003m
0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`003@3oool0103DP2/000000000000[P=@20?oo
o`030?ooZP1E000002^00080oooo00H0oonZ05D00000000000000000:`20e?l30?ooo`030000003o
ool0oooo0?`0oooo000=0?ooo`05081EP03oool0oooo080[E@2Zool0203oool00`3oZUD0:h3D0?oo
o`040?ooo`030000003oool0oooo0?`0oooo000<0?ooo`060?ooZP1E:h00oooo0?ooo`2ZEB/0P=Co
203oool00`3oZUD0:h3D0?ooo`040?ooo`800000o@3oool000`0oooo00H0oonZ05D[P03oool0oooo
0:YE:`20e?l80?ooo`030?nZE@0[P=@0oooo00@0oooo00<000000?ooo`3oool0o03oool000d0oooo
00D0P2/[083Do`3oojX0E@1E0:[oo`070?ooo`03080[E@2ZZUD0:h3D00D0oooo00<000000?ooo`3o
ool0G03oool3000009d0oooo000=0?ooo`040?oDP00[0000000005FZo`P0oooo00<0ojYE0000000[
P=@01@3oool00`000000oooo0?ooo`1K0?ooo`D00000W03oool00240oooo00<000000?ooo`3oool0
F`3oool5000009`0oooo000Q0?ooo`800000G03oool5000009`0oooo000Q0?ooo`030000003oool0
oooo05`0oooo0`00002M0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool00`000000
oooo0?ooo`3l0?ooo`008@3oool200000?d0oooo000Q0?ooo`030000003oool0oooo0?`0oooo000Q
0?ooo`030000003oool0oooo0?`0oooo000Q0?ooo`030000003oool0oooo0?`0oooo000Q0?ooo`80
0000o@3oool00240oooo00<000000?ooo`3oool0o03oool00240oooo00<000000?ooo`3oool0o03o
ool00240oooo00<000000?ooo`3oool0o03oool00240oooo00<000000?ooo`3oool0o03oool00240
oooo0P00003m0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`0000D0oooo0=B0:`0000000000
02^0e0020?ooo`030?ooZP1E000002^00080oooo00L0oonZ05D00000000000000000:`20e?l0ojYE
00<0000000@0001E0:[oo`3oool0e80[0P0000000`0[P=@0oooo0?ooo`020?ooo`030000003oool0
oooo0?`0oooo00001P3oool0P5F00?ooo`3oool0P2]E0:[oo`P0oooo00<0ojYE02^0e03oool00P3o
ool00`20:`00001E0:[oo`020?ooo`060?oDP00[:h00oooo0?ooo`20:b/0P=Co0`3oool00`000000
oooo0?ooo`0/0?ooo`<00000c@3oool000060?ooZP1E:h00oooo0?ooo`2ZEB/0P=Co203oool00`3o
ZUD0:h3D0?ooo`030?ooo`030?nZE@000000EJ[o00D0oooo00<0ZUD[083Do`3oool00P3oool20000
02`0oooo1@00003<0?ooo`0000H0oonZ05D[P03oool0oooo0:YE:`20e?l80?ooo`030?nZE@0[P=@0
oooo00@0oooo00D0oonZ0:ZZo`3oool0oooo0:YE000200000003001EZP3oool0oooo0080oooo00<0
00000?ooo`3oool0:`3oool500000<`0oooo00001P3oool0P2/[083Do`3oojX0E@1E0:[oo`L0oooo
00<0P2]E0:ZZE@0[P=@00P3oool02@3oe800:b^00?ooo`3oojX0E@1E0:[oo`3oool0ZUD[083Do`06
0?ooo`030000003oool0oooo02/0oooo1@00003<0?ooo`0000D0oooo0?oDP00[0000000005FZo`08
0?ooo`030?nZE@000000:h3D00<0oooo00@0e80[000000000000:h3D0P3oool0102ZE@0000000000
0000EJX40?ooo`030000003oool0oooo02`0oooo0`00003=0?ooo`008@3oool00`000000oooo0?oo
o`3l0?ooo`008@3oool200000?d0oooo000Q0?ooo`030000003oool0oooo0?`0oooo000Q0?ooo`03
0000003oool0oooo0?`0oooo000Q0?ooo`030000003oool0oooo0?`0oooo000Q0?ooo`800000o@3o
ool00240oooo00<000000?ooo`3oool0o03oool00240oooo00<000000?ooo`3oool0o03oool00240
oooo00<000000?ooo`3oool0o03oool00240oooo00<000000?ooo`3oool0o03oool00240oooo0P00
003m0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool00`000000oooo0?ooo`3l0?oo
o`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool200000?d0oooo000Q0?ooo`030000003o
ool0oooo0?`0oooo00070?ooo`040=B0:`000000000002^0e080oooo00<0oonZ05D00000:h000P3o
ool0203oojX0E@00000000000000000[083Do`3oool0e80[0P0000000`0[P=@0oooo0?ooo`020?oo
o`030000003oool0oooo0?`0oooo00070?ooo`05081EP03oool0oooo080[E@2Zool0203oool01P3o
ZUD0:h3D0?ooo`3oool0omB002/[P080oooo00<0P2/[083Do`3oool00P3oool00`000000oooo0?oo
o`3l0?ooo`001P3oool01P3oojX0EB^00?ooo`3oool0ZUD[083Do`P0oooo00<0ojYE02^0e03oool0
1@3oool00`2ZEB/0P=Co0?ooo`020?ooo`800000o@3oool000H0oooo00H0oonZ05D[P03oool0oooo
0:YE:`20e?l80?ooo`030?nZE@0[P=@0oooo0080oooo00@0ZUD000000000000005FZ103oool00`00
0000oooo0?ooo`3l0?ooo`001`3oool01@20:b/0P=Co0?ooZP1E05D0Z_oo00L0oooo00<0P2]E0:ZZ
E@0[P=@00`3oool00`2ZEB/0P=Co0?ooo`050?ooo`030000003oool0oooo0?`0oooo00070?ooo`04
0?oDP00[0000000005FZo`P0oooo00<0ojYE0000000[P=@00`3oool0102ZE@00000000000000EJX4
0?ooo`030000003oool0oooo0?`0oooo000Q0?ooo`030000003oool0oooo0?`0oooo000Q0?ooo`80
0000o@3oool00240oooo00<000000?ooo`3oool0o03oool00240oooo00<000000?ooo`3oool0o03o
ool00240oooo00<000000?ooo`3oool0o03oool00240oooo0P00003m0?ooo`008@3oool00`000000
oooo0?ooo`3l0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool00`000000oooo0?oo
o`3l0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`008@3oool200000?d0oooo000Q0?ooo`03
0000003oool0oooo04@0oooo0`00002e0?ooo`008@3oool00`000000oooo0?ooo`130?ooo`D00000
]03oool00240oooo00<000000?ooo`3oool0@`3oool500000;@0oooo000Q0?ooo`800000A03oool5
00000;@0oooo000Q0?ooo`030000003oool0oooo04@0oooo0`00002e0?ooo`008@3oool00`000000
oooo0?ooo`3l0?ooo`008@3oool00`000000oooo0?ooo`3l0?ooo`00o`3ooolQ0?ooo`00o`3ooolQ
0?ooo`00o`3ooolQ0?ooo`00o`3ooolQ0?ooo`00o`3ooolQ0?ooo`00\
\>"],
  ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-2.74464, -0.020299, \
0.0827344, 0.00112857}}],

Cell[BoxData[
    TagBox[\(\[SkeletonIndicator]  Graphics  \[SkeletonIndicator]\),
      False,
      Editable->False]], "Output"],

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
2.77556e-017 0.047619 0.0147151 6.71918 [
[.2381 .00222 -3 -9 ]
[.2381 .00222 3 0 ]
[.47619 .00222 -6 -9 ]
[.47619 .00222 6 0 ]
[.71429 .00222 -6 -9 ]
[.71429 .00222 6 0 ]
[.95238 .00222 -6 -9 ]
[.95238 .00222 6 0 ]
[-0.0125 .1491 -24 -4.5 ]
[-0.0125 .1491 0 4.5 ]
[-0.0125 .28348 -24 -4.5 ]
[-0.0125 .28348 0 4.5 ]
[-0.0125 .41787 -24 -4.5 ]
[-0.0125 .41787 0 4.5 ]
[-0.0125 .55225 -24 -4.5 ]
[-0.0125 .55225 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
.2381 .01472 m
.2381 .02097 L
s
[(5)] .2381 .00222 0 1 Mshowa
.47619 .01472 m
.47619 .02097 L
s
[(10)] .47619 .00222 0 1 Mshowa
.71429 .01472 m
.71429 .02097 L
s
[(15)] .71429 .00222 0 1 Mshowa
.95238 .01472 m
.95238 .02097 L
s
[(20)] .95238 .00222 0 1 Mshowa
.125 Mabswid
.04762 .01472 m
.04762 .01847 L
s
.09524 .01472 m
.09524 .01847 L
s
.14286 .01472 m
.14286 .01847 L
s
.19048 .01472 m
.19048 .01847 L
s
.28571 .01472 m
.28571 .01847 L
s
.33333 .01472 m
.33333 .01847 L
s
.38095 .01472 m
.38095 .01847 L
s
.42857 .01472 m
.42857 .01847 L
s
.52381 .01472 m
.52381 .01847 L
s
.57143 .01472 m
.57143 .01847 L
s
.61905 .01472 m
.61905 .01847 L
s
.66667 .01472 m
.66667 .01847 L
s
.7619 .01472 m
.7619 .01847 L
s
.80952 .01472 m
.80952 .01847 L
s
.85714 .01472 m
.85714 .01847 L
s
.90476 .01472 m
.90476 .01847 L
s
.25 Mabswid
0 .01472 m
1 .01472 L
s
0 .1491 m
.00625 .1491 L
s
[(0.02)] -0.0125 .1491 1 0 Mshowa
0 .28348 m
.00625 .28348 L
s
[(0.04)] -0.0125 .28348 1 0 Mshowa
0 .41787 m
.00625 .41787 L
s
[(0.06)] -0.0125 .41787 1 0 Mshowa
0 .55225 m
.00625 .55225 L
s
[(0.08)] -0.0125 .55225 1 0 Mshowa
.125 Mabswid
0 .04831 m
.00375 .04831 L
s
0 .08191 m
.00375 .08191 L
s
0 .1155 m
.00375 .1155 L
s
0 .18269 m
.00375 .18269 L
s
0 .21629 m
.00375 .21629 L
s
0 .24989 m
.00375 .24989 L
s
0 .31708 m
.00375 .31708 L
s
0 .35067 m
.00375 .35067 L
s
0 .38427 m
.00375 .38427 L
s
0 .45146 m
.00375 .45146 L
s
0 .48506 m
.00375 .48506 L
s
0 .51865 m
.00375 .51865 L
s
0 .58585 m
.00375 .58585 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
.02 w
.09524 .01472 Mdot
.19048 .60332 Mdot
.28571 .14213 Mdot
.38095 .03235 Mdot
.47619 .01658 Mdot
.57143 .01488 Mdot
.66667 .01473 Mdot
.7619 .01472 Mdot
.85714 .01472 Mdot
.95238 .01472 Mdot
% 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/B000`400?l00000o`00003oo`3ooolQ
0?ooo`00o`3ooolQ0?ooo`00o`3ooolQ0?ooo`00o`3ooolQ0?ooo`00o`3ooolQ0?ooo`00E`3oool0
103DP2/000000000000[P=@e0?ooo`080?ooZP1E000000000000000002/0P=Co0?ooo`3DP2/20000
000302^0e03oool0oooo0340oooo00P0oonZ05D00000000000000000:`20e?l0oooo0=B0:`800000
00<0:h3D0?ooo`3oool0<@3oool0203oZUD00000000000000000001E0:[oo`3oool0e80[0P000000
0`0[P=@0oooo0?ooo`070?ooo`00EP3oool01P3oe800:b^00?ooo`3oool0P2/[083DocH0oooo00<0
ojYE02^0e03oool00P3oool01@20EH00oooo0?ooo`20:eD0Z_oo03@0oooo00H0ojYE02^0e03oool0
oooo0?oDP00[:h020?ooo`03080[:`20e?l0oooo0380oooo00<0P2/00000E@2Zool00`3oool01@20
EH00oooo0?ooo`20:eD0Z_oo00P0oooo001J0?ooo`030:YE:`20e?l0oooo03D0oooo00H0ojYE02^0
e03oool0oooo0?ooZP1E:h020?ooo`030:YE:`20e?l0oooo03<0oooo00<0ojYE02^0e03oool01@3o
ool00`2ZEB/0P=Co0?ooo`0c0?ooo`060?nZE@000000EJ[o0?ooo`3oojX0EB^00P3oool00`2ZEB/0
P=Co0?ooo`070?ooo`00E`3oool0102ZE@00000000000000EJXg0?ooo`060?nZE@0[P=@0oooo0?oo
o`3oojX0EB^00P3oool00`2ZEB/0P=Co0?ooo`0c0?ooo`030?nZE@0[P=@0oooo0080oooo00@0ZUD0
00000000000005FZ=P3oool01@3oojX0ZZ[o0?ooo`3oojX0EB^00080oooo00<0ZUD[083Do`3oool0
1`3oool005L0oooo00<0ZUD[083Do`3oool0=`3oool00`20:eD0ZZYE02^0e0030?ooo`05080[:`20
e?l0oonZ05D0E@2Zool0<`3oool00`20:eD0ZZYE02^0e0030?ooo`030:YE:`20e?l0oooo03@0oooo
00`0omB002/[P03oool0oonZ05D0E@2Zool0oooo080[:`20e?l0oonZ05D0E@2Zool80?ooo`00E`3o
ool0102ZE@00000000000000EJXf0?ooo`030?nZE@000000:h3D00<0oooo00@0omB002/000000000
EJ[o=03oool00`3oZUD0000002^0e0030?ooo`040:YE000000000000001EZS@0oooo00@0e80[0000
00000000:h3D0P3oool0103oe800:`000000001EZ_l90?ooo`00o`3ooolQ0?ooo`006`3oool00`00
0000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo
00<000000?ooo`3oool0503oool300000600oooo0`00000F0?ooo`<000005P3oool3000001H0oooo
0`00000E0?ooo`<000005P3oool3000000`0oooo000K0?ooo`030000003oool0oooo01<0oooo1@00
001N0?ooo`D00000503oool5000001@0oooo1@00000D0?ooo`D000004`3oool5000001@0oooo1@00
000;0?ooo`006`3ooooo000000H00000000K0?ooo`030000003oool0oooo00T0oooo00<000000?oo
o`3oool01`3oool5000000X0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`0:0?oo
o`030000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`0:0?oo
o`030000003oool0oooo00T0oooo00<000000?ooo`3oool01`3oool5000000X0oooo00<000000?oo
o`3oool01`3oool5000000X0oooo00<000000?ooo`3oool01`3oool5000000T0oooo00<000000?oo
o`3oool0203oool5000000T0oooo00<000000?ooo`3oool01`3oool5000000X0oooo00<000000?oo
o`3oool01`3oool5000000/0oooo000K0?ooo`030000003oool0oooo01@0oooo0`0000180?ooo`<0
00005@3oool3000001H0oooo0`00000F0?ooo`<000005P3oool3000001D0oooo0`00000F0?ooo`<0
0000303oool001/0oooo00<000000?ooo`3oool0GP3oool5000009l0oooo000K0?ooo`030000003o
ool0oooo05h0oooo1@00002O0?ooo`006`3oool00`000000oooo0?ooo`1N0?ooo`D00000W`3oool0
01/0oooo00<000000?ooo`3oool0G`3oool300000:00oooo000K0?ooo`030000003oool0oooo0?l0
oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool200000?l0oooo103o
ool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?oo
o`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0
o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0
oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool200000?l0
oooo103oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?oo
o`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?oo
o`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000
003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool0
0`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`800000o`3oool40?ooo`006`3oool00`000000
oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<0
00000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?oo
o`030000003oool0oooo04H0oooo0`00002i0?ooo`006`3oool00`000000oooo0?ooo`150?ooo`D0
0000^03oool000050?ooo`3DP2/000000000000[P=@00P3oool00`3oojX0E@00000[P0030?ooo`06
0=B0:`000000000002^0e03oool0ojYE0`0000000`0005D0Z_oo0?ooo`020?ooo`030000003oool0
oooo04D0oooo1@00002h0?ooo`0000H0oooo081EP03oool0oooo080[E@2Zool70?ooo`09081EP03o
ool0oooo080[E@2Zool0oooo080[000005D0Z_oo00D0oooo00<000000?ooo`3oool0A@3oool50000
0;P0oooo00001P3oojX0EB^00?ooo`3oool0ZUD[083Do`H0oooo00H0oonZ05D[P03oool0oooo0:YE
:`20e?l20?ooo`030?nZE@000000EJ[o00@0oooo0P0000170?ooo`<00000^@3oool000060?ooZP1E
:h00oooo0?ooo`2ZEB/0P=Co1P3oool01P3oojX0EB^00?ooo`3oool0ZUD[083Do`<0oooo00<0oonZ
0:ZZo`3oool00`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo00001P3oool0P2/[083Do`3oojX0
E@1E0:[oo`L0oooo00/0P2/[083Do`3oojX0E@1E0:[oo`3oe800:b^00?ooo`3oojX0E@1E0:[oo`03
0?ooo`030000003oool0oooo0?l0oooo0`3oool000050?ooo`3oe800:`000000001EZ_l0203oool0
103oe800:`000000001EZ_l20?ooo`040=B0:`000000000002^0e0@0oooo00<000000?ooo`3oool0
o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0
oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000
oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`800000o`3oool40?ooo`006`3oool00`000000oooo0?oo
o`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?oo
o`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000
003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool0
0`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0
oooo0P00003o0?ooo`@0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<0
00000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?oo
o`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`00
6`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3o
ool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool200000?l0oooo103oool001/0
oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo
000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool3
0?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0
oooo0`3oool000050?ooo`3DP2/000000000000[P=@00P3oool00`3oojX0E@00000[P0030?ooo`04
0=B0:`000000000002^0e0<0oooo00@0e80[0000000002/0P=Co0`3oool00`000000oooo0?ooo`3o
0?ooo`<0oooo00001P3oool0P5F00?ooo`3oool0P2]E0:[oo`L0oooo00D0P5F00?ooo`3oool0P2]E
0:[oo`030?ooo`030?nZE@0[P=@0oooo00<0oooo00<000000?ooo`3oool0o`3oool30?ooo`0000H0
oonZ05D[P03oool0oooo0:YE:`20e?l60?ooo`080?ooZP1E:h00oooo0?ooo`2ZEB/0P=Co0?ooZP1E
0002000000030000:`20e?l0oooo0080oooo0P00003o0?ooo`@0oooo00001P3oojX0EB^00?ooo`3o
ool0ZUD[083Do`H0oooo00/0oonZ05D[P03oool0oooo0:YE:`20e?l0oooo0:YE001EZ_l0ojYE02^0
e0040?ooo`030000003oool0oooo0?l0oooo0`3oool000060?ooo`20:b/0P=Co0?ooZP1E05D0Z_oo
1`3oool02P20:b/0P=Co0?ooZP1E05D0Z_oo0?ooo`3oojX0E@0[0820E@0[P=@40?ooo`030000003o
ool0oooo0?l0oooo0`3oool000050?ooo`3oe800:`000000001EZ_l0203oool0103oe800:`000000
001EZ_l30?ooo`030?oDP00[0000:h3D00@0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3o
ool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool0
01/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0
oooo000K0?ooo`800000o`3oool40?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K
0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?oo
o`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo
0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o
0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo0P00003o0?ooo`@0
oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3o
ool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo
0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo
0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<00000
0?ooo`3oool0o`3oool30?ooo`006`3oool200000?l0oooo103oool001/0oooo00<000000?ooo`3o
ool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003o
ool0oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`00
0000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool000050?oo
o`3DP2/000000000000[P=@00P3oool00`3oojX0E@00000[P0030?ooo`040=B0:`000000000002^0
e080oooo00D0oonZ05D000000000000[083Do`030?ooo`030000003oool0oooo0?l0oooo0`3oool0
00060?ooo`20EH00oooo0?ooo`20:eD0Z_oo1`3oool02`20EH00oooo0?ooo`20:eD0Z_oo0?ooo`2Z
E@00EJ[o0?ooo`3oojX0ZZ[o00<0oooo00<000000?ooo`3oool0o`3oool30?ooo`0000H0oonZ05D[
P03oool0oooo0:YE:`20e?l60?ooo`0<0?ooZP1E:h00oooo0?ooo`2ZEB/0P=Co0?ooZP1E0000:h3D
0?ooo`3DP2/0EJ[o0`3oool200000?l0oooo103oool000060?ooZP1E:h00oooo0?ooo`2ZEB/0P=Co
1P3oool02`3oojX0EB^00?ooo`3oool0ZUD[083Do`3oool0P2]E02/[0000000002^000@0oooo00<0
00000?ooo`3oool0o`3oool30?ooo`0000H0oooo080[:`20e?l0oonZ05D0E@2Zool70?ooo`08080[
:`20e?l0oonZ05D0E@2Zool0oooo0?nZE@00:h060?ooo`030000003oool0oooo0?l0oooo0`3oool0
00050?ooo`3oe800:`000000001EZ_l0203oool0103oe800:`000000001EZ_l30?ooo`040=B0:`00
0000000005FZo`<0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?oo
o`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?oo
o`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`800000
o`3oool40?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0
oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000
oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<0
00000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?oo
o`030000003oool0oooo0?l0oooo0`3oool001/0oooo0P00003o0?ooo`@0oooo000K0?ooo`030000
003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool0
0`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0
oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo
000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool3
0?ooo`006`3oool200000?l0oooo103oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`00
6`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3o
ool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?ooo`3o0?oo
o`<0oooo00001@3oool0e80[000000000000:h3D0080oooo00<0oonZ05D00000:h000`3oool0103D
P2/000000000000[P=@20?ooo`040:YE00000000000002^0e0@0oooo00<000000?ooo`3oool0o`3o
ool30?ooo`0000H0oooo081EP03oool0oooo080[E@2Zool70?ooo`07081EP03oool0oooo080[E@2Z
ool0oonZ05EEZP020?ooo`03081EP03oool0oooo0080oooo00<000000?ooo`3oool0o`3oool30?oo
o`0000H0oonZ05D[P03oool0oooo0:YE:`20e?l60?ooo`0;0?ooZP1E:h00oooo0?ooo`2ZEB/0P=Co
0?ooo`20EH00oooo0?ooZP1EEJX0103oool200000?l0oooo103oool000060?ooZP1E:h00oooo0?oo
o`2ZEB/0P=Co1P3oool0203oojX0EB^00?ooo`3oool0ZUD[083Do`3oool0ZUD00P0000000`0[P=@0
oooo0?ooo`020?ooo`030000003oool0oooo0?l0oooo0`3oool000060?ooo`20:b/0P=Co0?ooZP1E
05D0Z_oo1`3oool02P20:b/0P=Co0?ooZP1E05D0Z_oo0?ooZP1E:h00oooo0?ooZP1E:h040?ooo`03
0000003oool0oooo0?l0oooo0`3oool000050?ooo`3oe800:`000000001EZ_l0203oool0103oe800
:`000000001EZ_l20?ooo`040=B0:`000000000005FZo`@0oooo00<000000?ooo`3oool0o`3oool3
0?ooo`006`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0
oooo0`3oool001/0oooo00<000000?ooo`3oool0o`3oool30?ooo`006`3oool00`000000oooo0?oo
o`3o0?ooo`<0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo0P00003o0?oo
o`@0oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<000000?ooo`3oool0
o`3oool30?ooo`006`3oool00`000000oooo0?ooo`0]0?ooo`<00000dP3oool001/0oooo00<00000
0?ooo`3oool0;03oool500000=40oooo000K0?ooo`030000003oool0oooo02`0oooo1@00003A0?oo
o`006`3oool00`000000oooo0?ooo`0/0?ooo`D00000d@3oool001/0oooo00<000000?ooo`3oool0
;@3oool300000=80oooo000K0?ooo`030000003oool0oooo0?l0oooo0`3oool001/0oooo00<00000
0?ooo`3oool0o`3oool30?ooo`00o`3ooolQ0?ooo`00o`3ooolQ0?ooo`00o`3ooolQ0?ooo`00\
\>"],
  ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-2.20293, -0.00930258, \
0.0808469, 0.000572964}}],

Cell[BoxData[
    TagBox[\(\[SkeletonIndicator]  Graphics  \[SkeletonIndicator]\),
      False,
      Editable->False]], "Output"]
}, Open  ]]
},
FrontEndVersion->"5.0 for Microsoft Windows",
ScreenRectangle->{{0, 1280}, {0, 717}},
WindowSize->{842, 559},
WindowMargins->{{0, Automatic}, {Automatic, 0}}
]

(*******************************************************************
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[1754, 51, 26, 0, 33, "Text"],
Cell[1783, 53, 177, 4, 33, "Text"],
Cell[1963, 59, 75, 1, 30, "Input"],
Cell[2041, 62, 37, 0, 33, "Text"],
Cell[2081, 64, 112, 2, 30, "Input"],
Cell[2196, 68, 157, 3, 33, "Text"],
Cell[2356, 73, 151, 3, 30, "Input"],
Cell[2510, 78, 60, 0, 33, "Text"],
Cell[2573, 80, 271, 5, 90, "Input"],
Cell[2847, 87, 107, 2, 30, "Input"],
Cell[2957, 91, 246, 4, 52, "Text"],
Cell[3206, 97, 185, 3, 70, "Input"],
Cell[3394, 102, 52, 0, 33, "Text"],
Cell[3449, 104, 569, 10, 190, "Input"],
Cell[4021, 116, 192, 4, 52, "Text"],

Cell[CellGroupData[{
Cell[4238, 124, 540, 11, 90, "Input"],
Cell[4781, 137, 15915, 411, 186, 3384, 252, "GraphicsData", "PostScript", \
"Graphics"],
Cell[20699, 550, 130, 3, 29, "Output"],
Cell[20832, 555, 14711, 347, 186, 2724, 195, "GraphicsData", "PostScript", \
"Graphics"],
Cell[35546, 904, 130, 3, 29, "Output"]
}, Open  ]]
}
]
*)



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