(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 23771, 927] NotebookOptionsPosition[ 22748, 893] NotebookOutlinePosition[ 23172, 909] CellTagsIndexPosition[ 23129, 906] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{"LiH", " ", "on", " ", "x"}], "-", "axis"}], ";", " ", RowBox[{"with", " ", "polarization"}]}], ",", " ", RowBox[{ RowBox[{"Li", "-", RowBox[{"cloud", " ", "at", " ", "X"}]}], "=", "0"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"1", " ", "Li", " ", RowBox[{"(", RowBox[{"x", " ", "from", " ", "center", " ", "of", " ", "P"}], ")"}]}], ",", " ", RowBox[{"2", " ", "H", " ", RowBox[{"(", RowBox[{"Q", " ", "from", " ", "center", " ", "of", " ", "R"}], ")"}]}], ",", " ", RowBox[{ RowBox[{"3", " ", "Li"}], "-", RowBox[{"cloud", " ", RowBox[{"(", "P", ")"}]}]}], ",", " ", RowBox[{ RowBox[{"4", " ", "H"}], "-", RowBox[{"cloud", " ", RowBox[{"(", "R", ")"}]}]}], ",", " ", RowBox[{"Z", "=", RowBox[{"3", " ", "inserted"}]}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"c2", "=", RowBox[{"{", RowBox[{ RowBox[{"k1", "\[Rule]", " ", "1.02480344"}], ",", " ", RowBox[{"k2", "\[Rule]", " ", "1.232443643"}], ",", RowBox[{"s1", "\[Rule]", " ", "0.27877144"}], ",", RowBox[{"s2", "\[Rule]", " ", "0.28887416"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"T", " ", "=", " ", RowBox[{ RowBox[{"k2", "*", RowBox[{"2.25", "/", RowBox[{"R", "^", "2"}]}]}], " ", "+", RowBox[{"k1", "*", RowBox[{"2.25", "/", RowBox[{"P", "^", "2"}]}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"d12", " ", "=", RowBox[{"P", "+", "R", "+", "Q", "-", "x"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"d13", " ", "=", " ", "x"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"d14", " ", "=", " ", RowBox[{"P", "+", "R", "-", "x"}]}], ";"}], " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"d23", " ", "=", " ", RowBox[{"P", "+", "R", "+", "Q"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"d24", " ", "=", " ", "Q"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"d34", " ", "=", " ", RowBox[{"P", "+", "R"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Vee", " ", "=", " ", RowBox[{ RowBox[{"3", "*", RowBox[{"s2", "/", "R"}]}], "+", RowBox[{"3", "*", RowBox[{"s1", "/", "P"}]}], "+", RowBox[{"4", "/", "d34"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Vnn", " ", "=", " ", RowBox[{"3", "/", "d12"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Vne", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{"-", "3"}], "*", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{ RowBox[{"(", RowBox[{"d13", "/", "P"}], ")"}], "^", "2"}]}], ")"}], "/", "P"}]}], "-", RowBox[{"6", "/", "d14"}], "-", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{ RowBox[{"(", RowBox[{"d24", "/", "R"}], ")"}], "^", "2"}]}], ")"}], "/", "R"}], "-", RowBox[{"2", "/", "d23"}]}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"func", " ", "=", " ", RowBox[{ RowBox[{ "T", " ", "+", " ", "Vee", " ", "+", " ", "Vnn", " ", "+", " ", "Vne"}], " ", "/.", " ", "c2"}]}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{ "arbitrary", " ", "center", " ", "positions", " ", "on", " ", "x"}], "-", "axis"}], ",", " ", RowBox[{"4", " ", "variables"}]}], " ", "*)"}], " ", "\[IndentingNewLine]", RowBox[{"N", "[", RowBox[{ RowBox[{"t", " ", "=", " ", RowBox[{"FindMinimum", "[", RowBox[{"func", ",", " ", RowBox[{"{", RowBox[{"R", ",", RowBox[{"{", RowBox[{"1.8", ",", "2.2"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"P", ",", RowBox[{"{", RowBox[{"0.5", ",", "0.6"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Q", ",", RowBox[{"{", RowBox[{"0.4", ",", "0.5"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"x", ",", RowBox[{"{", RowBox[{"0.01", ",", "0.02"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"MaxIterations", " ", "\[Rule]", " ", "100"}], "}"}]}], "]"}]}], ",", "20"}], "]"}], " ", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"u", " ", "=", " ", RowBox[{"t", "[", RowBox[{"[", "2", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], RowBox[{"(*", " ", "lengths", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"d12", " ", "/.", "u"}], "\[IndentingNewLine]", RowBox[{"d13", " ", "/.", " ", "u"}], "\[IndentingNewLine]", RowBox[{"d14", " ", "/.", " ", "u"}], "\[IndentingNewLine]", RowBox[{"d23", " ", "/.", " ", "u"}], "\[IndentingNewLine]", RowBox[{"d24", " ", "/.", " ", "u"}], "\[IndentingNewLine]", RowBox[{"d34", " ", "/.", "u"}], "\[IndentingNewLine]", RowBox[{"N", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"Vnn", "+", "Vee", "+", "Vne"}], ")"}], "/", "T"}], " ", "/.", " ", "u"}], " ", "/.", " ", "c2"}], ",", " ", "10"}], "]"}], " ", RowBox[{"(*", " ", "Virial", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"N", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "6"}], "*", RowBox[{"x", "/", RowBox[{"P", "^", "3"}]}]}], "-", RowBox[{"3", "/", RowBox[{"d12", "^", "2"}]}], "+", RowBox[{"6", "/", RowBox[{"d14", "^", "2"}]}]}], " ", "/.", " ", "u"}], " ", ",", " ", "10"}], "]"}], " ", RowBox[{"(*", " ", RowBox[{ RowBox[{"Forces", " ", "on", " ", "Li3"}], "+"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"N", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"2", "*", RowBox[{"Q", "/", RowBox[{"R", "^", "3"}]}]}], "+", RowBox[{"2", "/", RowBox[{"d23", "^", "2"}]}], "-", RowBox[{"3", "/", RowBox[{"d12", "^", "2"}]}]}], " ", "/.", " ", "u"}], ",", " ", "10"}], "]"}], RowBox[{"(*", " ", RowBox[{ RowBox[{"Forces", " ", "on", " ", "H"}], "+"}], " ", "*)"}]}]}]], "Input", CellChangeTimes->{3.5726328768465796`*^9}], Cell[BoxData[ RowBox[{ FractionBox["2.3058077399999997`", SuperscriptBox["P", "2"]], "+", FractionBox["0.8363143199999999`", "P"], "+", FractionBox["2.77299819675`", SuperscriptBox["R", "2"]], "+", FractionBox["0.86662248`", "R"], "-", FractionBox[ RowBox[{"3", "-", FractionBox[ SuperscriptBox["Q", "2"], SuperscriptBox["R", "2"]]}], "R"], "+", FractionBox["4", RowBox[{"P", "+", "R"}]], "-", FractionBox["2", RowBox[{"P", "+", "Q", "+", "R"}]], "-", FractionBox["6", RowBox[{"P", "+", "R", "-", "x"}]], "+", FractionBox["3", RowBox[{"P", "+", "Q", "+", "R", "-", "x"}]], "-", FractionBox[ RowBox[{"3", " ", RowBox[{"(", RowBox[{"3", "-", FractionBox[ SuperscriptBox["x", "2"], SuperscriptBox["P", "2"]]}], ")"}]}], "P"]}]], "Output"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "8.027595380866632`"}], ",", RowBox[{"{", RowBox[{ RowBox[{"R", "\[Rule]", "1.9868762698528695`"}], ",", RowBox[{"P", "\[Rule]", "0.5610511204557704`"}], ",", RowBox[{"Q", "\[Rule]", "0.45146091681570716`"}], ",", RowBox[{"x", "\[Rule]", "0.01765285575744501`"}]}], "}"}]}], "}"}]], "Output"], Cell[BoxData["2.981735451366902`"], "Output"], Cell[BoxData["0.01765285575744501`"], "Output"], Cell[BoxData["2.530274534551195`"], "Output"], Cell[BoxData["2.999388307124347`"], "Output"], Cell[BoxData["0.45146091681570716`"], "Output"], Cell[BoxData["2.54792739030864`"], "Output"], Cell[BoxData[ RowBox[{"-", "1.9999973540798617`"}]], "Output"], Cell[BoxData["9.48002020662031`*^-7"], "Output"], Cell[BoxData[ RowBox[{"-", "9.093399527815293`*^-8"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"plot1", " ", "=", " ", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "P"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "0"}], "}"}], ",", "0.03"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"P", " ", "+", " ", "R"}], ",", "0"}], "}"}], ",", "R"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"P", " ", "+", "R", "+", " ", "Q"}], ",", "0"}], "}"}], ",", "0.03"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Dashing", "[", RowBox[{"{", RowBox[{"0.03", ",", "0.03"}], "}"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"P", "+", "R"}], ",", "0"}], "}"}], ",", "Q"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "x"}], "]"}], "}"}]}], "}"}]}], "}"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"/.", "u"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{"plot1", ",", RowBox[{"{", RowBox[{ RowBox[{"AspectRatio", " ", "->", " ", "Automatic"}], ",", RowBox[{"PlotRange", " ", "->", " ", "All"}], ",", RowBox[{"Axes", " ", "->", " ", "True"}], ",", RowBox[{"GridLines", " ", "->", " ", "Automatic"}], ",", RowBox[{"Frame", " ", "->", " ", "True"}]}], "}"}]}], "]"}]}], "Input"], Cell[BoxData[ TagBox[ RowBox[{"\[SkeletonIndicator]", "Graphics", "\[SkeletonIndicator]"}], False, Editable->False]], "Output"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .7798 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 0.128666 0.186893 0.3899 0.186893 [ [.12867 -0.0125 -3 -9 ] [.12867 -0.0125 3 0 ] [.31556 -0.0125 -3 -9 ] [.31556 -0.0125 3 0 ] [.50245 -0.0125 -3 -9 ] [.50245 -0.0125 3 0 ] [.68935 -0.0125 -3 -9 ] [.68935 -0.0125 3 0 ] [.87624 -0.0125 -3 -9 ] [.87624 -0.0125 3 0 ] [ 0 0 -0.125 0 ] [-0.0125 .01611 -12 -4.5 ] [-0.0125 .01611 0 4.5 ] [-0.0125 .20301 -12 -4.5 ] [-0.0125 .20301 0 4.5 ] [-0.0125 .3899 -6 -4.5 ] [-0.0125 .3899 0 4.5 ] [-0.0125 .57679 -6 -4.5 ] [-0.0125 .57679 0 4.5 ] [-0.0125 .76369 -6 -4.5 ] [-0.0125 .76369 0 4.5 ] [ 0 0 -0.125 0 ] [ 0 .7798 .125 0 ] [ 1 0 .125 0 ] [ 0 0 0 0 ] [ 1 .7798 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 .5 r .25 Mabswid [ ] 0 setdash .12867 0 m .12867 .7798 L s .31556 0 m .31556 .7798 L s .50245 0 m .50245 .7798 L s .68935 0 m .68935 .7798 L s .87624 0 m .87624 .7798 L s 0 .20301 m 1 .20301 L s 0 .3899 m 1 .3899 L s 0 .57679 m 1 .57679 L s 0 g .12867 0 m .12867 .00625 L s [(0)] .12867 -0.0125 0 1 Mshowa .31556 0 m .31556 .00625 L s [(1)] .31556 -0.0125 0 1 Mshowa .50245 0 m .50245 .00625 L s [(2)] .50245 -0.0125 0 1 Mshowa .68935 0 m .68935 .00625 L s [(3)] .68935 -0.0125 0 1 Mshowa .87624 0 m .87624 .00625 L s [(4)] .87624 -0.0125 0 1 Mshowa .125 Mabswid .16604 0 m .16604 .00375 L s .20342 0 m .20342 .00375 L s .2408 0 m .2408 .00375 L s .27818 0 m .27818 .00375 L s .35294 0 m .35294 .00375 L s .39032 0 m .39032 .00375 L s .4277 0 m .4277 .00375 L s .46507 0 m .46507 .00375 L s .53983 0 m .53983 .00375 L s .57721 0 m .57721 .00375 L s .61459 0 m .61459 .00375 L s .65197 0 m .65197 .00375 L s .72672 0 m .72672 .00375 L s .7641 0 m .7641 .00375 L s .80148 0 m .80148 .00375 L s .83886 0 m .83886 .00375 L s .09129 0 m .09129 .00375 L s .05391 0 m .05391 .00375 L s .01653 0 m .01653 .00375 L s .91362 0 m .91362 .00375 L s .951 0 m .951 .00375 L s .98838 0 m .98838 .00375 L s .25 Mabswid 0 0 m 1 0 L s 0 .01611 m .00625 .01611 L s [(-2)] -0.0125 .01611 1 0 Mshowa 0 .20301 m .00625 .20301 L s [(-1)] -0.0125 .20301 1 0 Mshowa 0 .3899 m .00625 .3899 L s [(0)] -0.0125 .3899 1 0 Mshowa 0 .57679 m .00625 .57679 L s [(1)] -0.0125 .57679 1 0 Mshowa 0 .76369 m .00625 .76369 L s [(2)] -0.0125 .76369 1 0 Mshowa .125 Mabswid 0 .05349 m .00375 .05349 L s 0 .09087 m .00375 .09087 L s 0 .12825 m .00375 .12825 L s 0 .16563 m .00375 .16563 L s 0 .24039 m .00375 .24039 L s 0 .27776 m .00375 .27776 L s 0 .31514 m .00375 .31514 L s 0 .35252 m .00375 .35252 L s 0 .42728 m .00375 .42728 L s 0 .46466 m .00375 .46466 L s 0 .50204 m .00375 .50204 L s 0 .53942 m .00375 .53942 L s 0 .61417 m .00375 .61417 L s 0 .65155 m .00375 .65155 L s 0 .68893 m .00375 .68893 L s 0 .72631 m .00375 .72631 L s .25 Mabswid 0 0 m 0 .7798 L s .12867 .77355 m .12867 .7798 L s .31556 .77355 m .31556 .7798 L s .50245 .77355 m .50245 .7798 L s .68935 .77355 m .68935 .7798 L s .87624 .77355 m .87624 .7798 L s .125 Mabswid .16604 .77605 m .16604 .7798 L s .20342 .77605 m .20342 .7798 L s .2408 .77605 m .2408 .7798 L s .27818 .77605 m .27818 .7798 L s .35294 .77605 m .35294 .7798 L s .39032 .77605 m .39032 .7798 L s .4277 .77605 m .4277 .7798 L s .46507 .77605 m .46507 .7798 L s .53983 .77605 m .53983 .7798 L s .57721 .77605 m .57721 .7798 L s .61459 .77605 m .61459 .7798 L s .65197 .77605 m .65197 .7798 L s .72672 .77605 m .72672 .7798 L s .7641 .77605 m .7641 .7798 L s .80148 .77605 m .80148 .7798 L s .83886 .77605 m .83886 .7798 L s .09129 .77605 m .09129 .7798 L s .05391 .77605 m .05391 .7798 L s .01653 .77605 m .01653 .7798 L s .91362 .77605 m .91362 .7798 L s .951 .77605 m .951 .7798 L s .98838 .77605 m .98838 .7798 L s .25 Mabswid 0 .7798 m 1 .7798 L s .99375 .01611 m 1 .01611 L s .99375 .20301 m 1 .20301 L s .99375 .3899 m 1 .3899 L s .99375 .57679 m 1 .57679 L s .99375 .76369 m 1 .76369 L s .125 Mabswid .99625 .05349 m 1 .05349 L s .99625 .09087 m 1 .09087 L s .99625 .12825 m 1 .12825 L s .99625 .16563 m 1 .16563 L s .99625 .24039 m 1 .24039 L s .99625 .27776 m 1 .27776 L s .99625 .31514 m 1 .31514 L s .99625 .35252 m 1 .35252 L s .99625 .42728 m 1 .42728 L s .99625 .46466 m 1 .46466 L s .99625 .50204 m 1 .50204 L s .99625 .53942 m 1 .53942 L s .99625 .61417 m 1 .61417 L s .99625 .65155 m 1 .65155 L s .99625 .68893 m 1 .68893 L s .99625 .72631 m 1 .72631 L s .25 Mabswid 1 0 m 1 .7798 L s 0 .3899 m 1 .3899 L s .12867 0 m .12867 .7798 L s .5 Mabswid newpath .12867 .3899 .10486 0 365.73 arc s .13197 .3899 m .13197 .3899 .00561 0 365.73 arc F newpath .60486 .3899 .37133 0 365.73 arc s .68923 .3899 m .68923 .3899 .00561 0 365.73 arc F [ .03 .03 ] 0 setdash newpath .60486 .3899 .08438 0 365.73 arc s newpath .12867 .3899 .0033 0 365.73 arc s 0 0 m 1 0 L 1 .7798 L 0 .7798 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{574, 447.563}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}},ImageCache->GraphicsData["CompressedBitmap", "\<\ eJztnWd3VEcShgcQJphgckZCiJxFjhIgckYGgzEIEXzsD3t2j9ff+Wn707zc llRXGh4N7/St1vQEDgz31HRNP9W3b+juqupHk3//8flfk3//+XFy4M5fk//5 48+P/x24/e+/voqWLKrVFl+r1Rb9b6BWHP9Tq818/PP179THaPFRq70u/ltc fPe5OFpaHH0ojvqKo0/27e/F0ZLiaGxK8VX4L5SqTf+klastmSP+ALJPuvrN piv8CLLP84EtjTPqk1jHJP/krchW/KboRxbX482qszzlv889+XVH5bfTit90 nlwEG6YEM738aPGxaNZXdS35A8jWi7J1mevmzpd7u/QVn4t6HShbvtzbRepA YyCjhwc9ZFTZjeogX6CC5mU9kO+CLCv+C8/w5Vkh1VW6Ihc4aqUgCy9zNxYA 6ZrVNo309fup/6f+hPemPgChdq3ShgeLz52F5kC1U/3NK6R3V9xdfK4sNHfa 0eZKPSA0snenDEjLC82TxdGy4mhtLKb3HWaddbsRO1qZC9wqQ7pnR0tzgVtm SON2lAPXYqN5a0cfWgMyT82BMPzmRGquckBOhEvt219Tg0yYzYvF5gtXYWjD V6nh3lpV6tW1ysx5kRrujcEtE+HWmsZ4ariX1oNWiHDlDfdxarhxO0lrRLjN 1nIPU8M9s6rWiXBbzZx7qeGeGNwGEW6HadxJDffQ2mGTCLfL4G6lhrtvVW0V 4frNnBup4e4a3HYRbtA0RmW4wKEi3TKNnSLSkCFdg29His8+p/a6aVX1i3D7 TeNK6pNJgzIV86BhXkqNeR3KqQOrw6B7PjXwiLXNXhHziGkkh7til8s+Ee6Y wZ1NDXfJqjoowp0wc4ZTw10wuMMi3LBpnEwNdx7KqZhnQPdYauBzUO6ICHwW dI+mBj5tPe24iHnOTn9yuFNW1SkRrnFvdoU7CeVUzEugeyA18AkoR7cXAr5s 7Zocs/GNmeCumgbd/F3hGj/SCK7xY9MVTn0tIEz1dcQV+BCUuyACq695rsAH 7GReFjEbvyq7wu2HcirmLdClgYcr8D4oR8MDAr4Nujtk4KCnYu61Uzgiwt0x DUIKv+I1FBuEcirmPdCl0bnrSR+wtqFhPWHeh1/ekhpzt2GOiZgPTCM53K6G uo0xH4HuxtTAO6EcTTkR8GPQpdk3V+DtdjLvipiNpwZd4bZBORXzGej+lDPw c9ClVVJX4K1QjiaXCXgcdGme3RV4C5S7LwL/DLqrUwNvssvlkYj5wjSSw22E cirmL6BLC+euwKRLy0gE/Ap0adHKFZgc2p6IwK9Bd3lqYPLKeyoC/wq6tGbp CvwTlHsmAr8B3R9SA6+Fcs9F4N9Al5asXYHDbSjckGitmzAbr6e7wq2Ccirm O9Bdkhr4Ryj3UgSeAF1yp3AYDK6Ecr+ImO+n++Vs3YDxtUyYf/EaFFaB5DCS L2Oe55o86ciZhfjqY3yK71zhyBvxtQg3Ox5oRn7TE46cOslHieA+ga7rJUzR Cm+ahvti+q5wS6Hcb7nA9UG5txFwUxdEzRduCZR71xRc3xzZ1z/XPfkWQ7mJ pviWzpHNNOJoNUj+UfJ7VM6qGVp6eMSjfXM+Plagou5xxev8Fn9UEJLRhXXZ A25GXgWObkmXcoGjm/nF6nC1pkFIRo/BC7Fws5+LM5VUieKgF4jzsXD1EcZF Rb/nAseRwl+q8NGr4blYvsnpy2y2zKMR6f36LEKGMguJRsOo4JUQM7Z4DzLV Tb0K8JnYEz4BMhq5VgGmkfXpWGAaavc5A6+GOoZzBl4DdZyKBX4LMjWaoWOB aa7tZCwwTb7RbGE2wDS9qcaQqDKafj2RMzBNcB+PBaYZb5qizwaY1hTUyB1V Rmsex2KBadVGjc9UZcRyNGdgWrc7EgtMC3k/djvwJqjjcCzwS5Ctyhn4Bcho MboK8Gao41AsMC3tqzF/qoxcDw7WA5dB0WpagoVAJzePA/XoNCLtHCOm81gU Pzj17dT80ZfaOMjC8HQSvhgsPlMmqSCnGjVXgiojL6X9nr2BXJnI9yq5Ec3n tCC3MTU+V5Vthzr21aOrd76nIFvf7cA7oI6hWOAnIFOjolUZ+Y3uzRmYPHMH uwaYXHXJt7gK8G6oY0/XAJP3thrt37HA/VDHQCzwQ5CpyaM6FngA6uiPBX4A MgqZyAaYAlDULBaqbA/UsbtrgCkSaVu3A1No165Y4LsgU5Od+AOHMq3C3At1 hHMXs0R6B2QU9OcNvDO2IywE8NB8dXQFMIWmqkl8OhaYYn23xwJTtPKubgem 8O9tXQNMst3OwAegjq094G4GPgh1bIkFvgmy/m4Hphwhm7sGmLKcDDgDU9qY TV0DTIlv9nQ78BGoYyMChzI5YYZVqZiR3CjIBhcAmNu1B7zAwCPF56pCcmUB MI9CHRsUzBCC8UMhoeiRvuIzrMNT5sRsjDhjmOT9vcJMpBR7avJRVXYM6liv GBEcfIOIfD3LXOPHczbihGHSt+vMRHqCDeViRJkxkLy9Ntq39O6bjRFlZkFy qCoTsNOoORsjDhkm+aGQpxLNbXqbQ1fgOsWcMt0feU5ss2+zNoI6DJlTZqof gG/VtMrJzaF5OXITIccGknkbRllWf1IMK9MM9sO3ZT66rI3YY5i03EYda16H NQEzPILXFJpqA0QbRuhkIsnovqeaOFJ8BlX17S3aROp2tKRX7n1QxbDkXZHc WBrfqOsG54kNo5fbtYphdAMgI+hOSQEHqmHUtUdFXd3YUIZu6GQOPdsozIaS VhMmXeXXRV0yMUQzfG8ygh7GZBhNjlMQlGps8ylOo7ssecqSOfSGTqMr1cSd ZuJtUSPaRHqOkTk0PUzRjaqJZabSM3ak+g2fgnrXKMbSjZ8Mo2EjBcuqxlIj 07YJqld9dAPQGI2MJRnFY6sbg1DD01SPGhsR3QAUpkRzbySjCHq1AcqBcLkl QXJj6XWAJr9IRjNcqrFU79WGDdoFDXCtYR2Nf28YdFcrDUDvTTRLQjLKFqI2 ANU72rCORA1AMhrDk4yCjNQGULPTtsRYGptQgh3VWDWzraux9L5MhpGMIt8O icAtMZbel+mVj2SUEUs1Vk0B3BJj6bFAq0uqsWr6YFdjaZhAhnkbq6YeJt3T oLvK01hqzb4KxqqynmH1hWiIR0ZQBZRhsWdYasNonEo/RjJKSaruW+hvWCij mjO1bSIlpuMN/7xNCC9335syaxdjpI5G8wG0eeXUREd9tkXZjipJwQnnx55t nWsbTdHQRFtF26okgu/Z1rMNbavfg7cZw6ok/18Yw8KMJ+1jrJpTnyasKE8Z Z3vmzCr0nS5W/KNpeHXrZzJs9szXTFlKS521YTRB9LpnWM+wPAyjaTnXWzu9 vJERPcNaYVjjPGjzmhjGk/REq2JYuN2HF7LoK2vqZ795qaOHC9kWLrgfktkW Wi36VDWyLRxNv7/2WkPtxUGbbrIt7sWRF2U73Xc69obaVc/23ttYz7AuMqxj x6gtMazDJklaNTeXjWEVJ1Q72TZ6jatP/d+utk2iOu6Alvs6UweZosq63o4c 19E7yphudtKo4hmUlwONo2FZuzyphrWd912rnEN7hsUa1ipHbVXWdh7o1FOe ibptF1tAjfxU1G27qBFq5CeibtvFA5GxYw0bNFEDqBFh3g1ALCFEPUwSdVUg 3AjIkjdA14dCtjTyt063jAFWd9Vru4hvqvfifEakbIAqMf8dEfLeqgwPZZ4x WvlInuqgVWaX+ciG7WiDqBttbEsTlQjviWoDNJlvp1UpaB7amVV3rIrOstOq lEKqrO3SQSU3TE3gVSbOo2dlNub0GyYZUSbOq5IQT5W1SX6/8A4dZrlXWr3q dVctD6PQFftBRo+PppIZriw01VmOaBPp9kC3ETK78X20xd1TTQ5a5gWjs5iN OfsNk4woM39RlsYhZyOiE7YeNEy6Ouj2kLU5NLyh584WM5s6pbc51dJOBxGN rzfat/Tml40Rxw1z3knocCayzmIu5JMPIqogm3zyZQ5CWspeZUZkndm/dP2n afmwLhFeSmhxy9uI6D0Wwi4W6wsJzRZlsxUEzd2P9oC/lXXwTiyhTKsw6ZkQ 7hIxewhdB9meBQDOejOp7t5frO2A226PvB4wyFz3eSRZ1jtp9oBB1nabq7Yd cHdvwdx2u3K33b7nbQd8B2Q7nIFpMntHD9gRmFZEdsYC352vf7UEOJTJCTPc fWOGnvfm+zFHYJqY3xXbEdoO+D7ItjoD06rq7q4BfgCyLc7AA1BHfyzwQ5Cp niwdC9wPdQzEAj8C2aYesCPwY5BtdAYmR4I9PWBHYHLfGIwFfgIy1fOwY4HJ BWNvLPBTkKm7tqkycuocyhmY/EP2xQI/A9m6VgCX68UU0Uboz0Gmunm7olOc Uk5GzOtbKBkRzsmN8INT3xZHxb9xkIVcGJPwxWDxudSp0cZBpsY1qDKKpzjg eeZ/BpkaneJqRONMgq1CJ2exg/Xo6l3uBchWOwOTY9ihWOD6xD/FP3X7QlVG oXKHY4HrszAV/9QYu44FpriBI7HAtMWfup9hxwITy9FYYNpqT91EsWOBKajn WCwwJRtVQ9BVGQVaHY8Fpj361A0JOxaYHG9PxALTxoDqLoiqjOIrT8YCvwWZ upOhKiOv4FOxwO9A1tftwBRqPRwLPAGyJc7AlBPgdCzwe5AtdgamLA5nEDiU IczJ6Ytrtiyo1TgNZhW00FtjVhRTQVIakLOxJ/zD9EU0W1bjrJUqHw0Wz8Xy fayTVW08ikg4Hwv3aZZsphLKctwSuM8NgZuHo+mLC9Xhvpi8Chxl9rqYCxwl irvkATd1QfA+GKqsD+q4XA2ub04FX/98rMBHCR+vVONbOqeCmUb8kBfk3Aoo n+dEBWD6vauewNQi75oC5rM0mhfkN139uicfXZtvm+Kbe5+44QlHd7XfIuBm 9F3h6HnwJhe4xrutqHClritclR08Z7+szchvesJV2Tc1vI6H1Yzp6z4JYZXd ht9PX1ezdWdAxxAy1KOi0eDmpYg2Abo0LhwpPmMGSwRMI9sXIjBNFdDI2/Xa obmDn0Vgmj2iuQ1XYJqdGReBaX6OprtcgWnC7nnOwGFKNNx1VEyaqKV5T1fM Kjlwae6eZpZdgUn3sQj8ys4JrTq5YtK62SMRkxYikwPTUupDEZjWpmnl1BWY VtcfiMC0+k+L6a7A5L9wXwQm/wpyV3AFJl+ReyLwc7vUyHfJFZOcme6KmOTs lhyYXMjuiMDkTkjeea7AZUZRFZP8Ssnr0RWTPGPHRGByNSZHWFdgcpa+KQI3 zgDqitkP5W6ImBSZkhx4wNpGxaSIHwqgYcygp8INGtyoCHfXNCiQbqT49Bp5 DUG5qyImRVQSsOuppqjbKyIwRQVTCKgrcJmaUMUcMw0Ku3eFo9QMF0VMSs6R HJjSi1wQgSnBTH9q4MN2MlXMUdOgDE6ucEetqnMi3DXTGEoNR4knT4uYVwyT ksq6YlLO0mER8zLoJgcObk+h2CkR86K1JiXcdYU7bVWdEOHOmwZtY+wKR9ui qpsI0o4EyYHVSglYNdYVuPHJJMxh683UYVzhGl8GBHfSNOiO4ApXbvCi5v0+ bhpnUsNdtarUjNGUkjQ55giUU7MoUprMs6mBG78qEOYhu1zodcQV7oZV1S/C HTBzLstwoQIV6ZZVoKZb2mcaNCoKHcZrKHbHqlLT0gxaA4zAt64n855VpebF aDwmd4VrfnOU3aZB80WucI+tKjWSfYe19e3UcE+tKjXit9xjiWaGXeHGrSo1 snOzmUMLA65wL6wqNShvo5lDy1eucI3XvQiuTP1Ou3+6woVVxOD7oMZMrDYN Wlp1hZuwdlC991daRyDvD1e4SatK4CpjesnjyJXrk50fcq1cYt+S05g/SJ1s sbXDe4T7+meyFVx91iyv7WjeWauUICus+id2pEaCJIdbY0i37EgNZksOF35v eaEZBtrLiiP1aZAcLrxFhF2SBu1IzfTyDVxo8vCiS16DVTDDC3aRGkJ+JWe4 uurVPAZVgjgkOGqv5daVaUraG+ma1eaQsiJ5e02B1IcpuXe7auezqVQZyZG8 7xwLCFKDCpqXSSDkKE7OcCSj+OycdHPny71d+nodKG++3NuFO1B4coWPo7O+ qi36P12tx1Q=\ \>"],ImageRangeCache->{{{0, 573}, {446.563, 0}} -> {-0.87987, -2.24032, \ 0.0096886, 0.0096886}}], Cell[BoxData[ TagBox[ RowBox[{"\[SkeletonIndicator]", "Graphics", "\[SkeletonIndicator]"}], False, Editable->False]], "Output"] }, Open ]] }, WindowSize->{941, 740}, WindowMargins->{{Automatic, 460}, {Automatic, -13}}, PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}}, FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (January 25, 2013)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[579, 22, 6727, 195, 652, "Input"], Cell[7309, 219, 844, 27, 62, "Output"], Cell[8156, 248, 383, 10, 31, "Output"], Cell[8542, 260, 45, 0, 31, "Output"], Cell[8590, 262, 47, 0, 31, "Output"], Cell[8640, 264, 45, 0, 31, "Output"], Cell[8688, 266, 45, 0, 31, "Output"], Cell[8736, 268, 47, 0, 31, "Output"], Cell[8786, 270, 44, 0, 31, "Output"], Cell[8833, 272, 63, 1, 31, "Output"], Cell[8899, 275, 48, 0, 31, "Output"], Cell[8950, 277, 66, 1, 31, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[9053, 283, 1820, 52, 152, "Input"], Cell[10876, 337, 134, 4, 31, "Output"], Cell[11013, 343, 11582, 541, 456, 5102, 432, "GraphicsData", "PostScript", \ "Graphics"], Cell[22598, 886, 134, 4, 31, "Output"] }, Open ]] } ] *) (* End of internal cache information *)