(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 12.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 94957, 2276] NotebookOptionsPosition[ 88074, 2163] NotebookOutlinePosition[ 88407, 2178] CellTagsIndexPosition[ 88364, 2175] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"\[CapitalPhi]", "[", "N_", "]"}], "[", "X_", "]"}], ":=", RowBox[{ RowBox[{"-", SuperscriptBox["N", "2"]}], "+", RowBox[{ FractionBox["N", "2"], RowBox[{"Tr", "[", RowBox[{ RowBox[{"Transpose", "[", "X", "]"}], ".", "X"}], "]"}]}]}]}]], "Input",\ CellChangeTimes->{{3.793462980655712*^9, 3.793463026272648*^9}}, CellLabel->"In[1]:=",ExpressionUUID->"aca4f188-900e-4e2f-82cb-6708cc7e7dd7"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.793463471723394*^9, 3.7934634727823687`*^9}},ExpressionUUID->"2eb28450-94b1-4d41-8878-\ 74ef319b339f"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ssmat", "[", "N_", "]"}], "[", "v_", "]"}], ":=", RowBox[{"FoldList", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"#1", "+", "#2"}], ",", RowBox[{"Take", "[", RowBox[{"v", ",", RowBox[{"{", RowBox[{"#1", ",", RowBox[{"#1", "+", "#2", "-", "1"}]}], "}"}]}], "]"}]}], "}"}], "&"}], ",", "1", ",", RowBox[{"Range", "[", "N", "]"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.793463230474427*^9, 3.79346334132347*^9}}, CellLabel->"In[7]:=",ExpressionUUID->"74ea7e40-fb7c-42ad-8f65-2bd70fc9b5c0"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"ssmat", "[", "3", "]"}], "[", RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}], "]"}]], "Input", CellChangeTimes->{{3.793463327164769*^9, 3.793463335123438*^9}}, CellLabel->"In[8]:=",ExpressionUUID->"4e9ad724-362c-4e7a-9eba-cdeeee19cbcf"], Cell[BoxData[ TemplateBox[{ "Take","seqs", "\"Sequence specification (+n, -n, {+n}, {-n}, {m, n}, or {m, n, s}) \ expected at position \\!\\(\\*RowBox[{\\\"2\\\"}]\\) in \ \\!\\(\\*RowBox[{\\\"Take\\\", \\\"[\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\ \\\"a\\\", \\\",\\\", \\\"b\\\", \\\",\\\", \\\"c\\\"}], \\\"}\\\"}], \\\",\\\ \", RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\\\"2\\\", \ \\\",\\\", RowBox[{\\\"{\\\", \\\"a\\\", \\\"}\\\"}]}], \\\"}\\\"}], \ \\\",\\\", RowBox[{\\\"{\\\", RowBox[{\\\"3\\\", \\\",\\\", \ RowBox[{\\\"{\\\", RowBox[{\\\"1\\\", \\\"+\\\", \\\"a\\\"}], \\\"}\\\"}]}], \ \\\"}\\\"}]}], \\\"}\\\"}]}], \\\"]\\\"}]\\).\"",2,8,4,31323197559230362610, "Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{{3.7934633353696213`*^9, 3.793463342933799*^9}}, CellLabel-> "During evaluation of \ In[8]:=",ExpressionUUID->"4e796e7b-8de1-4aff-a02c-0d0b747b2413"], Cell[BoxData[ TemplateBox[{ "Take","seqs", "\"Sequence specification (+n, -n, {+n}, {-n}, {m, n}, or {m, n, s}) \ expected at position \\!\\(\\*RowBox[{\\\"2\\\"}]\\) in \ \\!\\(\\*RowBox[{\\\"Take\\\", \\\"[\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\ \\\"a\\\", \\\",\\\", \\\"b\\\", \\\",\\\", \\\"c\\\"}], \\\"}\\\"}], \\\",\\\ \", RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \ RowBox[{\\\"4\\\", \\\",\\\", RowBox[{\\\"{\\\", RowBox[{\\\"2\\\", \ \\\"+\\\", \\\"a\\\"}], \\\"}\\\"}]}], \\\"}\\\"}], \\\",\\\", \ RowBox[{\\\"Take\\\", \\\"[\\\", RowBox[{RowBox[{\\\"{\\\", \ RowBox[{\\\"a\\\", \\\",\\\", \\\"b\\\", \\\",\\\", \\\"c\\\"}], \\\"}\\\"}], \ \\\",\\\", RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\\\"2\\\", \ \\\",\\\", RowBox[{\\\"{\\\", \\\"a\\\", \\\"}\\\"}]}], \\\"}\\\"}], \ \\\",\\\", RowBox[{\\\"{\\\", RowBox[{\\\"3\\\", \\\",\\\", \ RowBox[{\\\"{\\\", RowBox[{\\\"Plus\\\", \\\"[\\\", RowBox[{\\\"\ \[LeftSkeleton]\\\", \\\"2\\\", \\\"\[RightSkeleton]\\\"}], \\\"]\\\"}], \ \\\"}\\\"}]}], \\\"}\\\"}]}], \\\"}\\\"}]}], \\\"]\\\"}]}], \\\"}\\\"}], \ \\\",\\\", RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\\\"6\\\", \ \\\",\\\", RowBox[{\\\"{\\\", RowBox[{\\\"4\\\", \\\"+\\\", \\\"a\\\"}], \ \\\"}\\\"}]}], \\\"}\\\"}], \\\",\\\", RowBox[{\\\"2\\\", \\\"+\\\", RowBox[{\ \\\"Take\\\", \\\"[\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\\\"a\\\", \ \\\",\\\", \\\"b\\\", \\\",\\\", \\\"c\\\"}], \\\"}\\\"}], \\\",\\\", \ RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\\\"2\\\", \\\",\\\", \ RowBox[{\\\"{\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \\\"1\\\", \\\"\ \[RightSkeleton]\\\"}], \\\"}\\\"}]}], \\\"}\\\"}], \\\",\\\", \ RowBox[{\\\"{\\\", RowBox[{\\\"3\\\", \\\",\\\", RowBox[{\\\"{\\\", \ RowBox[{\\\"\[LeftSkeleton]\\\", \\\"1\\\", \\\"\[RightSkeleton]\\\"}], \\\"}\ \\\"}]}], \\\"}\\\"}]}], \\\"}\\\"}]}], \\\"]\\\"}]}]}], \\\"}\\\"}]}], \\\"}\ \\\"}]}], \\\"]\\\"}]\\).\"",2,8,5,31323197559230362610,"Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{{3.7934633353696213`*^9, 3.793463342938555*^9}}, CellLabel-> "During evaluation of \ In[8]:=",ExpressionUUID->"99833ccf-f7f6-4574-bc6e-56a9fa33fd14"], Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", RowBox[{"{", RowBox[{"2", ",", RowBox[{"{", "a", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"4", ",", RowBox[{"{", RowBox[{"2", "+", "a"}], "}"}]}], "}"}], ",", RowBox[{"Take", "[", RowBox[{ RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", RowBox[{"{", "a", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", RowBox[{"{", RowBox[{"1", "+", "a"}], "}"}]}], "}"}]}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"7", ",", RowBox[{"{", RowBox[{"5", "+", "a"}], "}"}]}], "}"}], ",", RowBox[{"3", "+", RowBox[{"Take", "[", RowBox[{ RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", RowBox[{"{", "a", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", RowBox[{"{", RowBox[{"1", "+", "a"}], "}"}]}], "}"}]}], "}"}]}], "]"}]}]}], "}"}], ",", RowBox[{"Take", "[", RowBox[{ RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"4", ",", RowBox[{"{", RowBox[{"2", "+", "a"}], "}"}]}], "}"}], ",", RowBox[{"Take", "[", RowBox[{ RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", RowBox[{"{", "a", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", RowBox[{"{", RowBox[{"1", "+", "a"}], "}"}]}], "}"}]}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"6", ",", RowBox[{"{", RowBox[{"4", "+", "a"}], "}"}]}], "}"}], ",", RowBox[{"2", "+", RowBox[{"Take", "[", RowBox[{ RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", RowBox[{"{", "a", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", RowBox[{"{", RowBox[{"1", "+", "a"}], "}"}]}], "}"}]}], "}"}]}], "]"}]}]}], "}"}]}], "}"}]}], "]"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{{3.793463335405059*^9, 3.7934633429439383`*^9}}, CellLabel->"Out[8]=",ExpressionUUID->"4aada9fb-0136-4a39-9c2a-913465c6acfe"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"xx", "=", "\[IndentingNewLine]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "a", ",", "b", ",", "c"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"0", ",", "0", ",", "d", ",", "e"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "f"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";"}]], "Input", CellChangeTimes->{{3.793463374110407*^9, 3.793463394189417*^9}}, CellLabel->"In[9]:=",ExpressionUUID->"debf31e8-beab-4af1-a670-3db5979cd1c2"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"x4", "=", RowBox[{"xx", "-", RowBox[{"Transpose", "[", "xx", "]"}]}]}]], "Input", CellChangeTimes->{{3.7934633974629793`*^9, 3.793463402821336*^9}}, CellLabel->"In[10]:=",ExpressionUUID->"8886b158-c9fd-464d-85c7-fa6c18e364ab"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "a", ",", "b", ",", "c"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "a"}], ",", "0", ",", "d", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "b"}], ",", RowBox[{"-", "d"}], ",", "0", ",", "f"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "c"}], ",", RowBox[{"-", "e"}], ",", RowBox[{"-", "f"}], ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.7934634032724943`*^9}, CellLabel->"Out[10]=",ExpressionUUID->"8f8dddef-1985-4a97-a6bc-505f27bcc547"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Transpose", "[", "x4", "]"}], ".", "x4"}], "//", "Tr"}]], "Input",\ CellChangeTimes->{{3.793463405254016*^9, 3.793463412421341*^9}}, CellLabel->"In[11]:=",ExpressionUUID->"54e4a5a1-16be-4de6-9f0d-ce2e33df826d"], Cell[BoxData[ RowBox[{ RowBox[{"2", " ", SuperscriptBox["a", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["b", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["c", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["d", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["e", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["f", "2"]}]}]], "Output", CellChangeTimes->{3.793463412635048*^9}, CellLabel->"Out[11]=",ExpressionUUID->"a214a07c-8435-4ab9-8f4c-9012e4af817a"] }, Open ]], Cell[BoxData["Skew"], "Input", CellChangeTimes->{{3.793463029318808*^9, 3.793463043063738*^9}, { 3.793463202738372*^9, 3.7934632034497747`*^9}},ExpressionUUID->"60ab5996-56b2-4116-a22b-\ 4351bfe6a76c"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{"x3", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "a", ",", "b", ",", "d"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "a"}], ",", "0", ",", "c"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "b"}], ",", RowBox[{"-", "c"}], ",", "0"}], "}"}]}], "}"}]}], ")"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.793463132972478*^9, 3.793463166081422*^9}},ExpressionUUID->"7d739818-5a8a-4e64-8a11-\ c3eb86c80f79"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "a", "b"}, { RowBox[{"-", "a"}], "0", "c"}, { RowBox[{"-", "b"}], RowBox[{"-", "c"}], "0"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.793463135335209*^9, 3.793463144677956*^9}}, CellLabel-> "Out[3]//MatrixForm=",ExpressionUUID->"5e118c38-3841-4e44-a4f4-\ 4c504b5cc22c"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Tr", "[", RowBox[{ RowBox[{"Transpose", "[", "x3", "]"}], ".", "x3"}], "]"}]], "Input", CellChangeTimes->{{3.7934631023473177`*^9, 3.7934631552982683`*^9}}, CellLabel->"In[4]:=",ExpressionUUID->"33d7f345-4f7e-463b-8a47-f9a31fac8992"], Cell[BoxData[ RowBox[{ RowBox[{"2", " ", SuperscriptBox["a", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["b", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["c", "2"]}]}]], "Output", CellChangeTimes->{3.79346315553784*^9}, CellLabel->"Out[4]=",ExpressionUUID->"b8e16ebb-99fc-421d-8b9f-17c8b7116188"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "\[Beta]"}], " ", "n", " ", SuperscriptBox["x", "2"]}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "\[Infinity]"}], ",", "\[Infinity]"}], "}"}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"\[Beta]", ">", "0"}], ",", RowBox[{"n", ">", "0"}]}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.7934637531788597`*^9, 3.793463806724815*^9}}, CellLabel->"In[14]:=",ExpressionUUID->"a5e5313a-3cbe-4ee7-bf9f-86d6d149c6fe"], Cell[BoxData[ FractionBox[ SqrtBox["\[Pi]"], SqrtBox[ RowBox[{"n", " ", "\[Beta]"}]]]], "Output", CellChangeTimes->{{3.793463799306137*^9, 3.793463807151404*^9}}, CellLabel->"Out[14]=",ExpressionUUID->"9fbd9d22-95ab-435b-9d32-a01694cee41c"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ FractionBox[ SuperscriptBox["c", "2"], RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "-", SuperscriptBox["b", "2"]}], ")"}], " ", SuperscriptBox["\[ExponentialE]", RowBox[{"-", SqrtBox[ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}]]}]]}], RowBox[{"2", " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "-", SuperscriptBox["b", "2"]}], ")"}], " ", SuperscriptBox["\[ExponentialE]", SqrtBox[ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}]]]}], RowBox[{"2", " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}]}]]}], "/.", RowBox[{"c", "\[Rule]", "0"}]}], "/.", RowBox[{"b", "\[Rule]", "0"}]}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{"{", RowBox[{"a", ">", "0"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.793464485231653*^9, 3.7934645207379704`*^9}}, CellLabel->"In[26]:=",ExpressionUUID->"c80114c3-359b-4431-b57c-41ec3ec86c28"], Cell[BoxData[ RowBox[{"Cos", "[", "a", "]"}]], "Output", CellChangeTimes->{3.793464520980328*^9}, CellLabel->"Out[26]=",ExpressionUUID->"ecb93ba9-a956-4222-b24f-e0206d97dee4"] }, Open ]], Cell[BoxData[ RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]}]], "Input", CellChangeTimes->{{3.793464559625558*^9, 3.793464565208747*^9}},ExpressionUUID->"1e05e21d-787c-426a-9b90-\ e83b24238655"], Cell[BoxData[ RowBox[{"Clear", "[", "b", "]"}]], "Input", CellChangeTimes->{{3.7934667475081577`*^9, 3.793466752977477*^9}}, CellLabel->"In[73]:=",ExpressionUUID->"66f37bdc-cf01-4316-9982-d4a449b28fe5"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"b", " ", "c"}], RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}]]}], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "b"}], " ", "c"}], "+", RowBox[{"a", " ", SqrtBox[ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}]]}]}], ")"}], " ", SuperscriptBox["\[ExponentialE]", RowBox[{"-", SqrtBox[ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}]]}]]}], RowBox[{"2", " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "b"}], " ", "c"}], "-", RowBox[{"a", " ", SqrtBox[ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}]]}]}], ")"}], " ", SuperscriptBox["\[ExponentialE]", SqrtBox[ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}]]]}], RowBox[{"2", " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}]}]]}], "/.", RowBox[{"c", "\[Rule]", "0"}]}], "/.", RowBox[{"b", "\[Rule]", "0"}]}], ",", RowBox[{"{", RowBox[{"a", ",", RowBox[{"-", "20"}], ",", "20"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.793464222606069*^9, 3.793464305454688*^9}, { 3.793464449270852*^9, 3.793464461038485*^9}, {3.793466655978685*^9, 3.7934666677943993`*^9}}, CellLabel->"In[68]:=",ExpressionUUID->"4c3c31ca-4388-4656-980a-b8756fc51dde"], Cell[BoxData[ GraphicsBox[{{{}, {}, TagBox[ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ 1.], LineBox[CompressedData[" 1:eJwUmnc8Vf8fx+2d7ES4xrXXRSjyOd+shkoSUtkrpJJQ2QmVNERmyCg0ZUTy +ZSVhp2dvbn3INnjd35/3cf7cT6f936c83o+HlfS6ZKFKwMdHZ0+Mx3d/3+D J44tbG9rIjn3yINd2lQwflPoX++GJkq6a37ZeAcVHOcZWC5b1USXPI/xPxme BaR9lzcv/dVEESGKNn13ZsHXu4/ZBsc10cPGl6mHf8wAJYmznJUjmsie3X1k IWkGPPkgzZ00qInSjVNW7rnOANe+Yn7zHk00klsenrA+DdhUO8XRL020aDK7 AxOdBle+ZkimfddEoacd/LMGp0CPlYdMYL0m6mXRymbMnQKFoasK6l800YHm qlttilPgeIvo3sxiTfSM5sY7qjgJnvg5HA1L1UQ/ub8lbWyNgU02hePnkjRR /QulB49LxoBb+ry5boImEpoMdLPwGgM6dRFWc3GaSHWvJeVs+yjo2ZXr6BCh ifw9KWYjaSOA9GkqALugib7Jp9oGcAyBQvqrOXQ6mihFljzR1NcBdE8VsCRr aqKA2SPadTwdoC5nyIOiroleVs99qjT8DQZNzVWcFDTRBWb15Ka8NiAUp1Ja LaqJeCMZ98c7NYMIkcn6KDpNtCKrE//jSjWw0Tw/w/VdA/nTrvw93/MGjkc+ OZZbp4Emvoge7mwtglc7frw9UK2BLNnKnHN1SmHc9f1+PpUaqMBs7qXgViWs hrs2m95oIPUpQ4Et/VqoatbKHR+vgXztzlr9PdgCmV1NNXaf10A3niXSHRz5 A1vtKNYzZzTQCxtOxieJ/fCZjWjQZysNVCygPvju0ADUNsNrHc01UMRPg3tP LQehm+bTMwWGGmiuK73rwOsh+I1+IkxPUQMp+ShJ7tcfhU/Wm3N3yGmgJ57X Xj+/Owod/lV8H5DWQLYPjjzT6xqFq5NxApFiGmjj0ojfwuUxqNis/fInjwby mrb+j5Q0DmOfRTWdX6agAgOOlPWKSWiTdHlRbZGCImVEOnasT0KZx7a7GeYp yLTJMFl6/xT8fFvVOW+agvbRP/92omQK0rw7lmh/KIjrUn2ce8Y0rHBDol96 KEi8rjLconMaRjkUYPGdFNTy7qiqKvcMlLAMuavTQkHOa0aCbwNnoLmerHhY DQXNb+yXTsdm4Z69PIYWX4j4vZJZbZdm4aTqmrtMFQUpP6X7OJ0+C8OlGt9/ K6Mg/f8a/D4szcLjez52pBRTUFOWU7KjJBWKCD1f935PQeXq/pZTR6iwiN3f mLeQgvh3/uIITaHCEEYHz5EXFPTpTPnQHUSFRzYPPyjJoaDjdx+xeIxR4fCc WPeZZxSUZRd+NUmJBvm7ar2fP6Igbss2zpx8GkRKWTGRcRR0//Vl/qe1NOgd GpTjdo+CmLSvqtkP0mCdrGaf4m0KSmZzy/Dkw+HVG9wrXBEU5DeqseOVAg5J jVP8eAgF7bqtXl0FcHjjWubRD4EUtNX+pNzSA4dyDTfdE65RUGB4xaWOGzhs 32N9K8CXgpaG08/IxuIw/LJGxplLFPR4la/JMA2HqjU7Pul5U5DJhzhN1UIc 9u6a6hC7QEF3+pSXRj/iMMarZmHblehPRskj91oc7oUZ3MNOFJQe/zy2pBmH w3w3FWvsKWintfT1xh4cPnCzMsk7R0GplZL/3o/gUL+C4hRzhoK6I4wL7Gdw OLVjR4inFQUdSl0+1jmPw0THyWSzUxQ0teWSJbyMQ8OS6hJVcwoK4wm/Ir2O wzm2jBaeYxTkH8v6dHkTh+nnblAXDlPQKZaQpSfbODzy7jT7bxMKyvurFbZO 2MuMFHKZIQV5GB1SVyLsHGuu/5IxCqqKyeCWIe6fLJw4d/MAsX85VNXxVRxu bX0NPL+fgkK437278g+HhRbPngAdCrLMUoF1OA5t8q6/k9Qi9nfR79HYJA6Z 1yx/MlKIeoxtPRsHcVh0TH1yTIWCDBf8ksI7cWifxcn0TZGC+AL3+G//xCHX v3GJAjkKiudwvXDoCw7LD33Vi5WhIKki0dFzxTh0S0u39pGkoNa1L84H8nDI Pxd41VycgiQpd65MJ+IQGVo+0BCloLMqx567ROFQZIajfkmAgnQNLq59dcRh vcH4cBcvBX0oyrz98hgO/R5/2argpiBhZd/187o4bNwXqB3KRkFJJz9T9Thw ePP+KQtHZgo6Nmqr6DZPg/JDqj6GDBT0y/RXi3MnDUbEjOWybqgjtk4V+z8Z NKjWh75MraijVI8gh7MRNNinlvbnxz91pCxhxvjemQa1Oy0EH+LqiI+sNjgh RYPTZBQpPKKONlMXj7yIp8Kn11Mz1wbU0cFv0ueZL1Kh0S//yr4+dbS0YyzR 2JgKn/mpLGZ2EPevXnjiuzALLapTnBW+q6P/5t2fFoJZKNM+2l9fp46kD3hn aXPNwqVRVVu3anV0P/gHb3jnDExmqTbPrlRHHI3f0897zsDBwzMHxN6qI9GA 2i83wqdhke3e8k+F6ihzx4MVY6NpeMsrVMv2pToSSraaH2WehrL3+ZWeZqkj 0+v/2ebfnoIXm/WEeZ+oo3sOzYbpAZPQYOh2/NuH6uh1DpObNWUS8iw0cR+/ r4461bi2N6YmYDG/C/O9KHVkbqLlsMtmAq5ZxS4wXVdHWtmpXGNy4zDmT9/P lfPq6EXzhxszSSPQliZ76KmtOiJV12wuHhyBytuXq/daq6NqZqfTUrPDsInE XOFrro7cP2fvWNEbhkIuKi9mD6qjqKT5yK2WQZg9HRw+KKeOHDNc4K7SXngT P+D9cEQNbd7V+xW1+QumOepMYn/U0GkV0o6Tfj9hZZu6y3yHGqqre8tIN/0d bpVJn7P4roZyTuz1P9xaDyPC2M0E3quhM2152P6kL/Au72+lpBA19Idl5ujb PTkwRdN7JmO3GhJZEX0jIFkDPuW6upvzqyGd5IQLMW9rQd8u+xG6HWrIc4ge yByoB+IbJ3sd6dTQvj3pbomnv4PnNTo/pCdUkSzTWeZe/WaQf5qx8EWxKnoY SytvwDrAx4AUz7cnVJHohMLo7u+DQMrlSm7XIVW0ZDjF0y87BO6bHxqkP6iK LlpNvuuOGAJOCkunLbVUUXDr1G033WHA2Xvyv1VhVcSRL7vPOXkE2BmwCxsO q6D4/UfeXlIbB98UBy28e1WQOXX73bfgcaCxq+x+QrsKCl0TLxP5MQ5Y51wY J+tU0LbxtcpUpwnwLgvRYgtVkC3fzpb3kZOAkTmwtsNPBR3sWrQ/83ga+Mwf p6PzUUH5Z32fljZOg64/ZD0FdxWkLdR+tod9BrwqbXt384wKUosr/eEZNAOs PNTSSAYq6OoD7/3uFrMAWbJ0HtZRQedSOTzeRc4Cxf/+8F5VV0Gds/6Sr0pm wfbue9G1UirIOUjIsoifCl7+GPf1ZFVBgwp8A1WQCvg+fn4dT6eCDASRnOME FQTnPJmsXFVGUkGr33J30IBF8EG7nbPKSPHCEbmdVjRQeWF3su6YMooM+5Cg HkgDslZzbY79yuj70BVITaKBddVnh4ublVFbFrft3g4acBO9FvmnQRn5NLhv VS7QQDOrGWSpVkYfopRre3bgYP+i1JpapTISOHzsyn05HOQMrmqdKVFGodLm HW0AB9y/mi9FvFFGL27bdb2ywsH18hcFhS+UUbuGhfcubxwcf3yatJWsjLof cFxJf4yDGxo7D5vGK6PB6y5Jntk4yGv9duVhrDK6g3OqtRXhoNU3IqX7tjIK PnomugPhYItPv1oqVBkxctsz+v3CgeKHfzNegcpooHlOoLALB1an3gqUXCHi 38k/cHMYBxF/PQ5seSojdZF57tFpHLyOl3IzdVFGW6r0imPzOOjS7It7eF4Z nfWaAiHLOGBqTyjrtlJGG8OPed+u40Dd78SglLky4hn6eilgCwfnBNjZvQ8r oysbe/Q6t3EQU/yVUnJQGe2/LuPSSNjFlkG2W3rEPJb1Z84R5wcX994y3auM /rtYMBhB+ONKwAsfqiqjQt+HLhgRT3dvfnu3nDIybp/LSyDycfnttCklqYze BORPRBD5Pry2R9ZbhJjfvSv+bEQ9lYIdx0v4ifyYOopkiXonSx4EbHER9Xju 5er/iQMBq8OZpizKiBuvoFcj+oUtMTQ83FZC3O02UiJEP70SK+e7V5SQsfRX rsznOEjU9heRXlBCP946X/ryCAdfO9QMvWeUUIvHObbQUBzQ/Ke8SkaV0NCa X263Fw5EdmU/2fqjhMqRkEwrMV+TsnOfTTuV0CrjwSsXMBz4WguNP2xWQjJx t+5kyuPg+9M7OtLVSsj247LtwiINLOkYOnhXKiGz+RTbnd00INW1EVNSooSG t0SLmj/RwA3hyz2mL5VQI7J4ZhxMA3kfFRgfZSmhE51jf9fP0kCrzYhST4oS +huyIHVuHw0oJFsFe99XQtiF03tJc1RguY8nryRKCfFfY7aIbqCCsO6Gxq1Q JZR0vKriWRYVdO0+QHrkq4Taj/FHjR2jgpgU6eoSayX04ERUE+vTWVC8/8/M ljnRj2MZb8lus2CwJ1Hg0BElZCAxHcaoNQt0RTncevSV0BFRkW7WnzNgMnWO bVtSCbm/XH/qR50Gpumfjx+aVUTGnI53BFYmwdz9vg2mcUWUY/DBgfZxEqSE rBd8GVBEr1gEvv8OnASz9vtY9doUkUjaSdXOfxPgsVQJVKlQRAIJ5vtmRsdB /4tX6vwxiujY7kyu18mjwL8ola9fWhExmr4ObRrpB6TsCpQipogO69mnFmn2 g4b4bh/rXYpI1ST0/sWIP2DPtV0/mjkUkfclN4WoPX3gq078rep5BcR/xoGL 0agbcH++u/gSKiB3PY5UC7c2kFd/vePqWQUkwbTA0vKqEiRr+BvmWyog33FJ WUezchCb7vuu/5gCqiZ/f/xrugT4XvW6exhTQOyyj5+/OfwGHJA4byBBVkAr bzb9TCSug3Z/LO87TR4dUTJrvni/HDLIsvpLRsijzTERzzsv2+C/h4wjVjfl EV2ph8uEfzucXN8+Eesnj3oTnnucMfoNG1tWFJbd5NHMRmSiZV8HTA6e/vPz qDyaJtuAF9vdUP33L+NAQXk0qXyiaIF5EEpj34tec8sjW23v0znOg1CosE5i hFUefWN9vJ2EBuFGGFw9tiaHMgKvFO0PHIL1yu9fSw/IoTuyvlGzf4ahXeQT waaXckhn54uUh6FjsBEssQY+l0PKlPr7pt/HIFi3XiOlyaGUQqk70gLjkOQr OuD7QA7F9nuzgdxxOGz//KWQvxxSGPGRLamcgBaiTKnwkhxK3yEmZkw3Cas7 XO97XJBDzsneoyMHJ2HOMQXfinNyqPzky0DD2knopvdOz85QDp2uURgwrJqC HUu8qqwH5BDfSB/GuDYFTYuukt5pE/HtmJI/a01DeQUdZgZFOWQl7bm1+8U0 nBaqaszlkUMR165laYbOQNtWiS/HOeTQpdWoq7FFM/DH/fAPy4xyaEFcar5x dAa+YjJOOrwsi+7OfRJkN5mFPgs/HKl/ZNHpbNMwsfVZ2P9axTKxUxYt6Pr0 x5Gp8MSFByagRRYZhfRb9x6nQvVBC6VHNbIoVFdaeTudCjNTi8X2V8mieyvv vdqqqZDXWohnpEwW6WqLPwyapMKFX92LWoWyqCkBtZiq0qDTHb2JPzmyqLUl leJ+ggbbjNK7o57JojumFeunL9Fg8SeHqq5Hsmg6QqMzrZAGZQK+vgu/J4tW ktvvLtTTYIKGTLbibVlkY+lE5RuhQf/8ieigQFn0kYH3zltBHI67HL5B9pVF v7qTaxVUcGhNKvRu9JJFmrwLZZ6GOPzWy2Uf4CqL6i9cD7tig0Pdpz4nSfay aG/e6NED3jh8adFs2GAji1Q7jE/9CsHhbm4NbV8Lol9kgT7SQxyuRf4TqTGW RdrNq7U73+LQE7PecRHIopu3defyKwmeWv+4LbhPFhX9B1SZG3BoViayUKUh i279GmaUbMdhpW/QqLuyLGrJC6ff/INDZdX+Dh5ZWRToxFaTNE7wzhRoKJeQ RSMP/i3+peKQOzfrk9NuWeQhfv4I9yIOQxwY33DyyyJeo5moiRUcvmsyjWvn kkWrmodvXN4g+Mwg1iedRRaZHZOLqtnCocCb5uNudIRtzP5khOAjEzFBNbU1 MjIYE0n+RdiBsWd2rvwlo3Vf9cQI4nzBejqOqGQ09bLuKQPhr89zuOnOBBld O8BQeoyIx90j+85iiIx+rr4RcPmLQ+yw10PRXjI64mAwYkzk6/vx7eXRdjJS Ga4993eM4DG5RfPXjWTEk7tR703U25GoS/H/RkaLnboBRW04ZGMJ5gVfyYg3 yftbzTcc7r/2ZZ61koyeu0qRc4h+eo8ytzaXkFGs/HWGk0S/n506UpT8loys aiWGfmTisPlr3GOnfDJyP2h+TPARDhk02nyVssmoNvh7v0oYwVs85zQ/J5JR mKAQR5MtDpNCM/mjHpKR3YdGrjMmOPxOG/17/C4Zif17xFKiTvDxr4vFg8Fk VPbkgeo4PQ4d9Iue5AeQkXPVb9LnSRp8XLjk53uFjGYFVR5faKTBpTuhe5lc yUj4ktGSSSINQpNHpXJmZJT7r+mUhjANLpT8TpwzJupzoIS2/aNCGbJIQDkg I8j04NSpViqMYczWOapJnP8Rcn4xmgrNUfFHHxEyqpJ2kRgdm4URaqtJOgJk lH+H9dLzillY/OzAdTpuYj7HUo4ejZuFwsF1+x7Tk9Hhry1uzhqzcHBfV0XJ pAzKDrSI7r84A/ny96SGDMugb0evWUntn4FGwo43Tftk0JZmm6Y98wx8uTSl 190kg96XHdn9M2kaXv6wXrlRKoPIr92KXn2YgnQqEtDwtgxqrnvvdf3TBAwS +s/udogMOtTgyv/YdwIubztt1gXIIHZkIZcpPwFprXl6RzxlCN47/DX/0Tjs DVT9aH5CBpVb7n/YYj0GS2sOvD+/WwbFxZirxpUNw4vnzmUHvJZGmik2hQB2 w0njkIPledIoeivgmPhqF3RRyxxay5BGQfPZjEOULmjLMCoR8lgaXdrDJqad 2QEPvfRKiwyQRoY79d/tvtIGZRZvJDz6TxqNje59FtTZAHvuJUcX/pZC3Kd6 jQuiQ0BbLemVQ5MUyjZL5zHXeQJ+br9oFmyQQv6f6SqWXDNB1dXS3WGVUmiG NX3GZ+UVeH62rdAyWwrtMfJL2WL5BDyVdjRvXpZC4uc8JKznG8D69zBhcy4p lG56Wld/uQssMrEdYGaRQg2P16Xl3nUDmsEDx4ptSVTs/rqB36MHDBalF8j8 lURZqky9v9t7QU1Khf5qtyTyJl8O183qB7Geiw7PX0gi4TmPnZXbQ+B2zs3b 1lmSKGPLKi/TYhiE9DMUcKVKogt8CgNNOcPgsgXvX/84SXTIMCWa3nQEWO5X vX30miRaZ10Lt40YBXs4PPIXD0oiR/Gdzw62jgO7qp+xUvqSyN2U6dEB8QmQ 5Uu5bL6XOF+9nq10YQLI9q5pv5KTREF2F5Pa1ieA2qv7Nc5ckqjgDR68xD8F fB0WXjxilkTq+qwDKtZToFjA+h7cIiFp4d3RBslTQDeYZCE6T0IZdPs+Duye BgePfxho/U1CL6wL8WauGRDJIFxN10RCvVtLQeEmM6C+NChP9RsJvfl8pnkx ZAaYSZhcvFtBQtaHKhN2zxI8Nde19l8GCU1+MnLdVTYLknIO9F9KIqGGfM87 yeOzoNfm+Zf0RyT0W/ZQ7A8BKnD44hWzeouEast8urQvUsGFx1uC7z1IqMlv Jv4vwUuvTJxX+x1JqGZ1yeyzBg3Q1ur7uM6SkK38t19yBD/5Oj/K9jhGQhu9 0vVdBC8V71qKSjQhIfI1Vt09H2lg+YetZw0goTNiUY5rv2kgSEuGQtIg8gsT Cw8neKlqMkbguBIJ1Ye4zssRvESfTl2+KUPU617D7ULwktFJi958MRJ66Hwe ahF6Ooq5rKpTiMjfvWM1idDb38pFnzPzkJCJqUvtA0KPc/iE3dZkJ6GOrd/7 hAl+MpMa83BkIKF9BzNCKQQ/ib+OTxJflkAjJsNNPYTezxY8b39jSgLN/Az0 4/+CA/kQWdmOXgkU6bpR30Pw06txfJbSKIFeL/3aq96NA8qJ8g/3kQT6fHPP fv4RHJSWRdyYKpJAQQwzjrdmCP4jmf1nnCuBgkcFj4Yt4ADGCLJlPSX86Vvn sK8Q9cz3N27ckUBNT4+oSGzgoOHMywSbIAm0NHypFBE8dPzrlXPFPhLo7GMV SRrBS22KetI8jhJIiqXV/gVh28QzTXudkkB2Ck+uzW7i4M/6r3f1xhKozCze //MaDpxcngZI60qgi/od0SJLOBj/6WAQqiiBUh4dHmCcI/hmryJz7x4JpAA+ V1+fJHiEufyF/04JRBq7/C9/gODN36ZH+BgkUJaM3pDfb4IPcztmXy+Ko0re qNWeBhzcveb64PCEODK/eBb1VeLgsfEiZaxbHLn9tau/8QYHKYK32sN+iqPS tfq3Jc9wUFCSufvje3GUNWq3zHQTB0W31SpP5Ygjp3sp4yLuOKg4XWWHJ4oj lzLjzuaTBA/9682WDRJHHtotUSRpgm9rPU2++oij9w6sJyvZcdCTsDp53lEc fWj/T3ODRgNTe3epJpiIozuip7e8S2hgjjmvWX2fOIo9et47M5EGVn5rXf2p JI6qwauNIH8aYPO3+MjIK45sVNi0dIh95jEZss1gFEfKMrZdu7hpQFjo8ub+ JTG01+Zs8otJKpAvvX/Qt1cMGea/5+5NpgL1qD1jOxrFUJTTYe2Iy1Sga1UY nY/EEMsYzWHAmAoOLX37OZgrhiznnY2rZ2eBuzaT9YnLYkhy4LPABaVZ4MMS vzrtJIawpYqPy8szwL9DMi3qtBgKDffpM6ueAVH+YOjzfjGUbUg3fcpqBuSV 3vBSZhZDyTs0mXb7TIMx7flQ9pQ9SHigLaPBjeAjljCp3Ng96JxmDf0CaRIs dnDXYqF70O4uGRpnzwRgClDmCHTZg+63VfWRDk8AmTL3J+Oqe1BhQnOHvOg4 cNbpf1ldLYrGV6T6sx+NALeXOlYmZaLIRfN7pvbBEeC5+xFjQ4EoOiv7N2vH AvH+XDe0a3wkihze/kp7cmIYBMF8/m57UXR0nTP7PMMQeGJ6LYS2LoI87Dde nI7vA3XWXJa7tUTQ7dPbR99Qm0HDN1f6NDkR1Cm03pur3Ax+7oNvxEVF0Naa fOD270bQKurLLsMgguT02UbxHz/AwEBnlWrzblT4rEDoSWEtWHHPVjDy3o3y VAOlOOKKgGLg/m2fHGF0gOvDy+XjEKI/xxVHEoWR1u9Hvjanv0ArQ+fT1neE 0dnOjyY+DNUwgju2EPgII6HNxNKVM3WwO+ePNY+uMJrO/LvzysZPGNMS9u79 j11oj/cRZbXtdiiuk9BLrtqF7J8QgPDjNyxOy2dJebcLecb8R/2c2AEH3VvP RSTsQv8CXW5gil1QZ0ua/ZT9LnS5gzOGzqgXjivWOy4uCKFba3Pfz6YPwqCH vbEeY0IotXOMMWV1EPIt4WV9nULIIPJfnODpIWjwRZi7tlIIiXMmg2L2YZhg 7VmREEWc91a/LXFhBBpF7uDXERFC51WKJQ9vjsGeKUmDQi4h9JBV2+f20XF4 +YT2BYltQZTWGMP+NWkcporYQ9ZRQbTGz+2oqj4BF9698+p6LYh2hu1PuGYx CbP+nKq5/h/x/Lye4ZLjNNQY1Vhr1xJEbkUuJu9SpmHNNK+6urwgsul5e92h dRqOLzeljnMLIpYT0Q0pBjNQkc/s6qk+AeQ18eC7Pscs/CSslP+mSQANLjBV X9w/C80kOAbYqwXQN+2m95EXCH5S/nYE5QsgrgOR0udrZmGRiZGUSoAAOnI/ LyPamwoNj0nbxHgKoJhz50zK4qmw/RRD3Mh5AfReL+oCLKfCJQe0mmwkgBpi u7FTDDQY7Z6h9k9HAJkl/pHok6FBYZ8QV3MlAcSuLNeiY0KDejf1W1j4BJBj oEq4020a/BkuyurELIC0Lv1gU8umQbuYNf3PK/zITuCuXwOkwbCEjy+vDvAj 6TXD+87/aJA37Wl/Yys/4lF+L+XIjcPnz/0FFOv40dhvnYvysjiseasVNviK H41fdAvgscDh6VL+Ur1MfvTpnH2YmhvBV5ULM4nx/KhtRKZF4DoOA6pbJBei +JFL3cwreJfQ89/fWR+7wY+2MlSd1VJxmNz84P7Li/zo4LfiE84FOFTs9Klm dORHWZ+Semw/Ejz059iqnSWRD/vxQMFaHB4bVVarMOVHxjV5+Y+bcdg/zekq qMePLgR1rbf04PDy/HTKZVV+xFoWxtY2gkP6lYbmH5L8aIX28lrCDA4fb71k kRPkR0d3ff8nvIBDaeYY/Qg2ftSS1WR6fhmHxZzuvn/W+ZAru4iO0zoOjflM XurifKhgICxVjuCfDmFyf/wwHzpuZ3nmNcFH7hJMAvhvPpR5087xL2GvkEcO H2ngQ2kRI+9WifN3lL+G5lbyISnV5ycRwUsimlkldO/40FvTtjOmqzgs3Bc2 czabD51okJ+NI/hNH7OXLEvkQ7MRP3We0nD4y8TAmu8uH5I0tAt0mMCh3TGx +xeD+VDgrfl/0/04xE9tfP12mQ+dTOJg1vmNwzDb3hVpFyJ/l1QW4+845HWs UA215kMGD7fdBauIebonu/QcIe4brzx/+Q6Hmj6BKXsN+NA5nxcHtrOI+fpZ Nz+k8KGi63e/736Mw4lwQX1TYT5EQjEH031wyBH8Fo/n4EM1A8Znrc4QPBR4 OHtwgxfJFU++zziIQ3+fYI4bQ7zISS301AQPDlMu7Kqqa+NF+0o/jk0Q+1Xl 8v4Kfx0vsl0+ZBTcTYMsZ8e6XhXwouc8V155pdGgolVo7GoaLzI6fDmi/iYN Hj+5GzN5wItm5f0+fz5D8L3psRcDV3lRlj3/u1Begv+1Sq7xHeBFXFqDmncu U+EhtRMK9mq8SEN00HPCiAq9Faf6CiV50S7TRmPaLiosJokZGbPwonCOK3u3 ymeh4Y7bfIFNPOikLH2kC20GurFJ1NV84UEd3OV/jT7OwLuM5dd5i3nQ/Y3T WoNhM7B1dXawIIkH/fK1tjvJPQOdxi3f/nHkQeTv9swXRKZh1BDNSdGSB5V3 TB/07JmCBX0xQgEmPMgiQkxHP3kKLrRWBvMo8SC8rdrQjn8KMoQeToqa3ImS P/dOz69OQECZajm5YyeiG2MM2x8/BqPkxPbNzHMjlmrBvO//jcFGsZOZkR3c SM1k8qIjPgrtOMp9yjK4kaSDHHuR6SgMGonhFNPgRr1XO8aPUodhRYK88aTV DnRf1PXG5M5ByHZ2wplefwcKFN6eXXEZgFakvAgRyR2oruvR6OeX/XChQBqZ zXChi9Yc0pjyH6iAxPXeh3IhzsYMWz6ZHpg0LUC58ZITDZZUFoX0t8FrgF6M a40dbXy38TH9VwG/MiE98gA7si0BN5+nlUGe7yG2BjXsaBflVszCwWL4ynLj 6eU4dvRMlf8Kn0ghHL2wzPdbih3FtQTadujoQYsnVLZnR9mQU9zDLBlYAdSn uhfV0lmQSdyxG3EtbcBvTkVhVyQLig4bzOF/2A4+Loef3/JkQXtfb11pPPYb /MeiWPdTlwU9EFNoqq/rABbSN55eaGdGn45i7tuvu8G18yL7szmZUZgu0+Dx owOgwsXH5+4CE1qhGsZ2rA6ALa+vz690M6GYa3dqHp0aBFE3PDmxF0xI9aXN xdWtQZD0tKKv7yATmhUVKu08NgwqWmxDhW4wokescbZsDaNgq+vNh00HRgT5 ocM/gTFwcJBhctSUEWlsQyqfwxj4QSsw/yDIiHbIWO9q/zsG+jjXJc3fM6Az wX0tErwTgMR/wkoniQF1Wl+lO2g1AVxFsu+KhzKgdumAyJCUCUCTP/p31owB TbyN26VP6J9t49SaO5P0SEhcWC2CNAWMjuErl5voEX86+yM1uykQY2moYlNK j8pls46OpEwBHueZBNlIenQzdjTEkncaSIXpuVdL0KNnllw08YVp4Bb9ILWA hR6Rzg0OQ7kZUBA30vSISocynloknz43AzTT7+k6fKJDIk/cgfXXGWBU0cu+ aUWHpk8/cgsOnwVvCnL31evRoZgAnRKzolkgnHrpwiMSHbJEUhzNQ7OgY5nl 8dH2bej4whBM61NBQVfK/ED6NswUi6MP9qCCkHLVk37u2/A0Z0Dcp8dUQL5p xZO+tgW9dRr8tEaoYOXs9CVKzRbsrcOUvNhp4Kd+SFPt/S0YG57uZqJKA35b uXE00hY8e/pE68hVGjg0sI8WMb0Jq5SP/Xn+hAZE0a9ju4o3YQxPnhRdMQ18 Df/HhZluQmkg+uUBoa8Tne54t/NsQtZ+5AcJ/X3BUOynR88GfN+4sCuG0Of6 Mu+VNrM3oO6dC2GTejjgYTa+9+jiBhzvkHkyYIGD0bGuabLOBrzzMPCwtwcO PtZ5H6mg24AdGcIv7gfhwD7mCftI/DqUTFD/djcTBxoX5C8EnF+HHCctZlze 4YDlSOU3Trl1ONQv699cReh/RXP5zLk1qJTa9+XnDxy84RyN1qpYg/KO+3XP dBK8Mhsw8e3WGiy0zDt1bQgHp39xmp4/tgbfzChlkKYJvnuTkTcvtAZP6ISX 2s7jYCNOkyVqcBUuenGaSC/joPlSvatIwSp89nKY48Y6wYfmZ2vfXF2FXzfa W+0IPvOn4DKGB1Yh82uPoBaCx47w3YrsZFmF90r/LP3fFv8rNOrVvAILH6oe dCDOL7QVGNKlrEBMhedSEOGvrtgg+4nzChF//pksES85oZVBQWUFnnm4wmhP 5OPt7+b0eWkZinAxDpGJfDHrtS8n0TLc7ZV55yZRj4BunOT4nWVIi9/p5EDU OyksFX7j1DJ8wrl/oJ3oR+VqySC32DKcfvUmqpvo14Oew1j2+BLMyEil+RD9 dPr0J0Pn3RLsiav/nED0WzvtyvaP60uwX+Ju4fEHBD8HM9s7GC5B9vzq0BRi Pn/OJ1ctci3BewrtfDeI+UVKfAkWy/wHr87pK6wQ87ahO/3n/YV/MLEh4G0S sQ/KQ5P6Jpr/oORNnbVmYl/anvNs+NQtQj4X38QdrTSQdyvnLOPDRSgfz3JR gNi3Gy66n56eWYSKzlp8H4l9lJJ1uIFm/0KxmTu3ek/SwOX8tyu8/H9hNa0h teoTwV/cPrcODi5A2bSgk0kJVDDvq8x99fUCPJrg+MbUhwp89fOl200X4L3Y s6kqe6jgWtPz44lB85Ah1SvIyHMWaGs5dtcdnodxZNNTq/tnwVKShMuy0Dzc 5zwQ+IhjFgQ4pV23eT8HK8RYzl3NmwF/p5UO7/2Jw5aRiYy9LdPAr/ilXSKh 6/baHfmknzwNloLJfst0OFz0I6XoOEyDFR6JjPK9NDhQ8ukl78wU2NDm+3cg Yxb2yHsHJy1OApZbK5kmvlOQv8u/Qqx7HESbXSt9wTUFEw6zdUc+GgdsQgs/ 2F5Mwq+Kd+zZDo8DjvyZpe+9EzDSUW335ZIxsLOp3+yE8Ti872dsKxA5CoRF a1eshUfguuJJu3PrQ8DKTTqrNagb0t/WWi5t6QJ3r1yNeVzSBTPpOf2f7u4C n4OqL1nQOiGDWJhdnEMnkIl3Nmi174BPpZ/f6J35DRZgdm/LwTb4eK5CsHyl FYhrHlJ+zvsdys6/w5+ONIC5pGSX+eQIqOnWkDWYHAGCGJ7UmuheAFE7tBWM dC9A1RTnegHtB+CtvlxK7d4H8JRmV2XUfzmAYYk5UBnLgVfcvKZqnpSCVYNT aSb3SyEdXcm2c1U9ENz8cPlpaj2s/9l9V/NUF8jXS2k7U9UJPQJ76s8qdQNR nk9isVFdkE2mlymSsQf0lWnk5B3rhkdu9oW0f+gF+lymS5e7euBPhQHfawID YFlbMMp14A/0MPR93Ts9DC5YuZkV/B6CuskLP3CrEZByo9SfTm0YsuG+04zV I4CRS3dvdPQwzE+5KqecOgrUpmjvhLRH4PS8X1bQ0XGgrSt3ryVmFHpnBiSI vZoC6Rr7jwbQT0D9peUPFOFpMPDSWoXfbAJymQW2GkdOA0ej7eO5CRPw9XLg Th/iOxEAGbAM8iSkHb9xp4qLCowDq9kf6U7Bqpy1F62BVBDxkVx/+8YUjFu7 UTc+Suxx7O8h609TUC3vJuPOzzSgF3nvTcy+afgxpKrqrfYc+Mv7halJbgZm 5m/9KveeA/NkuSIHhxkY027wp/r5HHgv+lao4ukMtFGE653c82Ay9u3eCoZZ uPob6tJNzIOsxETtNw2zcJiO7hCH2ALQj/F9obcyC78rYdYCpxaAFCdTdgiZ ClPC0TV5uACSro/oiAVR4X6VL0XmT/+C9EZjjpjdNLi3vSOxquEv0PP7Y6+m R4PqN2dvKG/8Bf33lVwLztKgbMMuQzbHRRCbtBEqlEyDkpdV5PzjFwFP32lN 5lIa3LPLkHO0dhH0jCm0fm2hQX5Xnzao+A94BHc9yGPGITdXZJnK+X9g5L1e 4XcxQm9/SE5NffAP5KwZFJZr4ZDZ9m0o+9d/4I8nzyvfIziko691Dlj8B5gf jv1etMPh+ose0zHZJRDWwnge+OJw6fic0qkzS+Cizbfwk5E4nE0TXVStWgKP G84ON+QQ+t6Q0pU2twSSHdN6VT/gcHjapJJDehksi1+l2iCCrx6dyww8vQzS +UQSTIn3Qreub+R4NPE8me3cWgcO2weiPSwrlkHYynLn5UEcNkelm32dXQZe ARMFBZM4/KHyQV1dYgUEc5JuvcBxWNf+TeDZyRXwK0xH1P0fDr/c7F/hjFwB lsr8+6cIHqqUWuy7XroCFKSni1Q2cVjWwP5lYnIFXF02cdUi+KroskTuadFV 8GON7cAmYb/etfdO9bFVoM3iqhFD2C+rjlykhK2C+Pqxw7+J+zmuDiczilZB wBOvJ6NrOMzg8t+7Y2wVRH9VUitdIvjkw73dN3etAdvbbw2P/P//h7ZZm5OH 10DTyVbWrGkcPqIvG7IKWgOC9fBzxTAOY1/+rK15swasxOY/PO3GYfSJ4XyN oTUgKqJorNuEw4il5fuZ/Ovg491rXWnVOAxO3+HLbbIOXhlJDtWW4jDQSNoq KHAdqL4q7//wEodXZ3T3TxesA4UvTOfdk3Ho8/i4uM2fdVBWtPF3MAaHnvtc GOp2bgDX1QZTyQAcug5eH9c8uAEiVyrZFFxw6BD94HuW3wZIkzX9u3ICh+dU c9/sfLEBwj//bXq0H4cWQc3+M5ybwKJYo0qSi+Bn6XHbMwabwGWZP13kLw0e +r5uUH95E6xGZLMNdtGggbAca/bvTUBnP5XdnkmD+6D+DA/bFjiPnadjuUWD Wm4WTSH7t0Do/OhBNhcaVCoOfmqbsQXUi21PR0oR+382/ua3li3wwEv0HR0d DUox5NtrM20Dvs2bLKf6qFDYvF2O78I2mFuw0At9RIUM/oJ9LrvpsJwXRmcl aLPQ1qGg9aMWHeb5oGqmqmoWFh0BDVzmdFjC0NbOnXGz0EniQmlxFB0WejSU 8bv8LPz6rfIh0yIdVlbddXn2+AwU+XAy2mYnPZbtwcptITgDfdPHg18p0mOH onWyb/ZMQylfHi9LR3psZVMhhOw4DW+JuhjnNNJjZ+Lp70k5TME+5lW9lSl6 zOvR7l1Le6ag1tx9DTNmBqyOPSwpp2sSjtaUSSzqMWABA/s2n5lNQiMfzjXD fAYs77/TH53lJiDTl6I3I7cYsYOfQbxC4Sg8V2iaq5PBiN2tXVs/YD0KixP6 Uu9VMGLXLIQ5XBlGoYsnyx3NeUYs+Ytn8trpEVjLb+t8y44Jy6KbdypaGIJR bvTC0vuYsf43yludnP2Qlcs83InGgvXvzm0TcGmBNnK2SJudFTu1vMElm9AM Cw66bHPIsGKfUypiV+82wePXA4M/nGHFuq15QwwO/YSJ45nXmWpZsV+DamJX i2uh7Jf5K3mpbNht13mX6Pp30Ng/3mn6EAfW7OiVmGv3FSQ+Ss+qcubA1Klv 4naw1oDJVy8GH4dwYN8K/A49eVMLYkc+2ekVc2DwMOnZh7VvoN181DZWghML 6ivJ07zdBFyU9p5SXeLEyt8A/lSFDnBrsMPQN3sHRokek60VHAL95UcvBlbu wODCUA2/5xDYH48SQ37vwApfZm6XfR4Cc8YFU3dZuTEu9eiYRadhYFcY/CDb ixszkqZwj+eMgP3+Mr3tmjsxKbXTtxiZxkHiiWSmXrOd2LP5j4V6ZuNgXp5b dch1J6Yl8fdlcvw4eNm7HEZ9uhMrTzD4r1JiAgj990OWZWMnlsfNkH1SZRKs Mu8rF3XiwU4u79wZIzoN8nz//nrmw4NtCbE7TllOA8uB18OSN3mw1I/fdx6+ Pw3efZTikn/CgyV8NcLX1gh+8uKy16rjwd7yTnTSGmaAQFfd1bJWHsxz730q 2/oM+GoUHrN/gAe71f7jAK/SLBATX3qPrfBgiSwQG4ueBe3NA0zHFHkxx+oR Jk8t4jt5IGV3szYv1nhmuKfmHKEHCyxVTxnyYkGRF93oIqng3q0G6zPneDHS 4ap8/iYq0J275d3nwYsdjlqMmFyggvFzBuH213ixI++LLZMEaeCg9ocC1zhe 7CJ9dMYtaxqYe34RTqbwYl/mMuIr/Wng2U75dq8XvNg82wX/H4Q+XZ1M27yC eLE3kUI33X4Reva0Nd+/n7xYsrrU1bkJGrD8yisX2M2LCX35j8WMHgfvUqPM QxaIfA3H5f3UcfCDP2piJx0fZvZqlJvtEA7G790OydrBh5HO9zNo2eGAnum2 oKYoH1bS9YF52RcHe4IiX9XI82HFQyHy5lE40Fm8ZWilzYf91UmPNUjCgYX3 rZ4JQz4MS6lw/vISBxdHI65cP8mHPeHqwTvLcBBzLoKN054Pk3ayuxVeS/BM e3hGmjcfRubkC//cgoMqs3Bt1Rt8WANZ9dy9Phx014T9gtF8GE+rQ9L0GA4W 9cNcTibwYae/tTb0UHGwsyR0ffg5H6auoZxwdhEHiiqhj/3e8WFRtUlvvVdx YJwbosBSxYfdkfzRv2MTBw5iIejpDz7szcXtFQOCj24mBFsrdBP57N8c3Sbs xB3BtIpxPkz4uXCKOWG/vx1022yRDwt5q0GiEPd/bt7c00/Pj7nSlT/IIvxP XLv54dJOfqzrdQ7vcyI+A+3GEXoxfuyqX+CABg0HYm43hh4r8mNp4gaGluM4 0O2/Hiijy489VL/1lOUPDk5ZXd9ZasyP+XdYmh5pxYFPY2Ce6Sl+LEpAr1Gi Dgd3TAIPdDvwY8n7ND9Gf8RBTlVAu6cPP+b2JD8rIh8HUDvAa+MmPxbu5avD m0zw6Bt/hrg7/BjU/aqtFU3wb8Y19fc5/JhWz7WP++1xoLTrWv3BIn5M07uN hXQYByYP/OzaIT8mVJ1olU7BQVDo1djlHn5sc+q+kcsWDTxd9pW+M8mPcY4r qL8bpoGiS74VIkv82ELYUFlSLQ1M2l+ZPMArgHXvuT9uFE0DjF2XQ5vEBbAp 6ltbTjcaEDe/LOSoLICFflFi9jMk9hG7ZBRpKoA9l1000lijAkS6mPk9WAAr eBff+MiaCnqTvHXO3RPAbC9mjSUpUcESj3cjNUkAu/TT9LT51ixQpvfa4CkW wLSp6Ve6MmZB0pCHjfW0AFYYH296t20GfDjjgU8uC2AhJ1SdzNNnQGOLe9QN ZkEsFR2v7HKdAUxf3YrTSYIYf/kh7f1/p8Gl5y48o1aCWGCTcdSd7SkQdz05 Lc5ZEMPUUo78rZ4Cb8wb5fddFsRYkyZKbKOnAG1L57+4O4LYD48WdmXOKeB9 ltNXt1IQk1CpuC/GOgk8BYraYiWFMKWT7xoiWsfA3Zlxex1VIaxiXxTbavQY KPgqOju0XwgTOHPI+an+GJi6fJtJx1IIG39tamSTPQo8ftnsHYoSwlzE8t2A +whwi9pO3DsrhPHVvwl0+jEIos5rSQ+uCGEXLQblGv0GQZ7Whbd3mXdhhnue /34iNgjGhlvrB8R3YU0/WT6F9/QDF5C3cufkLqz3YU7aFEcfcFoxs+0v3YWl ikaTW3Q7gJ1nilh0uDDGU77x+O5qNVjvZm+cvy+M2VlYzhZf/gqSDl8POZci jBVwPEhQmUCgRd5mgPJBGMPK7undzfkEjCYEs/pGhTEvpZSM4rtvgILLIxmN Q7sxtNvjtrFINlw8H6P0h1sEcy1Pe/rL5hd8+Gu511RUBPNVPn5kq6cRqhxw jy2SE8HuXyv4zaDaDN32mFCjMRHs+pthY7XXLbC7h/Gthq8Ipilev2WR3Q6r rEM1Yn6LYEw3xPIfefTAOyf992mmiWIWjaLU6Phh+PinoverfFHsj+Iz/uHp YZhmOvCMXCaKlQY7Jrn+NwLfHTjEJNwqikXsIF3unhmBXQoiTRuse7DQNkMP Tu0xOEyIDX/BPVgMk9gJ06gxOCtxSwuX2oNNsivRPfg9BumEZpOHDuzBuD3w z5pXxqE8Q5VL3dU92KXSKoaraRNQI9j3KQjfg72jlz76epTgsRXZ7x/jCP/e n4O7lCahOe2BWmH+HkxVdnLnv9JJGNDjuPZgYA/WeygnbR5OwbDTQirs1D1Y cD1f0vntKXi3+bt9xNoejDRLS39+YBo+q9Os9RMUw3Q+Kf18VToN64qYH545 KoYVPRgvCkiZgc0qFV9bbcQwT3mNF47NM7Dnpc+/o25i2N1VOg4e5llIe9Zp axAuhkl3+LS+85yFK7tj75fFiWFOQkxlz1JnIUMChtTTxLCnfPpsh37MQqF7 +WTpMjFM3Yo7tkaWCkksdjZpNWLYR5237+ItqFAxnO+eYKsYxsWhKisUTIUG ATfnWKliGN1JtzsqjVTo6nzs06yUOOYtvCxyzYEGffrpaa7q4th/jvRHXofT YOCZUtLAAXFM5SzH2XtZNBh7QiKqxUYcEwowitX8Q4OJ39s+HnETx9js0ljX V2gw0zhmpvqqOGYaaifqzI/DYr1589I4cSz74NmLPEY4rCrNvaWWJo4lDp+4 dcoWh98otqUv88Uxdw29IY1LOGx9xT0lWSaOXSEdS3kdgcM+uWrR1Boi/sqt lq9PcDj+POC4QKs49kGltPxKLg7nxJTD7w+IY7evpSaUF+NwLWnwAwtVHKPK /S5L/opDJoGE8dA1cYw09y+Cl+ALPloINx+rBOZ4nsbnQ/CH5DcP7Rx+CSxp VzDfQ4JP1J9b2GmTJDDfeB+5AIJfDIL0o74pS2B1CSWM0gTfHLOSfWO7TwLL 1PZxjSf455w6T8essQQ26jUo9I3gI0+Otc0QCwlsSTSChgh+uj46Qua1l8Co ZSuNwQRfxVT9OpbtJYE9Pi/yYouwE5PKru0NlMCaw2hXDAk71zcrvT5SAuvZ 80bbjLhfbHav9swj4rl3Ndtuwv9X2WvUmXQJbEOpgbWA4L8WOnvBkAIJrPz8 Hfttgg8Hew4d4CmTwEbS1k13T+GQVqzh+rxaAhP7e5B5heDLzbg997WaiXx1 CidSO3HIdYGlpK5PAnNdzj3K/AuHIoZzfTZTEtiTobpkrS84VBDrYZr5J4GB L9BEkehv2rpjogE9Cbu5frZtnOh/9qRVQTQrCXvx9OZPz0SCL79irbsFSBhZ idPvx1Uclr/dO+4kQsJ+il8KzHfAIUpTXCskkbAPepSEk2Y4bPIXkDJQIWGm 0T6mjCQcdjiza0drkjCvq+GPudkIfjbfOty8j4SVSPI6TtBocFZx8oqTCQn7 Yivrz1xOg4u7/twuNCNhGye7m83SaHCdqTV50YKEHT13otM1hAY5Bj59ibIn YTVvAh/yAhrk/fnud5MrCfPLzCvOE6NB4fLcKWFvEhbf4efOt06FcvEPeAsD SZjdfzd6fIuoUDUskrwYQsJkTi+7e8ZSofbF6/sO3CZhB2GkuIErFRqZOjs2 PSJhMfUpYmH8VOi0rv3+bwFR/6zA1VSnWXhhUqlW/z0JaytSZM/SnIWXf5O6 b5eRsJP6uYIPGWdh6FsOeuEaEnZexJlVI3MGpjn3m+v/IWF9l/s7Pv2chp0/ bs9F7pTEJDTNXD8vTsInBunGp4UkMX3jykL87SS0eF+cQhaTxH53brkzek7C xsQRozpFSSyfUW6zt2cC1jn+l8xqIomle14Kff12HJYub/x3N0gSk3H3lu6W H4WJ0n7xD6YkMcqbPErRRB+0TLw3aT8nienEmj6IkOmDfOzZB9SXJbGx5gJT LodeGEdrmWhmksJ26hwLvNTWDaPK1fT5SFKY56fVkiuvOqD/iZnRJ1ZSWH3T hLS/WjM8fdNJO6VaCnMLiVR+MpgLE9MFWJYbpLAC8+6cCvYM2AHrfp9qlsKc DzG08Z18DK2YlK7t+COFXYx9n5kZHQRs7v/9ELYkhW2MRa7tp3sNbDMiKe4K 0tiZfbY2tLFq4FCdp6z1QBpTe6gimXugA2SO2Ww8TJDGRmzaGvdsdIAhVs6f 1FRpLH5dYqCwvBM4mV3yevFSGsujj9NZoHQD5986BSJfpTFq7qituVAfcJv4 Jkf/Txrzbdi5a7ON+H6z31w+vy6NzdV4/TqgOAQmlFTqK+hlMIbogJ/NoUPA 4/IjNz9uGcz8y1XpQflhcGH1TO6EnAyWW3VU39R3BHhzzkg12spgT/8dE/YY GAMz1yuYOB1lsIPRrDs75caB5+SdcVN3GexeGHu4z6Vx4F4rX/Dlqgx2iufx JufGOHAKdaOUxMpgjn0BB8o4JsEQdS//wmMZjOPugwoJs0ngcI75n2qyDLan 99af1NhJYLcv5+PLXBlMl37dvJZjCpz5OwTSqmQwOx3V+JT1KdDl+F6yu0YG O2w6l3t+7zSwag5jFPohg7XnB9RL+hB89lqi/kGnDHZJuzMjp28amLufP35r TgZ72+T5yvb1DGj6rayOlmSwVNu0lZn+GXDcaIN3c0MGQ+0bcj47Z8FRydTf /uxkDIhr9h64OAtMervOeUqRsYyDF2O6Ramg9vBLgxfyZOxbnl0qMqICo48B pFFVMraQVrxy15sK/ksQGj2vR8bufVN7VP2R0J+M47Up/5Ex7cTRcdU/VGDg W/Ki05SM5VnsqwygowH9E5ZeJy3JGP6MFp9G6NdPn6WPxdmSsascSuz+zjSw X/mv6g8HMhZP7RyRi6ABHfbHC0YXCf+e1xR5KmmgNMCxPfwqGbsoJ+ps1EkD WuPqpVXXyZgt+/sUs3ka0Khuuq4bRcbU/mmJ/ZYkeIOScfZaLBlrbGJ9eEoX B+qZPgeKHhPnHfNOPj+GgzfcBhJ4EhlrzfjxGDniQCV4B71yBhnzvFvz4LUf Dl7N9A175JKxvckBDz0IPlO0fVWTW0jGNj55Tc4l4iD/28284fdkbHOicck4 DwfyOkdjJD6SMV2tIFn3Yhy8yBXxPFdFxswj6WmnvuBAVmD6aHINGYv+ktPE +QsHuRHlKh3fyVhplseZuE4cyMzH7ORvIWMKGzzk3kGC5+xt5k90kjGxV7Jd 85M4kGqUa4v9Q8Yq6dalW3EcZOovFzeMkLFbFQW1N//hQKKwLpFlmowNJ5Ci aARPWWZ8LP8+R8b0+TU5nAjeuhtf0Be3TMw374SPO8FjMDpt22KLjK19tkwl vm9g8Wac1C5mWWxEMuyuHGErXg4z7uWUxdYOXjIe3sCBvYuvRwafLPb9h/i4 KuH/iY3LPefdstiVgKn/tXDn0VRtfwDAUVKGXpFnKBK6N+693HMvorz2t8Gj 0iRDEs1lKEUlKqWEZIqUypAkKhVFItVGKCpjSObhmu5wMj1Dht9prd+fe63v +u69z3evs76ftfbat+Uor5VZ2r6ga9CghhkYdZHypNhaiyo+jQYpTpLaVyhv GhquGk5n0WBzxrcUZcqjrjpMpdMGNChsjQlcR3k1UU19lfFqGuQOuyAxyrN1 Cxc4Tq6lwYrXkY5WlHdl5kj45VvQIGhvgq8J5WGYGEq6uo0GvKf2ltkxJPIS 8YotbGngKpcfWBpA1a+jvlfWkQZ7No6Nn6K83V5XKlN1kAZ6azf5ZzuSyBI/ 32HvQQPD80XxUpTfr2TeP63mTeW/XGyirESiN6mRMe0XafDL7Zx48aQIad44 0+wSSgP5ScmG0Y8itOvqUTG9mzTYPmfE0++RCIV522sN3qXBtudplk8DRGhs 3z8u51Jp8DQh2K9nrQh9IyRHrhfSQFcy8A73qRBJ0EaVtpXSoFqn6eSAnxAZ q/atUqikQVvsznhHWyFKkvjmF9tMg7CfzQkWUwLkXRMt+2yMBmvlgv9JWi1A Lz4F6p+cocFw3kszmbkC1JnnbWUwhw6+F+LPcym/bU3ec+edAh2QpfZgGeU1 7TPa2t/06DAg2f3U4UI/2u3yt3mkIR2uJ7fumYX6UYTjXFcbUzqQMg5pF8X6 0YSZIL15Ix3mfkD2vy/1ocq/s1aLDtGhYMDnnJNHLzqfs37nX7F0aGhWyr6s 0Y04eyp/7X1Ah2uyh43/rueh/pk94RmpdODfkpmpDOWh3eZepTuy6PBX0Lmh opEutKruMYr+RgexoWjf8fedaGxIjqkitgKEqxQUzan/t5f+j9lah1dAbUS7 /ZB8PTqZcizbSF8HErH5+lle93BLxeJb84104En8o0JyYTLeMl52qttUB2Ru GQkGe55iXUsd4vYmHYjvrdaaNM/CXQO8tJHDOnAwYl9K5UA+tvtn74OsOB3w OlWfb32wHJccme8X+lAHPmj5CebOqcQGN947HXqqA7OcitrSGirxgs7FSxbl 6MCNyyrWdy5W47JrP26fqtGBOrj4Zvp9LV7zfUcoR1oXvgW+jMfSTfjZlJib 9EJdGDz/W2mwvAkvpmds7FDShaipM1tqIpvxmM98qajlulBY8WHnRYVW/Grp l8sDoAsf+MH38yXa8XK3DWczzuqCSeh48cHyThwdPWRz7SIVHyHdJNLqwhIf kgz2BeiC+rwJerh3F25ZID74101dOCyeMDCuzsN3st8fO/FCFzR333+2ZF83 lpVYeUCPpwsNZ1coOWf04tyzs3Z283Xhnvrvm4jqV44IK9YnDOqCsWab95RR H87/4bx8vhgDTEvqCzVy+/Cp9Hu9QlUG3Jd7sSg7vR9rLD/a8GgZA+4+Ikw8 +vvx13vcMscVDNAcLkua1OJjWuDXtG+GDFj6dCvr3E3KT3um3Z9vZ4D0uJrn 14MCHFRdtvewHQMyu0uziqMF2MAiZruaEwOkjJI9LhQJcDiXzQlzY4Cso9+0 ioYQr34yqWnmyQB+1POiyc1C3KteqjDlzQAJn7CBaC8hXit9YORYIANerneX afkkxKJLet3aYQwwyWIcDBEJ8b2Ribqmmwy45/DPaLcC1Y+23cyxfMCAes1F W5J2i/AD231PZj9mwM/i57+m/9zH+sq89+4Flb/2aPQsql99/Kb4PPMdA866 mP47Uy/CNqyoY12FDKg19kofGhJhiYdOjnGlDHjWwqy4Pp/E6cqMrdaV1Dh5 h89HOuWP8NE1svUMqIyyiIxDJJ43u0i/qJkB4xPD8xRtSZztc0PjQhcD3tsU 8xhuJP7rsI6EYIABh3oC1IlIEr/7OTL4cIwB/uNu5WpJJHbeXtjpMMMAdsLp oEcvSaxYEv5dYQ4TXg7tvfcJU/5Y7VD8RZYJsmMvj/p/JfGJl/RsfwUmNN7I 3fuD8sQS+nDKalUmPG+7LVHSTuLSuPyYIQ0qvh/aNlOe8pIPu5ZGZ8LnS9fv uFCe0rpm73NQjwnEFVqj+iiJK6eWuy42ZIKNS9pRt98k9j01uLtmNRPKFt+W 2zZNYt2+D5tD1jFhqbzls1LKS/VOIabrNzKhtmQJt5EaX/1ux/q9jQlJnuse +FPxxCZt9UxbJrAVOyQ/Uvla8K/5bo5MMCmT9rtLzRdi+H5G8xATpN2y1kgN ktg4LfjXT1cmXLjw3k+WT2Kehm17lAcTrrv0Rj+hfBh1W7N6kzcTAqV/NLT8 IDGSJQslLlH5fGQ+PKP8JLicl/k2gAnDRANWoPx0ZzQo2TOUCcLLLscXZZLY 7Lj1Ld2bTFi0PuNQ+sM/70vkiZ24y4RM4htrIeXb5DeaxzLvM8Fpo0G7qT+J JSQG1pk+Y0KBdXHqsCOJOfRdL/xeMSFfRkrnykYS77fEKsU5TIg+mnWyiUv5 6nbYry3FTPAetX05MZvEZN6wQ9QXJgQ/SvXK54uwervDp7oqaj3r58XaVomw L0M3YW8LExpqFFTH7ojwqvySzR6jTDBMDF6hryrCLjzWm9dTTHhyqeTL7VEh viN9S3NiFgte7Elm/KgR4lHrg+NXFrDguMO5x8JrQpzVN5MSrcMC+Y6leaE8 Ae6cf1S+QZ8FEquuKPNzBVjeoNxXzYgFGp95+/XDBNjjYpx1yjoqfsX5xJNs AdZTMJHIcWDB4pRKn7mufOxonHh8cj8LPNT6Yz4b8nGoo1QDOLOg5PKOAF8x Puan1qaXnmaBfe5ZyfKofvzY1NOxMYwFy7/RrM3S+rDWkbScacyCRrFRZsjz HmwVIq+9voQF7pcUDR+69OArGT4RQV9ZsOFYgG2tdg9umzA/sqCBBXExNy5E 3enGCRFdCpqDLJiWMd797gyP8qLaCTNtPRhNmnmycV4nnj6YunghQw8Kvhy4 4vWyA3fNJz43EXpQTmeFfNnVgTMObVh2GunBWmKF0XRyOzZf4FaTtFsPJPrf rhzjtmGvozkrxSL1QCmzubhx709cq7hTLG9KD67sqHKK/l2G3+Y3PQucrQ9a osT4uh2lONHtiL2VjD48ND0UOpzyCR8r8HnVp6wPAf/ZBS3YWoRnH088pGyg Dz/FLj/6ppWHDYqEn8+46gPHObYy/rI4jvK8Fsmu14dtfu/yT46XoYmvz3Ku NetD/GNOR1XAV3SAXtXa1qkP4TkvxBYtLEfcJhW9yF/6cGtXRth0ZCXqT7Lh jc1mg5Cp5dIQV4NCZXsu26uzobfMeeJ5SAPKN/G5FbCMDd6XlhzbYfYTDR+R efJSmw1rlvH9BVM/0Z4C/cp5DDbIzFJ5KnBrQiwvb/W3K9kQIUu3tlzVispb 5+Wp7mBDqn7VfKMtHUhCLq78X2tqvi9x69UTO5DRKr0OTzs2bLgxKLt5sAMl RFvN++LIhq5whs/h6E50YmOs3XlXNpzaIUUzq+hCCzKZw43+bPBvux8qqdaD NrR9kJobxIZc+tXMogM9yFtux2KD62wQUzW6die1B7UdPbMu9AYbJkZkPE/p 9aKXSz7cMI1nww7nqz+fsfuQVeA2Vnw2G1YOVWRISPJRiv2vjbm5bDBQNGuo NOGjcWbkkdp3bAhCI69jjvNRYk31fbmPbMj6TvsoVc1HQg1b+YsVbNDPres0 DRcgGP5P7141G2KMxTTi3gpQ9KeYzdm1bLgVtDSIxxOgVe4NV0WNbLj52MaW bSJE1/L2jDr1smGXc9GXc9VC1BQ+pXCez4bIpJS+mREh0j+QwI4RsQG83SwO KotQ3dw2l4phNqRk7nmA7UVIp8kvkD9K7S/PQyvbW4QupC97KPWbDfwAq/8C bouQlu3BJiROgLHzMeXn5SLkpTN73GE2Abu33bOQ6BOhsslkRW8pAjxVokKY EiQ6+bB7a4YcAUPVeUGTVL9b5BXk9nUBAem9RhcS/yWR0qYV13oVCBgxXzqh 6ECiD79cCjRUCRBbtzbQ049E8kXSLaZqBOwndRi7Ikl0OCZtYpcGAXkv+YGy D0iU42qpdEaLgGnnFPGIdBLJrhFyI2kErJw/96/Wd5QfFoZvf65DgK+Yld7k ZxK96tI7XsokgNbh2M+rIdGcnIpgnj4B9ySTGmKbSWQfcjJFnEvALFfDBLVu qp93WvhRzYgAb/ManusfX3BetZqYEPBIt8XFf4hEOyV3TtqYEnDj/gHyyBiJ Un4MKXsiAjrcVMwVKb9MpEUbhq+j1mfnsiV8mkRbLhlaPTUjYHuQc/+f+32J VnXuJRYEhO1tXtj2x0PLz4Z0bCZgeHrNxxwq3mJc6fH0VgJOr309bw+VL/Zr TpGqFQGfrZUnS6n5RPft241sCLjZSL6ToDy07tTElNUu6nvd9zg3R0SiW//G qp5wIKCp6pJ7LbWfXhXTlSFOBPCbUlpOtJDIVNi0M3U/AdqFqkvqvpMoIt/3 5MdDBITPy/KfW0aijpvqYa1HCUhFAl+pDyQyOoqf/HYlQHrWz4s1GSQKXrWv RMmdgIYHzDnHk0jUJCfeyfUg4Me/9Pvfoyj/tj+Y2XaagMTs2DbpKyTyz1q3 5NhZqj7xXccWnKS853DVJtmXgF2feCtCLajv75EtP/syAa0Y0pYRJLoW1Ftx 8CoBBhbGqtbKJOJlWm7SCiEgNEdtZXSHCC0quyjlH06Ag0uvRXKxCK1ryyjq iKTO3xzRfNtUEUqUVURJd6j6di5lJB8RoXJN80nxOAKCcMH+9RtEaMrYJ3f/ fQJezDjLXdcQod2Hm7nLUgiYUX3FWlQrRIofHq1IzCSgYPhY6WY9IdrwvZ43 k03VwzbhlK24EHn2z3u49y0BmiHtor9rBJRX3NWWFlD11VJ8UOApQNdPGMkn lFPnW9t48e8kPsoNcK6YqqLqcddHbsDtz3sW90Ida6n9fntc/4LLR2afp+eo NRHA224xKxT3I7Fln37H9hGgXnhe4+/SPqS/cjznt4CAMfqChpvX+pDTFoaX wy8Cus0ne0T/9qE8n4hfqqMEnO3OKbTI70Ve1Xa8u7M5IBfeYdb2qAfx/XvL Y5Zy4O6TR8ePIx5SvacaOqrJgWn93fUmoi5kkWG50Y7Ggdbn66aU4rpQSlPG x79ZHJi1clhLeaQT7TP0ybm1igObGVmpN+I6UF33vKSbNhy45RIWHRncikqs g+Nyd3FAnmdn96ChBWUXzo1pdeBAhvfn7ZdWtKDbCVKhjAMciJ1LP1BQ2IRs bCW9PrpzYOnasiqN/gb0vVhs01AQB8x8e94GSH9H1cmjA1ZvOXD/ePGRZkWM CuXPCrzfc6DU5FzphpE89Mrvv+6EfA7kFlrKxdTkoKg9I439JRxI7i9z9Q57 hXYsGiq+UsOBoba1H227Y1Clv+juKwEHiq9K7PQlMnH5Ad5a+aVceB+xzOub XhVun506dkuTC4oN8gw5qWo8nOKcrkLjQuOHLgP3lmqswucvWcbiQoq3TYHr 9e/40KnBUf3VVHwIJ4VVV48n/Geeb7HjgkrQmlhJgxYsRys4VLWbC5Xn/smN GW/BGp+vLLZx4kJmjTWkvW/FZrJzgvcc5kLS3ccH7iS24RvRsofcTnEB69d+ 3KXagWmPVFSDI7gQ715wta6jC5uYN1bK3uRCXM/Hy8ErediyLy7oxm0uTM8u cTcK4WEPlsZITDwXHlQFzRzX78bvXtMqU9K4YI+6tbtde3CFXW+gbjoXomqu n5rI7sEd40/+efGKC4Xyij/6xHux1BpW2utcLhSs4Z3bHN2LrUq4gUWfuND7 6vy5nKd9+LDziKnFFy60h19xWS/sw97Sb4a+lHNBfJFwcbheP47fump/TS0X TCOywPZ5P+6tA9OOTi4MVwQZOMby8YS3xNDhHi686RX5Rtbwsdzioid9/VxI CFVe5C4twJy95koDA1x4nd2dqHhagM3E55WfHuGCeXTIxcYUAd71sOzq2BgX HJM4Z9EPAXY1C119YZILbPGKFWiuEP//vU74/3ud+H+5JLkh "]]}, Annotation[#, "Charting`Private`Tag$852617#1"]& ]}, {}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{0, 0}, DisplayFunction->Identity, Frame->{{False, False}, {False, False}}, FrameLabel->{{None, None}, {None, None}}, FrameTicks->{{Automatic, Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, Charting`ScaledFrameTicks[{Identity, Identity}]}}, GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], ImagePadding->All, Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& )}}, PlotRange->{{-20, 20}, {-0.9999993575792578, 0.9999999496884054}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{ 3.7934642265558367`*^9, {3.79346425859669*^9, 3.793464306101451*^9}, { 3.7934644554334497`*^9, 3.793464461383195*^9}, 3.7934666695829*^9}, CellLabel->"Out[68]=",ExpressionUUID->"f8286c1f-f644-4bfb-83c7-8ed63b92cbce"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ".", RowBox[{ RowBox[{"MatrixExp", "[", "x3", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "//", "FullSimplify"}]], "Input", CellChangeTimes->{{3.7934641442183743`*^9, 3.793464156873516*^9}, { 3.79346671107231*^9, 3.793466764513672*^9}}, CellLabel->"In[76]:=",ExpressionUUID->"8bae4557-85bc-4792-906e-cdf5f9954a44"], Cell[BoxData[ FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"a", "+", "b", "-", "c"}], ")"}]}], " ", "c"}], "+", RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "+", RowBox[{"a", " ", "c"}], "+", RowBox[{"b", " ", RowBox[{"(", RowBox[{"b", "+", "c"}], ")"}]}]}], ")"}], " ", RowBox[{"Cosh", "[", SqrtBox[ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}]], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "a"}], "+", "b"}], ")"}], " ", SqrtBox[ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}]], " ", RowBox[{"Sinh", "[", SqrtBox[ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}]], "]"}]}]}], RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}]]], "Output", CellChangeTimes->{{3.7934641500492496`*^9, 3.7934641572882633`*^9}, { 3.7934667247489147`*^9, 3.793466766544986*^9}}, CellLabel->"Out[76]=",ExpressionUUID->"8c5d5347-5047-44ec-ab4e-1d6d37a085ad"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"a", "=", RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{ SuperscriptBox["r", RowBox[{ RowBox[{"n", RowBox[{ RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}], "/", "2"}]}], "-", "1"}]], " ", RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "\[Beta]"}], " ", "n", " ", SuperscriptBox["r", "2"]}], "]"}], "2", RowBox[{ RowBox[{ SuperscriptBox["\[Pi]", RowBox[{"n", RowBox[{ RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}], "/", "4"}]}]], "/", RowBox[{"Gamma", "[", RowBox[{"n", RowBox[{ RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}], "/", "4"}]}], "]"}]}], "/", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["\[Pi]", RowBox[{"1", "/", "2"}]], "/", RowBox[{"Sqrt", "[", RowBox[{"n", " ", "\[Beta]"}], "]"}]}], ")"}], RowBox[{"n", RowBox[{ RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}], "/", "2"}]}]]}]}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"\[Beta]", ">", "0"}], ",", RowBox[{"n", ">", "0"}]}], "}"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.793465164938962*^9, 3.793465276942292*^9}, { 3.793465394288927*^9, 3.793465415723238*^9}, {3.79346555100313*^9, 3.79346555531676*^9}, 3.793465637781562*^9, {3.7934657388041058`*^9, 3.7934657487124987`*^9}, {3.7934660943107843`*^9, 3.793466111187224*^9}, { 3.793466158296303*^9, 3.7934661605743647`*^9}}, CellLabel->"In[50]:=",ExpressionUUID->"e95aa855-0ec5-4b02-9a2b-7b9f8ad86b9a"], Cell[BoxData[ FractionBox[ RowBox[{"2", " ", SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "n"}], " ", SuperscriptBox["r", "2"], " ", "\[Beta]"}]], " ", SuperscriptBox["r", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}]}]], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"n", " ", "\[Beta]"}], ")"}], RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}]]}], RowBox[{"Gamma", "[", RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}], "]"}]]], "Output", CellChangeTimes->{{3.793465255105665*^9, 3.793465277477212*^9}, 3.793465453681077*^9, 3.793465555715981*^9, 3.7934656389289494`*^9, { 3.7934657395221357`*^9, 3.793465749034925*^9}, {3.793466094794734*^9, 3.7934661117947063`*^9}, 3.793466161150166*^9}, CellLabel->"Out[50]=",ExpressionUUID->"28fe16a3-13d3-4ad9-b940-beced42022e7"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"b", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{"a", "/.", RowBox[{"{", RowBox[{"r", "\[Rule]", RowBox[{ RowBox[{"\[Pi]", "/", "2"}], "+", RowBox[{"\[Pi]", " ", "m"}]}]}], "}"}]}], ",", RowBox[{"{", RowBox[{"m", ",", "0", ",", "5"}], "}"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.79346630866848*^9, 3.793466387235531*^9}, { 3.793466478960395*^9, 3.793466485768878*^9}}, CellLabel->"In[65]:=",ExpressionUUID->"980574f0-a6f2-4bdb-9087-5c4edf46b08f"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"LogLogPlot", "[", RowBox[{ RowBox[{"b", "/.", RowBox[{"{", RowBox[{"\[Beta]", "\[Rule]", "10"}], "}"}]}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "100"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input", CellChangeTimes->{{3.793466199858704*^9, 3.7934662491211367`*^9}, { 3.793466488996272*^9, 3.793466499921826*^9}}, CellLabel->"In[67]:=",ExpressionUUID->"d81a95b0-baac-41e2-85a1-56476d76e643"], Cell[BoxData[ TemplateBox[{ "General","munfl", "\"\\!\\(\\*RowBox[{\\\"Exp\\\", \\\"[\\\", RowBox[{\\\"-\\\", \ \\\"2985.836216774226`\\\"}], \\\"]\\\"}]\\) is too small to represent as a \ normalized machine number; precision may be lost.\"",2,67,17, 31323197559230362610,"Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{{3.79346649455048*^9, 3.79346650022822*^9}}, CellLabel-> "During evaluation of \ In[67]:=",ExpressionUUID->"0276ced0-3e05-4431-85ff-80d6cff2f239"], Cell[BoxData[ TemplateBox[{ "General","munfl", "\"\\!\\(\\*RowBox[{\\\"Exp\\\", \\\"[\\\", RowBox[{\\\"-\\\", \ \\\"1998.7829219728292`\\\"}], \\\"]\\\"}]\\) is too small to represent as a \ normalized machine number; precision may be lost.\"",2,67,18, 31323197559230362610,"Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{{3.79346649455048*^9, 3.793466500247039*^9}}, CellLabel-> "During evaluation of \ In[67]:=",ExpressionUUID->"683c37e9-522b-416a-9aec-0a641843f48a"], Cell[BoxData[ TemplateBox[{ "General","munfl", "\"\\!\\(\\*RowBox[{\\\"Exp\\\", \\\"[\\\", RowBox[{\\\"-\\\", \ \\\"1209.1402861317115`\\\"}], \\\"]\\\"}]\\) is too small to represent as a \ normalized machine number; precision may be lost.\"",2,67,19, 31323197559230362610,"Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{{3.79346649455048*^9, 3.793466500266004*^9}}, CellLabel-> "During evaluation of \ In[67]:=",ExpressionUUID->"4eb8e038-2070-460c-b6a7-fc43b0c32baf"], Cell[BoxData[ TemplateBox[{ "General","stop", "\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"General\\\", \ \\\"::\\\", \\\"munfl\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ during this calculation.\"",2,67,20,31323197559230362610,"Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{{3.79346649455048*^9, 3.793466500285001*^9}}, CellLabel-> "During evaluation of \ In[67]:=",ExpressionUUID->"be60879b-9aaf-4b71-b856-f45eacbe3f80"], Cell[BoxData[ GraphicsBox[{{{}, {}, TagBox[ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ 1.], LineBox[CompressedData[" 1:eJwVknk0lXsXx2U856lQZMh0q2NsUCkZOs/vV4aipMicMs/Oo+GNUJnJNZUx ERkj15SoLtlmQm9mtzQgkosrGcvlPe8fe+31WXuvtb/ru7877CgjR04ODo5C dv2/56Wlxnlr3CBfis03vF/XBiVVx2JnhhlyctPseXMIw4LwdfXDDGcUHNNO aQICt5YhAwmry2glJ0M8wAaBZcjamgTDG0U4/9SYkUagf+y3Uslpf9Q/8ir9 yzQJUuuZpfxWgUgwg7bpXAsJiR8O0GNRCFpMELq2mE/C5up6WwFGONI14Jgf iyYhJNX4ZSwtEu0ZUDL97E3Cqs+XrYLTUeh7pmveRkcSrpn9xz2uKxbdP/In 1XGehMXtXHY0q7tI0jTrW4kuCQcjT8Wc7LyHossufruoQQJrJf5lBEpAPJl+ fyQqk1DoMjTeWpaIuCNab0vLkTA+wBCiM5JRdt0ToTdSJOw84Yn0klJQlmDH WoAICRcrn7nfoaWimgD63+KCJKTKriW3+T5AYjJROgEECf0Juo306TSUmmSh ncFDwlbu2Fm9Sw9RXL+QouMGEs5cHZCM7MpAnKOtJfX/MkHneyxj7FEmmr8u 8LDwJxNGFSo0eKweIZFn+9y2LDMh0GbwrKxwFioZcp+fWmCCTMqqk05nFrKo PHLm0DwTav77203HsGxk3ykS9WmOCVZ8OvGhKAfJZU9lfP3OhBXStSB3OQc5 Boyp67I5+Xp0bVNZLmpZyi1emGXC4eKyvjG3PJTuVDk8y+aesb6/eRj5iG/Q SkWFve8l9XOD3Id8lKR69PJzNvObSIvpJj1GN9IM2vzZ94qiju9zMixAVErh K/8fTNBvdNIOoxUiOacVmWdsfRO/Ii3z6gpRU++u9Z2LTAhTKfFq9n2CiCXF woYlJjDce8LGVYqQcNhoTsIKE+qzltJ4p4vQSunv2fG/mGDzTuKpXN4f6IDF Sugrtl9rW3Cb7qVilN7uZizEQYJGYMRCWFcJWu0O8lNh++1xoT/UWKcUKVZZ Rf7iI0HTZyJu9FEpWt0k8XWc/Z+/Sjblc1mVoaere7fu3ELC43bp8viqMjSo OGJJCZPg/XV/zS7hchQ3XznyTpSEbTImPVqd5SjQ5RNFkyHhXEz6ejCqQLrb KN7sfST8VlhCCKdVIKJT37DlIAn/NNVty1muQPJ19jWcR0iI/ndsd2PZMxS1 cY9xNSKhzWOfOTejChXXKTEVjUhIiBO7Zx1RhSpqB5ytzUiwqeDsqJyqQmeV f57Iv8DO869+5PrsObqQ2dJ/w5mdx99vy7/RfYl4ndKojbdI8C94u5jsWoNw Qyj9ZjEJYldfvE4cqEP39/1H/+x2BGshxc719Ho06mgu5rMDwWhSNvc/mvUo pXFG/4kCguKX0eTJzHq05w9KQ+UIAh1Ou/KfLg2Il0wTbDqP4MpdIvXSz0bU 2jJa230XQXuJlauiVCtytJo+6E7HcC/Br4/zdCtCpcHeZzdjsLzx4NiQbyta NZBD6lswTB5/Lx472IouJyswt4ljoPVbvp6Pb0M3uIa0FhUwaK9a7AaiHf0w 5afM9DC8Omk+bbrciZRDgnmuRWH4y6tQrf5bFxJY4NU2kDgGI5ftDcPzB5BJ 7vtzRueOQ/FcmvGn4Q+oIFhlQrRdCz46pzycGBxGHh2Wz3PO6YBu0k5i9/oX lPUsQ2105wl4sUygFyITSD1f1S9SVA9O38l0El6ZRCMrQWY2QqegzmKR+4X4 DJoWke9KcTEApaJV/cSgWUSfYHzsaDAEX529yz9mv6O/j+4sGpM5B3+u1dh4 3/qBHDwyKmfvGcEmw9zjtt/nkdT2gv5rvOfhTO3UJyp4EYkpWxs9emYCiXqj tgz+ZSTL5yvJ8jWDKbf91ujWCnpeRjL8NS3gUNEHodubfyE37WMfvyAriAoZ 1pINWkVb5/c8Pc60hj5/HeXZbWtIe+vH1dNBl2BXrPm6TdY6cs+fVqWmbOCY pC1DMpIDj2/iztYWsIMJjma5VKMNOPGWypEBE3sQPdDv2L6ZE3srVZaGxzqA 3gwz2bCJE++K75Ld0eYIV/80kXOK4sIBC400oR3OINsrNqesy437UtM3bLBz gberv0tECfDgHu69yVPPXeFmuekRzT4erDhSv798zQ3Kn3bEpkfzYi/HD4EJ 0h7wuXFO554JHwZP40cOTE8wJl6N+ZvzYc7G5AmTY57QbHgn1NmKD48Ea6nr 6HhC0TuZpqO2fFjd8+iMlIEneM+e1v7qwYdTRJ3dqi54Ar9k/vGjIXy4ubyh KcLPEzSvWqHxcj6cOGedlVjlCUk7GtU0BGm42Cvh9F8KLGA2mTNEhGg423yH mdIeFnxxmRaY20bDO94Oz/kos+BgqcjXAgkaVuua7OVXZUEn6ZooLk/D6pqO XFJaLOC+wD+3zKThFPvt9LoLLLiSZP6kyp2Gw/rib4nGsEBcYzopnkXDgXOx aiJ3WQAfAoOoyzS8cdhSfWsCC/hln1jIe9PwdFAXD2cqCwqe/suXHMSeL2iG Qy4LPr/Ncrh+n4ZjxDsEq6pZYLhxWupwCw0f39dx6MYEC1SpZSPD1zQ8/7DC zuRvFkj2cEW4dtIw9wff9b0zLJhM3T6X3kPDgh2DPr0/WBCmdLKZ9zNbz7jU lsU1FlTrZbMGl2m4232c544wBQoRFrV+SnSs8G3xwMBRCgSmHOYT99LxTvW+ HxqIgkVDL8XS/XTsGcFTnXqMggbR8Pgvqmxe/XXujC4FF/MrnA206Fg45JJq qCEFCc0CgjIX6Lj/i/7MPlsKOHiabeqj6djy/f5TloEUbBNptMuPo+O62w5O YsEUKMnXO0TF03GZ9Lei7hAKzuu9cjG9T8djF1NKNSMoyI+u9JrMoeMD5Xpa n2IoOCOSH7C1mo7fMEzF3R5QYC+fG7T0io7b8ngSv6VR4KOWHTJUR8eXL/vx Oz6kIMsyIyKvhY570pj/GD6iYOFhcpxGDx37DseILuRRkCYfkWk3Scf2UO7v W0ZBmVpY1olpOlZ2b/J9Xk5Bs15Izp5ZOhYQsT4595SCWfeAx4sLdHwl+6qu RSUFWqU+pZEbCHxTMdh//iUF5nXXyyluAoct8eUKVlPg0X2t4jwfgR9nlYUq 1FCQNO/1XHozgd8/qLI/VUvBpJorlIsRWMvtJLZuoGBdz7k+WYLA8q/LB0wb KRC2cmz0lybwL++XAqebKCBv2rbqMghsWd9tothCwb06i7fvlAlcrXfxa/Fr tl/dZt21BwlMc5nZH9pOQfWoSW/OYQInHaC4zDooGOcxGmRpEnjol+2R6U4K 1PX1P3OeIPDk7rbw0bcUxEjU7pbTJzDxnjMqp4uCkSkVbz0DAtdsKjhk001B VKwUf5wxgXtLuBxaeigYtrln8dSUwNp520ev9FKgepAvt9+CwEs/bJbE+ij4 3DurKWVD4IfK3D3n+yk4nOcYju0JPFG/JXKSzZHe77rtnQgsez3wgc8ABR9P GkqHuxLYJP0MJTlIgcr2RtdCDwL3sLS5/YYoeK/JFVPBInA60zJkme3X/wAH ghje "]]}, Annotation[#, "Charting`Private`Tag$852402#1"]& ]}, {}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{9.398306502016513*^-8, -254.89001668325236`}, CoordinatesToolOptions:>{"DisplayFunction" -> ({ Exp[ Part[#, 1]], Exp[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ Exp[ Part[#, 1]], Exp[ Part[#, 2]]}& )}, DisplayFunction->Identity, Frame->{{False, False}, {False, False}}, FrameLabel->{{None, None}, {None, None}}, FrameTicks->{{Quiet[ Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , Charting`ScaledFrameTicks[{Log, Exp}]}, {Quiet[ Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , Charting`ScaledFrameTicks[{Log, Exp}]}}, GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], ImagePadding->All, Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None}, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks->FrontEndValueCache[{Quiet[ Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , Quiet[ Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& }, {{{0., FormBox["1", TraditionalForm], {0.01, 0.}, { AbsoluteThickness[0.1]}}, {0.6931471805599453, FormBox["2", TraditionalForm], {0.01, 0.}, { AbsoluteThickness[0.1]}}, {1.6094379124341003`, FormBox["5", TraditionalForm], {0.01, 0.}, { AbsoluteThickness[0.1]}}, {2.302585092994046, FormBox["10", TraditionalForm], {0.01, 0.}, { AbsoluteThickness[0.1]}}, {2.995732273553991, FormBox["20", TraditionalForm], {0.01, 0.}, { AbsoluteThickness[0.1]}}, {-0.6931471805599453, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {-0.5108256237659907, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {-0.35667494393873245`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {-0.2231435513142097, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {-0.10536051565782628`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {0.4054651081081644, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {1.0986122886681098`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {1.3862943611198906`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {1.791759469228055, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {1.9459101490553132`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {2.0794415416798357`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {2.1972245773362196`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {2.70805020110221, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {3.4011973816621555`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {3.6888794541139363`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {3.912023005428146, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {4.0943445622221, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {4.248495242049359, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {4.382026634673881, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {4.499809670330265, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {4.605170185988092, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {5.0106352940962555`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {5.298317366548036, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}}, {{-253.28436022934503`, FormBox[ TemplateBox[{"10", RowBox[{"-", "110"}]}, "Superscript", SyntaxForm -> SuperscriptBox], TraditionalForm], {0.01, 0.}, { AbsoluteThickness[0.1]}}, {-207.2326583694641, FormBox[ TemplateBox[{"10", RowBox[{"-", "90"}]}, "Superscript", SyntaxForm -> SuperscriptBox], TraditionalForm], {0.01, 0.}, { AbsoluteThickness[0.1]}}, {-161.1809565095832, FormBox[ TemplateBox[{"10", RowBox[{"-", "70"}]}, "Superscript", SyntaxForm -> SuperscriptBox], TraditionalForm], {0.01, 0.}, { AbsoluteThickness[0.1]}}, {-115.12925464970229`, FormBox[ TemplateBox[{"10", RowBox[{"-", "50"}]}, "Superscript", SyntaxForm -> SuperscriptBox], TraditionalForm], {0.01, 0.}, { AbsoluteThickness[0.1]}}, {-69.07755278982137, FormBox[ TemplateBox[{"10", RowBox[{"-", "30"}]}, "Superscript", SyntaxForm -> SuperscriptBox], TraditionalForm], {0.01, 0.}, { AbsoluteThickness[0.1]}}, {-23.025850929940457`, FormBox[ TemplateBox[{"10", RowBox[{"-", "10"}]}, "Superscript", SyntaxForm -> SuperscriptBox], TraditionalForm], {0.01, 0.}, { AbsoluteThickness[0.1]}}, {-230.25850929940458`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {-184.20680743952366`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {-138.15510557964274`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {-92.10340371976183, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}, {-46.051701859880914`, FormBox[ TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { AbsoluteThickness[0.1]}}}}]]], "Output", CellChangeTimes->{{3.793466220564404*^9, 3.793466249380309*^9}, { 3.793466494667863*^9, 3.79346650031164*^9}}, CellLabel->"Out[67]=",ExpressionUUID->"92a6d277-5c42-4f63-b117-58768a23e8fc"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FullSimplify", "[", RowBox[{"a", "/.", RowBox[{"r", "\[Rule]", RowBox[{"\[Pi]", "/", "2"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.793466168378406*^9, 3.7934661818634033`*^9}}, CellLabel->"In[53]:=",ExpressionUUID->"19fa357b-b8b2-42f2-86cf-c70cabcec230"], Cell[BoxData[ FractionBox[ RowBox[{ SuperscriptBox["2", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"4", "+", "n", "-", SuperscriptBox["n", "2"]}], ")"}]}]], " ", SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", FractionBox["1", "4"]}], " ", "n", " ", SuperscriptBox["\[Pi]", "2"], " ", "\[Beta]"}]], " ", SuperscriptBox["\[Pi]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}]}]], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"n", " ", "\[Beta]"}], ")"}], RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}]]}], RowBox[{"Gamma", "[", RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}], "]"}]]], "Output", CellChangeTimes->{{3.793466174263611*^9, 3.793466182245388*^9}}, CellLabel->"Out[53]=",ExpressionUUID->"17ffa7ee-f62f-4e9a-b461-02cd24382398"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{"a", ",", RowBox[{"{", RowBox[{"r", ",", "0", ",", "\[Infinity]"}], "}"}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"\[Beta]", ">", "0"}], ",", RowBox[{"n", ">", "1"}]}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.793465454645339*^9, 3.793465462602173*^9}, { 3.793465562788645*^9, 3.793465581416975*^9}}, CellLabel->"In[51]:=",ExpressionUUID->"ba8f198a-690c-424d-9cc7-343746fa1b85"], Cell[BoxData["1"], "Output", CellChangeTimes->{ 3.793465483432444*^9, {3.793465561747189*^9, 3.793465583809306*^9}, 3.793465641281439*^9, {3.793465740366543*^9, 3.793465751406748*^9}, { 3.7934660976848183`*^9, 3.79346611407049*^9}, 3.7934661640146103`*^9}, CellLabel->"Out[51]=",ExpressionUUID->"b1226115-e262-43fa-91ef-96afd5531fd9"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Series", "[", RowBox[{"a", ",", RowBox[{"{", RowBox[{"\[Beta]", ",", "\[Infinity]", ",", "1"}], "}"}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"n", ">", "0"}], ",", RowBox[{"\[Beta]", ">", "0"}]}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.793465280424767*^9, 3.793465297775216*^9}}, CellLabel->"In[31]:=",ExpressionUUID->"a69d3ea3-6c53-4757-98a9-c615f36923a6"], Cell[BoxData[ RowBox[{ SuperscriptBox["2", RowBox[{ RowBox[{"-", FractionBox["1", "2"]}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}]}]], " ", SuperscriptBox["\[ExponentialE]", InterpretationBox[ RowBox[{ RowBox[{"-", RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{"n", " ", SuperscriptBox["\[Pi]", "2"]}], ")"}], " ", "\[Beta]"}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", FractionBox["1", "\[Beta]"], "]"}], "2"], SeriesData[$CellContext`\[Beta], DirectedInfinity[1], {}, -1, 2, 1], Editable->False]}], SeriesData[$CellContext`\[Beta], DirectedInfinity[1], {Rational[-1, 4] $CellContext`n Pi^2}, -1, 2, 1], Editable->False]], " ", SuperscriptBox["\[Pi]", RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}]], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"n", " ", "\[Beta]"}], ")"}], RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}]], " ", RowBox[{"Gamma", "[", RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}], "]"}]}]], "Output", CellChangeTimes->{{3.793465287033741*^9, 3.793465298181282*^9}}, CellLabel->"Out[31]=",ExpressionUUID->"de5bf86e-f71c-4d66-a846-9cdd3eec0bfa"] }, Open ]], Cell[BoxData[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"6", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}]}], "-", RowBox[{"s", "[", RowBox[{"0", ",", "1", ",", "1"}], "]"}], "-", RowBox[{"s", "[", RowBox[{"1", ",", "0", ",", "1"}], "]"}], "-", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "0"}], "]"}], "-", RowBox[{"s", "[", RowBox[{"2", ",", "1", ",", "1"}], "]"}], "-", RowBox[{"s", "[", RowBox[{"1", ",", "2", ",", "1"}], "]"}], "-", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "2"}], "]"}]}], ")"}], "2"], "//", "Expand"}]], "Input", CellChangeTimes->{{3.793536642823517*^9, 3.793536686774036*^9}}, CellLabel->"In[79]:=",ExpressionUUID->"76a5a6bf-8a98-4d15-942b-df42914ad53b"], Cell[BoxData["7"], "Input", CellChangeTimes->{ 3.7936296303941603`*^9},ExpressionUUID->"56f2956b-d07d-4363-8656-\ bbcfe2c5f5f3"], Cell[BoxData[ RowBox[{ SuperscriptBox[ RowBox[{"s", "[", RowBox[{"0", ",", "1", ",", "1"}], "]"}], "2"], "+", "cl", "+", SuperscriptBox[ RowBox[{"s", "[", RowBox[{"1", ",", "0", ",", "1"}], "]"}], "2"], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"0", ",", "1", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "0"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"1", ",", "0", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "0"}], "]"}]}], "+", SuperscriptBox[ RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "0"}], "]"}], "2"], "-", RowBox[{"12", " ", RowBox[{"s", "[", RowBox[{"0", ",", "1", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}]}], "-", RowBox[{"12", " ", RowBox[{"s", "[", RowBox[{"1", ",", "0", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}]}], "-", RowBox[{"12", " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "0"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}]}], "+", RowBox[{"36", " ", SuperscriptBox[ RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], "2"]}], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"0", ",", "1", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "2"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"1", ",", "0", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "2"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "0"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "2"}], "]"}]}], "-", RowBox[{"12", " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "2"}], "]"}]}], "+", SuperscriptBox[ RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "2"}], "]"}], "2"], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"0", ",", "1", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "2", ",", "1"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"1", ",", "0", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "2", ",", "1"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "0"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "2", ",", "1"}], "]"}]}], "-", RowBox[{"12", " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "2", ",", "1"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "2"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"1", ",", "2", ",", "1"}], "]"}]}], "+", SuperscriptBox[ RowBox[{"s", "[", RowBox[{"1", ",", "2", ",", "1"}], "]"}], "2"], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"0", ",", "1", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"2", ",", "1", ",", "1"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"1", ",", "0", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"2", ",", "1", ",", "1"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "0"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"2", ",", "1", ",", "1"}], "]"}]}], "-", RowBox[{"12", " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"2", ",", "1", ",", "1"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"1", ",", "1", ",", "2"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"2", ",", "1", ",", "1"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"s", "[", RowBox[{"1", ",", "2", ",", "1"}], "]"}], " ", RowBox[{"s", "[", RowBox[{"2", ",", "1", ",", "1"}], "]"}]}], "+", SuperscriptBox[ RowBox[{"s", "[", RowBox[{"2", ",", "1", ",", "1"}], "]"}], "2"]}]], "Input", CellChangeTimes->{{3.7935394747462997`*^9, 3.7935394748445168`*^9}},ExpressionUUID->"5ab2d411-f76c-439c-b4a8-\ 69e4391bfc67"], Cell[BoxData[ RowBox[{ RowBox[{"A", "=", RowBox[{"Sqrt", "[", RowBox[{"1", "-", RowBox[{ FractionBox[ RowBox[{"8", "g"}], SuperscriptBox["b", "2"]], RowBox[{"\[Eta]", "[", "x", "]"}], "\[Delta]Fo\[Delta]\[Eta]"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.793741067148281*^9, 3.7937411136426697`*^9}}, CellLabel->"In[80]:=",ExpressionUUID->"fead141c-7cf2-478d-a297-838bebe09fc8"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Series", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"1", "-", RowBox[{ FractionBox[ RowBox[{"8", "g"}], SuperscriptBox["b", "2"]], RowBox[{"\[Eta]", "[", "x", "]"}], "\[Delta]Fo\[Delta]\[Eta]"}]}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Eta]", "[", "x", "]"}], ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.793743846800037*^9, 3.793743856039771*^9}}, CellLabel->"In[98]:=",ExpressionUUID->"f60f6ced-d698-434d-b1b6-259a8d3625bf"], Cell[BoxData[ InterpretationBox[ RowBox[{"1", "-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{"g", " ", "\[Delta]Fo\[Delta]\[Eta]"}], ")"}], " ", RowBox[{"\[Eta]", "[", "x", "]"}]}], SuperscriptBox["b", "2"]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", RowBox[{"\[Eta]", "[", "x", "]"}], "]"}], "2"], SeriesData[ $CellContext`\[Eta][$CellContext`x], 0, {}, 0, 2, 1], Editable->False]}], SeriesData[ $CellContext`\[Eta][$CellContext`x], 0, { 1, (-4) $CellContext`b^(-2) $CellContext`g $CellContext`\[Delta]Fo\[Delta]\ \[Eta]}, 0, 2, 1], Editable->False]], "Output", CellChangeTimes->{3.793743859432831*^9}, CellLabel->"Out[98]=",ExpressionUUID->"ce625025-4360-455f-82b5-b9530ae4d111"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Series", "[", RowBox[{ RowBox[{ FractionBox[ SuperscriptBox["b", "2"], RowBox[{"4", "g"}]], RowBox[{"(", RowBox[{"A", "-", SuperscriptBox["A", "2"]}], ")"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Eta]", "[", "x", "]"}], ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.793741117161496*^9, 3.7937411420266447`*^9}}, CellLabel->"In[81]:=",ExpressionUUID->"16de18cb-0c52-4dab-9a12-e27dcf2d6fc9"], Cell[BoxData[ InterpretationBox[ RowBox[{ RowBox[{"\[Delta]Fo\[Delta]\[Eta]", " ", RowBox[{"\[Eta]", "[", "x", "]"}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", RowBox[{"\[Eta]", "[", "x", "]"}], "]"}], "2"], SeriesData[ $CellContext`\[Eta][$CellContext`x], 0, {}, 1, 2, 1], Editable->False]}], SeriesData[ $CellContext`\[Eta][$CellContext`x], 0, {$CellContext`\[Delta]Fo\[Delta]\[Eta]}, 1, 2, 1], Editable->False]], "Output", CellChangeTimes->{3.793741142658823*^9}, CellLabel->"Out[81]=",ExpressionUUID->"5c86022f-2a97-426d-a105-27ca644556d3"] }, Open ]], Cell[BoxData[ RowBox[{"cc", "=", RowBox[{"CC", "-", RowBox[{"b", RowBox[{"(", RowBox[{"2", "-", "A"}], ")"}], RowBox[{"(", FractionBox["1", RowBox[{"b", " ", "A", " ", "\[Chi]"}]]}]}]}]}]], "Input", CellChangeTimes->{{3.793742041190386*^9, 3.793742111131962*^9}},ExpressionUUID->"b204065d-c0d3-474e-bf46-\ 960ca97915f9"], Cell[BoxData[ RowBox[{"Clear", "[", "A", "]"}]], "Input", CellChangeTimes->{{3.793742928617783*^9, 3.793742934416638*^9}}, CellLabel->"In[82]:=",ExpressionUUID->"e6e51249-1961-4ba0-8491-cc8826f3a222"], Cell[BoxData[ RowBox[{"A", "[", "g"}]], "Input", CellChangeTimes->{{3.793742935137989*^9, 3.7937429381919527`*^9}},ExpressionUUID->"a1f9a74f-6349-479f-a0d8-\ 3afa27dbc2cf"], Cell[BoxData[ RowBox[{"CCC", "[", RowBox[{"CC_", ",", "b_", ",", "g_", ","}]}]], "Input", CellChangeTimes->{{3.793742911774315*^9, 3.793742922296541*^9}},ExpressionUUID->"2d175ba3-8b08-40f4-9f18-\ 393040950671"], Cell[BoxData[ RowBox[{"FourierTransform", "[", RowBox[{ RowBox[{"1", "-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{"g", " ", "\[Delta]Fo\[Delta]\[Eta]"}], ")"}], " ", RowBox[{"\[Eta]", "[", "x", "]"}]}], SuperscriptBox["b", "2"]]}], ","}]}]], "Input", CellChangeTimes->{{3.7937439219808197`*^9, 3.7937439253542013`*^9}},ExpressionUUID->"f35dc126-7704-4357-98fe-\ 523e0d2f75a7"], Cell[BoxData[ RowBox[{"A", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"1", "-", RowBox[{ FractionBox[ RowBox[{"8", "g"}], SuperscriptBox["b", "2"]], RowBox[{"\[Eta]", "[", "x", "]"}], RowBox[{"(", RowBox[{ RowBox[{"2", " ", "g", " ", SuperscriptBox[ RowBox[{"\[Epsilon]", "[", "x", "]"}], "2"], RowBox[{"\[Eta]", "[", "x", "]"}]}], "-", RowBox[{"b", " ", RowBox[{"\[Epsilon]", "[", "x", "]"}]}]}], ")"}]}]}], "]"}], "/.", RowBox[{"ss", "[", RowBox[{"[", "1", "]"}], "]"}]}], "/.", RowBox[{ RowBox[{"\[Eta]", "[", "x", "]"}], "\[Rule]", RowBox[{"\[Eta]s", " ", RowBox[{"Cos", "[", RowBox[{"qs", " ", "x"}], "]"}]}]}]}], "//", "Simplify"}]}]], "Input", CellChangeTimes->{{3.793743184168146*^9, 3.793743186360269*^9}, { 3.793743225022057*^9, 3.79374323424545*^9}, {3.793743279128126*^9, 3.793743292535133*^9}, {3.793743365160321*^9, 3.79374340324955*^9}, { 3.793743451180779*^9, 3.7937434597540073`*^9}, {3.793743495073674*^9, 3.793743544284822*^9}}, CellLabel->"In[91]:=",ExpressionUUID->"86367330-ecad-4848-a0ba-bdf293b66e9d"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AA", "=", SqrtBox[ FractionBox[ RowBox[{"1", "+", RowBox[{"12", " ", "b", " ", SuperscriptBox[ RowBox[{"Cos", "[", RowBox[{"qs", " ", "x"}], "]"}], "2"]}], "+", RowBox[{"4", " ", SuperscriptBox["b", "2"], SuperscriptBox[ RowBox[{"Cos", "[", RowBox[{"qs", " ", "x"}], "]"}], "4"]}]}], SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", "b", " ", SuperscriptBox[ RowBox[{"Cos", "[", RowBox[{"qs", " ", "x"}], "]"}], "2"]}]}], ")"}], "2"]]]}]], "Input", CellChangeTimes->{{3.793743642172892*^9, 3.793743771520555*^9}}, CellLabel->"In[96]:=",ExpressionUUID->"e00b5722-fae6-4282-a0c0-7c74db5258e3"], Cell[BoxData[ SqrtBox[ FractionBox[ RowBox[{"1", "+", RowBox[{"12", " ", "b", " ", SuperscriptBox[ RowBox[{"Cos", "[", RowBox[{"qs", " ", "x"}], "]"}], "2"]}], "+", RowBox[{"4", " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Cos", "[", RowBox[{"qs", " ", "x"}], "]"}], "4"]}]}], SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", "b", " ", SuperscriptBox[ RowBox[{"Cos", "[", RowBox[{"qs", " ", "x"}], "]"}], "2"]}]}], ")"}], "2"]]]], "Output", CellChangeTimes->{{3.793743748383366*^9, 3.793743772054668*^9}}, CellLabel->"Out[96]=",ExpressionUUID->"acca43d1-2cf7-4c66-8f61-f765de6fa91f"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FourierTransform", "[", RowBox[{"AA", ",", "x", ",", "k", ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"b", ">", "0"}], ",", RowBox[{"k", ">", "0"}], ",", RowBox[{"qs", ">", "0"}]}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.7937435458307056`*^9, 3.793743551747511*^9}, { 3.7937437747541113`*^9, 3.7937437845120173`*^9}}, CellLabel->"In[97]:=",ExpressionUUID->"0c450611-0015-4363-aeb9-daa06cff2241"], Cell[BoxData["$Aborted"], "Output", CellChangeTimes->{3.793743633712516*^9, 3.793743858452667*^9}, CellLabel->"Out[97]=",ExpressionUUID->"45be489a-043b-499f-bfbc-dadd66a9398a"] }, Open ]], Cell[BoxData[ RowBox[{"Convolve", "[", RowBox[{ FractionBox["1", RowBox[{ RowBox[{"d", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["qs", "2"], "-", SuperscriptBox["q", "2"]}], ")"}], "2"]}], "+", "\[CapitalDelta]r"}]], ",", RowBox[{"Sqrt", "[", RowBox[{"1", "-", FractionBox[ RowBox[{"8", "g"}], SuperscriptBox["b", "2"]]}]}]}]}]], "Input", CellChangeTimes->{{3.793743101140671*^9, 3.793743172813489*^9}},ExpressionUUID->"b8eeb8b8-eb37-49ca-9ce4-\ c9bfc4c7af57"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ss", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{"0", "==", RowBox[{ RowBox[{"CC", " ", RowBox[{"\[Epsilon]", "[", "x", "]"}]}], "-", RowBox[{"b", " ", RowBox[{"\[Eta]", "[", "x", "]"}]}], "+", RowBox[{"2", " ", "g", " ", RowBox[{"\[Epsilon]", "[", "x", "]"}], " ", SuperscriptBox[ RowBox[{"\[Eta]", "[", "x", "]"}], "2"]}]}]}], ",", RowBox[{"\[Epsilon]", "[", "x", "]"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.7937433173696737`*^9, 3.793743362030386*^9}}, CellLabel->"In[84]:=",ExpressionUUID->"7f8d0483-ea86-4a53-88fb-5f6501e09115"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"\[Epsilon]", "[", "x", "]"}], "\[Rule]", FractionBox[ RowBox[{"b", " ", RowBox[{"\[Eta]", "[", "x", "]"}]}], RowBox[{"CC", "+", RowBox[{"2", " ", "g", " ", SuperscriptBox[ RowBox[{"\[Eta]", "[", "x", "]"}], "2"]}]}]]}], "}"}], "}"}]], "Output", CellChangeTimes->{{3.793743357437993*^9, 3.793743362322541*^9}}, CellLabel->"Out[84]=",ExpressionUUID->"475ec955-d0ca-4d2e-aea6-c5be3d43ec81"] }, Open ]] }, WindowSize->{954, 1055}, WindowMargins->{{Automatic, 3}, {3, Automatic}}, FrontEndVersion->"12.0 for Linux x86 (64-bit) (April 8, 2019)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[558, 20, 474, 14, 49, "Input",ExpressionUUID->"aca4f188-900e-4e2f-82cb-6708cc7e7dd7"], Cell[1035, 36, 154, 3, 31, "Input",ExpressionUUID->"2eb28450-94b1-4d41-8878-74ef319b339f"], Cell[1192, 41, 639, 18, 31, "Input",ExpressionUUID->"74ea7e40-fb7c-42ad-8f65-2bd70fc9b5c0"], Cell[CellGroupData[{ Cell[1856, 63, 287, 6, 31, "Input",ExpressionUUID->"4e9ad724-362c-4e7a-9eba-cdeeee19cbcf"], Cell[2146, 71, 921, 17, 23, "Message",ExpressionUUID->"4e796e7b-8de1-4aff-a02c-0d0b747b2413"], Cell[3070, 90, 2214, 34, 43, "Message",ExpressionUUID->"99833ccf-f7f6-4574-bc6e-56a9fa33fd14"], Cell[5287, 126, 3189, 97, 105, "Output",ExpressionUUID->"4aada9fb-0136-4a39-9c2a-913465c6acfe"] }, Open ]], Cell[8491, 226, 734, 18, 170, "Input",ExpressionUUID->"debf31e8-beab-4af1-a670-3db5979cd1c2"], Cell[CellGroupData[{ Cell[9250, 248, 259, 5, 31, "Input",ExpressionUUID->"8886b158-c9fd-464d-85c7-fa6c18e364ab"], Cell[9512, 255, 618, 18, 35, "Output",ExpressionUUID->"8f8dddef-1985-4a97-a6bc-505f27bcc547"] }, Open ]], Cell[CellGroupData[{ Cell[10167, 278, 260, 6, 31, "Input",ExpressionUUID->"54e4a5a1-16be-4de6-9f0d-ce2e33df826d"], Cell[10430, 286, 499, 15, 37, "Output",ExpressionUUID->"a214a07c-8435-4ab9-8f4c-9012e4af817a"] }, Open ]], Cell[10944, 304, 207, 4, 31, "Input",ExpressionUUID->"60ab5996-56b2-4116-a22b-4351bfe6a76c"], Cell[CellGroupData[{ Cell[11176, 312, 574, 18, 31, "Input",ExpressionUUID->"7d739818-5a8a-4e64-8a11-c3eb86c80f79"], Cell[11753, 332, 741, 23, 83, "Output",ExpressionUUID->"5e118c38-3841-4e44-a4f4-4c504b5cc22c"] }, Open ]], Cell[CellGroupData[{ Cell[12531, 360, 265, 5, 31, "Input",ExpressionUUID->"33d7f345-4f7e-463b-8a47-f9a31fac8992"], Cell[12799, 367, 323, 9, 37, "Output",ExpressionUUID->"b8e16ebb-99fc-421d-8b9f-17c8b7116188"] }, Open ]], Cell[CellGroupData[{ Cell[13159, 381, 613, 16, 39, "Input",ExpressionUUID->"a5e5313a-3cbe-4ee7-bf9f-86d6d149c6fe"], Cell[13775, 399, 251, 6, 62, "Output",ExpressionUUID->"9fbd9d22-95ab-435b-9d32-a01694cee41c"] }, Open ]], Cell[CellGroupData[{ Cell[14063, 410, 1943, 59, 108, "Input",ExpressionUUID->"c80114c3-359b-4431-b57c-41ec3ec86c28"], Cell[16009, 471, 178, 3, 35, "Output",ExpressionUUID->"ecb93ba9-a956-4222-b24f-e0206d97dee4"] }, Open ]], Cell[16202, 477, 223, 6, 33, "Input",ExpressionUUID->"1e05e21d-787c-426a-9b90-e83b24238655"], Cell[16428, 485, 205, 3, 31, "Input",ExpressionUUID->"66f37bdc-cf01-4316-9982-d4a449b28fe5"], Cell[CellGroupData[{ Cell[16658, 492, 2445, 74, 115, "Input",ExpressionUUID->"4c3c31ca-4388-4656-980a-b8756fc51dde"], Cell[19106, 568, 30019, 511, 238, "Output",ExpressionUUID->"f8286c1f-f644-4bfb-83c7-8ed63b92cbce"] }, Open ]], Cell[CellGroupData[{ Cell[49162, 1084, 452, 11, 31, "Input",ExpressionUUID->"8bae4557-85bc-4792-906e-cdf5f9954a44"], Cell[49617, 1097, 1376, 45, 71, "Output",ExpressionUUID->"8c5d5347-5047-44ec-ab4e-1d6d37a085ad"] }, Open ]], Cell[CellGroupData[{ Cell[51030, 1147, 1713, 48, 71, "Input",ExpressionUUID->"e95aa855-0ec5-4b02-9a2b-7b9f8ad86b9a"], Cell[52746, 1197, 1154, 33, 76, "Output",ExpressionUUID->"28fe16a3-13d3-4ad9-b940-beced42022e7"] }, Open ]], Cell[53915, 1233, 564, 15, 31, "Input",ExpressionUUID->"980574f0-a6f2-4bdb-9087-5c4edf46b08f"], Cell[CellGroupData[{ Cell[54504, 1252, 482, 11, 31, "Input",ExpressionUUID->"d81a95b0-baac-41e2-85a1-56476d76e643"], Cell[54989, 1265, 501, 11, 23, "Message",ExpressionUUID->"0276ced0-3e05-4431-85ff-80d6cff2f239"], Cell[55493, 1278, 503, 11, 23, "Message",ExpressionUUID->"683c37e9-522b-416a-9aec-0a641843f48a"], Cell[55999, 1291, 503, 11, 23, "Message",ExpressionUUID->"4eb8e038-2070-460c-b6a7-fc43b0c32baf"], Cell[56505, 1304, 469, 10, 23, "Message",ExpressionUUID->"be60879b-9aaf-4b71-b856-f45eacbe3f80"], Cell[56977, 1316, 11646, 238, 228, "Output",ExpressionUUID->"92a6d277-5c42-4f63-b117-58768a23e8fc"] }, Open ]], Cell[CellGroupData[{ Cell[68660, 1559, 295, 6, 31, "Input",ExpressionUUID->"19fa357b-b8b2-42f2-86cf-c70cabcec230"], Cell[68958, 1567, 1165, 37, 77, "Output",ExpressionUUID->"17ffa7ee-f62f-4e9a-b461-02cd24382398"] }, Open ]], Cell[CellGroupData[{ Cell[70160, 1609, 509, 12, 31, "Input",ExpressionUUID->"ba8f198a-690c-424d-9cc7-343746fa1b85"], Cell[70672, 1623, 345, 5, 35, "Output",ExpressionUUID->"b1226115-e262-43fa-91ef-96afd5531fd9"] }, Open ]], Cell[CellGroupData[{ Cell[71054, 1633, 463, 11, 31, "Input",ExpressionUUID->"a69d3ea3-6c53-4757-98a9-c615f36923a6"], Cell[71520, 1646, 1608, 51, 56, "Output",ExpressionUUID->"de5bf86e-f71c-4d66-a846-9cdd3eec0bfa"] }, Open ]], Cell[73143, 1700, 825, 22, 33, "Input",ExpressionUUID->"76a5a6bf-8a98-4d15-942b-df42914ad53b"], Cell[73971, 1724, 131, 3, 31, "Input",ExpressionUUID->"56f2956b-d07d-4363-8656-bbcfe2c5f5f3"], Cell[74105, 1729, 4309, 126, 176, InheritFromParent,ExpressionUUID->"5ab2d411-f76c-439c-b4a8-69e4391bfc67"], Cell[78417, 1857, 439, 12, 50, "Input",ExpressionUUID->"fead141c-7cf2-478d-a297-838bebe09fc8"], Cell[CellGroupData[{ Cell[78881, 1873, 550, 16, 50, "Input",ExpressionUUID->"f60f6ced-d698-434d-b1b6-259a8d3625bf"], Cell[79434, 1891, 787, 22, 55, "Output",ExpressionUUID->"ce625025-4360-455f-82b5-b9530ae4d111"] }, Open ]], Cell[CellGroupData[{ Cell[80258, 1918, 496, 15, 56, "Input",ExpressionUUID->"16de18cb-0c52-4dab-9a12-e27dcf2d6fc9"], Cell[80757, 1935, 619, 17, 37, "Output",ExpressionUUID->"5c86022f-2a97-426d-a105-27ca644556d3"] }, Open ]], Cell[81391, 1955, 361, 11, 50, "Input",ExpressionUUID->"b204065d-c0d3-474e-bf46-960ca97915f9"], Cell[81755, 1968, 203, 3, 31, "Input",ExpressionUUID->"e6e51249-1961-4ba0-8491-cc8826f3a222"], Cell[81961, 1973, 177, 4, 31, "Input",ExpressionUUID->"a1f9a74f-6349-479f-a0d8-3afa27dbc2cf"], Cell[82141, 1979, 219, 5, 31, "Input",ExpressionUUID->"2d175ba3-8b08-40f4-9f18-393040950671"], Cell[82363, 1986, 437, 12, 51, "Input",ExpressionUUID->"f35dc126-7704-4357-98fe-523e0d2f75a7"], Cell[82803, 2000, 1260, 33, 50, "Input",ExpressionUUID->"86367330-ecad-4848-a0ba-bdf293b66e9d"], Cell[CellGroupData[{ Cell[84088, 2037, 762, 22, 73, InheritFromParent,ExpressionUUID->"e00b5722-fae6-4282-a0c0-7c74db5258e3"], Cell[84853, 2061, 726, 21, 75, "Output",ExpressionUUID->"acca43d1-2cf7-4c66-8f61-f765de6fa91f"] }, Open ]], Cell[CellGroupData[{ Cell[85616, 2087, 496, 11, 31, "Input",ExpressionUUID->"0c450611-0015-4363-aeb9-daa06cff2241"], Cell[86115, 2100, 178, 2, 35, "Output",ExpressionUUID->"45be489a-043b-499f-bfbc-dadd66a9398a"] }, Open ]], Cell[86308, 2105, 568, 19, 56, "Input",ExpressionUUID->"b8eeb8b8-eb37-49ca-9ce4-c9bfc4c7af57"], Cell[CellGroupData[{ Cell[86901, 2128, 646, 16, 39, "Input",ExpressionUUID->"7f8d0483-ea86-4a53-88fb-5f6501e09115"], Cell[87550, 2146, 508, 14, 58, "Output",ExpressionUUID->"475ec955-d0ca-4d2e-aea6-c5be3d43ec81"] }, Open ]] } ] *) (* End of internal cache information *)