(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. 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[ 118095, 2957]*) (*NotebookOutlinePosition[ 118751, 2980]*) (* CellTagsIndexPosition[ 118707, 2976]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[ \(<< DiscreteMath`ComputationalGeometry`\)], "Input"], Cell[BoxData[ \(Needs["\"]\)], "Input"], Cell[BoxData[ \(<< Graphics`Shapes`\)], "Input"], Cell[BoxData[ \(\(testData\ = \ Table[{Random[], Random[]}, {20}];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(hull = \ ConvexHull[testData];\)\)], "Input"], Cell[BoxData[ \(General::"spell" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(hull\)\" is similar to \ existing symbols \!\({hul, Hull}\)."\)], "Message"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[ Graphics[ {PointSize[0.02], Point\ /@ \ testData, \[IndentingNewLine]Line[\ testData[\([hull]\)]\ ]}\[IndentingNewLine]], PlotRange \[Rule] All, Axes \[Rule] True, AspectRatio \[Rule] Automatic];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.11724 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 -0.0926311 1.08464 0.0168986 1.08464 [ [.1243 .0044 -9 -9 ] [.1243 .0044 9 0 ] [.34123 .0044 -9 -9 ] [.34123 .0044 9 0 ] [.55815 .0044 -9 -9 ] [.55815 .0044 9 0 ] [.77508 .0044 -9 -9 ] [.77508 .0044 9 0 ] [.97951 .23383 -18 -4.5 ] [.97951 .23383 0 4.5 ] [.97951 .45076 -18 -4.5 ] [.97951 .45076 0 4.5 ] [.97951 .66768 -18 -4.5 ] [.97951 .66768 0 4.5 ] [.97951 .88461 -18 -4.5 ] [.97951 .88461 0 4.5 ] [.97951 1.10154 -6 -4.5 ] [.97951 1.10154 0 4.5 ] [ 0 0 0 0 ] [ 1 1.11724 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .1243 .0169 m .1243 .02315 L s [(0.2)] .1243 .0044 0 1 Mshowa .34123 .0169 m .34123 .02315 L s [(0.4)] .34123 .0044 0 1 Mshowa .55815 .0169 m .55815 .02315 L s [(0.6)] .55815 .0044 0 1 Mshowa .77508 .0169 m .77508 .02315 L s [(0.8)] .77508 .0044 0 1 Mshowa .125 Mabswid .17853 .0169 m .17853 .02065 L s .23276 .0169 m .23276 .02065 L s .28699 .0169 m .28699 .02065 L s .39546 .0169 m .39546 .02065 L s .44969 .0169 m .44969 .02065 L s .50392 .0169 m .50392 .02065 L s .61239 .0169 m .61239 .02065 L s .66662 .0169 m .66662 .02065 L s .72085 .0169 m .72085 .02065 L s .82931 .0169 m .82931 .02065 L s .88355 .0169 m .88355 .02065 L s .93778 .0169 m .93778 .02065 L s .07007 .0169 m .07007 .02065 L s .01583 .0169 m .01583 .02065 L s .25 Mabswid 0 .0169 m 1 .0169 L s .99201 .23383 m .99826 .23383 L s [(0.2)] .97951 .23383 1 0 Mshowa .99201 .45076 m .99826 .45076 L s [(0.4)] .97951 .45076 1 0 Mshowa .99201 .66768 m .99826 .66768 L s [(0.6)] .97951 .66768 1 0 Mshowa .99201 .88461 m .99826 .88461 L s [(0.8)] .97951 .88461 1 0 Mshowa .99201 1.10154 m .99826 1.10154 L s [(1)] .97951 1.10154 1 0 Mshowa .125 Mabswid .99201 .07113 m .99576 .07113 L s .99201 .12536 m .99576 .12536 L s .99201 .17959 m .99576 .17959 L s .99201 .28806 m .99576 .28806 L s .99201 .34229 m .99576 .34229 L s .99201 .39652 m .99576 .39652 L s .99201 .50499 m .99576 .50499 L s .99201 .55922 m .99576 .55922 L s .99201 .61345 m .99576 .61345 L s .99201 .72192 m .99576 .72192 L s .99201 .77615 m .99576 .77615 L s .99201 .83038 m .99576 .83038 L s .99201 .93884 m .99576 .93884 L s .99201 .99308 m .99576 .99308 L s .99201 1.04731 m .99576 1.04731 L s .25 Mabswid .99201 0 m .99201 1.11724 L s .02 w .57767 .27993 Mdot .72924 .89215 Mdot .06891 .16382 Mdot .02381 .0266 Mdot .76039 1.00858 Mdot .37991 .85354 Mdot .97619 .58065 Mdot .50099 .84394 Mdot .18763 1.09064 Mdot .91725 .13454 Mdot .71651 1.01771 Mdot .12697 .66953 Mdot .04621 .75468 Mdot .38974 .87892 Mdot .96931 .60777 Mdot .2733 .86922 Mdot .11629 .70073 Mdot .8854 .03258 Mdot .13211 .13698 Mdot .29178 .29018 Mdot .5 Mabswid .97619 .58065 m .96931 .60777 L .76039 1.00858 L .71651 1.01771 L .18763 1.09064 L .04621 .75468 L .02381 .0266 L .8854 .03258 L .91725 .13454 L s 0 0 m 1 0 L 1 1.11724 L 0 1.11724 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{257.75, 287.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg000^goo00<007ooOol017oo0007Ool4000dOom/000dOol2000I Ool00`00Oomoo`04Ool000Qoo`800:5oocL001Qoo`03001oogoo00Aoo`002Goo00<007ooOol0dWoo 100067oo00<007ooOol017oo0009Ool00`00Oomoo`3COol3000HOol00`00Oomoo`04Ool000Uoo`03 001oogoo0=Eoo`03001oogoo01Ioo`03001oogoo00Aoo`002Goo00<007ooOol0eGoo00<007ooOol0 5Woo00<007ooOol017oo0009Ool00`00Oomoo`3FOol00`00Oomoo`0EOol00`00Oomoo`04Ool000Uo o`03001oogoo0=Ioo`03001oogoo01Eoo`03001oogoo00Aoo`002Goo00<007ooOol0eWoo00<007oo Ool05Goo00<007ooOol017oo0009Ool00`00Oomoo`3GOol00`00Oomoo`0DOol00`00Oomoo`04Ool0 00Uoo`03001oogoo0=Moo`03001oogoo01Aoo`8000Eoo`002Goo00<007ooOol0egoo00<007ooOol0 57oo00<007ooOol017oo0009Ool00`00Oomoo`3HOol00`00Oomoo`0COol00`00Oomoo`04Ool000Uo o`03001oogoo0=Qoo`03001oogoo01=oo`03001oogoo00Aoo`002Goo00<007ooOol0f7oo00<007oo Ool04goo00<007ooOol017oo000:Ool00`00Oomoo`3GOol00`00Oomoo`0COol00`00Oomoo`04Ool0 00Yoo`03001oogoo0=Qoo`03001oogoo019oo`03001oogoo00Aoo`002Woo00<007ooOol0f7oo00<0 07ooOol04Woo00<007ooOol017oo000:Ool00`00Oomoo`3HOol00`00Oomoo`0BOol00`00Oomoo`04 Ool000Yoo`03001oogoo0=Uoo`03001oogoo015oo`03001oogoo00Aoo`002Woo00<007ooOol0fGoo 00<007ooOol04Goo00<007ooOol017oo000:Ool00`00Oomoo`3IOol00`00Oomoo`0AOol00`00Oomo o`04Ool000Yoo`03001oogoo0=Yoo`03001oogoo011oo`03001oogoo00Aoo`002Woo00<007ooOol0 fWoo00<007ooOol047oo00<007ooOol017oo000:Ool00`00Oomoo`3JOol00`00Oomoo`0@Ool20005 Ool000Yoo`03001oogoo0=Yoo`80015oo`03001oogoo00Aoo`002Woo00<007ooOol05Woo0P00`Goo 100047oo00<007ooOol017oo000:Ool00`00Oomoo`0EOol40030Ool4000@Ool00`00Oomoo`04Ool0 00Yoo`03001oogoo01Eoo`@00<5oo`80015oo`03001oogoo00Aoo`002Woo00<007ooOol05Woo0P00 eGoo00<007ooOol017oo000:Ool00`00Oomoo`3]Ool00`00Oomoo`04Ool000Yoo`03001oogoo0>eo o`03001oogoo00Aoo`002Woo00<007ooOol01goo0P00i7oo00<007ooOol017oo000:Ool00`00Oomo o`06Ool4003SOol00`00Oomoo`04Ool000Yoo`03001oogoo00Ioo`@00>=oo`03001oogoo00Aoo`00 2Woo00<007ooOol01goo0P00i7oo00<007ooOol017oo000:Ool00`00Oomoo`3]Ool00`00Oomoo`04 Ool000Yoo`03001oogoo0>eoo`8000Eoo`002Woo00<007ooOol0kGoo00<007ooOol017oo000:Ool0 0`00Oomoo`3]Ool00`00Oomoo`04Ool000Yoo`03001oogoo0>eoo`03001oogoo00Aoo`002Woo00<0 07ooOol0kGoo00<007ooOol017oo000:Ool00`00Oomoo`3]Ool00`00Oomoo`04Ool000Yoo`03001o ogoo0>eoo`03001oogoo00Aoo`002Woo00<007ooOol0kGoo00<007ooOol017oo000;Ool00`00Oomo o`3/Ool00`00Oomoo`04Ool000]oo`03001oogoo0>aoo`03001oogoo00Aoo`002goo00<007ooOol0 k7oo00<007ooOol017oo000;Ool00`00Oomoo`3/Ool00`00Oomoo`04Ool000]oo`03001oogoo0=Uo o`8000Aoo`8000=oo`@000Aoo`03001oogoo00Aoo`002goo00<007ooOol0f7oo00@007ooOol000Qo o`03001oogoo00Eoo`03001oogoo00Aoo`002goo00<007ooOol0f7oo00@007ooOol000Uoo`03001o ogoo00Aoo`<000Aoo`002goo00<007ooOol0f7oo00@007ooOol000Yoo`03001oogoo00=oo`03001o ogoo00Aoo`002goo00<007ooOol0f7oo00@007ooOol000Qoo`04001oogoo0004Ool00`00Oomoo`04 Ool000]oo`03001oogoo0=Uoo`8000Yoo`8000Eoo`03001oogoo00Aoo`002goo00<007ooOol0k7oo 00<007ooOol017oo000;Ool00`00Oomoo`3/Ool00`00Oomoo`04Ool000]oo`03001oogoo0>aoo`03 001oogoo00Aoo`002goo00<007ooOol0k7oo00<007ooOol017oo000;Ool00`00Oomoo`3/Ool00`00 Oomoo`04Ool000]oo`03001oogoo0>aoo`03001oogoo00Aoo`002goo00<007ooOol0Q7oo0P00IWoo 00<007ooOol017oo000;Ool00`00Oomoo`23Ool4001UOol00`00Oomoo`04Ool000]oo`03001oogoo 08=oo`@006Eoo`03001oogoo00Aoo`002goo00<007ooOol0?Goo0P00AGoo0P00IWoo0P001Goo000; Ool00`00Oomoo`0lOol4002/Ool00`00Oomoo`04Ool000]oo`03001oogoo03aoo`@00:aoo`03001o ogoo00Aoo`002goo00<007ooOol0?Goo0P00[Goo00<007ooOol017oo000;Ool00`00Oomoo`3/Ool0 0`00Oomoo`04Ool000]oo`03001oogoo0>aoo`03001oogoo00Aoo`002goo00<007ooOol0k7oo00<0 07ooOol017oo000;Ool00`00Oomoo`3/Ool00`00Oomoo`04Ool000]oo`03001oogoo0>aoo`03001o ogoo00Aoo`002goo00<007ooOol0k7oo00<007ooOol017oo000;Ool00`00Oomoo`3/Ool00`00Oomo o`04Ool000aoo`03001oogoo0>]oo`03001oogoo00Aoo`0037oo00<007ooOol0jgoo00<007ooOol0 17oo000]oo`8000Eoo`0037oo 00<007ooOol0jgoo00<007ooOol017oo000]oo`03001oogoo00Aoo`0037oo00<007ooOol0jgoo00<007ooOol017oo000]oo`03001oogoo00Aoo`0037oo00<007oo Ool0jgoo00<007ooOol017oo000]oo`03001oogoo00Aoo`0037oo00<007ooOol0jgoo00<007ooOol017oo000]oo`03001oogoo00Aoo`0037oo00<007ooOol0jgoo 0P001Goo000]oo`03001oogoo 00Aoo`0037oo00<007ooOol0jgoo00<007ooOol017oo000]oo`03001oogoo00Aoo`0037oo00<007ooOol0jgoo00<007ooOol017oo 000]oo`03001oogoo00Aoo`00 37oo00<007ooOol0jgoo00<007ooOol017oo000]oo`03001oogoo00Aoo`0037oo00<007ooOol0f7oo0P0017oo0P001Goo0`000goo 00<007ooOol017oo000Yoo`03001oogoo00Aoo`003Goo00<007ooOol0jWoo00<007ooOol017oo000=Ool00`00Oomoo`3Z Ool00`00Oomoo`04Ool000eoo`03001oogoo0>Yoo`03001oogoo00Aoo`003Goo00<007ooOol0jWoo 00<007ooOol017oo000=Ool00`00Oomoo`3ZOol00`00Oomoo`04Ool000eoo`03001oogoo0>Yoo`03 001oogoo00Aoo`003Goo00<007ooOol0jWoo00<007ooOol017oo000=Ool00`00Oomoo`3ZOol20005 Ool000eoo`03001oogoo0>Yoo`03001oogoo00Aoo`003Goo00<007ooOol0jWoo00<007ooOol017oo 000=Ool00`00Oomoo`3ZOol00`00Oomoo`04Ool000eoo`03001oogoo0>Yoo`03001oogoo00Aoo`00 3Goo00<007ooOol0jWoo00<007ooOol017oo000=Ool00`00Oomoo`3ZOol00`00Oomoo`04Ool000eo o`03001oogoo0>Yoo`03001oogoo00Aoo`003Goo00<007ooOol0jWoo00<007ooOol017oo000=Ool0 0`00Oomoo`3ZOol00`00Oomoo`04Ool000eoo`03001oogoo0>Yoo`03001oogoo00Aoo`003Goo00<0 07ooOol0jWoo00<007ooOol017oo000=Ool00`00Oomoo`3ZOol00`00Oomoo`04Ool000eoo`03001o ogoo0>Yoo`03001oogoo00Aoo`003Goo00<007ooOol0jWoo0P001Goo000=Ool00`00Oomoo`3ZOol0 0`00Oomoo`04Ool000eoo`03001oogoo0>Yoo`03001oogoo00Aoo`003Goo00<007ooOol0jWoo00<0 07ooOol017oo000>Ool00`00Oomoo`3UOol20002Ool00`00Oomoo`04Ool000ioo`03001oogoo0>Ao o`@00003Ool007oo00Eoo`003Woo00<007ooOol0i7oo100000=oo`00Ool01Goo000>Ool00`00Oomo o`3UOol20002Ool00`00Oomoo`04Ool000ioo`03001oogoo0>Eoo`05001oogooOol00006Ool000io o`03001oogoo0>Eoo`05001oogooOol00006Ool000ioo`03001oogoo0>Eoo`05001oogooOol00006 Ool000ioo`03001oogoo0>=oo`8000Aoo`03001oogoo00Aoo`003Woo00<007ooOol0hWoo10000goo 00<007ooOol017oo000>Ool00`00Oomoo`3ROol40003Ool20005Ool000ioo`03001oogoo0>=oo`80 00Aoo`03001oogoo00Aoo`003Woo00<007ooOol0hWoo00<007ooOol017oo00<007ooOol017oo000> Ool00`00Oomoo`3ROol00`00Oomoo`04Ool00`00Oomoo`04Ool000ioo`03001oogoo0>5oo`03001o ogoo00Eoo`03001oogoo00Aoo`003Woo00<007ooOol0hGoo00<007ooOol01Goo00<007ooOol017oo 000>Ool00`00Oomoo`3POol00`00Oomoo`06Ool00`00Oomoo`04Ool000ioo`03001oogoo0>1oo`03 001oogoo00Ioo`03001oogoo00Aoo`003Woo00<007ooOol0ggoo00<007ooOol01goo00<007ooOol0 17oo000>Ool00`00Oomoo`3OOol00`00Oomoo`07Ool00`00Oomoo`04Ool000ioo`03001oogoo0=io o`03001oogoo00Qoo`03001oogoo00Aoo`003Woo00<007ooOol0gWoo00<007ooOol027oo00<007oo Ool017oo000>Ool00`00Oomoo`3FOol20004Ool20003Ool30005Ool00`00Oomoo`04Ool000ioo`03 001oogoo015oo`800<9oo`04001oogoo0004Ool01@00Oomoogoo00000Woo00<007ooOol00Woo00<0 07ooOol017oo000>Ool00`00Oomoo`0@Ool40031Ool01000Oomoo`000goo00<007ooOol00Woo00@0 07ooOol000Aoo`<000Aoo`003Woo00<007ooOol047oo1000`Goo00@007ooOol000=oo`03001oogoo 009oo`<000Eoo`03001oogoo00Aoo`003Woo00<007ooOol04Goo0P00`Woo00@007ooOol0009oo`03 001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00Aoo`003Woo00<007ooOol0eWoo0P000goo00<0 07ooOol017oo0`0017oo00<007ooOol017oo000>Ool00`00Oomoo`3JOol00`00Oomoo`07oo1`00RGoo 00<007ooOol017oo000_Ool00`00Oomoo`0`Ool8002@Ool00`00Oomoo`04Ool002moo`03001oogoo 02Uoo`L009Qoo`03001oogoo00Aoo`00<7oo00<007ooOol08Goo1`00Wgoo00<007ooOol017oo000` Ool00`00Oomoo`0IOol8002VOol00`00Oomoo`04Ool0035oo`03001oogoo015oo`L00:ioo`03001o ogoo00Aoo`00"], ImageRangeCache->{{{0, 256.75}, {286.938, 0}} -> {0.071484, -0.0448223, 0.00369933, 0.00369933}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(redData\ = \ testData[\([hull]\)]\)], "Input"], Cell[BoxData[ \({{0.9854144480979308`, 0.5197559909336091`}, {0.9790666337506108`, 0.5447592159417597`}, {0.7864503652395413`, 0.9142900019898313`}, {0.7459980897444073`, 0.9227130073994213`}, {0.258391038463348`, 0.989953074822844`}, {0.12800478780748317`, 0.6802117765645495`}, {0.10735396431028531`, 0.00894527441596694`}, {0.9017056392536047`, 0.014461222122999957`}, {0.9310701765597696`, 0.10846213234160151`}}\)], "Output"] }, Open ]], Cell[BoxData[ \(\(InsideCircle[{x_, y_}, {{cx_, cy_}, r_}] := \[IndentingNewLine]\((x - cx)\)^2 + \((y - cy)\)^2 \[LessEqual] \ r^2;\)\)], "Input"], Cell[BoxData[ \(DefineCircle[p1_, p2_, p3_] := Module[\[IndentingNewLine]{m1, m2, center, t1, t2, radius}, \[IndentingNewLine]m1\ = \ \((p1 + p2)\)/2; \[IndentingNewLine]m2\ = \ \((p1 + p3)\)/2; \[IndentingNewLine]sol\ = \ Solve[{{x, y} - m1\ \[Equal] \ t1\ \((p1 - p2)\) . {{0, 1}, {\(-1\), 0}}, \[IndentingNewLine]{x, y} - m2\ \[Equal] \ t2\ \((p1 - p3)\) . {{0, 1}, {\(-1\), 0}}}, {x, y}, {t1, t2}]; \[IndentingNewLine]center\ = N[\ {x, y}\ /. \ sol[\([1]\)]\ ]; \[IndentingNewLine]radius\ = Max[\(N[Sqrt[\((# - center)\) . \((# - center)\)]\ ] &\)\ /@ \ {p1, p2, p3}]; \[IndentingNewLine]{\ center, radius}\[IndentingNewLine]]\)], "Input"], Cell[BoxData[{ \(\ \(Done\ = \ False;\)\), "\[IndentingNewLine]", \(\(circleList\ = \ {};\)\), "\[IndentingNewLine]", \(\({Di, Dj, Dk} = {1, 2, 3};\)\), "\[IndentingNewLine]", \(While[\ \(! Done\), \[IndentingNewLine]circle\ = \ DefineCircle[\ redData[\([Di]\)], redData[\([Dj]\)], redData[\([Dk]\)]\ ]; \[IndentingNewLine]works\ = \ \(! MemberQ[\ \(InsideCircle[#, circle] &\)\ /@ \ \ redData, \ False]\); \[IndentingNewLine]If[works, \ \(AppendTo[circleList, circle]\ ;\)\ \ ]; \ \[IndentingNewLine]\[IndentingNewLine]\(Dk++\); \ If[\ Dk > Length[redData], \[IndentingNewLine]\t\(Dj++\); \ If[\ Dj > Length[redData] - 1, \[IndentingNewLine]\t\(Di++\); \ If[\ Di > Length[redData] - 2, \ \[IndentingNewLine]\ \(Done = True;\)\[IndentingNewLine]]; \ Dj = Di + 1;\[IndentingNewLine]]; \ Dk = Dj + 1;\[IndentingNewLine]];\[IndentingNewLine]]\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(bestSolution\ = Reverse[\ First\ [Sort[\ Reverse\ /@ \ circleList\ ]\ ]]\)], "Input"], Cell[BoxData[ \({{0.5014835398271242`, 0.4503954575960198`}, 0.5917908300462131`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\ \)\(\(InsideCircle[#, bestSolution] &\) /@ \ \ redData\)\)\)], "Input"], Cell[BoxData[ \({True, True, True, True, True, True, True, True, True}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[ Graphics[ {PointSize[0.02], Point\ /@ \ testData, \[IndentingNewLine]Line[\ testData[\([hull]\)]\ ], \[IndentingNewLine]Circle\ @@ \ bestSolution\ }\[IndentingNewLine]], PlotRange \[Rule] All, Axes \[Rule] True, AspectRatio \[Rule] Automatic];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 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 0.0964762 0.80466 0.137585 0.80466 [ [.25741 .12508 -9 -9 ] [.25741 .12508 9 0 ] [.41834 .12508 -9 -9 ] [.41834 .12508 9 0 ] [.57927 .12508 -9 -9 ] [.57927 .12508 9 0 ] [.7402 .12508 -9 -9 ] [.7402 .12508 9 0 ] [.90114 .12508 -3 -9 ] [.90114 .12508 3 0 ] [.08398 .29852 -18 -4.5 ] [.08398 .29852 0 4.5 ] [.08398 .45945 -18 -4.5 ] [.08398 .45945 0 4.5 ] [.08398 .62038 -18 -4.5 ] [.08398 .62038 0 4.5 ] [.08398 .78131 -18 -4.5 ] [.08398 .78131 0 4.5 ] [.08398 .94224 -6 -4.5 ] [.08398 .94224 0 4.5 ] [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .25741 .13758 m .25741 .14383 L s [(0.2)] .25741 .12508 0 1 Mshowa .41834 .13758 m .41834 .14383 L s [(0.4)] .41834 .12508 0 1 Mshowa .57927 .13758 m .57927 .14383 L s [(0.6)] .57927 .12508 0 1 Mshowa .7402 .13758 m .7402 .14383 L s [(0.8)] .7402 .12508 0 1 Mshowa .90114 .13758 m .90114 .14383 L s [(1)] .90114 .12508 0 1 Mshowa .125 Mabswid .13671 .13758 m .13671 .14133 L s .17694 .13758 m .17694 .14133 L s .21718 .13758 m .21718 .14133 L s .29764 .13758 m .29764 .14133 L s .33787 .13758 m .33787 .14133 L s .37811 .13758 m .37811 .14133 L s .45857 .13758 m .45857 .14133 L s .49881 .13758 m .49881 .14133 L s .53904 .13758 m .53904 .14133 L s .61951 .13758 m .61951 .14133 L s .65974 .13758 m .65974 .14133 L s .69997 .13758 m .69997 .14133 L s .78044 .13758 m .78044 .14133 L s .82067 .13758 m .82067 .14133 L s .8609 .13758 m .8609 .14133 L s .05624 .13758 m .05624 .14133 L s .01601 .13758 m .01601 .14133 L s .94137 .13758 m .94137 .14133 L s .9816 .13758 m .9816 .14133 L s .25 Mabswid 0 .13758 m 1 .13758 L s .09648 .29852 m .10273 .29852 L s [(0.2)] .08398 .29852 1 0 Mshowa .09648 .45945 m .10273 .45945 L s [(0.4)] .08398 .45945 1 0 Mshowa .09648 .62038 m .10273 .62038 L s [(0.6)] .08398 .62038 1 0 Mshowa .09648 .78131 m .10273 .78131 L s [(0.8)] .08398 .78131 1 0 Mshowa .09648 .94224 m .10273 .94224 L s [(1)] .08398 .94224 1 0 Mshowa .125 Mabswid .09648 .17782 m .10023 .17782 L s .09648 .21805 m .10023 .21805 L s .09648 .25828 m .10023 .25828 L s .09648 .33875 m .10023 .33875 L s .09648 .37898 m .10023 .37898 L s .09648 .41922 m .10023 .41922 L s .09648 .49968 m .10023 .49968 L s .09648 .53991 m .10023 .53991 L s .09648 .58015 m .10023 .58015 L s .09648 .66061 m .10023 .66061 L s .09648 .70085 m .10023 .70085 L s .09648 .74108 m .10023 .74108 L s .09648 .82155 m .10023 .82155 L s .09648 .86178 m .10023 .86178 L s .09648 .90201 m .10023 .90201 L s .09648 .09735 m .10023 .09735 L s .09648 .05712 m .10023 .05712 L s .09648 .01689 m .10023 .01689 L s .09648 .98248 m .10023 .98248 L s .25 Mabswid .09648 0 m .09648 1 L s .02 w .59375 .33272 Mdot .70619 .7869 Mdot .21632 .24658 Mdot .18286 .14478 Mdot .7293 .87328 Mdot .44704 .75826 Mdot .8894 .55581 Mdot .53686 .75114 Mdot .30439 .93416 Mdot .84567 .22486 Mdot .69675 .88006 Mdot .25939 .62175 Mdot .19948 .68492 Mdot .45433 .77709 Mdot .88429 .57593 Mdot .36795 .76989 Mdot .25147 .6449 Mdot .82204 .14922 Mdot .2632 .22667 Mdot .38166 .34032 Mdot .5 Mabswid .8894 .55581 m .88429 .57593 L .7293 .87328 L .69675 .88006 L .30439 .93416 L .19948 .68492 L .18286 .14478 L .82204 .14922 L .84567 .22486 L s newpath .5 .5 .47619 0 365.73 arc s 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{260.5, 260.5}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgQoo`006Goo00<007ooOol0j7oo000IOol2 003YOol001Uoo`03001oogoo0>Qoo`006Goo00<007ooOol0GWoo4000NWoo000IOol00`00Oomoo`1D Ool:000@Ool9001aOol001Uoo`03001oogoo04ioo`H002=oo`H006]oo`006Goo00<007ooOol0BGoo 1@00;goo1P00IGoo000IOol00`00Oomoo`16Ool3000jOol3001ROol001Uoo`03001oogoo04=oo`<0 041oo`<005moo`006Goo00<007ooOol0@7oo0`00AWoo0`00G7oo000IOol00`00Oomoo`0mOol3001< Ool3001IOol001Uoo`03001oogoo03Yoo`<0059oo`8005Moo`006Goo0P00>7oo0`00Egoo0`00E7oo 000IOol00`00Oomoo`0dOol3001MOol3001AOol001Uoo`03001oogoo039oo`8006=oo`<004ioo`00 6Goo00<007ooOol0<7oo0P00J7oo0P00C7oo000IOol00`00Oomoo`0^Ool2001/Ool2001:Ool001Uo o`03001oogoo02aoo`80071oo`03001oogoo04Moo`006Goo00<007ooOol0:Woo0P00Lgoo0P00Agoo 000IOol00`00Oomoo`0XOol2001gOol20015Ool001Uoo`03001oogoo02Moo`03001oogoo07Uoo`80 04=oo`006Goo00<007ooOol07goo0P0017oo0P000goo10006goo0P0017oo0P001Goo0`006Woo0P00 17oo0P000goo0`0077oo0P0017oo10000Woo0P0087oo1@0067oo000IOol2000OOol01@00Oomoo`00 Ool00P001Goo00<007ooOol06goo00@007ooOol000]oo`03001oogoo01Qoo`04001oogoo0008Ool0 1000Oomoo`006Woo00@007ooOol000Moo`80009oo`03001oogoo01moo`03001oogoo01Qoo`006Goo 00<007ooOol07Woo00<007ooOol00P0027oo00<007ooOol06Woo00@007ooOol000Qoo`D001Uoo`04 001oogoo0008Ool01000Oomoo`006Woo00@007ooOol000Qoo`04001oogoo000QOol00`00Oomoo`0H Ool001Uoo`03001oogoo01ioo`04001oogoo000:Ool00`00Oomoo`0IOol01000Oomoo`0027oo00@0 07ooOol001Yoo`04001oogoo0008Ool3000KOol01000Oomoo`002Goo0P008Woo00<007ooOol067oo 000IOol00`00Oomoo`0NOol40008Ool01000Oomoo`006Woo00@007ooOol000Uoo`03001oo`0001Yo o`04001oogoo0009Ool00`00Oomoo`0JOol01000Oomoo`0027oo00@007ooOol0025oo`03001oogoo 01Qoo`006Goo00<007ooOol07Goo10002Woo0P0077oo0P002goo0P006goo0P002Woo0`006goo0P00 2Woo0P0000=oo`0000007Woo0P006Woo000IOol00`00Oomoo`0LOol00`00Oomoo`2?Ool2000hOol0 01Uoo`03001oogoo01]oo`03001oogoo099oo`03001oogoo03Eoo`006Goo00<007ooOol06Goo0P00 UWoo00<007ooOol0=7oo000IOol00`00Oomoo`0HOol00`00Oomoo`2GOol00`00Oomoo`0cOol001Uo o`03001oogoo01Moo`03001oogoo09Uoo`8003=oo`006Goo00<007ooOol05Woo00<007ooOol0W7oo 00<007ooOol0<7oo003o0005000000Aoo`03001oogoo00Moo`03001oogoo00Qoo`03001oogoo00Mo o`03001oogoo00Moo`D000Ioo`03001oogoo00Moo`03001oogoo00Qoo`03001oogoo00Moo`03001o ogoo00Qoo`03001oogoo00Moo`03001oogoo00Qoo`03001oogoo00Moo`03001oogoo00Moo`03001o ogoo00Qoo`03001oogoo00Moo`03001oogoo00Qoo`03001oogoo00Moo`03001oogoo00Qoo`03001o ogoo00Moo`03001oogoo00Ioo`@000Qoo`03001oogoo00Moo`03001oogoo00Qoo`03001oogoo00Mo o`03001oogoo00=oo`006Goo00<007ooOol04GooE@00DGoo1@00;7oo000IOol00`00Oomoo`0AOol5 001@OomF000/Ool001Uoo`03001oogoo011oo`03001oo`0000800:9oo`D002aoo`006Goo00<007oo Ool03goo00D007ooOomoo`000:Aoo`<00003Ool007oo02Yoo`006Goo00<007ooOol03Woo00<007oo Ool00Woo00<007ooOol0Y7oo00@007ooOol002Yoo`006Goo00<007ooOol03Goo00<007ooOol00goo 00<007ooOol0Y7oo00D007ooOomoo`0002Uoo`006Goo00<007ooOol037oo00<007ooOol017oo00<0 07ooOol0YGoo00D007ooOomoo`0002Qoo`006Goo00<007ooOol037oo00<007ooOol017oo00<007oo Ool0YGoo00D007ooOomoo`0002Qoo`006Goo0P0037oo00<007ooOol01Goo00<007ooOol0YGoo00<0 07ooOol00Woo00<007ooOol09Goo000IOol00`00Oomoo`0:Ool00`00Oomoo`06Ool00`00Oomoo`2V Ool00`00Oomoo`02Ool00`00Oomoo`0TOol001Uoo`03001oogoo00Uoo`03001oogoo00Moo`03001o ogoo0:Ioo`03001oogoo00=oo`03001oogoo02=oo`006Goo00<007ooOol027oo00<007ooOol027oo 00<007ooOol0YWoo00<007ooOol017oo00<007ooOol08Woo000IOol00`00Oomoo`07Ool00`00Oomo o`09Ool00`00Oomoo`2VOol00`00Oomoo`05Ool00`00Oomoo`0QOol001Uoo`03001oogoo00Ioo`03 001oogoo00Yoo`03001oogoo0:Moo`03001oogoo00Eoo`03001oogoo021oo`006Goo00<007ooOol0 1Woo00<007ooOol02Woo00<007ooOol0Ygoo00<007ooOol01Goo00<007ooOol087oo000IOol00`00 Oomoo`05Ool00`00Oomoo`0;Ool00`00Oomoo`2WOol00`00Oomoo`06Ool00`00Oomoo`0OOol001Uo o`03001oogoo00Aoo`03001oogoo00aoo`03001oogoo0:Qoo`03001oogoo00Ioo`03001oogoo01io o`006Goo00<007ooOol00goo00<007ooOol03Goo00<007ooOol0Z7oo00<007ooOol01goo00<007oo Ool07Goo000IOol00`00Oomoo`02Ool00`00Oomoo`0?Ool00`00Oomoo`2WOol30008Ool00`00Oomo o`0LOol001Uoo`8000=oo`03001oogoo00moo`03001oogoo011oo`<009=oo`D000Moo`03001oogoo 01aoo`006Goo00D007ooOomoo`00019oo`03001oogoo00moo`D0099oo`D000Qoo`03001oogoo01]o o`006Goo00@007ooOol001=oo`03001oogoo00moo`D0099oo`D000Uoo`03001oogoo01Yoo`006Goo 00<007oo000057oo00<007ooOol03goo1@00Tgoo0`002Woo00<007ooOol06Woo000IOol2000EOol0 0`00Oomoo`0@Ool3002ROol00`00Oomoo`0IOol001Uoo`8001Eoo`03001oogoo00Aoo`<00:ioo`03 001oogoo01Uoo`006Goo00<007ooOol057oo00<007ooOol00goo1@00[Woo00<007ooOol067oo000H Ool2000FOol00`00Oomoo`03Ool5002_Ool00`00Oomoo`0GOol001Qoo`8001Ioo`03001oogoo00=o o`D00;1oo`03001oogoo01Ioo`005goo00<007oo00005Woo00<007ooOol017oo0`00/Goo00<007oo Ool05Woo000GOol01000Ool000005Goo00<007ooOol0^Goo00<007ooOol05Goo000FOol01000Oomo o`005Woo00<007ooOol0^Goo00<007ooOol05Goo000FOol01000Oomoo`005Woo00<007ooOol0^Woo 00<007ooOol057oo000EOol01@00Oomoogoo00005Woo00<007ooOol0^Woo00<007ooOol057oo000E Ool01@00Oomoogoo00005Woo00<007ooOol0^goo00<007ooOol04goo000DOol00`00Oomoo`02Ool0 0`00Oomoo`0DOol00`00Oomoo`2lOol00`00Oomoo`0BOol001=oo`03001oogoo00=oo`03001oogoo 01Aoo`03001oogoo0;aoo`03001oogoo019oo`004goo00<007ooOol00goo00<007ooOol057oo00<0 07ooOol0_Goo00<007ooOol04Goo0005Ool20004Ool20003Ool40005Ool00`00Oomoo`0DOol00`00 Oomoo`2mOol00`00Oomoo`0AOol000Aoo`04001oogoo0008Ool00`00Ool00006Ool00`00Oomoo`0D Ool00`00Oomoo`2nOol00`00Oomoo`0@Ool000Aoo`04001oogoo0009Ool20006Ool2000EOol00`00 Oomoo`2nOol00`00Oomoo`0@Ool000Aoo`04001oogoo0009Ool20006Ool00`00Oomoo`0DOol00`00 Oomoo`2oOol00`00Oomoo`0?Ool000Aoo`04001oogoo0008Ool200000goo001oo`04Ool00`00Oomo o`0DOol00`00Oomoo`2oOol00`00Oomoo`0?Ool000Eoo`8000Uoo`<000Ioo`03001oogoo01Aoo`03 001oogoo0;moo`03001oogoo00moo`0047oo00<007ooOol01Woo00<007ooOol057oo00<007ooOol0 `7oo00<007ooOol03Woo000?Ool00`00Oomoo`07Ool00`00Oomoo`0DOol00`00Oomoo`30Ool00`00 Oomoo`0>Ool000moo`03001oogoo00Moo`03001oogoo01Aoo`03001oogoo0<1oo`03001oogoo00io o`003Woo00<007ooOol027oo00<007ooOol057oo00<007ooOol0IWoo0`00F7oo00<007ooOol03Goo 000>Ool00`00Oomoo`08Ool00`00Oomoo`0DOol00`00Oomoo`1UOol5001GOol00`00Oomoo`0=Ool0 00eoo`03001oogoo00Uoo`03001oogoo01Aoo`03001oogoo02ioo`<003Aoo`D005Moo`03001oogoo 00eoo`003Goo00<007ooOol02Goo00<007ooOol057oo00<007ooOol0;Goo1@00Ool00`00Oomoo`0EOol00`00Oomoo`37Ool00`00 Oomoo`06Ool000Qoo`03001oogoo00ioo`03001oogoo01Eoo`03001oogoo0Ool00`00Oomoo`0FOol00`00Oomoo`2^ Ool00`00Oomoo`0DOol00`00Oomoo`07Ool000Qoo`03001oogoo00ioo`03001oogoo01Ioo`03001o ogoo0:eoo`03001oogoo01Eoo`03001oogoo00Moo`0027oo00<007ooOol03Woo00<007ooOol05Woo 00<007ooOol0[Goo00<007ooOol05Goo00<007ooOol01goo0009Ool00`00Oomoo`0=Ool00`00Oomo o`0FOol00`00Oomoo`2/Ool00`00Oomoo`0FOol00`00Oomoo`07Ool000Uoo`03001oogoo00eoo`03 001oogoo01Ioo`03001oogoo0:aoo`03001oogoo01Ioo`03001oogoo00Moo`002Goo00<007ooOol0 3Goo00<007ooOol05Woo00<007ooOol0Zgoo00<007ooOol05goo00<007ooOol01goo0005Ool20002 Ool01000Ool000000goo0`001Woo00<007ooOol05Woo00<007ooOol03Goo0`00Vgoo00<007ooOol0 5Woo00<007ooOol027oo0004Ool01P00Oomoo`00Ool000Ioo`04001oogoo0005Ool00`00Oomoo`0F Ool00`00Oomoo`0Ool00`00Oomoo`08Ool00`00 Oomoo`0GOol00`00Oomoo`2ROol00`00Oomoo`0IOol00`00Oomoo`0=Ool000ioo`03001oogoo00Qo o`03001oogoo01Moo`03001oogoo0:9oo`03001oogoo01Uoo`03001oogoo00eoo`003Woo00<007oo Ool027oo00<007ooOol05Woo0`00XWoo00<007ooOol06Woo00<007ooOol03Goo000?Ool00`00Oomo o`07Ool00`00Oomoo`0EOol5002QOol00`00Oomoo`0IOol00`00Oomoo`0>Ool000moo`03001oogoo 00Moo`03001oogoo01Eoo`D00:1oo`03001oogoo01Yoo`03001oogoo00ioo`0047oo00<007ooOol0 1Woo00<007ooOol05Goo1@00X7oo00<007ooOol06Woo00<007ooOol03Woo000@Ool00`00Oomoo`06 Ool00`00Oomoo`0FOol3002POol00`00Oomoo`0JOol00`00Oomoo`0?Ool0015oo`03001oogoo00Eo o`03001oogoo01Qoo`03001oogoo09ioo`03001oogoo01Yoo`03001oogoo00moo`004Woo00<007oo Ool017oo0P006Woo00<007ooOol0W7oo00<007ooOol06Woo00<007ooOol047oo000BOol00`00Oomo o`04Ool00`00Oomoo`0IOol00`00Oomoo`2LOol00`00Oomoo`0JOol00`00Oomoo`0@Ool0019oo`03 001oogoo00Aoo`03001oogoo01Yoo`03001oogoo09Yoo`03001oogoo01Yoo`03001oogoo015oo`00 4goo00<007ooOol00goo00<007ooOol06Woo00<007ooOol0VWoo00<007ooOol06Woo00<007ooOol0 4Goo000COol00`00Oomoo`03Ool00`00Oomoo`0JOol00`00Oomoo`2IOol00`00Oomoo`0JOol00`00 Oomoo`0BOol001Aoo`03001oogoo009oo`03001oogoo01]oo`03001oogoo09Qoo`03001oogoo01Yo o`03001oogoo019oo`0057oo00<007ooOol00Woo00<007ooOol06goo00<007ooOol0Ugoo00<007oo Ool06Woo00<007ooOol04goo000EOol01@00Oomoogoo00007Woo00<007ooOol0UGoo00<007ooOol0 6goo00<007ooOol04goo000EOol01@00Oomoogoo00007Woo00<007ooOol0UGoo00<007ooOol06Woo 00<007ooOol057oo000FOol01000Oomoo`007Woo00<007ooOol0U7oo00<007ooOol06goo00<007oo Ool057oo000FOol00`00Oomoo`02000NOol00`00Oomoo`2COol00`00Oomoo`0JOol00`00Oomoo`0E Ool001Moo`03001oo`0001moo`03001oogoo04ioo`<0045oo`03001oogoo01Yoo`03001oogoo01Io o`0067oo0P0087oo00<007ooOol0C7oo1@00@7oo00<007ooOol06Woo00<007ooOol05Woo000HOol2 000POol00`00Oomoo`0eOol3000DOol5000oOol00`00Oomoo`0JOol00`00Oomoo`0GOol001Uoo`03 001oogoo01moo`03001oogoo03=oo`D001=oo`D003moo`03001oogoo01Yoo`03001oogoo01Moo`00 6Goo00<007ooOol07goo00<007ooOol0Ool00`00Oomoo`0HOol00`00 Oomoo`0NOol000Eoo`8000Yoo`8000Ioo`03001oogoo00Aoo`03001oogoo01aoo`03001oogoo07Ao o`<000moo`03001oogoo01Qoo`03001oogoo01ioo`006Goo00<007ooOol01Goo00<007ooOol06goo 00<007ooOol0QGoo00<007ooOol067oo00<007ooOol07goo000IOol00`00Oomoo`06Ool00`00Oomo o`0KOol00`00Oomoo`24Ool00`00Oomoo`0GOol00`00Oomoo`0POol001Uoo`03001oogoo00Moo`03 001oogoo01Yoo`03001oogoo08=oo`03001oogoo01Moo`03001oogoo025oo`006Goo00<007ooOol0 27oo00<007ooOol06Woo00<007ooOol0PWoo00<007ooOol05Woo00<007ooOol08Woo000IOol00`00 Oomoo`08Ool00`00Oomoo`0JOol00`00Oomoo`21Ool00`00Oomoo`0GOol00`00Oomoo`0ROol001Uo o`03001oogoo00Uoo`03001oogoo01Uoo`03001oogoo085oo`03001oogoo01Ioo`03001oogoo02=o o`006Goo0P002goo00<007ooOol06Goo00<007ooOol0Ogoo00<007ooOol05Woo00<007ooOol097oo 000IOol00`00Oomoo`0;Ool00`00Oomoo`0HOol00`00Oomoo`1oOol00`00Oomoo`0EOol00`00Oomo o`0UOol001Uoo`03001oogoo00aoo`03001oogoo01Qoo`03001oogoo07eoo`03001oogoo01Eoo`03 001oogoo02Ioo`006Goo00<007ooOol03Goo00<007ooOol05goo00<007ooOol0OGoo00<007ooOol0 57oo00<007ooOol09goo000IOol00`00Oomoo`0>Ool00`00Oomoo`0FOol00`00Oomoo`1lOol00`00 Oomoo`0DOol00`00Oomoo`0XOol001Uoo`03001oogoo00moo`03001oogoo01Ioo`03001oogoo07]o o`03001oogoo01=oo`03001oogoo02Uoo`006Goo00<007ooOol047oo00<007ooOol05Goo00<007oo Ool0NWoo00<007ooOol04Woo0P00;7oo000IOol00`00Oomoo`0AOol00`00Oomoo`0EOol00`00Oomo o`1iOol00`00Oomoo`0AOol00`00Oomoo`0/Ool001Uoo`03001oogoo019oo`03001oogoo01Aoo`03 001oogoo07Qoo`03001oogoo015oo`03001oogoo02eoo`006Goo00<007ooOol04goo00<007ooOol0 57oo00<007ooOol0Mgoo00<007ooOol047oo00<007ooOol0;Woo000IOol00`00Oomoo`0DOol2000D Ool00`00Oomoo`1fOol00`00Oomoo`0@Ool00`00Oomoo`0_Ool001Uoo`8001Moo`03001oogoo015o o`03001oogoo07Ioo`03001oogoo00moo`03001oogoo031oo`006Goo00<007ooOol05goo00<007oo Ool04Goo00<007ooOol0LWoo0`0047oo0P00Ool00`00Oomoo`0cOol001Uoo`03001oogoo01Uoo`80015oo`03 001oogoo06Moo`D0009oo`L000eoo`03001oogoo03Aoo`006Goo00<007ooOol06goo00<007ooOol0 3Woo00<007ooOol0IWoo20000Woo1@0037oo00<007ooOol0=Goo000IOol00`00Oomoo`0LOol00`00 Oomoo`0>Ool00`00Oomoo`1NOol700000goo000000030005Ool3000;Ool2000hOol001Uoo`03001o ogoo01eoo`03001oogoo00eoo`03001oogoo05Ioo`P000Uoo`<001=oo`03001oogoo03Qoo`006Goo 00<007ooOol07Woo0P003Goo00<007ooOol0Cgoo1`009Woo00<007ooOol0>Goo000IOol00`00Oomo o`0POol00`00Oomoo`0;Ool00`00Oomoo`17Ool7000/Ool00`00Oomoo`0jOol001Uoo`03001oogoo 025oo`03001oogoo00Yoo`03001oogoo03moo`P0035oo`8003eoo`006Goo0P008goo0P002goo00<0 07ooOol0=goo1`00>7oo00<007ooOol0?Goo000IOol00`00Oomoo`0TOol20009Ool00`00Oomoo`0` Ool7000mOol20010Ool001Uoo`03001oogoo02Ioo`03001oogoo00Ioo`03001oogoo02Uoo`L0049o o`80049oo`006Goo00<007ooOol09goo0P001goo00<007ooOol087oo2000Agoo0P00A7oo000IOol0 0`00Oomoo`0YOol20005Ool00`00Oomoo`0IOol7001=Ool20016Ool001Uoo`03001oogoo02]oo`80 00Aoo`03001oogoo015oo`L005=oo`03001oogoo04Ioo`006Goo00<007ooOol0;Goo0P000Woo0`00 2Goo2000F7oo0P00BGoo000IOol00`00Oomoo`0_Ool600000goo00000005001MOol3001;Ool001Uo o`03001oogoo031oo`H0069oo`8004ioo`0047oo1@0017oo00<007ooOol0<7oo1@00HGoo0P00D7oo 000BOol00`00Oomoo`04Ool00`00Oomoo`0aOol300000goo0000001MOol2001BOol0019oo`03001o ogoo00Aoo`8003Qoo`<005Qoo`8005Aoo`004Woo00<007ooOol017oo00<007ooOol0>Woo0`00DWoo 0`00EWoo000BOol00`00Oomoo`04Ool00`00Oomoo`0mOol3001Woo1P00Ggoo000IOol00`00 Oomoo`19Ool2000eOol3001UOol001Uoo`03001oogoo04]oo`H002Yoo`D006Qoo`006Goo00<007oo Ool0DGoo1`007Goo1P00KGoo000IOol00`00Oomoo`1HOolM001cOol001Uoo`03001oogoo0>Qoo`00 6Goo0P00jGoo000IOol00`00Oomoo`3XOol001Uoo`03001oogoo0>Qoo`006Goo00<007ooOol0j7oo 000IOol00`00Oomoo`3XOol00001\ \>"], ImageRangeCache->{{{0, 259.5}, {259.5, 0}} -> {-0.119903, -0.170991, 0.00478911, 0.00478911}}] }, Open ]], Cell[BoxData[ \(\(testData3D\ = \ Table[\ {Random[], \ Random[], \ Random[]}, {100}]; \)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(ch3D = ConvexHull3D[testData3D]\)], "Input"], Cell[BoxData[ \({{4, 22, 32}, {4, 24, 92}, {4, 32, 24}, {4, 64, 22}, {4, 92, 64}, {6, 15, 63}, {6, 50, 97}, {6, 55, 15}, {6, 63, 50}, {6, 97, 55}, {9, 17, 32}, {9, 22, 61}, {9, 32, 22}, {9, 61, 99}, {9, 99, 17}, {15, 49, 84}, {15, 55, 49}, {15, 84, 63}, {16, 24, 95}, {16, 32, 44}, {16, 34, 24}, {16, 44, 91}, {16, 91, 97}, {16, 95, 32}, {16, 97, 34}, {17, 44, 32}, {17, 49, 69}, {17, 69, 91}, {17, 84, 49}, {17, 88, 84}, {17, 91, 44}, {17, 99, 88}, {22, 64, 61}, {24, 32, 95}, {24, 34, 68}, {24, 68, 92}, {34, 97, 68}, {49, 55, 97}, {49, 97, 69}, {50, 63, 66}, {50, 66, 68}, {50, 68, 97}, {61, 63, 84}, {61, 64, 92}, {61, 84, 99}, {61, 92, 63}, {63, 92, 66}, {66, 92, 68}, {69, 97, 91}, {84, 88, 99}} \)], "Output"] }, Open ]], Cell[BoxData[ \(\(InsideSphere[{x_, y_, z_}, {{cx_, cy_, cz_}, r_}] := \[IndentingNewLine]\((x - cx)\)^2 + \((y - cy)\)^2 + \((z - cz)\)^2 \[LessEqual] \ r^2;\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(DefineSphere[a_, b_, c_, d_] := Module[\n\t\t{m, normal}, \n\t\tm\ = \ Det[{\((b - a)\), \((c - a)\), \((d - a)\)}]; \n\t center\ = \ \tIf[ m < 1000, \ (*bad\ Matrix, \ find\ the\ circle\ *) \n\t\tnormal\ = \ Cross[b - a, c - a]; \n\t\tInverse[{normal, b - a, c - a}] . {\((a . normal)\), \((b - a)\) . \((b + a)\)/ 2, \n\t\t\t\t\((c - a)\) . \((c + a)\)/2}\n\t\t, \ (*\ Good\ Matrix\ find\ the\ inverse\ *) \n\t\t\tInverse[ {\((b - a)\), \((c - a)\), \((d - a)\)}] . {\((b - a)\) . \((b + a)\)/ 2, \n\t\t\t\t\((c - a)\) . \((c + a)\)/2, \((d - a)\) . \((d + a)\)/ 2}\n\t\t\t]; \[IndentingNewLine]radius\ = Max[\(N[Sqrt[\((# - center)\) . \((# - center)\)]\ ] &\)\ /@ \ {a, b, c, d}]; \[IndentingNewLine]{\ center, radius}\n\t\t]; \)\), "\n", \(DefineSphere\ @@ \ redData[\([{1, 2, 3, 4}]\)]\)}], "Input"], Cell[BoxData[ \({{0.598576101762027`, 0.299018434909257`, 0.6009353165416556`}, 0.8447962728280928`}\)], "Output"] }, Open ]], Cell[BoxData[ \(\(redData\ = \ testData3D[\([\ Union[Flatten[ch3D]]]\)];\)\)], "Input"], Cell[BoxData[{ \(\ \(Done\ = \ False;\)\), "\[IndentingNewLine]", \(\(sphereList\ = \ {};\)\), "\[IndentingNewLine]", \(\({Di, Dj, Dk, Dl} = {1, 2, 3, 4};\)\), "\[IndentingNewLine]", \(While[\ \(! Done\), \[IndentingNewLine]sphere\ = \ DefineSphere[\ redData[\([Di]\)], redData[\([Dj]\)], redData[\([Dk]\)], redData[\([Dl]\)]\ ]; \[IndentingNewLine]works\ = \ \(! MemberQ[\ \(InsideSphere[#, sphere] &\)\ /@ \ \ redData, \ False]\); \[IndentingNewLine]If[works, \ \(AppendTo[sphereList, sphere]\ ;\)\ \ ]; \[IndentingNewLine]\(Dl++\); \ If[Dl > Length[redData], \[IndentingNewLine]\(Dk++\); \ If[\ Dk > Length[redData] - 1, \[IndentingNewLine]\t\(Dj++\); \ If[\ Dj > Length[redData] - 2, \[IndentingNewLine]\t\(Di++\); \ If[\ Di > Length[redData] - 3, \ \[IndentingNewLine]\ \(Done = True;\)\[IndentingNewLine]]; \ Dj = Di + 1;\[IndentingNewLine]]; \ Dk = Dj + 1;\[IndentingNewLine]]; \ Dl = Dk + 1;\[IndentingNewLine]];\[IndentingNewLine]]\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Length[redData]\)], "Input"], Cell[BoxData[ \(27\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(bestSolution\ = Reverse[\ First\ [Sort[\ Reverse\ /@ \ sphereList\ ]\ ]]\)], "Input"], Cell[BoxData[ \({{0.46046441812242367`, 0.5109882594225997`, 0.5514747799223599`}, 0.7434243073146426`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\ \)\(\(InsideSphere[#, bestSolution] &\) /@ \ \ redData\)\)\)], "Input"], Cell[BoxData[ \({True, True, True, True, True, True, True, True, True, True, True, True, True}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Graphics", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[ Graphics3D[ {PointSize[0.02], Point\ /@ \ testData3D\[IndentingNewLine], \ \[IndentingNewLine]TranslateShape[ Sphere[\ bestSolution[\([2]\)], 10, 10], \[IndentingNewLine]bestSolution[ \([1]\)]\ ]\ \ }\[IndentingNewLine]], PlotRange \[Rule] {{0, 1}, {0, 1}, {0, 1}}, Axes \[Rule] True, AspectRatio \[Rule] Automatic];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.0855 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics3D %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.0567234 1.16608 0 1.16608 [ [.07825 .23514 -5.94197 -9 ] [.07825 .23514 .05803 0 ] [.18503 .19003 -17.1654 -9 ] [.18503 .19003 .83459 0 ] [.29671 .14287 -16.5049 -9 ] [.29671 .14287 1.49509 0 ] [.41365 .09351 -15.8444 -9 ] [.41365 .09351 2.15559 0 ] [.53622 .0418 -15.1839 -9 ] [.53622 .0418 2.8161 0 ] [.66483 -0.01242 -4.84113 -9 ] [.66483 -0.01242 1.15887 0 ] [-0.00228 .81813 -3.47541 0 ] [-0.00228 .81813 2.52459 9 ] [.09305 .88497 -10.1461 0 ] [.09305 .88497 7.85393 9 ] [.17993 .94589 -9.90012 0 ] [.17993 .94589 8.09988 9 ] [.25946 1.00164 -9.68248 0 ] [.25946 1.00164 8.31752 9 ] [.33252 1.05285 -9.48852 0 ] [.33252 1.05285 8.51148 9 ] [.39987 1.10006 -3.10486 0 ] [.39987 1.10006 2.89514 9 ] [.07502 .2512 -6 -2.6079 ] [.07502 .2512 0 6.3921 ] [.0597 .34709 -18 -2.69294 ] [.0597 .34709 0 6.30706 ] [.04328 .44988 -18 -2.78472 ] [.04328 .44988 0 6.21528 ] [.02563 .56035 -18 -2.88407 ] [.02563 .56035 0 6.11593 ] [.00662 .67939 -18 -2.99197 ] [.00662 .67939 0 6.00803 ] [-0.01393 .80804 -6 -3.10957 ] [-0.01393 .80804 0 5.89043 ] [ 0 0 0 0 ] [ 1 1.0855 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .08846 .24555 m .67245 0 L s .08846 .24555 m .09356 .25076 L s [(0)] .07825 .23514 .98066 1 Mshowa .19482 .20083 m .19972 .20623 L s [(0.2)] .18503 .19003 .90727 1 Mshowa .30604 .15406 m .31071 .15966 L s [(0.4)] .29671 .14287 .83388 1 Mshowa .42247 .10511 m .42688 .11091 L s [(0.6)] .41365 .09351 .76049 1 Mshowa .54447 .05381 m .5486 .05982 L s [(0.8)] .53622 .0418 .6871 1 Mshowa .67245 0 m .67627 .00621 L s [(1)] .66483 -0.01242 .61371 1 Mshowa .125 Mabswid .11461 .23456 m .11764 .23771 L s .14105 .22344 m .14405 .22662 L s .16779 .2122 m .17076 .21541 L s .22216 .18933 m .22506 .1926 L s .2498 .17771 m .25268 .18101 L s .27776 .16595 m .2806 .16928 L s .33465 .14204 m .33741 .14542 L s .36358 .12987 m .36631 .13329 L s .39286 .11756 m .39554 .12101 L s .45243 .09251 m .45504 .09602 L s .48275 .07977 m .48531 .08331 L s .51343 .06687 m .51595 .07044 L s .57589 .0406 m .57832 .04424 L s .60769 .02723 m .61007 .0309 L s .63987 .0137 m .64221 .0174 L s .25 Mabswid 0 .80374 m .40037 1.0855 L s 0 .80374 m .00114 .79654 L s [(0)] -0.00228 .81813 .15847 -1 Mshowa .09489 .87051 m .09581 .86328 L s [(0.2)] .09305 .88497 .12734 -1 Mshowa .18139 .93139 m .18211 .92413 L s [(0.4)] .17993 .94589 .10001 -1 Mshowa .26056 .9871 m .26111 .97984 L s [(0.6)] .25946 1.00164 .07583 -1 Mshowa .33331 1.0383 m .3337 1.03102 L s [(0.8)] .33252 1.05285 .05428 -1 Mshowa .40037 1.0855 m .40063 1.07821 L s [(1)] .39987 1.10006 .03495 -1 Mshowa .125 Mabswid .02457 .82103 m .02522 .81671 L s .04857 .83792 m .04918 .83359 L s .072 .85441 m .07258 .85007 L s .11725 .88625 m .11777 .88191 L s .13911 .90164 m .13961 .89729 L s .16049 .91668 m .16095 .91233 L s .20183 .94577 m .20224 .94142 L s .22183 .95985 m .22221 .95549 L s .2414 .97362 m .24176 .96926 L s .27932 1.0003 m .27963 .99594 L s .29769 1.01323 m .29797 1.00887 L s .31568 1.02589 m .31594 1.02153 L s .35058 1.05045 m .35079 1.04609 L s .36751 1.06237 m .3677 1.058 L s .3841 1.07404 m .38428 1.06968 L s .25 Mabswid .08846 .24555 m 0 .80374 L s .08846 .24555 m .09517 .24273 L s [(0)] .07502 .2512 1 -0.42047 Mshowa .07323 .34166 m .07999 .33894 L s [(0.2)] .0597 .34709 1 -0.40157 Mshowa .0569 .44469 m .06371 .44209 L s [(0.4)] .04328 .44988 1 -0.38117 Mshowa .03935 .55542 m .04621 .55296 L s [(0.6)] .02563 .56035 1 -0.3591 Mshowa .02044 .67476 m .02735 .67244 L s [(0.8)] .00662 .67939 1 -0.33512 Mshowa 0 .80374 m .00696 .80159 L s [(1)] -0.01393 .80804 1 -0.30899 Mshowa .125 Mabswid .08475 .26897 m .08878 .26729 L s .08097 .29278 m .08502 .29112 L s .07713 .31701 m .08118 .31536 L s .06925 .36674 m .07332 .36512 L s .06521 .39226 m .06928 .39067 L s .06109 .41824 m .06517 .41666 L s .05263 .47162 m .05672 .47008 L s .04829 .49904 m .05239 .49752 L s .04386 .52697 m .04797 .52547 L s .03476 .58441 m .03888 .58296 L s .03008 .61396 m .03421 .61252 L s .0253 .64406 m .02944 .64265 L s .01548 .70606 m .01963 .70469 L s .01042 .73797 m .01458 .73663 L s .00526 .77053 m .00943 .76921 L s .25 Mabswid .08846 .24555 m 0 .80374 L s 0 .80374 m .40037 1.0855 L s .40037 1.0855 m .41799 .58158 L s .41799 .58158 m .08846 .24555 L s .67245 0 m .92713 .41497 L s .92713 .41497 m 1 .94814 L s 1 .94814 m .70644 .58546 L s .70644 .58546 m .67245 0 L s .08846 .24555 m 0 .80374 L s 0 .80374 m .70644 .58546 L s .70644 .58546 m .67245 0 L s .67245 0 m .08846 .24555 L s .41799 .58158 m .92713 .41497 L s .92713 .41497 m 1 .94814 L s 1 .94814 m .40037 1.0855 L s .40037 1.0855 m .41799 .58158 L s 0 0 m 1 0 L 1 1.0855 L 0 1.0855 L closepath clip newpath .5 Mabswid .38306 .59926 m .49277 .60772 L .44799 .67171 L p .727 .568 .675 r F P 0 g s .49277 .60772 m .38306 .59926 L p .55895 .52556 L .723 .609 .729 r F P 0 g s .55895 .52556 m .56165 .54662 L .49277 .60772 L p .723 .609 .729 r F P 0 g s .56165 .54662 m .55895 .52556 L .65305 .49459 L p .64 .549 .737 r F P 0 g s .633 .52343 m .56165 .54662 L p .65305 .49459 L .64 .549 .737 r F P 0 g s .49666 .5205 m .55895 .52556 L p .37914 .58961 L .723 .609 .729 r F P 0 g s .38306 .59926 m .37914 .58961 L p .55895 .52556 L .723 .609 .729 r F P 0 g s .37269 .57373 m .39213 .51201 L .49666 .5205 L p .723 .609 .729 r F P 0 g s .37914 .58961 m .37269 .57373 L p .49666 .5205 L .723 .609 .729 r F P 0 g s .40577 .69175 m .38306 .59926 L p .44799 .67171 L .727 .568 .675 r F P 0 g s .39213 .51201 m .37269 .57373 L .31755 .48918 L p .797 .691 .747 r F P 0 g s .44799 .67171 m .4131 .72158 L .40577 .69175 L p .727 .568 .675 r F P 0 g s .34347 .48473 m .39213 .51201 L p .31755 .48918 L .797 .691 .747 r F P 0 g s .65305 .49459 m .71122 .47545 L p .633 .52343 L .64 .549 .737 r F P 0 g s .71122 .47545 m .72255 .49433 L .633 .52343 L p .64 .549 .737 r F P 0 g s .31755 .48918 m .29803 .45926 L .34347 .48473 L p .797 .691 .747 r F P 0 g s .72255 .49433 m .71122 .47545 L .76585 .41224 L p .53 .504 .772 r F P 0 g s .76148 .50207 m .72255 .49433 L p .76585 .41224 L .53 .504 .772 r F P 0 g s .02 w .47276 .69274 Mdot .5 Mabswid .76585 .41224 m .80058 .37205 L p .76148 .50207 L .53 .504 .772 r F P 0 g s .80088 .50991 m .76148 .50207 L p .80058 .37205 L .53 .504 .772 r F P 0 g s .84498 .53872 m .80088 .50991 L .87442 .43109 L p .464 .405 .706 r F P 0 g s .80058 .37205 m .87442 .43109 L .80088 .50991 L p .53 .504 .772 r F P 0 g s .02 w .55862 .55207 Mdot .5 Mabswid .24042 .39468 m .24498 .40516 L .21432 .38805 L p .862 .81 .798 r F P 0 g s .15092 .35265 m .20754 .31897 L .24042 .39468 L p .862 .81 .798 r F P 0 g s .21432 .38805 m .15092 .35265 L p .24042 .39468 L .862 .81 .798 r F P 0 g s .93721 .55126 m .90772 .57972 L .84498 .53872 L p .464 .405 .706 r F P 0 g s .92166 .49625 m .93721 .55126 L p .84498 .53872 L .464 .405 .706 r F P 0 g s .87442 .43109 m .92166 .49625 L p .84498 .53872 L .464 .405 .706 r F P 0 g s .36686 1.04257 m .40446 .96868 L .44915 1.01684 L p .694 .362 .41 r F P 0 g s .87442 .43109 m .80058 .37205 L .79045 .29445 L p .353 .478 .847 r F P 0 g s .02 w .44747 .68603 Mdot .36078 .51553 Mdot .7534 .47571 Mdot .30169 .39671 Mdot .40716 .46325 Mdot .50274 .52436 Mdot .82481 .39809 Mdot .5 Mabswid .92166 .49625 m .87442 .43109 L .8679 .36176 L closepath p .094 .253 .737 r F P 0 g s .79045 .29445 m .78395 .24467 L p .87442 .43109 L .353 .478 .847 r F P 0 g s .8679 .36176 m .87442 .43109 L p .78395 .24467 L .353 .478 .847 r F P 0 g s .02 w .81088 .63351 Mdot .77984 .3497 Mdot .5 Mabswid .92005 .60623 m .90772 .57972 L p .93957 .56357 L .38 .277 .611 r F P 0 g s .90772 .57972 m .93721 .55126 L .93957 .56357 L p .38 .277 .611 r F P 0 g s .02 w .35139 .45944 Mdot .33884 .74299 Mdot .5 Mabswid .44915 1.01684 m .48793 1.05862 L p .36686 1.04257 L .694 .362 .41 r F P 0 g s .02 w .57215 .49691 Mdot .5 Mabswid .23121 .27455 m .20754 .31897 L p .21338 .23036 L .844 .962 .883 r F P 0 g s .18298 .25751 m .21338 .23036 L p .20754 .31897 L .844 .962 .883 r F P 0 g s .13447 .35371 m .18298 .25751 L p .20754 .31897 L .844 .962 .883 r F P 0 g s .20754 .31897 m .15092 .35265 L .13447 .35371 L p .844 .962 .883 r F P 0 g s .02 w .39355 1.00356 Mdot .5 Mabswid .96273 .6846 m .9583 .68848 L .92005 .60623 L p .38 .277 .611 r F P 0 g s .93957 .56357 m .96273 .6846 L p .92005 .60623 L .38 .277 .611 r F P 0 g s .02 w .72604 .45404 Mdot .1875 .38384 Mdot .7687 .43549 Mdot .42834 .77761 Mdot .52699 .85268 Mdot .50562 1.02397 Mdot .5 Mabswid .48793 1.05862 m .49825 1.06307 L .35736 1.05522 L p .612 .162 .159 r F P 0 g s .35736 1.05522 m .36227 1.0516 L .48793 1.05862 L p .612 .162 .159 r F P 0 g s .48793 1.05862 m .36227 1.0516 L .36686 1.04257 L p .694 .362 .41 r F P 0 g s .24425 .20279 m .27314 .19588 L .23121 .27455 L p .844 .962 .883 r F P 0 g s .21338 .23036 m .24425 .20279 L p .23121 .27455 L .844 .962 .883 r F P 0 g s .02 w .36719 .68171 Mdot .51644 .99745 Mdot .5 Mabswid .78395 .24467 m .8181 .25777 L .8679 .36176 L p .353 .478 .847 r F P 0 g s .02 w .37459 .33021 Mdot .5 Mabswid .18298 .25751 m .13447 .35371 L .12849 .35882 L p .833 .98 .688 r F P 0 g s .12976 .32691 m .18298 .25751 L p .12849 .35882 L .833 .98 .688 r F P 0 g s .12849 .35882 m .0695 .40913 L p .12976 .32691 L .833 .98 .688 r F P 0 g s .95396 .71824 m .9583 .68848 L p .96395 .70258 L .257 .093 .457 r F P 0 g s .9583 .68848 m .96273 .6846 L .96395 .70258 L p .257 .093 .457 r F P 0 g s .02 w .38948 1.00073 Mdot .5 Mabswid .8181 .25777 m .78395 .24467 L .70109 .18329 L p .058 .477 .888 r F P 0 g s .02 w .77491 .36846 Mdot .37241 .50991 Mdot .5 Mabswid .97057 .80041 m .93813 .82663 L .95396 .71824 L p .257 .093 .457 r F P 0 g s .96395 .70258 m .97057 .80041 L p .95396 .71824 L .257 .093 .457 r F P 0 g s .02 w .27743 .814 Mdot .76602 .76314 Mdot .31641 .3522 Mdot .5 Mabswid .80268 .24123 m .8181 .25777 L p .70109 .18329 L .058 .477 .888 r F P 0 g s .02 w .76034 .29066 Mdot .51603 .34718 Mdot .19902 .54818 Mdot .79182 .44964 Mdot .35093 .4261 Mdot .5 Mabswid .33648 .16961 m .27314 .19588 L p .37456 .1486 L .446 .881 .844 r F P 0 g s .27314 .19588 m .24425 .20279 L .37456 .1486 L p .446 .881 .844 r F P 0 g s .70109 .18329 m .64883 .14459 L p .80268 .24123 L .058 .477 .888 r F P 0 g s .89398 .89648 m .93813 .82663 L p .96954 .80747 L .048 0 .169 r F P 0 g s .93813 .82663 m .97057 .80041 L .96954 .80747 L p .048 0 .169 r F P 0 g s .7707 .20693 m .80268 .24123 L p .64883 .14459 L .058 .477 .888 r F P 0 g s .02 w .7742 .36673 Mdot .71155 .91374 Mdot .59963 .88525 Mdot .5 Mabswid .4375 .12243 m .44561 .12434 L .33648 .16961 L p .446 .881 .844 r F P 0 g s .37456 .1486 m .4375 .12243 L p .33648 .16961 L .446 .881 .844 r F P 0 g s .02 w .50679 .30051 Mdot .5 Mabswid .93094 .90976 m .84322 .97677 L .89398 .89648 L p .048 0 .169 r F P 0 g s .96582 .83289 m .93094 .90976 L p .89398 .89648 L .048 0 .169 r F P 0 g s .96954 .80747 m .96582 .83289 L p .89398 .89648 L .048 0 .169 r F P 0 g s .02 w .79505 .25309 Mdot .15739 .60279 Mdot .5 Mabswid .91621 .92238 m .83204 .98661 L p .93094 .90976 L 0 0 0 r F P 0 g s .83204 .98661 m .84322 .97677 L .93094 .90976 L p 0 0 0 r F P 0 g s .02 w .7646 .19001 Mdot .5 Mabswid .64883 .14459 m .68972 .14612 L .7707 .20693 L p .058 .477 .888 r F P 0 g s .68972 .14612 m .64883 .14459 L .52233 .13198 L p 0 .561 .755 r F P 0 g s .0695 .40913 m .07426 .39928 L .12976 .32691 L p .833 .98 .688 r F P 0 g s .02 w .38281 .95153 Mdot .36394 .37704 Mdot .5 Mabswid .07426 .39928 m .0695 .40913 L .05737 .44304 L p 0 0 0 r F P 0 g s .02 w .58629 .89449 Mdot .5 Mabswid .52233 .13198 m .44561 .12434 L p .68972 .14612 L 0 .561 .755 r F P 0 g s .02 w .775 .53203 Mdot .41549 .44061 Mdot .5 Mabswid .05743 .44295 m .07426 .39928 L p .05737 .44304 L 0 0 0 r F P 0 g s .02 w .34383 .52949 Mdot .77631 .74559 Mdot .5 Mabswid .50076 .12727 m .68972 .14612 L p .44561 .12434 L 0 .561 .755 r F P 0 g s .44561 .12434 m .4375 .12243 L .50076 .12727 L p 0 .561 .755 r F P 0 g s .75082 .19669 m .7707 .20693 L .68972 .14612 L p .625 .084 0 r F P 0 g s .02 w .108 .43942 Mdot .95325 .7892 Mdot .5685 .49058 Mdot .5 Mabswid .05737 .44304 m .05699 .44409 L .05743 .44295 L p 0 0 0 r F P 0 g s .93094 .90976 m .96582 .83289 L .94199 .84311 L p .959 .915 .558 r F P 0 g s .02 w .38659 .77153 Mdot .52537 .9359 Mdot .62305 .41709 Mdot .92518 .91825 Mdot .57602 .51621 Mdot .37255 .35792 Mdot .5 Mabswid .68972 .14612 m .71716 .17936 L .75082 .19669 L p .625 .084 0 r F P 0 g s .02 w .14494 .78434 Mdot .5 Mabswid .68972 .14612 m .50076 .12727 L .54317 .15056 L p .572 .067 .017 r F P 0 g s .71716 .17936 m .68972 .14612 L p .54317 .15056 L .572 .067 .017 r F P 0 g s .02 w .65579 .30718 Mdot .5147 .16634 Mdot .5 Mabswid .93094 .90976 m .92377 .91662 L .91621 .92238 L p 0 0 0 r F P 0 g s .92377 .91662 m .93094 .90976 L .92583 .85004 L p .919 .959 .794 r F P 0 g s .94199 .84311 m .92583 .85004 L .93094 .90976 L p .959 .915 .558 r F P 0 g s .92583 .85004 m .91731 .84598 L .92377 .91662 L p .919 .959 .794 r F P 0 g s .02 w .46346 .6594 Mdot .92286 .82818 Mdot .75927 .4294 Mdot .18363 .74051 Mdot .33166 .38149 Mdot .50604 .68002 Mdot .28662 .71952 Mdot .24448 .76431 Mdot .60402 .73157 Mdot .5 Mabswid .02969 .61639 m .02902 .66842 L .03398 .6592 L closepath p 0 0 .369 r F P 0 g s .02 w .41613 .74687 Mdot .5 Mabswid .70791 .19393 m .71716 .17936 L p .54317 .15056 L .572 .067 .017 r F P 0 g s .54317 .15056 m .61367 .18927 L p .70791 .19393 L .572 .067 .017 r F P 0 g s .02 w .62872 .74949 Mdot .5 Mabswid .03398 .6592 m .02902 .66842 L .0401 .71846 L p .185 .2 .642 r F P 0 g s .02 w .6115 .14585 Mdot .5 Mabswid .0857 .71844 m .03398 .6592 L p .0401 .71846 L .185 .2 .642 r F P 0 g s .0401 .71846 m .06769 .84306 L p .0857 .71844 L .185 .2 .642 r F P 0 g s .02 w .49035 .83134 Mdot .5 Mabswid .06769 .84306 m .07296 .85508 L .13208 .76293 L p .35 .415 .789 r F P 0 g s .02 w .14821 .63741 Mdot .5 Mabswid .13208 .76293 m .12096 .75882 L .06769 .84306 L p .35 .415 .789 r F P 0 g s .06769 .84306 m .12096 .75882 L .0857 .71844 L p .185 .2 .642 r F P 0 g s .02 w .02394 .72612 Mdot .13342 .67894 Mdot .5 Mabswid .61367 .18927 m .70521 .19818 L .70791 .19393 L p .572 .067 .017 r F P 0 g s .02 w .87306 .7326 Mdot .77314 .71211 Mdot .5 Mabswid .70521 .19818 m .61367 .18927 L .64505 .2659 L p .703 .357 .387 r F P 0 g s .70035 .28823 m .70521 .19818 L p .64505 .2659 L .703 .357 .387 r F P 0 g s .02 w .46988 .76921 Mdot .84907 .71575 Mdot .5 Mabswid .64505 .2659 m .66025 .30301 L p .70035 .28823 L .703 .357 .387 r F P 0 g s .66025 .30301 m .69935 .30661 L .70035 .28823 L p .703 .357 .387 r F P 0 g s .69935 .30661 m .66025 .30301 L .63515 .4076 L p .732 .484 .554 r F P 0 g s .72073 .45318 m .69935 .30661 L p .63515 .4076 L .732 .484 .554 r F P 0 g s .72773 .67867 m .82804 .73568 L p .72121 .65944 L .847 .757 .764 r F P 0 g s .82804 .73568 m .81617 .71395 L .72121 .65944 L p .847 .757 .764 r F P 0 g s .02 w .43981 .58293 Mdot .60221 .40176 Mdot .5 Mabswid .74286 .54245 m .72121 .65944 L .81617 .71395 L closepath p .887 .715 .663 r F P 0 g s .02 w .488 .58046 Mdot .5 Mabswid .63515 .4076 m .62243 .46063 L p .72073 .45318 L .732 .484 .554 r F P 0 g s .62243 .46063 m .72306 .46914 L .72073 .45318 L p .732 .484 .554 r F P 0 g s .72306 .46914 m .62243 .46063 L .55899 .55169 L p .737 .563 .657 r F P 0 g s .74286 .54245 m .72306 .46914 L p .55899 .55169 L .737 .563 .657 r F P 0 g s .72121 .65944 m .74286 .54245 L p .55899 .55169 L .737 .563 .657 r F P 0 g s .72121 .65944 m .71687 .6725 L .72773 .67867 L p .847 .757 .764 r F P 0 g s .49579 .64242 m .48171 .6549 L .71687 .6725 L p .732 .626 .741 r F P 0 g s .71687 .6725 m .72121 .65944 L .49579 .64242 L p .732 .626 .741 r F P 0 g s .55899 .55169 m .49579 .64242 L .72121 .65944 L p .737 .563 .657 r F P 0 g s .25 Mabswid .67245 0 m .92713 .41497 L s .92713 .41497 m 1 .94814 L s 1 .94814 m .70644 .58546 L s .70644 .58546 m .67245 0 L s .08846 .24555 m 0 .80374 L s 0 .80374 m .70644 .58546 L s .70644 .58546 m .67245 0 L s .67245 0 m .08846 .24555 L s .08846 .24555 m .67245 0 L s .08846 .24555 m .09356 .25076 L s [(0)] .07825 .23514 .98066 1 Mshowa .19482 .20083 m .19972 .20623 L s [(0.2)] .18503 .19003 .90727 1 Mshowa .30604 .15406 m .31071 .15966 L s [(0.4)] .29671 .14287 .83388 1 Mshowa .42247 .10511 m .42688 .11091 L s [(0.6)] .41365 .09351 .76049 1 Mshowa .54447 .05381 m .5486 .05982 L s [(0.8)] .53622 .0418 .6871 1 Mshowa .67245 0 m .67627 .00621 L s [(1)] .66483 -0.01242 .61371 1 Mshowa .125 Mabswid .11461 .23456 m .11764 .23771 L s .14105 .22344 m .14405 .22662 L s .16779 .2122 m .17076 .21541 L s .22216 .18933 m .22506 .1926 L s .2498 .17771 m .25268 .18101 L s .27776 .16595 m .2806 .16928 L s .33465 .14204 m .33741 .14542 L s .36358 .12987 m .36631 .13329 L s .39286 .11756 m .39554 .12101 L s .45243 .09251 m .45504 .09602 L s .48275 .07977 m .48531 .08331 L s .51343 .06687 m .51595 .07044 L s .57589 .0406 m .57832 .04424 L s .60769 .02723 m .61007 .0309 L s .63987 .0137 m .64221 .0174 L s .25 Mabswid 0 .80374 m .40037 1.0855 L s 0 .80374 m .00114 .79654 L s [(0)] -0.00228 .81813 .15847 -1 Mshowa .09489 .87051 m .09581 .86328 L s [(0.2)] .09305 .88497 .12734 -1 Mshowa .18139 .93139 m .18211 .92413 L s [(0.4)] .17993 .94589 .10001 -1 Mshowa .26056 .9871 m .26111 .97984 L s [(0.6)] .25946 1.00164 .07583 -1 Mshowa .33331 1.0383 m .3337 1.03102 L s [(0.8)] .33252 1.05285 .05428 -1 Mshowa .40037 1.0855 m .40063 1.07821 L s [(1)] .39987 1.10006 .03495 -1 Mshowa .125 Mabswid .02457 .82103 m .02522 .81671 L s .04857 .83792 m .04918 .83359 L s .072 .85441 m .07258 .85007 L s .11725 .88625 m .11777 .88191 L s .13911 .90164 m .13961 .89729 L s .16049 .91668 m .16095 .91233 L s .20183 .94577 m .20224 .94142 L s .22183 .95985 m .22221 .95549 L s .2414 .97362 m .24176 .96926 L s .27932 1.0003 m .27963 .99594 L s .29769 1.01323 m .29797 1.00887 L s .31568 1.02589 m .31594 1.02153 L s .35058 1.05045 m .35079 1.04609 L s .36751 1.06237 m .3677 1.058 L s .3841 1.07404 m .38428 1.06968 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{271.438, 294.625}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00`00Oomoo`02Ool00`00Oomoo`1=Ool00:Aoo`8001Aoo`03 001oogoo00=oo`03001oogoo04aoo`00XWoo0P005goo00<007ooOol00Woo00<007ooOol0C7oo002O Ool4000HOol00`00Oomoo`03Ool00`00Oomoo`1;Ool009eoo`8001aoo`03001oogoo00=oo`03001o ogoo04]oo`00VWoo0`007Woo00<007ooOol017oo00<007ooOol0BWoo002HOol200000goo001oo`0N Ool00`00Oomoo`05Ool00`00Oomoo`19Ool006aoo`8000Aoo`8000=oo`<001aoo`8000=oo`03001o ogoo01eoo`03001oogoo00Eoo`03001oogoo04Uoo`00Jgoo00@007ooOol000Qoo`04001oogoo000H Ool3000UOol00`00Oomoo`06Ool00`00Oomoo`18Ool006]oo`04001oogoo0008Ool01000Oomoo`00 5Woo0`009goo00<007ooOol01Woo00<007ooOol0B7oo001[Ool01000Oomoo`0027oo0`005Goo0P00 :Woo00<007ooOol01goo00<007ooOol0Agoo001[Ool01000Oomoo`002Goo00<007ooOol04Goo0`00 ;7oo00<007ooOol027oo00<007ooOol0AWoo001/Ool2000:Ool3000?Ool2000_Ool00`00Oomoo`08 Ool00`00Oomoo`16Ool008Moo`<00003Ool007oo02ioo`03001oogoo00Uoo`03001oogoo04Eoo`00 QGoo0P00=7oo00<007ooOol02Goo00<007ooOol0AGoo0023Ool2000fOol00`00Oomoo`0:Ool00`00 Oomoo`14Ool0081oo`<00003Ool007oo03Eoo`03001oogoo00]oo`03001oogoo04=oo`00OWoo0P00 >goo00<007ooOol02goo00<007ooOol0@goo001lOol2000mOol00`00Oomoo`000000002`00:7oo00<007ooOol03Woo00<007ooOol0?goo001>Ool2000;Ool2 000@Ool3000:Ool20002=gX20006Ool200080SL200000d@PA2400009000NOol00`00Oomoo`0?Ool0 0`00Oomoo`0nOol006]oo`800003Ool007oo00Qoo`800004>iX00000000BOol400002TQ1A218@D@P B45484Q1A218@D@P2@005Goo00<007ooOol03goo00<007ooOol0?Woo001XOol3000;Ool200000cMj 0000000IOol200004D@PA25484@QA2148D@PA25484@QA2148D@PA25484@QA2002@0037oo00<007oo Ool047oo00<007ooOol0?Goo001VOol2000iX0000002ioo`80000RA218@D@PB45484Q1A218@D@PB454 84Q1A218@D@PB45484Q1A218@D@PB45484Q1A218@D@PB4548000A218@D@PB442000?Ool00`00Oomo o`0jOol0035oo`04001oogoo0008Ool00`00Oomoo`0JOol30003Ool00`00Oomoo`05Ool200000cMj 0000000UOol2000;Ool08`00A2148D@PA25484@QA2148D@PA25484@QA2148D@PA25484@QA2148D@P A25484@QA2148D@PA24004@QA2148D@PA2400P003Woo00<007ooOol0>Woo000aOol01000Oomoo`00 2Goo00<007ooOol05goo0P002goo0`00007oo000bOol2000:Ool2000AOol2000;Ool50013Ool08000A25484@QA2148D@PA25484@QA2148D@P A25484@QA2148D@PA25484@Q00148D@PA25484@QA2148D@P0002C402000;Ool00`00Oomoo`0gOol0 04ioo`<00003Ool007oo00Qoo`@004Moo`80000MA218@D@PB45484Q1A218@D@PB45484Q1A218@D@P B45484Q1A20004@PB45484Q1A218@D@P0005f`020002C4000`00Oomoo`09Ool00`00Oomoo`0fOol0 04aoo`8000]oo`D004]oo`80000NA25484@QA2148D@PA25484@QA2148D@PA25484@QA2148D@P0014 84@QA2148D@P0005f`Gk1M/5o0000Ta000<007ooOol00Woo0P0017oo00<007ooOol0=Woo001:Ool2 000;Ool200000cMj001oo`1?Ool6000064@PB45484Q1A218@D@PB45484Q1A218@@00B45484Q1A218 @@001O`5f`Gl1M/5o0800004C4000000Ool40004Ool00`00Oomoo`0eOol004Moo`<00003Ool007oo 00Moo`D0059oo`03001EJeU/00=EJ`d00005A2148D@PA2400002Ool01PGl1M/5n`GK1O`5f`800003 C400000000<000Aoo`03001oogoo03Eoo`00AGoo0P002goo1@00EGoo014005E;FFaEBeU/ED]IK5E; FFaEBeU/ED]IK5E;FFaEBeU/00H000=oo`070005f`Gl1M/5o0GK1O`01@001Woo00<007ooOol0=7oo 000ROol2000NOol3000;Ool20004Jm/00`00Oomoo`1COol01000EF]EJeU/0eE[00EIK5E[EF]EJeU/ 00=EJ`05FFaEJ`00EF]IK002EF/00`00Oomoo`02Ool020001M/5n`GK1O`5f`Gk1M/30007Ool00`00 Oomoo`0cOol0025oo`04001oogoo000KOol20002Ool20009Ool01`00Jma[ff_LJm][g00005Moo`0F 001IK5E;FFaEBeU/ED]IK5E;FFaEBeU/ED]IK5E;FF`005U/ED]IK5E;0005Ool200001`Gl1M/5o0GK 1O`5f`Gl008000Ioo`03001oogoo03=oo`008Goo00@007ooOol001Uoo`8000ioo`03001[ff_K00A[ f`03001oogoo05Eoo`05001EJeE[EF]IK003EF/01EU/EF]EJeE[FF`00eE[00H005E[EF]EJeU/0007 Ool02P001O/5f`Gl1M/5n`GK1O`5f`001Woo00<007ooOol0Jma[ff_LJm][g6_KJma[ff_L Jm][g6_KJm`006Qoo`0>001EBeU/ED]IK5E;FFaEBeU/ED/005E;FF`001Aoo`0;000YfRgj:MX]nRWJ ;OXYfRgj:MX00003Ool00`00Oomoo`0XOol002Qoo`03001oogoo00Moo`03001oogoo00Ioo`03001W e@0000e[f`03001oogoo06Moo`03001EJeU/00=EJ`07FFaEJeE[001IK5E[00005Goo00/002WJ:OXY fRWj:MXYnRWJ:OXYfP0000=oo`03001oogoo02Moo`009goo00<007ooOol02Goo00<007ooOol01Goo 0P0000i[ff_LJm][g6_KJma[ff_LJm][g6_KJma[f`00JWoo00d005U/ED]IK5E;FFaEBeU/ED/005E; FF`0000 000]nRWJ;OXYfRgj:MX]nRWJ;OXYfRgj:MX000Aoo`03001oogoo02=oo`009Woo0P003Goo00D006_E JoEWe@0000e[f`03001oogoo06]oo`80000:GO5Il5WaFO5MlEW`FO4005ga000GOol03@00:OXYfRWj :MXYnRWJ:OXYfRWj:MXYnP0000Eoo`03001oogoo029oo`009Woo00<007ooOol037oo018006_eImD0 06_KJma[ff_LJm][g6_KJma[ff_LJm][g6_K001_Ool03000FM1MlEW@GO5Id5gaFM0005W@GO4001Io o`0>000YfRgj:MX]nRWJ;OXYfRgj:MX]nRWJ;OX000Aoo`03001oogoo029oo`009Woo00<007ooOol0 2goo00D006_eImE[m@0000][f`<006moo`05001IlEWaGO5Il002FO401Ega001IlEWa00005Woo00h0 02Wj:MXYnRWJ:OXYfRWj:MXYnRWJ:OXYfP001Goo00<007ooOol08Goo000VOol00`00Oomoo`0:Ool0 3`00JoEWeF_e001[g6_KJma[ff_LJm][g6_KJma[f`02000016liJcQ_>@009goo0P00A7oo00d005ga FM1MlEW@GO5Id5gaFM0005W@GO40000FOol03`00:MX]nRWJ;OXYfRgj:MX]nRWJ;OXYfRgj:MX00005 Ool00`00Oomoo`0POol002Ioo`03001oogoo00Uoo`06001[mFOEJoE[e@0026_K0P0000I[>6liJcQ_ >F/h000VOol40013Ool01000FO5MlEW`0UWa00MMlEW`FO5Il@00FO00000FOol03`00:OXYfRWj:MXY nRWJ:OXYfRWj:MXYnRWJ:OX00005Ool00`00Oomoo`0POol002Eoo`03001oogoo00Uoo`0H001[mFOE JoEWe@00Jm][g6_KJma[ff_LJm][g000KcU[>6liJcQ_>F/hKcU[>0009Goo1000@goo00d005gaFM1M lEW@GO5Id5gaFM1Ml@00GO40000FOol04000:MX]nRWJ;OXYfRgj:MX]nRWJ;OXYfRgj:MX]nP001Goo 00<007ooOol07goo000UOol00`00Ool00009Ool01P00ImE[mF_EJoD000I[f`80000:KcU[>6liJcQ_ >F/hKcU[>6li000VOol20014Ool01P00FO1IlEWaGO5Il09Il@05GO5Il000FO40000FOol04000:OXY fRWj:MXYnRWJ:OXYfRWj:MXYnRWJ:OXYfP001Goo00<007ooOol07goo000UOol20009Ool02`00ImE[ mFOEJoD006_LJm][g6_KJm`00P0000e[>6liJcQ_>F/hKcU[>6liJcQ_>F/hKcT00018Ool2000POol0 3`00FM1MlEW@GO5Id5gaFM1MlEW@GO4005gaFM00000EOol04@00:MX]nRWJ;OXYfRgj:MX]nRWJ;OXY fRgj:MX]nRWJ00001Goo00<007ooOol07Woo000BOol20004Ool20003Ool40004Ool00`00Oomoo`07 Ool01`00ImE[mF_EJoEWe@0000=[f`80000?KcU[>6liJcQ_>F/hKcU[>6liJcQ_>F/hKcU[>00001Io o`8002moo`@001moo`05001IlEWaGO5Il002FO4025gaFO1IlEWa001Il5Wa000@Ool20003Ool04@00 :OXYfRWj:MXYnRWJ:OXYfRWj:MXYnRWJ:OXYfRWj00001Woo00<007ooOol07Goo000AOol01000Oomo o`0027oo00<007ooOol01Goo00<007ooOol01Woo00T006OEJoEWeF_eImD006_KJm`00P00019[>6li JcQ_>F/hKcU[>6liJcQ_>F/hKcU[>6liJcQ_>F/h000DOol4000^Ool4000OOol03`00FM1MlEW@GO5I d5gaFM1MlEW@GO4005gaFM00000?Ool40002Ool04P00:MX]nRWJ;OXYfRgj:MX]nRWJ;OXYfRgj:MX] nRWJ;OX000Eoo`03001oogoo01eoo`004Goo00@007ooOol000Uoo`03001oogoo00Aoo`03001oogoo 00Ioo`06001[mF_EJoEWeF_e0`000Woo0P00011_>F/hKcU[>6liJcQ_>F/hKcU[>6liJcQ_>F/hKcT0 01Aoo`@000]oo`80029oo`8001moo`04001IlEgaFO02FO402UgaFO1IlEWaGO5Il000FO5Ml@003goo 10000goo014002WJ:OXYfRWj:MXYnRWJ:OXYfRWj:MXYnRWJ:OXYfP0000Ioo`03001oogoo01aoo`00 4Goo00@007ooOol000Yoo`03001oogoo00=oo`03001oogoo00Eoo`07001[mFOEJoEWeF_e00001goo 0P0000m[>6liJcQ_>F/hKcU[>6liJcQ_>F/hKcU[>6li000057oo0P002goo1000@Woo010005gaFM1M lEW@GO5Id5gaFM1MlEW@GO4005gaFM00011oo`8000Aoo`0B000]nRWJ;OXYfRgj:MX]nRWJ;OXYfRgj :MX]nRWJ;OXYfP001Goo00<007ooOol077oo000AOol01000Oomoo`0027oo00@007ooOol000=oo`80 00Ioo`07001[mF_EJoEWeF_e00002Woo0P0000e_>F/hKcU[>6liJcQ_>F/hKcU[>6liJcP0000QOol4 0012Ool01P00FO1IlEWaGO5Il09Il@08GO5Il5WaFO4005W`FO4000moo`8000Eoo`0B000YfRWj:MXY nRWJ:OXYfRWj:MXYnRWJ:OXYfRWj:MXYnP001Woo00<007ooOol06goo000BOol2000:Ool20004Ool0 0`00Oomoo`04Ool01@00JoEWeF_eImD00P003Goo00h006liJcQ_>F/hKcU[>6liJcQ_>F/hKcU[>000 8Goo0P00@goo014005gaFM1MlEW@GO5Id5gaFM1MlEW@GO4005gaFM1Ml@0000eoo`@000Aoo`0B000] nRWJ;OXYfRgj:MX]nRWJ;OXYfRgj:MX]nRWJ;OXYfP001goo00<007ooOol06Woo000TOol00`00Oomo o`03Ool01P00JoE[eF_eImD0011oo`80000;JcQ_>F/hKcU[>6liJcQ_>F/hKcT0000OOol20014Ool0 1@00FO5IlEgaFO000UWa00]MlEW`FO5IlEgaFO0005WaGO5Il00000eoo`@000Aoo`0A000YfRWj:MXY nRWJ:OXYfRWj:MXYnRWJ:OXYfRWj:MXYnP020006Ool00`00Oomoo`0JOol002Aoo`03001oogoo00=o o`05001WeF_eImD0000COol200002VliJcQ_>F/hKcU[>6liJcQ_>@005Woo0P001Goo1000@goo0180 05W@GO5Id5gaFM1MlEW@GO5Id5gaFM1Ml@00GO5Id5ga000>Ool20004Ool04P00@OL002WJ;OXYfRgj :MX]nRWJ;OXYfRgj:MX]nRWJ;OXYfP8000Moo`03001oogoo01Uoo`0097oo00<007ooOol00Woo00D0 06_EJoEWe@0001=oo`80000;Ool00000JcQ_>F/hKcU[>6liJcP0000EOol40004Ool40013Ool00`00 GO5Il002FO401UgaFO1IlEWaGO5Il09Il@05001Il5WaFO40000COol01000@OM1n47h0P00010YnRWJ :OXYfRWj:MXYnRWJ:OXYfRWj:MXYnP002?L000Ioo`03001oogoo01Uoo`0097oo00L007ooOomoo`00 ImE[m@02000COol40002Ool200001fliJcQ_>F/hKcU[>00001Aoo`@000Eoo`8004Aoo`0B001Id5ga FM1MlEW@GO5Id5gaFM1MlEW@GO4005gaFM1Ml@004goo01@0048H?OM2647g@QP002gj:MX]nRWJ;OXY fRgj:MX]nRWJ;OXYfRgj0P001goo00<007ooOol067oo000SOol02000Oomoogoo001[eF_e000EOol4 0004Ool01`00KcU[>6liJcQ_>@0001Eoo`8004]oo`06001Il5WaFO5MlEW`0UWa00]MlEW`FO5IlEga FO0005WaGO5Il000019oo`050011n47h@OQ1m`03@OP03@00:OXYfRWj:MXYnRWJ:OXYfRWj:MXYnRWJ 008000Qoo`03001oogoo01Moo`008goo0P000Woo00<006_e00005goo0P001Woo00L006liJcQ_>F/h KcT0000=Ool2001BOol05000GO5Id5gaFM1MlEW@GO5Id5gaFM1MlEW@GO4005gaFM1MlEW@000@Ool0 6@00@QPmmd8H@OM263gg@QQ1md8H000]nRWJ;OXYfRgj:MX]nRWJ;OXYfRgj0008m`0000Moo`03001o ogoo01Moo`008goo00H007ooOol006_e000ROol200000fliJcP0000000Ool02Woo1000AWoo10001goo01AId5gaFM1MlEW@GO5Id5gaFM1M lEW@GO5Id5ga001MlEW@GO5Id0003Woo00X0048H?OM2647g@QPmmd8H@OM260@0000>?OL002WJ;OXY fRgj:MX]nRWJ;OX000Sg2?H000Qoo`03001oogoo01Eoo`008goo0`00:Goo0P0037oo0P00Agoo1000 1Woo00<005gaFO000UWa00IMlEW`FO5IlEgaFO02FO4025gaFO1Il@00GO5Il5Wa000>Ool01000@OQ1 n47g0d7h00=1md7h@OP0100000i1n47g000YfRWj:MXYnRWJ:OXYfP002?H8m`0027oo00<007ooOol0 5Goo000SOol2000/Ool00`00Oomoo`1COol20007Ool05@00FM1MlEW@GO5Id5gaFM1MlEW@GO5Id5ga FM1MlEW@001Id5gaFM00000=Ool03000?OM2647g@QPmmd8H@OM263gg@QQ1m`800004@QQ1md8H?OL2 00002Bgj:MX]nRWJ;OX000Sg2?H00009Ool00`00Oomoo`0DOol0029oo`03001oo`0002eoo`03001o ogoo05Moo`80009oo`05001IlEWaGO5Il002FO401UgaFO1IlEWaGO5Il09Il@06GO4005WaFO5Ml@00 37oo00@0047h@OQ1m`=1n005@OM1n47h@OQ1m`03@OP0447g@OQ1n47h@OM1n000:OXYfRWj:MX000Sf 2?L8mP0027oo00<007ooOol057oo000ROol3000]Ool00`00Oomoo`1FOol400005goo001Id5gaFM1M lEW@GO5Id5gaFM1MlEW@GO5Id5gaFM0005W@GO5Id5ga00002Woo021263gg@QQ1md8H?OM2647g@QPm md8H@OM263gg@QQ1md8H?OM2647g@QPmmd8H000]nRWJ;OXYfP002?H8m`0027oo0P005Goo000ROol2 000_Ool00`00Oomoo`0COol20010Ool500000eWaGO5Il002FO401UgaFO1IlEWaGO5Il09Il@06GO5I l5Wa001MlEW`0UWa00<007ooOol01goo00@0047h@OQ1m`=1n005@OM1n47h@OQ1m`03@OP01D7g@OQ1 n47h@OL00d7h00]1md7h000YnRWJ:OX000Sg2?H8m`0000Aoo`<00003Ool007oo01Aoo`008Woo0P00 <7oo00<007ooOol04Goo1000@7oo0P0001Qoo`00GO5Id5gaFM1MlEW@GO5Id5gaFM1MlEW@GO5Id5ga FM0005W@GO5Id5ga0008Ool200006D8H@OM263gg@QQ1md8H?OM2647g@QPmmd8H@OM263gg@QQ1md8H ?OM2647g@QPmmd8H00800007:MX000Sf2?L8mP00Ool00`0017oo00<007ooOol04goo000ROol00`00 Oomoo`0`Ool00`00Oomoo`0@Ool40013Ool01P00FO1IlEWaGO5Il09Il@06GO5Il5WaFO5MlEW`0UWa 00MMl@00FO5IlEgaFO000007Ool40003@OP01D7g@OQ1n47h@OL00d7h00E1md7h@OQ1n47g00=1n005 @OM1n47h@OQ1m`02@OP01BWj0008m`Sf2?L00P001goo00<007ooOol04goo000ROol00`00Oomoo`0a Ool00`00Oomoo`0@Ool20014Ool05`00GO5Id5gaFM1MlEW@GO5Id5gaFM1MlEW@GO5Id5gaFM0005W@ GO5Id5ga00001goo1P0001m1md8H?OM2647g@QPmmd8H@OM263gg@QQ1md8H?OM2647g@QPmmd8H@OM2 63gg@QQ1m`002?H8m`Sf2?L00008Ool00`00Oomoo`0BOol0029oo`03001oogoo00Qoo`8002Qoo`03 001oogoo01moo`8003=oo`05001IlEWaGO5Il002FO401UgaFO1IlEWaGO5Il09Il@06GO5Il5Wa001M lEW`0UWa00<007ooOol017oo00<0047h00001@000T7h00E1md7h@OQ1n47g00=1n005@OM1n47h@OQ1 m`03@OP0347g@OQ1n47h@OL003VE0008mPSg2?H000Qoo`03001oogoo019oo`008Goo00<007oo0000 27oo1000:7oo00<007ooOol07Goo1000IHiUCVF0008m`Sf2?L00007Ool0 0`00Oomoo`0BOol0025oo`03001oogoo00Uoo`8002]oo`03001oogoo01aoo`8003=oo`0H001Id5ga FM1MlEW@GO5Id5gaFM1MlEW@GO5Id5gaFM1MlEW@001Id5gaFM1MlEW@0P0000eoo`00@QQ1md8H?OM2 647g@QPmmd8H@OM2600400006Sgg@QQ1md8H?OM2647g@QPmmd8H@OM263gg@QQ1m`00=IDiUSFE>IHe UCVF0008m`Sf0007Ool00`00Oomoo`0BOol000ioo`8000Aoo`8000Eoo`<000=oo`03001oogoo03Mo o`03001oogoo04moo`06001Il5WaFO5MlEW`0UWa00IMlEW`FO5IlEgaFO02FO401UgaFO1Il@00GO5I l09Il@06GO4000000011n47g0d7h00E1md7h@OQ1n47g0091n0@00003@OQ1md7h0091n005@OM1n47h @OQ1m`03@OP03T7g000iUCVF>IDiUSVE>IHiU@002?H8m`Sf0006Ool00`00Oomoo`0BOol000eoo`04 001oogoo000;Ool00`00Oomoo`02Ool00`00Oomoo`0hOol00`00Oomoo`0:Ool20012Ool06@00GO5I d5gaFM1MlEW@GO5Id5gaFM1MlEW@GO5Id5gaFM1MlEW@001Id5gaFM1MlEW@00<0000=@OM263gg@QQ1 md8H?OM2647g@QPmmd8H@OL00P0001a2647g@QPmmd8H@OM263gg@QQ1md8H?OM2647g000eUCVF=IDi USFE>IHeUCVF=ID000Sf2?L000Ioo`03001oogoo019oo`003Goo00@007ooOol000Qoo`D000=oo`03 001oogoo03Uoo`03001oogoo00Qoo`@000]oo`8003Aoo`L00005FO1IlEWaGO5Il002FO401UgaFO1I lEWaGO40009Il@03GO5Il5Wa00800005@OM1n47h@OQ1m`03@OP01D7g@OQ1n47h@OL00d7h00E1md7h @OQ1n47g00=1n00D@OM1n47h@OQ1m`00>IDiUSVE>IHiUCVF>IDiUSVE>IHiU@002?H000Moo`03001o ogoo015oo`003Goo00@007ooOol000Qoo`04001oogoo0003Ool00`00Oomoo`0kOol20008Ool4000: Ool4000bOol02000FSAN=5XdGSAJ=5hdFS@=0000=5W@GO5Id5gaFM00047g@QPmmd8H@OM263gg@QQ1 md8H?OM2647g@QPmmd8H@OM263gg@QQ1md8H?OM2647g@QPmmd8H@OL003FE>IHeUCVF=IDiUSFE>IHe UCVF=IDiUSFE0008mP001Woo00<007ooOol04Goo000=Ool01000Oomoo`002Goo00<007oo00000goo 0P00?7oo00@006Jg000000Moo`8000]oo`@0039oo`0D001N=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN =5XdGSAJ=5hdFSAN=0L000=1n005@OM1n47h@OQ1m`03@OP01D7g@OQ1n47h@OL00d7h00E1md7h@OQ1 n47g00=1n00C@OL003VE>IHiUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IH000Sg00001Woo00<007ooOol0 4Goo000>Ool2000;Ool20003Ool00`00Oomoo`0lOol00`00I[MR]`02000COol2000bOol08P00GSAJ =5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=000FSAN=5XdGSAJ=000?OM2647g@QPm md8H0P0002Lmmd8H@OM263gg@QQ1md8H?OM2647g@QPmmd8H@OM263gg@QQ1m`00=IDiUSFE>IHeUCVF =IDiUSFE>IHeUCVF=IDiUSFE>IH000Sg00001Goo00<007ooOol04Goo000POol00`00Oomoo`0mOol0 1000I[MR]fJg0P00A7oo01l005hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN =5Xd001J=5hdFSAN=5Xd0011m`03@OP400001D7g@OQ1n47h@OL00d7h00E1md7h@OQ1n47g00=1n00D @OL003VE>IHiUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF>IDiUP8000Eoo`03001oogoo015oo`00 87oo00<007ooOol0?Woo00D006JgH[MV]f:f0080049oo`0R001J=5hdFSAN=5XdGSAJ=5hdFSAN=5Xd GSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=000GSAJ=5hdFSAN=000@QPmmd8H@OL40000948H?OM2647g@QPm md8H@OM263gg@QQ1md8H?OM2647g000eUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHe U@8000Eoo`03001oogoo015oo`0087oo00<007ooOol0?Woo00P006:gI[MR]fJgH[MV]`00=Woo0P00 27oo01l005XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFS@005XdGSAJ =5hdFS@00002@OP00d7g@OQ1n0020003@OP01D7g@OQ1n47h@OL00d7h01]1md7h@OQ1n47g000iUCVF >IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF>ID00P0017oo00<007ooOol04Goo000O Ool00`00Oomoo`10Ool01`00H[IV]f:gI[MR]VJg008003=oo`@000Ioo`1?001J=5hdFSAN=5XdGSAJ =5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGS@005hdFSAN=5XdGS@0048H@OM263gg@QQ1 md8H?OM2647g@QPmmd8H@OM263gg@QQ1md8H?OM2647g000eUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHe UCVF=IDiUSFE>IHeUCVF=IDiUSFE000017oo00<007ooOol04Goo000OOol00`00Oomoo`11Ool02000 H[MV]f:gI[MR]fJgH[L2000aOol40006Ool08@00GSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hd FSAN=5XdGSAJ=5hdFSAN=5Xd001J=5hdFSAN=5XdGS@00003@OP01D7g@OQ1n47h@OL00d7h00E1md7h @OQ1n47g00=1n00J@OL003VE>IHiUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF >IDiUP8000Aoo`03001oogoo011oo`007goo0P00@Woo00/006JgH[IV]f:gI[MR]VJgH[MV]`00035o o`@000Aoo`0Q001N=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN =000GSAJ=5hdFSAN=5Xd00H0000Z@QQ1md8H?OM2647g@QPmmd8H@OM263gg@QQ1m`00=IDiUSFE>IHe UCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUP0017oo00<007ooOol047oo 000OOol00`00Oomoo`12Ool02P00I[MR]fJgH[MV]f:gI[MR]fJg0P00;goo10000goo02<005hdFSAN =5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFS@005XdGSAJ=5hdFSAN =00000Eoo`D000=1n00R@OM1n47h@OQ1m`00>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHi UCVF>IDiUSVE>IHiUCVF>IDiUSVE0004Ool00`00Oomoo`0@Ool001moo`03001oogoo049oo`0:001R ]fJgH[IV]f:gI[MR]VJgH[L4000^Ool20004Ool09000FSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN =5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=000GSAJ=5hdFSAN=5XdGS@000Uoo`@0000R?OM2647g000e UCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE0003 Ool00`00Oomoo`0@Ool001moo`03001oogoo04=oo`08001R]fJgH[MV]f:gI[MR]`@00003I[L00000 035oo`0U001J=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hd FS@005XdGSAJ=5hdFSAN=5Xd00003Goo0`0001liUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF>IDi USVE>IHiUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IH00003Ool00`00Oomoo`0@Ool001ioo`03001oogoo 04Eoo`05001R]fJgH[IV]`0600000f:fI[MR]`07000VOol20002Ool09@00GSAJ=5hdFSAN=5XdGSAJ =5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hd001N=5XdGSAJ=5hdFSAN=000011o o`80000M>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF =ID00003Ool00`00Oomoo`0@Ool001ioo`03001oogoo04Eoo`04001V]f:gI[L600001F:gI[MR]fJg 00001UYf3@0067oo1@0002EN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ =5hdFSAN=5XdGSAJ=000FSAN=5XdGSAJ=5hdFS@0000BOol07@00>IHiUCVF>IDiUSVE>IHiUCVF>IDi USVE>IHiUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF00000goo00<007ooOol047oo000NOol00`00 Oomoo`16Ool00`00I[MR]`0400006VJgH[IV]f:gI[L005igFUIJMeYFGWMJEUYgFUINMeYFFWMJEUig FUIJMeYFGWMJEUYgFUH>000:Ool400009ehdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ =5hdFSAN=5XdGSAJ=5hdFSAN=5XdGS@005hdFSAN=5XdGSAJ=5hdFS@0000BOol200006cFE>IHeUCVF =IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IH00003Ool00`00Oomoo`0? Ool001ioo`8004Moo`80000;I[MR]`00001V]f:gI[MR]fJgH[L0000JFWH40004FWH:0000:dhf0000 0000FSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ =000FSAN=5XdGSAJ=5hdFSAN=00001Aoo`80000I>IHiUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF >IDiUSVE>IHiUCVF>IDiUSVE00000goo00<007ooOol03goo000NOol00`00Oomoo`15Ool4000096Jg H[MV]f:fI[MR]fJgH[IV]`00FWMJEUigFUIJMeYFGWMJEUYgFUINMeYFFWMJEUigFUIJMeYFGWMJEUYg FUINMeYFFWMJEP@0000iGWMJEUYgFUINMeYFFWMJEUigFUIJMeYF001>=U8gCSH005XdGSAJ=5hdFSAN =5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=000GSAJ=5hdFSAN =5XdGSAJ=00000Moo`8000eoo`0I000iUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDi USFE>IHeUCVF00000goo00<007ooOol03goo000NOol00`00Oomoo`15Ool400002F:gI[MR]fJgH[MV ]f:gI[L0000LFWH2000=FWH0;@00CSM>=P00FSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ =5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFS@005XdGSAJ=5hdFSAN=5XdGS@00006Ool4000=Ool2 00005cVE>IHiUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF00000Woo00<007oo Ool03goo000NOol00`00Oomoo`16Ool30000HVJgH[IV]f:gI[MR]VJgH[L005YFGWMJEUYgFUINMeYF FWMJEUigFUIJMeYFGWMJEUYgFUINMeYFFWMJEUigFUIJMeYFGWMJEUYgFUINMeYFFWMJEUigFUIJMeYF GWMJEUYgFUINMeYF001>=U8g001N=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5Xd GSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=000GSAJ=5hdFSAN=5XdGSAJ=5hd0005Ool4000?Ool05cVF=IDi USFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE00000Woo00<007ooOol03goo000M Ool00`00Oomoo`1:Ool02@00I[MR]fJgH[MV]f:gI[L0000[FWH0;P00DSL005hdFSAN=5XdGSAJ=5hd FSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFS@005XdGSAJ=5hd FSAN=5XdGSAJ=0001Woo0P004Goo0P0001@iUSVE>IHiUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF >IDiUP000Woo00<007ooOol03goo000MOol00`00Oomoo`0SOol2000VOol0<`00I[MR]VJgH[MV]`00 GWMJEUYgFUINMeYFFWMJEUigFUIJMeYFGWMJEUYgFUINMeYFFWMJEUigFUIJMeYFGWMJEUYgFUINMeYF FWMJEUigFUIJMeYFGWMJEUYgFUINMeYFFWMJEP020000;5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hd FSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=000GSAJ=5hdFSAN=5XdGSAJ=5hd 000KOol05000>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE0002Ool00`00Oomoo`0? Ool001eoo`03001oogoo029oo`@002Eoo`07001R]fJgH[MV]f:g0000:UYf0P0002eoo`00FSAN=5Xd GSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5Xd GS@005hdFSAN=5XdGSAJ=5hdFS@00P006goo0P00018iUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF >IDiUSVE0002Ool00`00Oomoo`0>Ool001eoo`8002=oo`@002Ioo`0_001R]fJgH[IV]`00FWMJEUig FUIJMeYFGWMJEUYgFUINMeYFFWMJEUigFUIJMeYFGWMJEUYgFUINMeYFFWMJEUigFUIJMeYFGWMJEUYg FUINMeYFFWMJEUigFUIJM`040000;UXdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5Xd GSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFS@005XdGSAJ=5hdFSAN=5Xd001^e0007Goo0180 03FE>IHeUCVF=IDiUSFE>IHeUCVF=IDiUSFE>IHeUCVF0002Ool00`00Oomoo`0>Ool001eoo`03001o ogoo02=oo`8002Qoo`04001R]fJg000ZFWH30000<5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ =5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=000GSAJ=5hdFSAN=5XdGS@0 07;DK]@001eoo`0?000iUCVF>IDiUSVE>IHiUCVF>IDiUSVE>IHiUCVF0080009oo`03001oogoo00io o`002Goo0P0017oo0P000goo0`001Woo00<007ooOol0CGoo02l006JgH[L005YFGWMJEUYgFUINMeYF FWMJEUigFUIJMeYFGWMJEUYgFUINMeYFFWMJEUigFUIJMeYFGWMJEUYgFUINMeYFFWMJEUigFUIJMeYF GWMJEUYgFUH007oo0080000`GSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hd FSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5Xd001J=5hdFSAN=5XdGSAJ=000K]Abe0007Woo0P00 014iUSFE>IHeUCVF=IDiUSFE>IHeUCVF000a4bdB001oo`00011oo`0027oo00@007ooOol000Qoo`04 001oogoo0004Ool00`00Oomoo`1?Ool00`00I[L0000XFWH0IHiUCVF>IDiUSVE>IHiUCVF000]4bdB ;A<007oo000047oo0008Ool01000Oomoo`0027oo00@007ooOol000Aoo`03001oogoo04moo`80000Y GWMJEUYgFUINMeYFFWMJEUigFUIJMeYFGWMJEUYgFUINMeYFFWMJEUigFUIJMeYFGWMJEUYgFUINMeYF FWMJEUigFUIJMeYFGWMJEUYgFUH00002Ool0=000GSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hd FSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=000FSAN=5XdGSAJ=5hd FS@006kDL]E^e00087oo0P0000heUCVF=IDiUSFE>IH0034C;A8]4bdB001oo`0047oo0008Ool01000 Oomoo`0027oo0`001Goo00<007ooOol0D7oo00<005YfFWH09EYf03D007ooOol005hdFSAN=5XdGSAJ =5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ =5hdFSAN=000GSAJ=5hdFSAN=5XdGS@007;D009^e003001oogoo021oo`0>000iUCVF>IDiUP00;A<] 4RdC;A8]4`00Ool0011oo`0027oo00@007ooOol000Uoo`03001oogoo00Aoo`03001oogoo055oo`0? 001JEUigFUIJMeYFGWMJEUYgFUINMeYFFWMJEUig0080000:FUINMeYFFWMJEUigFUIJMeYFGWL20000 25YFGWMJEUYgFUINMeYFFWL20003Ool0=P00FSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ =5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5Xd001J=5hdFSAN=5XdGS@0 07;EK]Abe6kDL]D0029oo`800009>IH0034C;A8]4bdBOol0 01Yoo`8005Moo`0J001J=5XeFSAJ=EXdFSEJ=5XeFSAJ=EXdFSEJ=5XeFSAJ=EXdFSEJ=5XeFSAJ=EXd FSD000Ioo`0G001J=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=0030000 7EhdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=000L]@0 0fkD00Mbe6kDK]A^e7;DK]@0000TOol02BdB;A<]4RdC;A8]4`00Ool0000>Ool001Yoo`03001oogoo 05Ioo`0J001NEEXdGUEJ=5iEFSANEEXdGUEJ=5iEFSANEEXdGUEJ=5iEFSANEEXdGUEJ=5iEFS@000Eo o`0E001J=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hd00<0000ZGSAJ=5hdFSAN =5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5Xd001^e7;DK]Ab eFkDL]A^e7;EK]Abe00097oo00L002dB;A<]4S4C;A8]4`02000>Ool001Yoo`03001oogoo05Moo`0H 001J=EXdFSEJ=5XeFSAJ=EXdFSEJ=5XeFSAJ=EXdFSEJ=5XeFSAJ=EXdFSEJ=0001Woo018005hdFSAN =5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGS@300008EhdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hd FSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=00200000fkDL]A^e002K]@01G;D K]A^e6kD00009Goo00H]4bdB;A<]4RdC;A82000>Ool001Yoo`03001oogoo05Moo`0G001J=5iEFSAN EEXdGUEJ=5iEFSANEEXdGUEJ=5iEFSANEEXdGUEJ=5iEFS@00006Ool03`00GSAJ=5hdFSAN=5XdGSAJ =5hdFSAN=5XdGSAJ=0040000Ool001Yoo`03001oogoo01Yoo`8003]oo`0F001J=5iEFSANEEXdGUEJ=5iEFSAN EEXdGUEJ=5iEFSANEEXdGUEJ=5iE0005Ool02`00GSAJ=5hdFSAN=5XdGSAJ=5hdFS@00`0003UJ=5hd FSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hd FSAN=5XdGSAJ=5hdFSAN=5XdGS@007;EK]Abe6kD001^e7;DK]AbeFkDL]A^e7;E000017oo100077oo 00D002dBgoo01@005XdFSEJ=5XeFSAJ=EXdFSEJ=5Xe FSAJ=EXdFSEJ=5XeFSAJ=@001Woo00P005XdGSAJ=5hdFSAN=5Xd0`0002iJ=5hdFSAN=5XdGSAJ=5hd FSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hd FSAN=5XdGSAJ=5hdFS@000=^e005L]A^e000K]Abe003K]@00g;DK]@00004Ool4000LOol01P00;A<] 4RdC;A8]4`8000eoo`006Goo0`006Woo1000>goo01<005iEFSANEEXdGUEJ=5iEFSANEEXdGUEJ=5iE FSANEEXdGUD00006Ool90000?eXdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ =5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=000L]A^ e7;EK]Abe000L]E^e7;DK]AbeFkDL]@00005Ool2000NOol01@00;A<]4S4C;A800P003Goo000IOol3 000KOol2000lOol04P00FSAJ=EXdFSEJ=5XeFSAJ=EXdFSEJ=5XeFSAJ=EXdFSD000Ioo`03001JMUYg 00@00003FWL0000000`0000WGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hd FSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5Xd001^e7;D00=^e005L]@006kDK]Abe003K]@00g;D 001oo`0SOol01@00;A8]4bdB;A<00P003Goo000IOol3001IOol04P00GUEJ=5iEFSANEEXdGUEJ=5iE FSANEEXdGUEJ=5iEFS@000Aoo`D0000CGWMJMUigFWINMeYfGWMJMUigFWINMeYfGWMJMUigFWINMeYf GWL03P0002IJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFSAN=5XdGSAJ=5hdFS@006kDL]E^e7;D K]AbeFkDL]@007;EK]Abe6kDL]E^e0009Goo00@002dB;A<]4P8000eoo`006Goo0`00FWoo00l005Xe FSAJ=EXdFSEJ=5XeFSAJ=EXdFSEJ=5XeFS@00P000goo1P0000EJMUYgFWMNMeYf009JM`06GWMJMUYg FWMNMeYf0UYg00INMeYfFWMJMeigFWH2FWL01UigFWIJMeYgGWMJMP9JM`03GWMJMP0000d00009GSAJ =5hdFSAN=5XdGS@007;D00=^e006L]A^e6kDK]Abe0000VkD00Ebe6kDK]A^e00002Aoo`04000]4bdB ;A<2000=Ool001Uoo`<005Yoo`0>001J=5iEFSANEEXdGUEJ=5iEFSANEEXdGUEJ=0H000Ioo``0000S GWMJMUigFWINMeYfGWMJMUigFWINMeYfGWMJMUigFWINMeYfGWMJMUigFWINMeYfGWMJMUigFWINMeYf GWMJMUigFWINM`0800004FkDL]A^e7;EK]Abe6kDL]E^e7;D001beFkDL]A^e7;E00009Goo00D0034C ;A8]4`0000eoo`006Goo0P0000Goo0P00 0f[g00EZn6[g000007;D009^e005001be6kDK]@0000UOol00`00;A<0000Woo0`005Woo 00@005iEFS@005Eoo`<00004J_M[66[gJaP200000fkD001oo`0QOol00`0074hLC@02000;Ool001Mo o`03001oogoo00=oo`0:5=@DdaCD5=74d00P002goo000FOol00`00Oomoo`04Ool030005=0080 00]oo`005Woo00@007oo000000=oo`0=000De1Bc5=@@/aCD5;74d00P002goo000FOol50002Ool0 3P005=000@/aCD5;001oo`0000Yoo`005Woo00<007ooOol01Goo010001Bc5=@@/aCD5;74d007oo00002Woo000EOol00`00Oomoo`06Ool040005=@DdaCD5= 74dLCP00Ool0000:Ool001Eoo`03001oogoo00Moo`0@000De1Bc5=@@/aCD5;008000Yo o`005Goo00<007ooOol01goo018001CC5=@DdaCD5= 74d007oo0009Ool001Eoo`03001oogoo00Moo`0C000De1Bc5=@@/aCD5;74dPCQa=74h007oo00002Goo000DOol00`00Oomoo`09Ool03`005=@DdaCD5=001oo`0000Uoo`0057oo00<007ooOol02Goo 00T001CD5=74dLCP00Ool00009Ool001Aoo`03001oogoo 00Yoo`@0000=5=@DdaCD5=74d007oo0009Ool001Aoo`03001oogoo00Qoo`<0000?5=@D/aCD 4;0002Ool00`00Oomoo`06Ool001=oo`03001oo`00008000Yoo`0=000De1CC5=@DdaCD5=74dLCQa=74hLC@000Woo00<0 07ooOol01Woo000COol300074dLCQa=0P000Woo00<007ooOol01Woo000;Ool50004Ool2000< Ool030005=@DdaCD5=74d000@410D0009oo`03001oogoo00Ioo`003Goo00<007ooOol01goo00<007oo000027oo00/0 01CD5=008000<41005001oogooOol00007Ool000eoo`03001oogoo00Qoo`8000Uoo`09000De12c5=@D /`00:IP]^@0002Yoo`@001moo`03001oogoo07Eoo`03001oogoo00Moo`08000LCP0010D410@510@0 00Aoo`03001oogoo00Eoo`003Goo00<007ooOol02Woo00<007ooOol01Woo00P001CC5=@Dd`00:IPY ^000;7oo0P0087oo00<007ooOol0MWoo00<007ooOol00Woo0P000Woo0P0000H41@@410@410@50004 Ool00`00Oomoo`05Ool000aoo`8000eoo`8000Ioo`08000De1Bc000YV2fi:IP004ioo`03001oogoo 011oo`8006Eoo`03001oogoo00@00009Ool000@510@41@@410D4100000Aoo`03001oogoo00Eoo`00 7Goo00<007oo00000goo00L001CC5=@002Vh:IP0001?Ool00`00Oomoo`0?Ool4001TOol00`00Oomo o`0500001@@510@410@410D00P@400<007ooOol00Woo00<007ooOol01Goo000AOol2000;Ool20004 Ool01ACD000]^BVH0000Cgoo00<007ooOol047oo1000IGoo00<007ooOol00P0000Moo`0010@41@@4 10D410030004Ool00`00Oomoo`05Ool0011oo`04001oogoo000;Ool20003Ool01ACC000YV2Vh0000 Cgoo00<007ooOol04Goo0P00Igoo00D007ooOomoo`0000<4100510D00000Ni400005Ool00`00Oomo o`05Ool0011oo`04001oogoo000=Ool01`00Oomoo`00:IPY^000051oo`03001oogoo07]oo`06001o ogoo00041@@40P0000Ak/GN@Nk4000Eoo`03001oogoo00Eoo`0047oo00@007ooOol000ioo`<00003 :KP007oo051oo`03001oogoo01Yoo`8005moo`<0000810@00000Mi5k/G^ANk4000Moo`03001oogoo 00Aoo`0047oo00@007ooOol0011oo`<0055oo`03001oogoo01Uoo`@005ioo`@00007Nk5gT7^aMi1k /GN@00001goo00<007ooOol017oo000AOol2000BOol2001AOol00`00Oomoo`0IOol4001NOol02P00 LmP007^aMi5k/G^ANk5gT@0027oo00<007ooOol017oo000WOol00`00Oomoo`1>Ool00`00Oomoo`0J Ool2001OOol02P00LmP00000Nk5gT7^aMi1k/@0027oo00<007ooOol017oo000XOol01000Oomoo`00 C7oo00<007ooOol0Ngoo00X007OI001k/@00Nk5gTG^aNi4000Qoo`03001oogoo00Aoo`00:Goo0`00 C7oo00<007ooOol0NWoo00X000@5001gf@00Nk4007^aMi0000Uoo`03001oogoo00Aoo`00:goo00<0 07ooOol0BWoo00<007ooOol0NWoo00X000@4001cf000Mi5k/@00Nk4000Uoo`03001oogoo00Aoo`00 ;7oo0P00BWoo00<007ooOol0NGoo00P000@410D007OI001k/GN@0P002goo00<007ooOol00goo000^ Ool00`00Ool00017Ool00`00Oomoo`0/Ool2001:Ool02`0010@410@4001cf000Ni5k/GNA00002goo 00<007ooOol00goo000_Ool20017Ool00`00Oomoo`0[Ool40019Ool02P@410D410@5001gf@00Nk5g T7^a0P002Woo00<007ooOol00goo000`Ool20016Ool00`00Oomoo`0[Ool40018Ool02`0010@410@5 10@007?H001gTG^a00000Woo00<007ooOol01goo00<007ooOol00goo000bOol00`00Oomoo`13Ool0 0`00Oomoo`0XOol20002Ool20019Ool02`@510@41@@410D007OI001k/GN@00000goo00<007ooOol0 1Woo00<007ooOol00goo000cOol200000goo001oo`10Ool00`00Oomoo`0WOol4001;Ool210@01@@5 10@410@400000W?H0P0017oo00<007ooOol01Woo00<007ooOol00goo000ROol20004Ool20003Ool4 0004Ool00`00Oomoo`10Ool00`00Oomoo`0WOol4001:Ool02P0010@41@@410D410@510@007?H0P00 1Goo00<007ooOol01Goo00<007ooOol00goo000QOol01000Oomoo`0027oo00<007ooOol01Woo0P00 @7oo00<007ooOol0:7oo0P00Bgoo00<000@510@00P@400H41@@410@007OI0007Ool00`00Oomoo`05 Ool00`00Oomoo`02Ool0025oo`04001oogoo0009Ool00`00Oomoo`07Ool00`00Oomoo`0mOol00`00 Oomoo`17Ool2000[Ool0300010D410@510@41@@410D41000LmP000Qoo`03001oogoo00Aoo`03001o ogoo009oo`008Goo00@007ooOol000Yoo`03001oogoo00Moo`03001oo`0003aoo`03001oogoo04Io o`@002Uoo`0300041@@40084100410D410@410@3000:Ool00`00Oomoo`03Ool00`00Oomoo`02Ool0 025oo`04001oogoo0008Ool01000Oomoo`002Goo0P00?7oo00<007ooOol0AWoo1000:Goo00P000@4 10D410@510@41@@410002goo00<007ooOol00Woo00<007ooOol00Woo000ROol2000:Ool20007oo0P0017oo0P001Goo0`000Woo00<007ooOol0 97oo0P0017oo00<007ooOol0KGoo00<000@400004Woo1@003Woo000gOol01000Oomoo`002goo00<0 07ooOol00Woo0P00:Woo00<007ooOol0K7oo0`003goo10004goo000gOol01000Oomoo`0027oo1@00 1Goo00<007oo00009goo00<007ooOol0Jgoo0`002goo1@005goo000gOol01000Oomoo`0027oo00@0 07ooOol000Moo`8002Ioo`03001EK00006aoo`03001oogoo00Moo`@001aoo`00=goo00@007ooOol0 00Uoo`03001oo`0000Uoo`03001oogoo02=oo`04001EK5E/001YOol20006Ool4000POol003Qoo`80 00]oo`8000Yoo`04001oogoo000POol00`00FFaEK002EF`00`00Oomoo`1UOol20002Ool5000TOol0 059oo`<0021oo`03001EK5E/00=EK003001oogoo06=oo`D002Uoo`00E7oo00<007ooOol07Goo00D0 05E/EFaEK5U/00=EK003001oogoo05ioo`D002eoo`00EGoo0P007Goo00<005E/EF`01UE/00<007oo Ool04Woo0P00AGoo1000Ool01@00EFaEK5E/FF`00eE/00EIK5E/EFaEK5U/00=EK004FFaEK5E/000;Ool2000YOol5 001@Ool004]oo`04001oogoo0008Ool01000Oomoo`001Woo00<007ooOol037oo00<005E/EF`04EE/ 00<007ooOol01goo100097oo1000EGoo001;Ool01000Oomoo`0027oo0`0027oo00D007ooOomoo`00 00Qoo`04001EK5E/FF`3EF`01EU/EFaEK5E/FF`00eE/00EIK5E/EFaEK5U/009EK003001oogoo00Io o`@0021oo`@005Uoo`00Bgoo00@007ooOol000Uoo`03001oogoo00Qoo`800003Ool007oo00Moo`03 001EK5E/01AEK003001oogoo00Ioo`8001aoo`D005eoo`00C7oo0P002Woo0`002Woo0P001goo00<0 05E/FF`00eE/00EIK5E/EFaEK5U/00=EK005FFaEK5E/EFaIK003EF`015U/EFaEK0008Goo1000HWoo 001VOol20006Ool00`00EFaEK00GEF`00`00Oomoo`0JOol4001VOol006Qoo`03001oo`00009oo`03 001IK5E/009EK005FFaEK5E/EFaIK003EF`01EU/EFaEK5E/FF`00eE/00EIK5E/EFaEK5U/009EK003 001oogoo01Aoo`D006Yoo`00JGoo0P000Woo20005EE/00<007ooOol03goo1000Kgoo001ZOol30000 24R4C:A8Q4bTB8A"], ImageRangeCache->{{{0, 270.438}, {293.625, 0}} -> {-0.0189261, -0.0418083, 0.00346138, 0.00346138}}] }, Open ]] }, Open ]] }, FrontEndVersion->"4.0 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, WindowSize->{597, 521}, WindowMargins->{{146, Automatic}, {Automatic, 32}} ] (*********************************************************************** 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[1717, 49, 71, 1, 30, "Input"], Cell[1791, 52, 72, 1, 30, "Input"], Cell[1866, 55, 52, 1, 30, "Input"], Cell[1921, 58, 86, 1, 30, "Input"], Cell[CellGroupData[{ Cell[2032, 63, 67, 1, 30, "Input"], Cell[2102, 66, 184, 3, 42, "Message"] }, Open ]], Cell[CellGroupData[{ Cell[2323, 74, 303, 7, 70, "Input"], Cell[2629, 83, 18469, 414, 296, 3256, 222, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[21135, 502, 67, 1, 30, "Input"], Cell[21205, 505, 490, 9, 67, "Output"] }, Open ]], Cell[21710, 517, 171, 3, 50, "Input"], Cell[21884, 522, 823, 14, 210, "Input"], Cell[22710, 538, 1008, 18, 330, "Input"], Cell[CellGroupData[{ Cell[23743, 560, 114, 2, 30, "Input"], Cell[23860, 564, 102, 2, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[23999, 571, 100, 2, 30, "Input"], Cell[24102, 575, 88, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[24227, 581, 358, 7, 90, "Input"], Cell[24588, 590, 23403, 506, 269, 3688, 258, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[48006, 1099, 112, 2, 30, "Input"], Cell[CellGroupData[{ Cell[48143, 1105, 64, 1, 30, "Input"], Cell[48210, 1108, 789, 11, 200, "Output"] }, Open ]], Cell[49014, 1122, 199, 3, 50, "Input"], Cell[CellGroupData[{ Cell[49238, 1129, 1137, 21, 310, "Input"], Cell[50378, 1152, 125, 2, 29, "Output"] }, Open ]], Cell[50518, 1157, 92, 1, 30, "Input"], Cell[50613, 1160, 1137, 19, 370, "Input"], Cell[CellGroupData[{ Cell[51775, 1183, 48, 1, 30, "Input"], Cell[51826, 1186, 36, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[51899, 1192, 114, 2, 30, "Input"], Cell[52016, 1196, 128, 2, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[52181, 1203, 100, 2, 30, "Input"], Cell[52284, 1207, 119, 2, 48, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[52440, 1214, 27, 0, 53, "Section"], Cell[CellGroupData[{ Cell[52492, 1218, 471, 11, 130, "Input"], Cell[52966, 1231, 65101, 1722, 303, 18314, 1140, "GraphicsData", "PostScript", "Graphics"] }, Open ]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)