15074 lines
623 KiB
Mathematica
15074 lines
623 KiB
Mathematica
(* Content-type: application/vnd.wolfram.mathematica *)
|
|
|
|
(*** Wolfram Notebook File ***)
|
|
(* http://www.wolfram.com/nb *)
|
|
|
|
(* CreatedBy='Mathematica 11.2' *)
|
|
|
|
(*CacheID: 234*)
|
|
(* Internal cache information:
|
|
NotebookFileLineBreakTest
|
|
NotebookFileLineBreakTest
|
|
NotebookDataPosition[ 158, 7]
|
|
NotebookDataLength[ 637442, 15065]
|
|
NotebookOptionsPosition[ 616869, 14738]
|
|
NotebookOutlinePosition[ 617265, 14754]
|
|
CellTagsIndexPosition[ 617222, 14751]
|
|
WindowFrame->Normal*)
|
|
|
|
(* Beginning of Notebook Content *)
|
|
Notebook[{
|
|
|
|
Cell[CellGroupData[{
|
|
Cell["Initialization", "Title",
|
|
CellChangeTimes->{{3.726041770598298*^9,
|
|
3.726041773223225*^9}},ExpressionUUID->"f14a9b83-4155-4933-b4bd-\
|
|
86482283a3f0"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{"Needs", "[", "\"\<MaTeX`\>\"", "]"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"SetOptions", "[",
|
|
RowBox[{"MaTeX", ",",
|
|
RowBox[{"\"\<Preamble\>\"", "\[Rule]",
|
|
RowBox[{
|
|
"{", "\"\<\\\\usepackage{amssymb,amsmath,latexsym,amsfonts,amsthm,\
|
|
mathpazo,xcolor,bm,mhchem,siunitx}\>\"", "}"}]}]}], "]"}], ";"}]}], "Input",
|
|
InitializationCell->True,
|
|
CellChangeTimes->{{3.7288240181604652`*^9, 3.728824027007351*^9}, {
|
|
3.733131339213026*^9, 3.733131352923026*^9}, {3.8307412261178923`*^9,
|
|
3.8307412292891083`*^9}},
|
|
CellLabel->"In[1]:=",ExpressionUUID->"f63df8ff-a805-43cf-b25e-970437446449"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData["\<\"Ghostscript is not found at /usr/local/bin/gs\"\>"], "Print",
|
|
CellLabel->
|
|
"During evaluation of \
|
|
In[1]:=",ExpressionUUID->"5cb064db-9a96-49d8-b73d-03704506f017"],
|
|
|
|
Cell[BoxData["\<\"Please configure Ghostscript using \
|
|
ConfigureMaTeX[\\\"Ghostscript\\\" -> \\\"path to gs \
|
|
executable\[Ellipsis]\\\"]\"\>"], "Print",
|
|
CellLabel->
|
|
"During evaluation of \
|
|
In[1]:=",ExpressionUUID->"a1b2528f-5340-4604-8b03-168c2a162b5a"],
|
|
|
|
Cell[BoxData[
|
|
InterpretationBox["\<\"\\!\\(\\*TemplateBox[List[\\\"\\\\\\\"Click \
|
|
here\\\\\\\"\\\", \\\"paclet:MaTeX/tutorial/ConfiguringMaTeX\\\"], \
|
|
\\\"HyperlinkPaclet\\\"]\\) for documentation on configuring MaTeX.\"\>",
|
|
StringForm["`` for documentation on configuring MaTeX.",
|
|
Hyperlink["Click here", "paclet:MaTeX/tutorial/ConfiguringMaTeX"]],
|
|
Editable->False]], "Print",
|
|
CellLabel->
|
|
"During evaluation of \
|
|
In[1]:=",ExpressionUUID->"cd6f07bd-300c-4ba1-83eb-469c1e63eaf6"]
|
|
}, Open ]]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"J3", "[",
|
|
RowBox[{"i_", ",", "a_", ",", "l_"}], "]"}], ":=",
|
|
RowBox[{"ThreeJSymbol", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"i", ",", "0"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"a", ",", "0"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"l", ",", "0"}], "}"}]}], "]"}]}], ";"}]], "Input",
|
|
InitializationCell->True,
|
|
CellChangeTimes->{{3.600453124069656*^9, 3.6004531282446003`*^9}, {
|
|
3.60048222016492*^9, 3.6004822548645678`*^9}},
|
|
CellLabel->"In[3]:=",ExpressionUUID->"06b69520-f042-4fc6-9314-22d2e79542d6"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"J6", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"a_", ",", "b_", ",", "c_"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"e_", ",", "f_", ",", "g_"}], "}"}]}], "]"}], ":=",
|
|
RowBox[{"SixJSymbol", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"e", ",", "f", ",", "g"}], "}"}]}], "]"}]}], ";"}]], "Input",
|
|
InitializationCell->True,
|
|
CellLabel->"In[4]:=",ExpressionUUID->"a8c11cd4-a9a5-4079-8595-5294b1fb94c7"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]_", ",", "m_"}]], "[",
|
|
RowBox[{"\[Theta]_", ",", "\[Phi]_"}], "]"}], "=",
|
|
RowBox[{"SphericalHarmonicY", "[",
|
|
RowBox[{"\[ScriptL]", ",", "m", ",", "\[Theta]", ",", "\[Phi]"}], "]"}]}],
|
|
";"}]], "Input",
|
|
InitializationCell->True,
|
|
CellChangeTimes->{{3.6167931952908697`*^9, 3.616793207770255*^9}},
|
|
CellLabel->"In[5]:=",ExpressionUUID->"e29c6d12-164d-461c-b102-761d687a35f0"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y", "\[ScriptL]_"], "[", "\[Theta]_", "]"}], "=",
|
|
RowBox[{"SphericalHarmonicY", "[",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",", "\[Theta]", ",", "0"}], "]"}]}],
|
|
";"}]], "Input",
|
|
InitializationCell->True,
|
|
CellChangeTimes->{{3.6167931952908697`*^9, 3.616793207770255*^9}, {
|
|
3.743229365082172*^9, 3.743229372894492*^9}},
|
|
CellLabel->"In[6]:=",ExpressionUUID->"74769596-3e6e-4ca2-8edd-d3dad7f9f8d1"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]_"], "[", "\[Theta]_", "]"}], "=",
|
|
RowBox[{"LegendreP", "[",
|
|
RowBox[{"\[ScriptL]", ",", "\[Theta]"}], "]"}]}], ";"}]], "Input",
|
|
InitializationCell->True,
|
|
CellChangeTimes->{{3.6167931952908697`*^9, 3.616793207770255*^9}, {
|
|
3.7428781062377253`*^9, 3.74287811954315*^9}},
|
|
CellLabel->"In[7]:=",ExpressionUUID->"1fff622e-e162-45b8-93d8-03e2f95f6a4a"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptCapitalY]",
|
|
RowBox[{"\[ScriptL]_", ",", "m_"}]], "[",
|
|
RowBox[{"\[Theta]_", ",", "\[Phi]_"}], "]"}], ":=",
|
|
RowBox[{"FullSimplify", "[",
|
|
RowBox[{
|
|
RowBox[{"Which", "[",
|
|
RowBox[{
|
|
RowBox[{"m", "<", "0"}], ",",
|
|
RowBox[{
|
|
FractionBox["\[ImaginaryI]",
|
|
SqrtBox["2"]],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}], "-",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"-", "1"}], ")"}], "m"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",",
|
|
RowBox[{"-", "m"}]}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}]}]}], ")"}]}], ",",
|
|
RowBox[{"m", "\[Equal]", "0"}], ",",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "0"}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}], ",",
|
|
RowBox[{"m", ">", "0"}], ",",
|
|
RowBox[{
|
|
FractionBox["1",
|
|
SqrtBox["2"]],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}], "+",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"-", "1"}], ")"}], "m"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",",
|
|
RowBox[{"-", "m"}]}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}]}]}], ")"}]}]}], "]"}],
|
|
",",
|
|
RowBox[{
|
|
RowBox[{"0", "<", "\[Theta]", "<", "\[Pi]"}], "&&",
|
|
RowBox[{"0", "<", "\[Phi]", "<",
|
|
RowBox[{"2", "\[Pi]"}]}]}]}], "]"}]}], ";"}]], "Input",
|
|
InitializationCell->True,
|
|
CellChangeTimes->{
|
|
3.617400433527934*^9, {3.6174039018984203`*^9, 3.617403963513486*^9}, {
|
|
3.617404074545025*^9, 3.6174041117104883`*^9}},
|
|
CellLabel->"In[8]:=",ExpressionUUID->"7fc2e2a8-1267-4aa2-acf5-d2d12a58563c"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"a_", ",", "b_"}]], "=",
|
|
RowBox[{"KroneckerDelta", "[",
|
|
RowBox[{"a", ",", "b"}], "]"}]}], ";"}]], "Input",
|
|
InitializationCell->True,
|
|
CellLabel->"In[9]:=",ExpressionUUID->"76897437-158e-48b2-bca0-c92679d71862"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Delta]", "x_"], "=",
|
|
RowBox[{"KroneckerDelta", "[", "x", "]"}]}], ";"}]], "Input",
|
|
InitializationCell->True,
|
|
CellLabel->"In[10]:=",ExpressionUUID->"751041e2-0753-48c1-aa6c-9f69333e4db7"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]",
|
|
RowBox[{
|
|
RowBox[{"\[ScriptL]",
|
|
RowBox[{"(",
|
|
RowBox[{"\[ScriptL]", "+", "1"}], ")"}]}], "+", "m", "+", "1"}]],
|
|
"[",
|
|
RowBox[{"\[Theta]_", ",", "\[Phi]_"}], "]"}], "=",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptCapitalY]",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",", "5"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"m", ",",
|
|
RowBox[{"-", "\[ScriptL]"}], ",", "\[ScriptL]"}], "}"}]}], "]"}],
|
|
";"}]], "Input",
|
|
InitializationCell->True,
|
|
CellChangeTimes->{3.726076349075821*^9, 3.742817932502624*^9},
|
|
CellLabel->"In[11]:=",ExpressionUUID->"f13406bf-d041-4fbb-823f-f514d04fe27c"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"SortEigensystem", "[", "eigsys_", "]"}], ":=",
|
|
RowBox[{"Transpose", "[",
|
|
RowBox[{"Sort", "[",
|
|
RowBox[{"Transpose", "[", "eigsys", "]"}], "]"}], "]"}]}]], "Input",
|
|
InitializationCell->True,
|
|
CellLabel->"In[12]:=",ExpressionUUID->"183ae429-a997-4f0d-baef-2a20bbc5c8ff"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"YY", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]1_", ",", "m1_"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]2_", ",", "m2_"}], "}"}]}], "]"}], ":=",
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]3", "=",
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{"\[ScriptL]1", "-", "\[ScriptL]1"}], "]"}]}],
|
|
RowBox[{"\[ScriptL]1", "+", "\[ScriptL]2"}]],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"m3", "=",
|
|
RowBox[{"-", "\[ScriptL]3"}]}], "\[ScriptL]3"],
|
|
RowBox[{
|
|
SqrtBox[
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]1"}], "+", "1"}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]2"}], "+", "1"}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]3"}], "+", "1"}], ")"}]}],
|
|
RowBox[{"4", "\[Pi]"}]]],
|
|
RowBox[{"J3", "[",
|
|
RowBox[{"\[ScriptL]1", ",", "\[ScriptL]2", ",", "\[ScriptL]3"}], "]"}],
|
|
|
|
RowBox[{"ThreeJSymbol", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]1", ",", "m1"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]2", ",", "m2"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]3", ",", "m3"}], "}"}]}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"-", "1"}], ")"}], "m3"],
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]3", ",",
|
|
RowBox[{"-", "m3"}]}]]}]}]}]}]], "Input",
|
|
InitializationCell->True,
|
|
CellChangeTimes->{{3.7432300298738956`*^9, 3.74323016561016*^9}},
|
|
CellLabel->"In[13]:=",ExpressionUUID->"2fd619d6-5e78-47b6-adfc-2c3a75428669"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell["Transient uniform electron gases", "Title",
|
|
CellChangeTimes->{{3.726041069929246*^9, 3.726041082828075*^9}, {
|
|
3.7607264675564423`*^9,
|
|
3.760726469171418*^9}},ExpressionUUID->"c626dffe-68a4-4be1-b83c-\
|
|
a98638c384be"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell["Useful relations", "Section",
|
|
CellChangeTimes->{{3.743229812346977*^9,
|
|
3.743229815314281*^9}},ExpressionUUID->"e0a5c645-2143-460d-a4e6-\
|
|
085c89e142f8"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"L", "=", "1"}], "}"}], ",",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0", "\[Pi]"],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0",
|
|
RowBox[{"2", "\[Pi]"}]],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], ",",
|
|
SubscriptBox["m", "1"]}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], ",",
|
|
SubscriptBox["m", "2"]}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "3"], ",",
|
|
SubscriptBox["m", "3"]}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}],
|
|
RowBox[{"\[DifferentialD]", "\[Phi]"}],
|
|
RowBox[{"\[DifferentialD]", "\[Theta]"}]}]}]}], "\[Equal]",
|
|
RowBox[{
|
|
SqrtBox[
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
SubscriptBox["\[ScriptL]", "1"]}], "+", "1"}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
SubscriptBox["\[ScriptL]", "2"]}], "+", "1"}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
SubscriptBox["\[ScriptL]", "3"]}], "+", "1"}], ")"}]}],
|
|
RowBox[{"4", "\[Pi]"}]]],
|
|
RowBox[{"J3", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], ",",
|
|
SubscriptBox["\[ScriptL]", "2"], ",",
|
|
SubscriptBox["\[ScriptL]", "3"]}], "]"}],
|
|
RowBox[{"ThreeJSymbol", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], ",",
|
|
SubscriptBox["m", "1"]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], ",",
|
|
SubscriptBox["m", "2"]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "3"], ",",
|
|
SubscriptBox["m", "3"]}], "}"}]}], "]"}]}]}], "//", "Simplify"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], ",", "0", ",", "L"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], ",", "0", ",", "L"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "3"], ",", "0", ",", "L"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["m", "1"], ",",
|
|
RowBox[{"-",
|
|
SubscriptBox["\[ScriptL]", "1"]}], ",",
|
|
SubscriptBox["\[ScriptL]", "1"]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["m", "2"], ",",
|
|
RowBox[{"-",
|
|
SubscriptBox["\[ScriptL]", "2"]}], ",",
|
|
SubscriptBox["\[ScriptL]", "2"]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["m", "3"], ",",
|
|
RowBox[{"-",
|
|
SubscriptBox["\[ScriptL]", "3"]}], ",",
|
|
SubscriptBox["\[ScriptL]", "3"]}], "}"}]}], "]"}]}], "]"}]], "Input",
|
|
CellChangeTimes->{{3.743229347616185*^9, 3.7432293566229267`*^9}, {
|
|
3.7432293931406107`*^9, 3.743229582745933*^9}, {3.743229655069162*^9,
|
|
3.74322967376245*^9}, {3.743229823945314*^9, 3.7432298862913017`*^9},
|
|
3.743229927711697*^9},ExpressionUUID->"18ee6744-3e3b-4677-9588-\
|
|
1803214665ac"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{"{", "True", "}"}], "}"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], "}"}], "}"}]}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}]}], "}"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], "}"}],
|
|
"}"}]}], "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"{", "True", "}"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"{", "True", "}"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"{", "True", "}"}], "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], "}"}]}],
|
|
"}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}]}], "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], "}"}]}],
|
|
"}"}]}], "}"}]}], "}"}]}], "}"}]], "Output",
|
|
CellChangeTimes->{{3.743229886878755*^9,
|
|
3.743229929619356*^9}},ExpressionUUID->"cbca8ed1-5d8f-4e61-8033-\
|
|
cf95096b7059"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"L", "=", "2"}], "}"}], ",",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], ",",
|
|
SubscriptBox["m", "1"]}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], ",",
|
|
SubscriptBox["m", "2"]}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}]}], "\[Equal]",
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "3"], "=",
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], "-",
|
|
SubscriptBox["\[ScriptL]", "2"]}], "]"}]}],
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], "+",
|
|
SubscriptBox["\[ScriptL]", "2"]}]],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{
|
|
SubscriptBox["m", "3"], "=",
|
|
RowBox[{"-",
|
|
SubscriptBox["\[ScriptL]", "3"]}]}],
|
|
SubscriptBox["\[ScriptL]", "3"]],
|
|
RowBox[{
|
|
SqrtBox[
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
SubscriptBox["\[ScriptL]", "1"]}], "+", "1"}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
SubscriptBox["\[ScriptL]", "2"]}], "+", "1"}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
SubscriptBox["\[ScriptL]", "3"]}], "+", "1"}], ")"}]}],
|
|
RowBox[{"4", "\[Pi]"}]]],
|
|
RowBox[{"J3", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], ",",
|
|
SubscriptBox["\[ScriptL]", "2"], ",",
|
|
SubscriptBox["\[ScriptL]", "3"]}], "]"}],
|
|
RowBox[{"ThreeJSymbol", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], ",",
|
|
SubscriptBox["m", "1"]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], ",",
|
|
SubscriptBox["m", "2"]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "3"], ",",
|
|
SubscriptBox["m", "3"]}], "}"}]}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"-", "1"}], ")"}],
|
|
SubscriptBox["m", "3"]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "3"], ",",
|
|
RowBox[{"-",
|
|
SubscriptBox["m", "3"]}]}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}]}]}]}]}], "//",
|
|
"Simplify"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], ",", "0", ",", "L"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], ",", "0", ",", "L"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["m", "1"], ",",
|
|
RowBox[{"-",
|
|
SubscriptBox["\[ScriptL]", "1"]}], ",",
|
|
SubscriptBox["\[ScriptL]", "1"]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["m", "2"], ",",
|
|
RowBox[{"-",
|
|
SubscriptBox["\[ScriptL]", "2"]}], ",",
|
|
SubscriptBox["\[ScriptL]", "2"]}], "}"}]}], "]"}]}], "]"}]], "Input",
|
|
CellChangeTimes->{{3.743229347616185*^9, 3.7432293566229267`*^9}, {
|
|
3.7432293931406107`*^9, 3.743229582745933*^9}, {3.743229655069162*^9,
|
|
3.74322967376245*^9}},ExpressionUUID->"ea189845-c47e-4753-ae12-\
|
|
0c29bb7fe966"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"{", "True", "}"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}], "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}]}], "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}], ",",
|
|
RowBox[{"{", "True", "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}]}], "}"}]}], "}"}]}], "}"}]], "Output",
|
|
CellChangeTimes->{{3.743229554288212*^9, 3.743229584376692*^9}, {
|
|
3.743229656863202*^9,
|
|
3.743229675340521*^9}},ExpressionUUID->"92d6db72-9f08-4355-8160-\
|
|
14f066aceceb"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"L", "=", "5"}], "}"}], ",",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
SubscriptBox["\[ScriptL]", "1"]], "[", "\[Theta]", "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
SubscriptBox["\[ScriptL]", "2"]], "[", "\[Theta]", "]"}]}],
|
|
"\[Equal]",
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "3"], "=",
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], "-",
|
|
SubscriptBox["\[ScriptL]", "2"]}], "]"}]}],
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], "+",
|
|
SubscriptBox["\[ScriptL]", "2"]}]],
|
|
RowBox[{
|
|
SqrtBox[
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
SubscriptBox["\[ScriptL]", "1"]}], "+", "1"}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
SubscriptBox["\[ScriptL]", "2"]}], "+", "1"}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
SubscriptBox["\[ScriptL]", "3"]}], "+", "1"}], ")"}]}],
|
|
RowBox[{"4", "\[Pi]"}]]],
|
|
SuperscriptBox[
|
|
RowBox[{"J3", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], ",",
|
|
SubscriptBox["\[ScriptL]", "2"], ",",
|
|
SubscriptBox["\[ScriptL]", "3"]}], "]"}], "2"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
SubscriptBox["\[ScriptL]", "3"]], "[", "\[Theta]", "]"}]}]}]}], "//",
|
|
"Simplify"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], ",", "0", ",", "L"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], ",", "0", ",", "L"}], "}"}]}],
|
|
"]"}]}], "]"}]], "Input",
|
|
CellChangeTimes->{{3.743229754397874*^9,
|
|
3.743229790813179*^9}},ExpressionUUID->"c2d3be71-50b2-4d02-bc7c-\
|
|
fa8422bb9511"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
"True", ",", "True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
"True", ",", "True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
"True", ",", "True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
"True", ",", "True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
"True", ",", "True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
"True", ",", "True", ",", "True", ",", "True", ",", "True", ",", "True"}],
|
|
"}"}]}], "}"}]], "Output",
|
|
CellChangeTimes->{{3.743229787447109*^9,
|
|
3.7432297917507353`*^9}},ExpressionUUID->"3a86ae5d-84b5-4de4-bf01-\
|
|
e2f7182357aa"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]"}], "+", "1"}], ")"}],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0", "\[Pi]"],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}], "]"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"2", "R", " ",
|
|
RowBox[{"Sin", "[",
|
|
RowBox[{"\[Theta]", "/", "2"}], "]"}]}], ")"}], "n"],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}],
|
|
RowBox[{"\[DifferentialD]", "\[Theta]"}]}]}]}], "\[Equal]",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"2", "R"}], ")"}], "n"],
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]"}], "+", "1"}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"-", "1"}], ")"}], "\[ScriptL]"], "2", " ",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
FractionBox["n", "2"], ")"}], "!"}],
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
FractionBox["n", "2"], ")"}], "!"}]}],
|
|
RowBox[{" ",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox["n", "2"], "+", "\[ScriptL]", "+", "1"}], ")"}],
|
|
"!"}],
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox["n", "2"], "-", "\[ScriptL]"}], ")"}], "!"}]}]}]]}]}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",", "2"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"n", ",", "0", ",", "10"}], "}"}]}], "]"}], "//",
|
|
"MatrixForm"}]], "Input",
|
|
CellChangeTimes->{{3.742997563067418*^9, 3.742997629595066*^9}, {
|
|
3.743007488832282*^9, 3.7430074921039743`*^9}, {3.743008519262891*^9,
|
|
3.743008520697835*^9}, {3.743008552202379*^9, 3.74300856107659*^9}, {
|
|
3.743008673268701*^9, 3.743008689038439*^9}, {3.743010924076429*^9,
|
|
3.7430109261273117`*^9}},ExpressionUUID->"6d246081-7c23-4031-b117-\
|
|
f6e9dbc0e0a0"],
|
|
|
|
Cell[BoxData[
|
|
TagBox[
|
|
RowBox[{"(", "\[NoBreak]", GridBox[{
|
|
{"True", "True", "True", "True", "True", "True", "True", "True", "True",
|
|
"True", "True"},
|
|
{"True", "True", "True", "True", "True", "True", "True", "True", "True",
|
|
"True", "True"},
|
|
{"True", "True", "True", "True", "True", "True", "True", "True", "True",
|
|
"True", "True"}
|
|
},
|
|
GridBoxAlignment->{
|
|
"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
|
|
"RowsIndexed" -> {}},
|
|
GridBoxSpacings->{"Columns" -> {
|
|
Offset[0.27999999999999997`], {
|
|
Offset[0.7]},
|
|
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
|
|
Offset[0.2], {
|
|
Offset[0.4]},
|
|
Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
|
|
Function[BoxForm`e$,
|
|
MatrixForm[BoxForm`e$]]]], "Output",
|
|
CellChangeTimes->{3.743008697461802*^9,
|
|
3.743010934155423*^9},ExpressionUUID->"3f1ab4cb-673d-4ce6-aaea-\
|
|
91d682381bce"]
|
|
}, Open ]]
|
|
}, Closed]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell["Jacobian on a d-sphere", "Section",
|
|
CellChangeTimes->{{3.514962539137184*^9, 3.5149625496237373`*^9},
|
|
3.725888161913249*^9},ExpressionUUID->"f857da23-6512-4a44-801c-\
|
|
0238416ec25a"],
|
|
|
|
Cell[TextData[{
|
|
"For two particles on a d-sphere, we need to convert the Jacobian in the \
|
|
principal angle \[Theta] to a Jacobian in ",
|
|
Cell[BoxData[
|
|
FormBox["u", TraditionalForm]],ExpressionUUID->
|
|
"cb20c416-f00e-4253-a78d-8b716e51c9f1"]
|
|
}], "Text",
|
|
CellChangeTimes->{{3.514366347939295*^9, 3.5143663588893747`*^9}, {
|
|
3.514368123460621*^9, 3.5143681283725033`*^9}, {3.5144419641929693`*^9,
|
|
3.5144419660810423`*^9}, {3.5144420288335114`*^9, 3.514442066863542*^9}, {
|
|
3.5144421498400106`*^9,
|
|
3.5144421506088*^9}},ExpressionUUID->"2556e3c0-3c07-46c8-a4f0-e0d5f873e557"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"u", "=",
|
|
RowBox[{
|
|
RowBox[{"2", "R", " ",
|
|
RowBox[{
|
|
RowBox[{"Sin", "[",
|
|
FractionBox["\[Theta]", "2"], "]"}], "\t",
|
|
"\[DoubleLongLeftRightArrow]", "\t", "\[Theta]"}]}], "=",
|
|
RowBox[{"2",
|
|
RowBox[{"ArcSin", "[",
|
|
FractionBox["u",
|
|
RowBox[{"2", "R"}]], "]"}]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.514440997871438*^9,
|
|
3.514441038467401*^9}},ExpressionUUID->"52f037c3-c011-4459-9ec6-\
|
|
6f496c768a58"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}],
|
|
RowBox[{"d", "-", "1"}]],
|
|
RowBox[{"\[DifferentialD]", "\[Theta]"}]}],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0", "\[Pi]"],
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}],
|
|
RowBox[{"d", "-", "1"}]],
|
|
RowBox[{"\[DifferentialD]", "\[Theta]"}]}]}]], "=",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"\[CapitalGamma]", "[",
|
|
FractionBox[
|
|
RowBox[{"d", "+", "1"}], "2"], "]"}],
|
|
RowBox[{
|
|
SqrtBox["\[Pi]"], " ",
|
|
RowBox[{"\[CapitalGamma]", "[",
|
|
FractionBox["d", "2"], "]"}]}]],
|
|
SuperscriptBox[
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}],
|
|
RowBox[{"d", "-", "1"}]],
|
|
FractionBox[
|
|
RowBox[{"\[DifferentialD]", "\[Theta]"}],
|
|
RowBox[{"\[DifferentialD]", "u"}]],
|
|
RowBox[{"\[DifferentialD]", "u"}]}]}]], "Input",
|
|
CellChangeTimes->{{3.51436962491194*^9, 3.514369710622314*^9}, {
|
|
3.514369824804817*^9, 3.514369826492672*^9}, {3.514370361976281*^9,
|
|
3.514370393649591*^9}, {3.51444091636539*^9, 3.514440982678095*^9}, {
|
|
3.5144410180546293`*^9, 3.514441019516622*^9}, {3.5144411456978903`*^9,
|
|
3.514441162811365*^9}, {3.514441221975813*^9, 3.514441255639862*^9}, {
|
|
3.5144416987210093`*^9, 3.514441704046093*^9}, {3.514441741525853*^9,
|
|
3.5144417650487223`*^9}, {3.5144418247020273`*^9,
|
|
3.51444182582703*^9}},ExpressionUUID->"e939f164-90ed-4275-8c20-\
|
|
a3c9b35f02a0"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"\t\t\t",
|
|
RowBox[{"=",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"\[CapitalGamma]", "[",
|
|
FractionBox[
|
|
RowBox[{"d", "+", "1"}], "2"], "]"}],
|
|
RowBox[{
|
|
SqrtBox["\[Pi]"], " ",
|
|
RowBox[{"\[CapitalGamma]", "[",
|
|
FractionBox["d", "2"], "]"}]}]],
|
|
SuperscriptBox[
|
|
RowBox[{"Sin", "[",
|
|
RowBox[{"2",
|
|
RowBox[{"ArcSin", "[",
|
|
FractionBox["u",
|
|
RowBox[{"2", "R"}]], "]"}]}], "]"}],
|
|
RowBox[{"d", "-", "1"}]],
|
|
RowBox[{
|
|
FractionBox["\[DifferentialD]",
|
|
RowBox[{"\[DifferentialD]", "u"}]],
|
|
RowBox[{"(",
|
|
RowBox[{"2",
|
|
RowBox[{"ArcSin", "[",
|
|
FractionBox["u",
|
|
RowBox[{"2", "R"}]], "]"}]}], ")"}]}],
|
|
RowBox[{"\[DifferentialD]", "u"}]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.51436962491194*^9, 3.514369710622314*^9}, {
|
|
3.514369824804817*^9, 3.514369826492672*^9}, {3.514370361976281*^9,
|
|
3.514370393649591*^9}, {3.51444091636539*^9, 3.514440975890657*^9}, {
|
|
3.514441046579885*^9, 3.5144410552684402`*^9}, {3.5144411650853786`*^9,
|
|
3.514441165711499*^9}, {3.514441237939712*^9, 3.514441258974966*^9},
|
|
3.514441768412119*^9, {3.5144418200515213`*^9, 3.5144418393774023`*^9},
|
|
3.5144419717829742`*^9},ExpressionUUID->"abec2db9-74cd-44ab-8e15-\
|
|
ec3c2d9acd58"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"\t\t\t",
|
|
RowBox[{"=",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"\[CapitalGamma]", "[",
|
|
FractionBox[
|
|
RowBox[{"d", "+", "1"}], "2"], "]"}],
|
|
RowBox[{
|
|
SqrtBox["\[Pi]"], " ",
|
|
RowBox[{"\[CapitalGamma]", "[",
|
|
FractionBox["d", "2"], "]"}], "R"}]],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
FractionBox["u", "R"], ")"}],
|
|
RowBox[{"d", "-", "1"}]],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"1", "-",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
FractionBox["u",
|
|
RowBox[{"2", "R"}]], ")"}], "2"]}], ")"}],
|
|
FractionBox[
|
|
RowBox[{"d", "-", "2"}], "2"]],
|
|
RowBox[{"\[DifferentialD]", "u"}]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.514441348517651*^9, 3.514441350082279*^9}, {
|
|
3.514441788689559*^9, 3.514441817076388*^9}, {3.514441851341044*^9,
|
|
3.5144418681911297`*^9}, {3.5144419729582577`*^9, 3.514442001547876*^9}, {
|
|
3.5144436090329647`*^9,
|
|
3.514443609481625*^9}},ExpressionUUID->"6245dfde-4373-46ac-8f56-\
|
|
97c43c57cefd"]
|
|
}, Closed]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell["Spherium", "Section",
|
|
CellChangeTimes->{{3.4415144118152733`*^9, 3.441514417462728*^9}, {
|
|
3.441563463354508*^9, 3.4415634659050083`*^9}, {3.441648461308599*^9,
|
|
3.4416484613837833`*^9}, {3.4416489347610483`*^9, 3.44164894374827*^9}, {
|
|
3.442003673441472*^9, 3.442003679337524*^9}, {3.442384570530238*^9,
|
|
3.442384577341913*^9}, {3.4423851482723503`*^9, 3.442385148777483*^9},
|
|
3.705159142601218*^9, {3.716972358664538*^9, 3.7169723618822803`*^9}, {
|
|
3.725887700857214*^9, 3.7258877207683*^9}, {3.7258879529143953`*^9,
|
|
3.725887971537971*^9}, 3.725888164456431*^9, {3.742878203693392*^9,
|
|
3.742878210178339*^9}},ExpressionUUID->"d36161d9-7065-4d0c-9aa3-\
|
|
9e184ff60f78"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell["Legendre basis set", "Subsection",
|
|
CellChangeTimes->{{3.726073981425799*^9, 3.7260739868717747`*^9}, {
|
|
3.742878146737846*^9, 3.742878154661549*^9}, {3.742878200397444*^9,
|
|
3.74287820116363*^9}, {3.742878283137578*^9, 3.7428782911282177`*^9}, {
|
|
3.742878651086339*^9, 3.7428786516772127`*^9}, {3.7428787066524467`*^9,
|
|
3.74287871029501*^9}, {3.742898142501433*^9, 3.742898143278768*^9}, {
|
|
3.742898186664515*^9,
|
|
3.742898187434697*^9}},ExpressionUUID->"caba0f41-e4c2-48bd-b7f9-\
|
|
f49d444689e8"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox["1",
|
|
SuperscriptBox["R", "2"]]}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
SuperscriptBox["\[DifferentialD]", "2"],
|
|
RowBox[{"\[DifferentialD]",
|
|
SuperscriptBox["\[Theta]", "2"]}]],
|
|
RowBox[{"+",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
RowBox[{"Cot", "[", "\[Theta]", "]"}]}], "+",
|
|
FractionBox["1",
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]]}], ")"}]}]}],
|
|
FractionBox["\[DifferentialD]",
|
|
RowBox[{"\[DifferentialD]", "\[Theta]"}]]}], ")"}]}], "+",
|
|
FractionBox["1",
|
|
RowBox[{"2", "R", " ",
|
|
RowBox[{"Sin", "[",
|
|
RowBox[{"\[Theta]", "/", "2"}], "]"}]}]], "+",
|
|
FractionBox["1",
|
|
SuperscriptBox["R", "2"]], " \t",
|
|
RowBox[{"(*", " ",
|
|
RowBox[{
|
|
"Hamiltonian", " ", "for", " ", "the", " ", "triplet", " ", "P", " ",
|
|
"state"}], " ", "*)"}]}]], "Input",
|
|
CellChangeTimes->{{3.4415273614013968`*^9, 3.441527390402627*^9}, {
|
|
3.441558204848555*^9, 3.441558232195305*^9}, 3.441559730873198*^9, {
|
|
3.441648594035817*^9, 3.441648609697917*^9}, {3.44165798861795*^9,
|
|
3.441657994696912*^9}, {3.441658262370665*^9, 3.4416582626277857`*^9}, {
|
|
3.442003758893745*^9, 3.442003800036807*^9}, {3.4423846162448273`*^9,
|
|
3.442384679581851*^9}, {3.4423856499997*^9, 3.442385669539687*^9}, {
|
|
3.725887734569551*^9, 3.725887750488283*^9}, {3.725888167336578*^9,
|
|
3.7258881684004602`*^9}, {3.7428020206313257`*^9, 3.742802022722247*^9}, {
|
|
3.742802071248371*^9, 3.742802073411126*^9}, {3.742802113237672*^9,
|
|
3.742802114380064*^9}, {3.742878166458519*^9, 3.742878202392807*^9},
|
|
3.74287824976378*^9, {3.742878683723751*^9, 3.742878696595866*^9}, {
|
|
3.742878785782621*^9, 3.7428788081921873`*^9},
|
|
3.7428790684197273`*^9},ExpressionUUID->"19db6ad5-bc03-487e-a573-\
|
|
966ce5a1e931"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "\[ScriptL]_"], "[", "\[Theta]_", "]"}], "=",
|
|
RowBox[{
|
|
FractionBox[
|
|
SqrtBox[
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]"}], "+", "1"}]],
|
|
RowBox[{"4", "\[Pi]"}]],
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}], "]"}]}]}], ";", "\t",
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "3"}], "}"}], ",",
|
|
RowBox[{
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"8",
|
|
SuperscriptBox["\[Pi]", "2"],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0", "\[Pi]"],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "i"], "[", "\[Theta]", "]"}],
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "j"], "[", "\[Theta]", "]"}],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}],
|
|
RowBox[{"\[DifferentialD]", "\[Theta]"}]}]}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"i", ",", "0", ",", "M"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"j", ",", "0", ",", "M"}], "}"}]}], "]"}], "\[Equal]",
|
|
RowBox[{"IdentityMatrix", "[",
|
|
RowBox[{"M", "+", "1"}], "]"}]}]}], "]"}]}]], "Input",
|
|
CellChangeTimes->{{3.442384728507373*^9, 3.442384762544999*^9}, {
|
|
3.442384846108696*^9, 3.442384849245185*^9}, {3.725887836001515*^9,
|
|
3.72588783924848*^9}, {3.725887897025584*^9, 3.725887897520524*^9}, {
|
|
3.742878089764477*^9, 3.742878095672801*^9}, {3.7428781292961063`*^9,
|
|
3.742878137669608*^9}, {3.7428784349631367`*^9, 3.7428784475235558`*^9}, {
|
|
3.742878629235376*^9, 3.742878674283474*^9}, {3.742878761583694*^9,
|
|
3.742878772688912*^9}, {3.7429026540579042`*^9,
|
|
3.742902660217538*^9}},ExpressionUUID->"6cb4dcc6-ee3c-42a3-83e3-\
|
|
235f526f9182"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.7428786560165787`*^9, 3.742878674948601*^9},
|
|
3.742878773518346*^9, 3.742901391526465*^9, 3.742902661333044*^9,
|
|
3.742903268077057*^9,
|
|
3.7429231774546757`*^9},ExpressionUUID->"7a5608ac-da7f-4146-9663-\
|
|
314f8a925eb7"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "2"}], "}"}], ",",
|
|
RowBox[{
|
|
RowBox[{"H", "[", "\[Alpha]_", "]"}], "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"8",
|
|
SuperscriptBox["\[Pi]", "2"],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0", "\[Pi]"],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "i"], "[", "\[Theta]", "]"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Psi]", "j", "\[DoublePrime]"], "[",
|
|
"\[Theta]", "]"}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
RowBox[{"Cot", "[", "\[Theta]", "]"}]}], "+",
|
|
FractionBox["1",
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]]}], ")"}],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Psi]", "j", "\[Prime]"], "[",
|
|
"\[Theta]", "]"}]}]}], ")"}]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox["\[Alpha]",
|
|
RowBox[{"2", " ",
|
|
RowBox[{"Sin", "[",
|
|
RowBox[{"\[Theta]", "/", "2"}], "]"}]}]], "+", "1"}], ")"}],
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "j"], "[", "\[Theta]", "]"}]}]}], ")"}],
|
|
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}],
|
|
RowBox[{"\[DifferentialD]", "\[Theta]"}]}]}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"i", ",", "0", ",", "M"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"j", ",", "0", ",", "M"}], "}"}]}], "]"}]}]}], "]"}],
|
|
";"}]], "Input",
|
|
CellChangeTimes->{{3.742918604620111*^9, 3.7429186131351423`*^9},
|
|
3.742918719955948*^9, {3.74291885295679*^9, 3.742918854648775*^9},
|
|
3.742922362967875*^9, 3.742980439148241*^9,
|
|
3.742980540306929*^9},ExpressionUUID->"4538602f-e656-4a1f-8b53-\
|
|
fef84aa71ecb"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "2"}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{"Table", "[", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"\[Epsilon]", ",", "c"}], "}"}], "=",
|
|
RowBox[{"SortEigensystem", "[",
|
|
RowBox[{"Eigensystem", "[",
|
|
RowBox[{"N", "[",
|
|
RowBox[{
|
|
RowBox[{"H", "[", "\[Alpha]", "]"}], ",", "15"}], "]"}], "]"}],
|
|
"]"}]}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"f", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "n"], "[", "\[Theta]", "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"n", ",", "0", ",", "M"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"\[Rho]", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"8",
|
|
SuperscriptBox["\[Pi]", "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]"}], "+", "1"}], ")"}],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0", "\[Pi]"],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
"c", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
|
|
".", "f"}], ")"}], "2"],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}],
|
|
RowBox[{"\[DifferentialD]", "\[Theta]"}]}]}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",", "2"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"\"\<\[Alpha]: \>\"", ",",
|
|
RowBox[{"N", "[", "\[Alpha]", "]"}]}], "]"}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"\"\<\[Rho]: \>\"", ",", "\[Rho]"}], "]"}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
|
|
"-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}],
|
|
"+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "3",
|
|
"\[RightDoubleBracket]"}]}]}], "}"}], "]"}], ";"}],
|
|
"\[IndentingNewLine]", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Alpha]", ",",
|
|
RowBox[{"-", "10"}], ",", "0", ",", "1"}], "}"}]}], "]"}]}],
|
|
"\[IndentingNewLine]", "]"}]], "Input",
|
|
CellChangeTimes->{
|
|
3.7169719668102694`*^9, 3.725887849338797*^9, {3.725887899762218*^9,
|
|
3.725887922914515*^9}, {3.725887992098515*^9, 3.725888054354484*^9}, {
|
|
3.725888190363358*^9, 3.725888220466589*^9}, {3.725888405954722*^9,
|
|
3.7258884143609447`*^9}, {3.725888474666101*^9, 3.725888479977105*^9}, {
|
|
3.725888867994993*^9, 3.725888870697344*^9}, {3.7258889297858877`*^9,
|
|
3.725888934808717*^9}, {3.725888967938243*^9, 3.725889013634396*^9}, {
|
|
3.725889098059265*^9, 3.725889127921206*^9}, {3.725948058954719*^9,
|
|
3.7259480590574303`*^9}, 3.72594816605788*^9, {3.7259484228037577`*^9,
|
|
3.7259484452333307`*^9}, {3.7428020644337606`*^9,
|
|
3.7428020663834143`*^9}, {3.74280212730392*^9, 3.74280222326132*^9},
|
|
3.742813402384555*^9, {3.7428134755684967`*^9, 3.742813490200959*^9},
|
|
3.742814183560895*^9, {3.742819919975389*^9, 3.742819921001403*^9}, {
|
|
3.7428199815500298`*^9, 3.742819983199623*^9}, {3.742877775652999*^9,
|
|
3.7428779074014883`*^9}, {3.7428779855771227`*^9, 3.742878008161315*^9}, {
|
|
3.7428782383972187`*^9, 3.742878269832116*^9}, {3.742878722461308*^9,
|
|
3.7428787571128817`*^9}, {3.742878822183488*^9, 3.742878822578849*^9}, {
|
|
3.7428788828839493`*^9, 3.7428788901191797`*^9}, {3.74287901611771*^9,
|
|
3.742879142617798*^9}, {3.742879199059029*^9, 3.7428791995390997`*^9},
|
|
3.742901214891993*^9, {3.74290164400101*^9, 3.742901906207686*^9}, {
|
|
3.742901977623595*^9, 3.742902002095676*^9}, {3.742902032247851*^9,
|
|
3.742902129781516*^9}, {3.742902162525971*^9, 3.74290222166597*^9}, {
|
|
3.742902276796481*^9, 3.742902287956953*^9}, {3.74290235927039*^9,
|
|
3.7429024146277122`*^9}, {3.7429024507177353`*^9,
|
|
3.7429025388586197`*^9}, {3.742903006310214*^9, 3.7429030105077744`*^9}, {
|
|
3.742903134891645*^9, 3.742903234602419*^9}, {3.742903317285879*^9,
|
|
3.7429033173754187`*^9}, {3.742903361602311*^9, 3.74290336281636*^9}, {
|
|
3.742905076823636*^9, 3.7429050778905582`*^9}, {3.742918166486006*^9,
|
|
3.742918220012596*^9}, {3.742918311916502*^9, 3.742918313196629*^9}, {
|
|
3.7429183606868353`*^9, 3.742918373040654*^9}, 3.742918421383092*^9, {
|
|
3.742918494233326*^9, 3.742918623848249*^9}, {3.74291880637696*^9,
|
|
3.7429188584054213`*^9}, {3.742918994743949*^9, 3.742919000933652*^9}, {
|
|
3.742919057477284*^9, 3.7429190853953876`*^9}, {3.742919151618346*^9,
|
|
3.742919208160902*^9}, {3.742920743629745*^9, 3.742920743849949*^9},
|
|
3.742922144965681*^9, {3.742922177083435*^9, 3.742922183503256*^9},
|
|
3.742922225061594*^9, 3.742922262893311*^9, {3.742922314745081*^9,
|
|
3.7429223742620287`*^9}, {3.74292246647335*^9, 3.742922597303072*^9}, {
|
|
3.742922649922433*^9, 3.7429226518828707`*^9}, {3.742923296115052*^9,
|
|
3.742923318322493*^9}, {3.742980141599243*^9, 3.74298028080587*^9}, {
|
|
3.742980310806139*^9, 3.7429803255358543`*^9}, {3.742980357754479*^9,
|
|
3.742980398957408*^9}, {3.7429804420837727`*^9, 3.7429804467641287`*^9}, {
|
|
3.742980541432966*^9, 3.742980548122097*^9}, {3.742980578285955*^9,
|
|
3.742980578400919*^9}, {3.7429806326930037`*^9, 3.742980650442853*^9}, {
|
|
3.742980694195736*^9, 3.742980749099784*^9}, {3.742981142831009*^9,
|
|
3.742981146671338*^9}},ExpressionUUID->"1fc2dedb-8f1a-403e-a7e1-\
|
|
c8dbd76bc9e5"]
|
|
}, Closed]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell["Explicitly-correlated calculations for ground state", "Subsection",
|
|
CellChangeTimes->{{3.726073981425799*^9, 3.7260739868717747`*^9}, {
|
|
3.742878146737846*^9, 3.742878154661549*^9}, {3.742878200397444*^9,
|
|
3.74287820116363*^9}, {3.7429004809627247`*^9, 3.742900482248204*^9}, {
|
|
3.743008847489559*^9, 3.743008848427631*^9}, {3.760885320961331*^9,
|
|
3.760885323017894*^9}, {3.761038569984333*^9,
|
|
3.761038570679368*^9}},ExpressionUUID->"bdb8d3b4-c988-408c-865f-\
|
|
6a4aaefec0cc"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "10"}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{"tab", "=",
|
|
RowBox[{"Table", "[", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"\[Epsilon]", ",", "c"}], "}"}], "=",
|
|
RowBox[{"SortEigensystem", "[",
|
|
RowBox[{"Eigensystem", "[",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"N", "[",
|
|
RowBox[{
|
|
RowBox[{"H", "[", "R", "]"}], ",", "100"}], "]"}], ",",
|
|
RowBox[{"N", "[",
|
|
RowBox[{
|
|
RowBox[{"S", "[", "R", "]"}], ",", "100"}], "]"}]}], "}"}],
|
|
"]"}], "]"}]}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"Print", "[", "\[Epsilon]", "]"}], ";", "\[IndentingNewLine]",
|
|
|
|
RowBox[{"f", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "n"], "[", " ",
|
|
RowBox[{"R", " ",
|
|
SqrtBox[
|
|
RowBox[{"2", "-",
|
|
RowBox[{"2",
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}]]}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"n", ",", "M"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"\[Rho]", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"\[ScriptL]", "+",
|
|
FractionBox["1", "2"]}], ")"}],
|
|
RowBox[{"NIntegrate", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
"c", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
|
|
".", "f"}], ")"}], "2"],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}], ",",
|
|
RowBox[{"WorkingPrecision", "\[Rule]", "15"}]}], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",", "2"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"\"\<R: \>\"", ",",
|
|
RowBox[{"N", "[", "R", "]"}]}], "]"}], ";", "\[IndentingNewLine]",
|
|
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"\"\<\[Rho]: \>\"", ",", "\[Rho]"}], "]"}], ";"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"N", "[", "R", "]"}], ",",
|
|
RowBox[{"Chop", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
|
|
"-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "2",
|
|
"\[RightDoubleBracket]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "3",
|
|
"\[RightDoubleBracket]"}]}]}], "]"}]}], "}"}]}],
|
|
"\[IndentingNewLine]", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"-",
|
|
RowBox[{"Rationalize", "[", "5.3253", "]"}]}], "}"}]}], "}"}]}],
|
|
"]"}]}]}], "\[IndentingNewLine]", "]"}], "\[IndentingNewLine]",
|
|
RowBox[{"ListPlot", "[",
|
|
RowBox[{"tab", ",",
|
|
RowBox[{"Joined", "\[Rule]", "True"}], ",",
|
|
RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]}], "Input",
|
|
CellChangeTimes->{
|
|
3.7169719668102694`*^9, 3.725887849338797*^9, {3.725887899762218*^9,
|
|
3.725887922914515*^9}, {3.725887992098515*^9, 3.725888054354484*^9}, {
|
|
3.725888190363358*^9, 3.725888220466589*^9}, {3.725888405954722*^9,
|
|
3.7258884143609447`*^9}, {3.725888474666101*^9, 3.725888479977105*^9}, {
|
|
3.725888867994993*^9, 3.725888870697344*^9}, {3.7258889297858877`*^9,
|
|
3.725888934808717*^9}, {3.725888967938243*^9, 3.725889013634396*^9}, {
|
|
3.725889098059265*^9, 3.725889127921206*^9}, {3.725948058954719*^9,
|
|
3.7259480590574303`*^9}, 3.72594816605788*^9, {3.7259484228037577`*^9,
|
|
3.7259484452333307`*^9}, {3.7428020644337606`*^9,
|
|
3.7428020663834143`*^9}, {3.74280212730392*^9, 3.74280222326132*^9},
|
|
3.742813402384555*^9, {3.7428134755684967`*^9, 3.742813490200959*^9},
|
|
3.742814183560895*^9, {3.742819919975389*^9, 3.742819921001403*^9}, {
|
|
3.7428199815500298`*^9, 3.742819983199623*^9}, {3.742877775652999*^9,
|
|
3.7428779074014883`*^9}, {3.7428779855771227`*^9, 3.742878008161315*^9}, {
|
|
3.7428782383972187`*^9, 3.742878269832116*^9}, {3.742878722461308*^9,
|
|
3.7428787571128817`*^9}, {3.742878822183488*^9, 3.742878822578849*^9}, {
|
|
3.7428788828839493`*^9, 3.7428788901191797`*^9}, {3.74287901611771*^9,
|
|
3.742879142617798*^9}, {3.742879199059029*^9, 3.7428791995390997`*^9},
|
|
3.742901214891993*^9, {3.74290164400101*^9, 3.742901906207686*^9}, {
|
|
3.742901977623595*^9, 3.742902002095676*^9}, {3.742902032247851*^9,
|
|
3.742902129781516*^9}, {3.742902162525971*^9, 3.74290222166597*^9}, {
|
|
3.742902276796481*^9, 3.742902287956953*^9}, {3.74290235927039*^9,
|
|
3.7429024146277122`*^9}, {3.7429024507177353`*^9,
|
|
3.7429025388586197`*^9}, {3.742903006310214*^9, 3.7429030105077744`*^9}, {
|
|
3.742903134891645*^9, 3.742903234602419*^9}, {3.742903317285879*^9,
|
|
3.7429033173754187`*^9}, {3.742903361602311*^9, 3.74290336281636*^9}, {
|
|
3.742905076823636*^9, 3.7429050778905582`*^9}, {3.742918166486006*^9,
|
|
3.742918220012596*^9}, {3.742918311916502*^9, 3.742918313196629*^9}, {
|
|
3.7429183606868353`*^9, 3.742918373040654*^9}, 3.742918421383092*^9, {
|
|
3.742918494233326*^9, 3.742918623848249*^9}, {3.74291880637696*^9,
|
|
3.7429188584054213`*^9}, {3.742918994743949*^9, 3.742919000933652*^9}, {
|
|
3.742919057477284*^9, 3.7429190853953876`*^9}, {3.742919151618346*^9,
|
|
3.742919208160902*^9}, {3.742920743629745*^9, 3.742920743849949*^9},
|
|
3.742922144965681*^9, {3.742922177083435*^9, 3.742922183503256*^9},
|
|
3.742922225061594*^9, 3.742922262893311*^9, {3.742922314745081*^9,
|
|
3.7429223742620287`*^9}, {3.74292246647335*^9, 3.742922597303072*^9}, {
|
|
3.742922649922433*^9, 3.7429226518828707`*^9}, {3.742923296115052*^9,
|
|
3.742923318322493*^9}, {3.742980141599243*^9, 3.74298028080587*^9}, {
|
|
3.742980310806139*^9, 3.7429803255358543`*^9}, {3.742980357754479*^9,
|
|
3.742980398957408*^9}, {3.7429804420837727`*^9, 3.7429804467641287`*^9}, {
|
|
3.742980541432966*^9, 3.742980548122097*^9}, {3.742980578285955*^9,
|
|
3.742980578400919*^9}, {3.7429806326930037`*^9, 3.742980650442853*^9}, {
|
|
3.742980694195736*^9, 3.742980749099784*^9}, {3.742981142831009*^9,
|
|
3.742981146671338*^9}, {3.742995040906142*^9, 3.7429950736953487`*^9}, {
|
|
3.742995103988391*^9, 3.742995134262944*^9}, {3.742995247787807*^9,
|
|
3.742995324266892*^9}, {3.742995360656518*^9, 3.742995384384591*^9}, {
|
|
3.7429954237133417`*^9, 3.742995433990855*^9}, {3.74299547198099*^9,
|
|
3.742995484920415*^9}, {3.742995760731353*^9, 3.7429957673259373`*^9}, {
|
|
3.742995847653798*^9, 3.7429958543557777`*^9}, {3.7429960931764708`*^9,
|
|
3.742996100192951*^9}, {3.742996300021468*^9, 3.742996312749928*^9}, {
|
|
3.742996623983343*^9, 3.742996683485918*^9}, {3.742996763260223*^9,
|
|
3.7429967667513227`*^9}, {3.742996823435986*^9, 3.742996947881322*^9}, {
|
|
3.7429969858904467`*^9, 3.7429969890918093`*^9}, {3.742997154797719*^9,
|
|
3.742997179630937*^9}, {3.742997221183319*^9, 3.7429972234251423`*^9}, {
|
|
3.742997256190982*^9, 3.742997295285985*^9}, {3.742997325738884*^9,
|
|
3.7429973513749123`*^9}, {3.74299738735357*^9, 3.7429974112679663`*^9}, {
|
|
3.742997461552939*^9, 3.7429974669219646`*^9}, {3.743008210683326*^9,
|
|
3.743008225538146*^9}, 3.743009057265111*^9, {3.743009239073036*^9,
|
|
3.7430092656499767`*^9}, {3.743009361125576*^9, 3.743009373039097*^9}, {
|
|
3.7430094955856752`*^9, 3.7430095437002373`*^9}, {3.7430096137618933`*^9,
|
|
3.743009669733102*^9}, {3.743009863885*^9, 3.7430099872406483`*^9}, {
|
|
3.743010046219955*^9, 3.743010048241816*^9}, {3.7430103170795507`*^9,
|
|
3.743010344854659*^9}, {3.743011088494897*^9, 3.7430111264389553`*^9}, {
|
|
3.7430111611489353`*^9, 3.743011161959427*^9}, {3.743017152694162*^9,
|
|
3.743017214293683*^9}, {3.7430172717293787`*^9, 3.74301731611399*^9}, {
|
|
3.743050381548286*^9, 3.7430504265925217`*^9}, {3.743050459093212*^9,
|
|
3.743050513236857*^9}, {3.743058479430113*^9, 3.743058512638873*^9}, {
|
|
3.7430585676431007`*^9, 3.743058581876259*^9}, 3.743058631064424*^9, {
|
|
3.7430936684137993`*^9, 3.743093679241973*^9}, {3.743093711275429*^9,
|
|
3.7430937413274803`*^9}, {3.743093773814063*^9, 3.743093775701182*^9}, {
|
|
3.7430940895099916`*^9, 3.743094095858829*^9}, 3.743134557856875*^9, {
|
|
3.743134593968667*^9, 3.743134730681005*^9}, {3.743136067507962*^9,
|
|
3.7431360880238857`*^9}, {3.7432205013549223`*^9, 3.743220521207345*^9}, {
|
|
3.74324901832952*^9, 3.743249039226322*^9}, {3.743249141222273*^9,
|
|
3.7432491431661043`*^9}, 3.743249275352684*^9, {3.743250240903697*^9,
|
|
3.743250241066393*^9}},
|
|
CellLabel->"In[14]:=",ExpressionUUID->"fd4d7d77-fd44-443b-a877-600297ee2a20"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{
|
|
"-", "0.1221505895086752399672850481526467453951231674963393224824639187698\
|
|
510629717143679724801991059956225635619235945765`100."}], ",",
|
|
RowBox[{
|
|
"-", "0.0329776383481224696083465030844867425916092144997434553796738060473\
|
|
842476633084142694769402632462430048763648368884`100."}], ",",
|
|
"0.121189192074791677886199429384612372856196205110210467954297229577054057\
|
|
1299788262324991374025027180285762299667263`100.", ",",
|
|
"0.352824478791268842094551803605610560714169830756836675818144468000987186\
|
|
67601264685738820111391498215467923577726`100.", ",",
|
|
"0.658197287983287267972481670616492578263384688287338880906630524528966320\
|
|
4401974130248707878242182479787082595699135`100.", ",",
|
|
"1.036126198997539471845801990943954942866546829103444800341454650917282477\
|
|
5731944536633733689942485492001847246125242`100.", ",",
|
|
"1.493071436302994390071759619231425063440863301522365809679435088965429904\
|
|
2270506855869914221478548795637441650644614`100.", ",",
|
|
"2.305621582488911961576388232620486782796696540533005373783870191651545988\
|
|
9376808896048122639810653346546119604831802`100.", ",",
|
|
"5.800562289082376441214521876570322846101563848946398256812215108372655585\
|
|
7259092489543315160288367587772617431893314`100.", ",",
|
|
"61.05834835093963526398782194093927789728447678601293025105167285079751048\
|
|
35999222424279051681938080645134816458778736`100."}], "}"}]], "Print",
|
|
CellChangeTimes->{
|
|
3.7432491436528273`*^9, 3.743249275645846*^9, {3.743250241540782*^9,
|
|
3.743250269102879*^9}, 3.743252061783297*^9, 3.743252172287586*^9,
|
|
3.760885286003696*^9},
|
|
CellLabel->
|
|
"During evaluation of \
|
|
In[14]:=",ExpressionUUID->"eddb80e0-8314-4b81-a073-134184dae11a"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "5.3253`"}], ",",
|
|
RowBox[{"-", "9.219234834278800533326605743782`8.850010829569765*^-8"}]}],
|
|
"}"}], "}"}]], "Output",
|
|
CellChangeTimes->{
|
|
3.743134561955127*^9, 3.743134598396058*^9, {3.743134630792986*^9,
|
|
3.743134732201373*^9}, 3.7431360900707407`*^9, {3.743220514222476*^9,
|
|
3.743220523817198*^9}, {3.743249031908792*^9, 3.743249048224409*^9}, {
|
|
3.743249088261744*^9, 3.743249143757661*^9}, 3.7432492758447723`*^9, {
|
|
3.743250241623152*^9, 3.743250269175798*^9}, 3.743252061896006*^9,
|
|
3.7432521723645277`*^9, 3.76088528642432*^9},
|
|
CellLabel->"Out[14]=",ExpressionUUID->"77e73b0a-4204-439b-880c-363ddd8df3f0"],
|
|
|
|
Cell[BoxData[
|
|
GraphicsBox[{{}, {{}, {},
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.012833333333333334`],
|
|
AbsoluteThickness[1.6],
|
|
LineBox[{{-5.3253, -9.2192348342788*^-8}, {-5.3253, \
|
|
-9.2192348342788*^-8}}]}}, {}, {}, {}, {}},
|
|
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, Automatic}, {Automatic, Automatic}},
|
|
GridLines->{None, None},
|
|
GridLinesStyle->Directive[
|
|
GrayLevel[0.5, 0.4]],
|
|
ImageMargins->0.,
|
|
ImagePadding->All,
|
|
ImageSize->Automatic,
|
|
ImageSizeRaw->Automatic,
|
|
Method->{"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
|
|
(Identity[#]& )[
|
|
Part[#, 1]],
|
|
(Identity[#]& )[
|
|
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
|
|
(Identity[#]& )[
|
|
Part[#, 1]],
|
|
(Identity[#]& )[
|
|
Part[#, 2]]}& )}},
|
|
PlotRange->{{-10.6506, 0}, {-1.84384696685576*^-7, 0}},
|
|
PlotRangeClipping->True,
|
|
PlotRangePadding->{{
|
|
Scaled[0.02],
|
|
Scaled[0.02]}, {
|
|
Scaled[0.05],
|
|
Scaled[0.02]}},
|
|
Ticks->{Automatic, Automatic}]], "Output",
|
|
CellChangeTimes->{
|
|
3.743134561955127*^9, 3.743134598396058*^9, {3.743134630792986*^9,
|
|
3.743134732201373*^9}, 3.7431360900707407`*^9, {3.743220514222476*^9,
|
|
3.743220523817198*^9}, {3.743249031908792*^9, 3.743249048224409*^9}, {
|
|
3.743249088261744*^9, 3.743249143757661*^9}, 3.7432492758447723`*^9, {
|
|
3.743250241623152*^9, 3.743250269175798*^9}, 3.743252061896006*^9,
|
|
3.7432521723645277`*^9, 3.760885286702335*^9},
|
|
CellLabel->"Out[15]=",ExpressionUUID->"e954db0b-9de5-4b95-884f-97be0d9ee069"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"(*", " ",
|
|
RowBox[{"R", " ", "=", " ", "5.3253"}], " ", "*)"}]], "Input",
|
|
CellChangeTimes->{{3.742996084929338*^9, 3.742996087955208*^9},
|
|
3.743008844931081*^9},ExpressionUUID->"2a334965-e048-4730-b8d2-\
|
|
934066eee580"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], "\[Equal]", "0"}]], "Input",
|
|
CellChangeTimes->{{3.743008617221795*^9,
|
|
3.743008632732617*^9}},ExpressionUUID->"7e0bdb5b-809c-478e-a3d8-\
|
|
bbaf3faf9a2a"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"], "\[Proportional]",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]"}], "+", "1"}], ")"}],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0", "\[Pi]"],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"\[Psi]", "[", "u", "]"}], "2"],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}],
|
|
RowBox[{"\[DifferentialD]", "\[Theta]"}]}]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.743008638310566*^9,
|
|
3.7430087113463907`*^9}},ExpressionUUID->"efa3f2c4-c56a-4f0d-a231-\
|
|
57f12b695850"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"\[Psi]", "[", "u", "]"}], "2"], "=",
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"n", "=", "0"}], "\[Infinity]"],
|
|
RowBox[{
|
|
SubscriptBox["a", "n"],
|
|
SuperscriptBox["u", "n"]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.743008733842286*^9, 3.7430087532244596`*^9},
|
|
3.743009302480163*^9},ExpressionUUID->"6d2eae8e-6c4d-48f2-a1b2-\
|
|
4de4ecc2600b"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], "\[Equal]", "0"}]], "Input",
|
|
CellChangeTimes->{{3.743008826317938*^9, 3.743008876179605*^9}, {
|
|
3.743008923358904*^9, 3.7430089257474413`*^9}, 3.743008964749034*^9, {
|
|
3.7430110645813437`*^9,
|
|
3.7430110748797283`*^9}},ExpressionUUID->"ae82bc8b-92a9-43b2-ac92-\
|
|
6cd163b82739"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"a", "=",
|
|
RowBox[{"CoefficientList", "[",
|
|
RowBox[{
|
|
RowBox[{"1.`", "\[VeryThinSpace]", "+",
|
|
RowBox[{"0.6666467666189491`", " ", "u"}], "+",
|
|
RowBox[{"0.233711497250696`", " ",
|
|
SuperscriptBox["u", "2"]}], "+",
|
|
RowBox[{"0.057892269462279114`", " ",
|
|
SuperscriptBox["u", "3"]}], "+",
|
|
RowBox[{"0.011416060718727025`", " ",
|
|
SuperscriptBox["u", "4"]}], "+",
|
|
RowBox[{"0.0019001512003665785`", " ",
|
|
SuperscriptBox["u", "5"]}], "+",
|
|
RowBox[{"0.00027454051463773074`", " ",
|
|
SuperscriptBox["u", "6"]}], "+",
|
|
RowBox[{"0.00003485368552570877`", " ",
|
|
SuperscriptBox["u", "7"]}], "+",
|
|
RowBox[{"3.909550758995941`*^-6", " ",
|
|
SuperscriptBox["u", "8"]}], "+",
|
|
RowBox[{"3.886613919337475`*^-7", " ",
|
|
SuperscriptBox["u", "9"]}], "+",
|
|
RowBox[{"3.423932142765105`*^-8", " ",
|
|
SuperscriptBox["u", "10"]}], "+",
|
|
RowBox[{"2.6560194575496133`*^-9", " ",
|
|
SuperscriptBox["u", "11"]}], "+",
|
|
RowBox[{"1.7871244353862165`*^-10", " ",
|
|
SuperscriptBox["u", "12"]}], "+",
|
|
RowBox[{"1.017581390449739`*^-11", " ",
|
|
SuperscriptBox["u", "13"]}], "+",
|
|
RowBox[{"4.734306593585661`*^-13", " ",
|
|
SuperscriptBox["u", "14"]}], "+",
|
|
RowBox[{"1.714745687814212`*^-14", " ",
|
|
SuperscriptBox["u", "15"]}], "+",
|
|
RowBox[{"4.501929931069031`*^-16", " ",
|
|
SuperscriptBox["u", "16"]}], "+",
|
|
RowBox[{"7.574161874717616`*^-18", " ",
|
|
SuperscriptBox["u", "17"]}], "+",
|
|
RowBox[{"6.100436598427603`*^-20", " ",
|
|
SuperscriptBox["u", "18"]}]}], ",", "u"}], "]"}]}], ";"}]], "Input",
|
|
CellChangeTimes->{
|
|
3.7430101190494423`*^9, {3.743010352750772*^9, 3.743010358043541*^9}, {
|
|
3.7430111740999517`*^9, 3.7430111950267553`*^9},
|
|
3.7430113269559107`*^9},ExpressionUUID->"87275d0e-03a0-4d3c-9d6f-\
|
|
87d7d86f1997"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"NSolve", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"n", "=", "0"}],
|
|
RowBox[{
|
|
RowBox[{"Length", "[", "a", "]"}], "-", "1"}]],
|
|
RowBox[{
|
|
RowBox[{"a", "\[LeftDoubleBracket]",
|
|
RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{
|
|
SuperscriptBox["2",
|
|
RowBox[{"1", "+", "n"}]], " ",
|
|
SuperscriptBox["R", "n"], " ",
|
|
RowBox[{
|
|
FractionBox["n", "2"], "!"}]}],
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"1", "+",
|
|
FractionBox["n", "2"]}], ")"}], "!"}]], "-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
RowBox[{"(",
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
RowBox[{"3", " ",
|
|
SuperscriptBox["2",
|
|
RowBox[{"1", "+", "n"}]], " ",
|
|
SuperscriptBox["R", "n"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox["n", "2"], "!"}], ")"}], "2"]}],
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+",
|
|
FractionBox["n", "2"]}], ")"}], "!"}], " ",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"2", "+",
|
|
FractionBox["n", "2"]}], ")"}], "!"}]}]]}], ")"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
FractionBox[
|
|
RowBox[{"5", " ",
|
|
SuperscriptBox["2",
|
|
RowBox[{"1", "+", "n"}]], " ",
|
|
SuperscriptBox["R", "n"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox["n", "2"], "!"}], ")"}], "2"]}],
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+",
|
|
FractionBox["n", "2"]}], ")"}], "!"}], " ",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"3", "+",
|
|
FractionBox["n", "2"]}], ")"}], "!"}]}]]}]}], ")"}]}]}],
|
|
"\[Equal]", "0"}], ",", "R", ",", "Reals"}], "]"}]], "Input",
|
|
CellChangeTimes->{{3.743008903832117*^9, 3.743008967251095*^9}, {
|
|
3.743009196399331*^9, 3.743009223717544*^9}, {3.743009319245885*^9,
|
|
3.743009320852151*^9}, {3.743009404900145*^9, 3.7430094792063637`*^9}, {
|
|
3.743009571152327*^9, 3.7430095985464563`*^9}, {3.743009758354797*^9,
|
|
3.743009784554747*^9}, {3.743010107602206*^9, 3.743010110403318*^9}, {
|
|
3.7430101563715353`*^9, 3.743010219116867*^9}, {3.7430103802544622`*^9,
|
|
3.743010407153284*^9}, {3.743010971637995*^9, 3.74301100841931*^9}, {
|
|
3.7430111317461853`*^9, 3.743011139419375*^9}, {3.7430113023914213`*^9,
|
|
3.7430113086757936`*^9}, {3.74325075070501*^9, 3.7432507633530416`*^9}, {
|
|
3.743252178653953*^9,
|
|
3.743252191491788*^9}},ExpressionUUID->"3a93abe4-2ad3-486e-8c6e-\
|
|
7fdc2391862f"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"R", "\[Rule]",
|
|
RowBox[{"-", "7.90510513769442`"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"R", "\[Rule]",
|
|
RowBox[{"-", "5.3252580783808625`"}]}], "}"}]}], "}"}]], "Output",
|
|
CellChangeTimes->{{3.74300890102166*^9, 3.743008937590334*^9}, {
|
|
3.743008967830804*^9, 3.743008977460165*^9}, {3.743009202941248*^9,
|
|
3.743009224321291*^9}, {3.7430093127952747`*^9, 3.743009336272367*^9}, {
|
|
3.7430093977504263`*^9, 3.743009486065894*^9}, {3.743009566002088*^9,
|
|
3.743009598986909*^9}, {3.743009785285321*^9, 3.743009831584551*^9}, {
|
|
3.74301000669014*^9, 3.743010029742188*^9}, {3.743010110958336*^9,
|
|
3.743010120657176*^9}, {3.743010161125496*^9, 3.743010219470181*^9},
|
|
3.743010291783205*^9, {3.743010361433179*^9, 3.743010408716257*^9},
|
|
3.7430110099585543`*^9, {3.743011132333686*^9, 3.743011147105628*^9}, {
|
|
3.743011181862275*^9, 3.743011197086944*^9}, {3.7430113097387753`*^9,
|
|
3.743011328647744*^9}, 3.7432507526975203`*^9, {3.743252044458527*^9,
|
|
3.743252072024311*^9}, {3.74325218171531*^9,
|
|
3.74325219198354*^9}},ExpressionUUID->"3f0af36f-5a14-4009-9228-\
|
|
7f92279f21fd"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "2"}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{"tab", "=",
|
|
RowBox[{"Table", "[", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"\[Epsilon]", ",", "c"}], "}"}], "=",
|
|
RowBox[{"SortEigensystem", "[",
|
|
RowBox[{"Eigensystem", "[",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"N", "[",
|
|
RowBox[{
|
|
RowBox[{"H", "[", "R", "]"}], ",", "100"}], "]"}], ",",
|
|
RowBox[{"N", "[",
|
|
RowBox[{
|
|
RowBox[{"S", "[", "R", "]"}], ",", "100"}], "]"}]}], "}"}],
|
|
"]"}], "]"}]}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"f", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "n"], "[",
|
|
RowBox[{"2", " ", "R", " ",
|
|
RowBox[{"Sin", "[",
|
|
RowBox[{"\[Theta]", "/", "2"}], "]"}]}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"n", ",", "M"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"\[Rho]", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"\[ScriptL]", "+",
|
|
FractionBox["1", "2"]}], ")"}],
|
|
RowBox[{"NIntegrate", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
"c", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
|
|
".", "f"}], ")"}], "2"],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}], ",",
|
|
RowBox[{"WorkingPrecision", "\[Rule]", "15"}]}], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",", "2"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"\[Rho]", "=",
|
|
RowBox[{"Normalize", "[", "\[Rho]", "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"\"\<R: \>\"", ",",
|
|
RowBox[{"N", "[", "R", "]"}]}], "]"}], ";", "\[IndentingNewLine]",
|
|
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"\"\<\[Rho]: \>\"", ",", "\[Rho]"}], "]"}], ";"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"N", "[", "R", "]"}], ",",
|
|
RowBox[{"Chop", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
|
|
"-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "2",
|
|
"\[RightDoubleBracket]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "3",
|
|
"\[RightDoubleBracket]"}]}]}], "]"}]}], "}"}]}],
|
|
"\[IndentingNewLine]", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",",
|
|
RowBox[{"-", "8"}], ",",
|
|
RowBox[{"-", "1"}]}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]",
|
|
"]"}], "\[IndentingNewLine]",
|
|
RowBox[{"ListPlot", "[",
|
|
RowBox[{"tab", ",",
|
|
RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}]}], "Input",
|
|
CellChangeTimes->{
|
|
3.7169719668102694`*^9, 3.725887849338797*^9, {3.725887899762218*^9,
|
|
3.725887922914515*^9}, {3.725887992098515*^9, 3.725888054354484*^9}, {
|
|
3.725888190363358*^9, 3.725888220466589*^9}, {3.725888405954722*^9,
|
|
3.7258884143609447`*^9}, {3.725888474666101*^9, 3.725888479977105*^9}, {
|
|
3.725888867994993*^9, 3.725888870697344*^9}, {3.7258889297858877`*^9,
|
|
3.725888934808717*^9}, {3.725888967938243*^9, 3.725889013634396*^9}, {
|
|
3.725889098059265*^9, 3.725889127921206*^9}, {3.725948058954719*^9,
|
|
3.7259480590574303`*^9}, 3.72594816605788*^9, {3.7259484228037577`*^9,
|
|
3.7259484452333307`*^9}, {3.7428020644337606`*^9,
|
|
3.7428020663834143`*^9}, {3.74280212730392*^9, 3.74280222326132*^9},
|
|
3.742813402384555*^9, {3.7428134755684967`*^9, 3.742813490200959*^9},
|
|
3.742814183560895*^9, {3.742819919975389*^9, 3.742819921001403*^9}, {
|
|
3.7428199815500298`*^9, 3.742819983199623*^9}, {3.742877775652999*^9,
|
|
3.7428779074014883`*^9}, {3.7428779855771227`*^9, 3.742878008161315*^9}, {
|
|
3.7428782383972187`*^9, 3.742878269832116*^9}, {3.742878722461308*^9,
|
|
3.7428787571128817`*^9}, {3.742878822183488*^9, 3.742878822578849*^9}, {
|
|
3.7428788828839493`*^9, 3.7428788901191797`*^9}, {3.74287901611771*^9,
|
|
3.742879142617798*^9}, {3.742879199059029*^9, 3.7428791995390997`*^9},
|
|
3.742901214891993*^9, {3.74290164400101*^9, 3.742901906207686*^9}, {
|
|
3.742901977623595*^9, 3.742902002095676*^9}, {3.742902032247851*^9,
|
|
3.742902129781516*^9}, {3.742902162525971*^9, 3.74290222166597*^9}, {
|
|
3.742902276796481*^9, 3.742902287956953*^9}, {3.74290235927039*^9,
|
|
3.7429024146277122`*^9}, {3.7429024507177353`*^9,
|
|
3.7429025388586197`*^9}, {3.742903006310214*^9, 3.7429030105077744`*^9}, {
|
|
3.742903134891645*^9, 3.742903234602419*^9}, {3.742903317285879*^9,
|
|
3.7429033173754187`*^9}, {3.742903361602311*^9, 3.74290336281636*^9}, {
|
|
3.742905076823636*^9, 3.7429050778905582`*^9}, {3.742918166486006*^9,
|
|
3.742918220012596*^9}, {3.742918311916502*^9, 3.742918313196629*^9}, {
|
|
3.7429183606868353`*^9, 3.742918373040654*^9}, 3.742918421383092*^9, {
|
|
3.742918494233326*^9, 3.742918623848249*^9}, {3.74291880637696*^9,
|
|
3.7429188584054213`*^9}, {3.742918994743949*^9, 3.742919000933652*^9}, {
|
|
3.742919057477284*^9, 3.7429190853953876`*^9}, {3.742919151618346*^9,
|
|
3.742919208160902*^9}, {3.742920743629745*^9, 3.742920743849949*^9},
|
|
3.742922144965681*^9, {3.742922177083435*^9, 3.742922183503256*^9},
|
|
3.742922225061594*^9, 3.742922262893311*^9, {3.742922314745081*^9,
|
|
3.7429223742620287`*^9}, {3.74292246647335*^9, 3.742922597303072*^9}, {
|
|
3.742922649922433*^9, 3.7429226518828707`*^9}, {3.742923296115052*^9,
|
|
3.742923318322493*^9}, {3.742980141599243*^9, 3.74298028080587*^9}, {
|
|
3.742980310806139*^9, 3.7429803255358543`*^9}, {3.742980357754479*^9,
|
|
3.742980398957408*^9}, {3.7429804420837727`*^9, 3.7429804467641287`*^9}, {
|
|
3.742980541432966*^9, 3.742980548122097*^9}, {3.742980578285955*^9,
|
|
3.742980578400919*^9}, {3.7429806326930037`*^9, 3.742980650442853*^9}, {
|
|
3.742980694195736*^9, 3.742980749099784*^9}, {3.742981142831009*^9,
|
|
3.742981146671338*^9}, {3.742995040906142*^9, 3.7429950736953487`*^9}, {
|
|
3.742995103988391*^9, 3.742995134262944*^9}, {3.742995247787807*^9,
|
|
3.742995324266892*^9}, {3.742995360656518*^9, 3.742995384384591*^9}, {
|
|
3.7429954237133417`*^9, 3.742995433990855*^9}, {3.74299547198099*^9,
|
|
3.742995484920415*^9}, {3.742995760731353*^9, 3.7429957673259373`*^9}, {
|
|
3.742995847653798*^9, 3.7429958543557777`*^9}, {3.7429960931764708`*^9,
|
|
3.742996100192951*^9}, {3.742996300021468*^9, 3.742996312749928*^9}, {
|
|
3.742996623983343*^9, 3.742996683485918*^9}, {3.742996763260223*^9,
|
|
3.7429967667513227`*^9}, {3.742996823435986*^9, 3.742996947881322*^9}, {
|
|
3.7429969858904467`*^9, 3.7429969890918093`*^9}, {3.742997154797719*^9,
|
|
3.742997179630937*^9}, {3.742997221183319*^9, 3.7429972234251423`*^9}, {
|
|
3.742997256190982*^9, 3.742997295285985*^9}, {3.742997325738884*^9,
|
|
3.7429973513749123`*^9}, {3.74299738735357*^9, 3.7429974112679663`*^9}, {
|
|
3.742997461552939*^9, 3.7429974669219646`*^9}, {3.743008210683326*^9,
|
|
3.743008225538146*^9}, 3.743009057265111*^9, {3.743009239073036*^9,
|
|
3.7430092656499767`*^9}, {3.743009361125576*^9, 3.743009373039097*^9}, {
|
|
3.7430094955856752`*^9, 3.7430095437002373`*^9}, {3.7430096137618933`*^9,
|
|
3.743009669733102*^9}, {3.743009863885*^9, 3.7430099872406483`*^9}, {
|
|
3.743010046219955*^9, 3.743010048241816*^9}, {3.7430103170795507`*^9,
|
|
3.743010344854659*^9}, {3.743011088494897*^9, 3.7430111264389553`*^9}, {
|
|
3.7430111611489353`*^9, 3.743011161959427*^9}, {3.743017152694162*^9,
|
|
3.743017214293683*^9}, {3.7430172717293787`*^9, 3.74301731611399*^9}, {
|
|
3.743050381548286*^9, 3.7430504265925217`*^9}, {3.743050459093212*^9,
|
|
3.743050513236857*^9}, {3.743058479430113*^9, 3.743058512638873*^9}, {
|
|
3.7430585676431007`*^9, 3.743058581876259*^9}, 3.743058631064424*^9, {
|
|
3.7430936684137993`*^9, 3.743093679241973*^9}, {3.743093711275429*^9,
|
|
3.7430937413274803`*^9}, {3.743093773814063*^9, 3.743093775701182*^9}, {
|
|
3.7430940895099916`*^9, 3.743094095858829*^9}, {3.74324925746987*^9,
|
|
3.7432492932678623`*^9}},ExpressionUUID->"d1b1610f-85af-4346-ac50-\
|
|
e489107603e8"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "8.`"}], ",",
|
|
"0.05663767376625528048334848706351426913`13.802711341328264"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "7.`"}], ",",
|
|
"0.05515826077011463963622210991315024364`13.790751914580428"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "6.`"}], ",",
|
|
"0.05267761031337876002220813890081900529`13.769978140343293"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "5.`"}], ",",
|
|
"0.04771886253406148955033934815129399933`13.725422339701307"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "4.`"}], ",",
|
|
"0.03398178620477027569403537051987069279`13.573123108659425"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "3.`"}], ",",
|
|
RowBox[{
|
|
"-", "0.00668395560516228709635906989335329095`12.841363418604455"}]}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "2.`"}], ",",
|
|
"0.11793777599399517240707880748737754526`14.023145791709837"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "1.`"}], ",",
|
|
"0.5832241052451204458791142818175643314`14.68171816821296"}], "}"}]}],
|
|
"}"}]], "Output",
|
|
CellChangeTimes->{{3.742996657478889*^9, 3.742996694811885*^9},
|
|
3.742996774697028*^9, {3.742996831606791*^9, 3.742996930722329*^9}, {
|
|
3.742996979128537*^9, 3.742996998685197*^9}, {3.742997170258297*^9,
|
|
3.74299719396703*^9}, 3.742997236462091*^9, {3.742997281163794*^9,
|
|
3.7429973094529037`*^9}, {3.7429973429218388`*^9, 3.742997365255122*^9},
|
|
3.742997401406933*^9, 3.742997433942346*^9, 3.742997481668456*^9, {
|
|
3.743008209064024*^9, 3.743008227506484*^9}, 3.7430090700339823`*^9, {
|
|
3.743009243713592*^9, 3.74300927481546*^9}, {3.743009368158757*^9,
|
|
3.7430093778680067`*^9}, {3.743009503160977*^9, 3.743009544881068*^9}, {
|
|
3.743009615591918*^9, 3.743009674203759*^9}, {3.743009877875682*^9,
|
|
3.7430099570468187`*^9}, 3.743009988127508*^9, 3.743010048849511*^9, {
|
|
3.743010321582046*^9, 3.743010345691057*^9}, {3.743011108463632*^9,
|
|
3.7430111275578327`*^9}, 3.743011321093457*^9, {3.743017188499008*^9,
|
|
3.743017216540564*^9}, {3.743017266818322*^9, 3.7430173175941553`*^9}, {
|
|
3.743050388269188*^9, 3.7430504389575*^9}, {3.7430504717763042`*^9,
|
|
3.743050525568631*^9}, {3.743058489036425*^9, 3.743058522599071*^9}, {
|
|
3.743058573364636*^9, 3.743058631765682*^9}, {3.743093680652239*^9,
|
|
3.743093742800342*^9}, 3.743093782907002*^9, 3.743094097635339*^9, {
|
|
3.743249263535275*^9,
|
|
3.743249293845167*^9}},ExpressionUUID->"d46330e7-34f6-4fd6-87c7-\
|
|
9d62e37f39f0"],
|
|
|
|
Cell[BoxData[
|
|
GraphicsBox[{{}, {{}, {},
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.012833333333333334`],
|
|
AbsoluteThickness[1.6],
|
|
LineBox[{{-8., 0.05663767376625528}, {-7., 0.05515826077011464}, {-6.,
|
|
0.05267761031337876}, {-5., 0.04771886253406149}, {-4.,
|
|
0.03398178620477028}, {-3., -0.006683955605162287}, {-2.,
|
|
0.11793777599399517`}, {-1.7293408880365622`,
|
|
0.2438717606778325}}]}}, {}, {}, {}, {}},
|
|
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, Automatic}, {Automatic, Automatic}},
|
|
GridLines->{None, None},
|
|
GridLinesStyle->Directive[
|
|
GrayLevel[0.5, 0.4]],
|
|
ImagePadding->All,
|
|
Method->{"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
|
|
(Identity[#]& )[
|
|
Part[#, 1]],
|
|
(Identity[#]& )[
|
|
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
|
|
(Identity[#]& )[
|
|
Part[#, 1]],
|
|
(Identity[#]& )[
|
|
Part[#, 2]]}& )}},
|
|
PlotRange->{{-8., 0}, {-0.006683955605162287, 0.2438717606778325}},
|
|
PlotRangeClipping->True,
|
|
PlotRangePadding->{{
|
|
Scaled[0.02],
|
|
Scaled[0.02]}, {
|
|
Scaled[0.05],
|
|
Scaled[0.05]}},
|
|
Ticks->{Automatic, Automatic}]], "Output",
|
|
CellChangeTimes->{{3.742996657478889*^9, 3.742996694811885*^9},
|
|
3.742996774697028*^9, {3.742996831606791*^9, 3.742996930722329*^9}, {
|
|
3.742996979128537*^9, 3.742996998685197*^9}, {3.742997170258297*^9,
|
|
3.74299719396703*^9}, 3.742997236462091*^9, {3.742997281163794*^9,
|
|
3.7429973094529037`*^9}, {3.7429973429218388`*^9, 3.742997365255122*^9},
|
|
3.742997401406933*^9, 3.742997433942346*^9, 3.742997481668456*^9, {
|
|
3.743008209064024*^9, 3.743008227506484*^9}, 3.7430090700339823`*^9, {
|
|
3.743009243713592*^9, 3.74300927481546*^9}, {3.743009368158757*^9,
|
|
3.7430093778680067`*^9}, {3.743009503160977*^9, 3.743009544881068*^9}, {
|
|
3.743009615591918*^9, 3.743009674203759*^9}, {3.743009877875682*^9,
|
|
3.7430099570468187`*^9}, 3.743009988127508*^9, 3.743010048849511*^9, {
|
|
3.743010321582046*^9, 3.743010345691057*^9}, {3.743011108463632*^9,
|
|
3.7430111275578327`*^9}, 3.743011321093457*^9, {3.743017188499008*^9,
|
|
3.743017216540564*^9}, {3.743017266818322*^9, 3.7430173175941553`*^9}, {
|
|
3.743050388269188*^9, 3.7430504389575*^9}, {3.7430504717763042`*^9,
|
|
3.743050525568631*^9}, {3.743058489036425*^9, 3.743058522599071*^9}, {
|
|
3.743058573364636*^9, 3.743058631765682*^9}, {3.743093680652239*^9,
|
|
3.743093742800342*^9}, 3.743093782907002*^9, 3.743094097635339*^9, {
|
|
3.743249263535275*^9,
|
|
3.74324929392282*^9}},ExpressionUUID->"a1eff725-6cd6-4766-9c48-\
|
|
e4596ad8fcd8"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"Table", "[", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"\[Rho]", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"\[ScriptL]", "+",
|
|
FractionBox["1", "2"]}], ")"}],
|
|
RowBox[{"NIntegrate", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"1", "+",
|
|
RowBox[{"2", "R", " ",
|
|
RowBox[{
|
|
RowBox[{"Sin", "[",
|
|
RowBox[{"\[Theta]", "/", "2"}], "]"}], "/", "3"}]}]}], ")"}],
|
|
"2"],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}], ",",
|
|
RowBox[{"WorkingPrecision", "\[Rule]", "15"}]}], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",", "2"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"\[Rho]", "=",
|
|
RowBox[{"Normalize", "[", "\[Rho]", "]"}]}], ";", "\[IndentingNewLine]",
|
|
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"\"\<R: \>\"", ",",
|
|
RowBox[{"N", "[", "R", "]"}]}], "]"}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"\"\<\[Rho]: \>\"", ",", "\[Rho]"}], "]"}], ";"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"N", "[", "R", "]"}], ",",
|
|
RowBox[{"Chop", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}],
|
|
"+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "3", "\[RightDoubleBracket]"}]}]}],
|
|
"]"}]}], "}"}]}], "\[IndentingNewLine]", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",",
|
|
RowBox[{"-", "2"}], ",",
|
|
RowBox[{"-", "1"}], ",",
|
|
RowBox[{"1", "/", "10"}]}], "}"}]}], "]"}]], "Input",
|
|
CellChangeTimes->{{3.743249317434453*^9,
|
|
3.743249370435869*^9}},ExpressionUUID->"312998b8-f34f-4d8f-ada8-\
|
|
529ce8e4fc92"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "2.`"}], ",",
|
|
"0.13174565054273172613063877577446241472`14.189537982782927"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "1.9`"}], ",",
|
|
"0.0613071878644988213426676455054809456`13.83855598577885"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "1.8`"}], ",",
|
|
"0.01621148017165953868975934024109813171`13.244125144327507"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "1.7`"}], ",",
|
|
RowBox[{
|
|
"-", "0.00549819479807370640993893605019036912`12.75853216507087"}]}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "1.6`"}], ",",
|
|
RowBox[{
|
|
"-", "0.00614133775885803398953899157104994269`12.790728765694983"}]}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "1.5`"}], ",",
|
|
"0.01213213484544885266155837405930094013`13.070581074285709"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "1.4`"}], ",",
|
|
"0.04742473000348483674589975821544297506`13.647075731952729"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "1.3`"}], ",",
|
|
"0.09794465662280307408467795150154074992`13.947188398060387"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "1.2`"}], ",",
|
|
"0.16176959973608382395756211575824370712`14.151561216728714"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "1.1`"}], ",",
|
|
"0.23661760255479798428713987334398564266`14.305165344332528"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "1.`"}], ",",
|
|
"0.31970896888176448295241466594701653813`14.426982255443834"}], "}"}]}],
|
|
"}"}]], "Output",
|
|
CellChangeTimes->{{3.743249352275446*^9,
|
|
3.7432493714217453`*^9}},ExpressionUUID->"732834ed-bb17-43bb-807d-\
|
|
6b18ef0060a2"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{"c", "=",
|
|
RowBox[{"RecurrenceTable", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"a", "[", "0", "]"}], "\[Equal]", "1"}], ",",
|
|
RowBox[{
|
|
RowBox[{"a", "[", "1", "]"}], "\[Equal]", "\[Gamma]"}], ",",
|
|
RowBox[{
|
|
RowBox[{"a", "[",
|
|
RowBox[{"k", "+", "2"}], "]"}], "\[Equal]",
|
|
RowBox[{
|
|
FractionBox["\[Gamma]",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"k", "+", "2"}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"k", "+", "1"}], ")"}], "\[Gamma]"}], "+", "1"}],
|
|
")"}]}]],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"a", "[",
|
|
RowBox[{"k", "+", "1"}], "]"}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"k",
|
|
RowBox[{"(",
|
|
RowBox[{"k", "+", "\[Delta]", "-", "1"}], ")"}]}],
|
|
RowBox[{"4",
|
|
SuperscriptBox["R", "2"]}]], "-", "\[CapitalEpsilon]"}],
|
|
")"}],
|
|
RowBox[{"a", "[", "k", "]"}]}]}], ")"}]}]}]}], "}"}], "/.",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"\[Gamma]", "\[Rule]",
|
|
FractionBox["1", "3"]}], ",",
|
|
RowBox[{"\[Delta]", "\[Rule]", "5"}]}], "}"}]}], ",", "a", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"k", ",", "0", ",", "10"}], "}"}]}], "]"}]}],
|
|
";"}], "\[IndentingNewLine]",
|
|
RowBox[{"c2", "=",
|
|
RowBox[{
|
|
RowBox[{"CoefficientList", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"n", "=", "0"}],
|
|
RowBox[{
|
|
RowBox[{"Length", "[", "c", "]"}], "-", "1"}]],
|
|
RowBox[{
|
|
RowBox[{"c", "\[LeftDoubleBracket]",
|
|
RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}],
|
|
SuperscriptBox["u", "n"]}]}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"m", "=", "0"}],
|
|
RowBox[{
|
|
RowBox[{"Length", "[", "c", "]"}], "-", "1"}]],
|
|
RowBox[{
|
|
RowBox[{"c", "\[LeftDoubleBracket]",
|
|
RowBox[{"m", "+", "1"}], "\[RightDoubleBracket]"}],
|
|
SuperscriptBox["u", "m"]}]}], ")"}]}], "/.",
|
|
RowBox[{"\[CapitalEpsilon]", "->",
|
|
RowBox[{"-", "0.157412987479"}]}]}], "/.",
|
|
RowBox[{"R", "\[Rule]",
|
|
RowBox[{"-", "5.3253"}]}]}], ",", "u"}], "]"}], "//",
|
|
"N"}]}], "\[IndentingNewLine]",
|
|
RowBox[{"NSolve", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"n", "=", "0"}],
|
|
RowBox[{
|
|
RowBox[{"Length", "[", "c2", "]"}], "-", "1"}]],
|
|
RowBox[{
|
|
RowBox[{"c2", "\[LeftDoubleBracket]",
|
|
RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{
|
|
SuperscriptBox["2",
|
|
RowBox[{"1", "+", "n"}]], " ",
|
|
SuperscriptBox["R", "n"], " ",
|
|
RowBox[{
|
|
FractionBox["n", "2"], "!"}]}],
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"1", "+",
|
|
FractionBox["n", "2"]}], ")"}], "!"}]], "-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
RowBox[{"(",
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
RowBox[{"3", " ",
|
|
SuperscriptBox["2",
|
|
RowBox[{"1", "+", "n"}]], " ",
|
|
SuperscriptBox["R", "n"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox["n", "2"], "!"}], ")"}], "2"]}],
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+",
|
|
FractionBox["n", "2"]}], ")"}], "!"}], " ",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"2", "+",
|
|
FractionBox["n", "2"]}], ")"}], "!"}]}]]}], ")"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
FractionBox[
|
|
RowBox[{"5", " ",
|
|
SuperscriptBox["2",
|
|
RowBox[{"1", "+", "n"}]], " ",
|
|
SuperscriptBox["R", "n"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox["n", "2"], "!"}], ")"}], "2"]}],
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+",
|
|
FractionBox["n", "2"]}], ")"}], "!"}], " ",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"3", "+",
|
|
FractionBox["n", "2"]}], ")"}], "!"}]}]]}]}], ")"}]}]}],
|
|
"\[Equal]", "0"}], ",", "R", ",", "Reals"}], "]"}]}], "Input",
|
|
CellChangeTimes->{{3.743058256930421*^9, 3.743058272448606*^9}, {
|
|
3.743058311944397*^9, 3.743058377270937*^9}, {3.743058422125256*^9,
|
|
3.743058425331132*^9}, {3.743058546668931*^9, 3.743058546742296*^9}, {
|
|
3.743058641720284*^9, 3.7430586420763073`*^9}, {3.743058673176174*^9,
|
|
3.743058709883335*^9}, {3.743058815311449*^9, 3.743058908417449*^9}, {
|
|
3.743059013663269*^9, 3.74305901753706*^9}, {3.743059064286539*^9,
|
|
3.743059118971814*^9}, {3.743059238295856*^9, 3.7430592996460943`*^9}, {
|
|
3.743059386341751*^9, 3.743059412491478*^9}, {3.743059656942665*^9,
|
|
3.7430597753306503`*^9}, {3.7430598192186747`*^9, 3.743059838263276*^9}, {
|
|
3.743248912160686*^9, 3.743248940150074*^9}, {3.74324917661977*^9,
|
|
3.743249239136263*^9}, {3.7432493876767406`*^9, 3.743249393690229*^9}, {
|
|
3.743249547085828*^9, 3.743249553646801*^9}, {3.7432497666245327`*^9,
|
|
3.743249846178138*^9}, {3.74324987624471*^9, 3.743249889050623*^9}, {
|
|
3.743250192619252*^9, 3.74325020160819*^9}, 3.743250332485158*^9,
|
|
3.7432503778741083`*^9, {3.743250415497982*^9, 3.74325042068097*^9}, {
|
|
3.743250480403112*^9, 3.7432504891071577`*^9}, {3.743250553975196*^9,
|
|
3.743250588685631*^9}, {3.743250649758428*^9, 3.743250675590646*^9}, {
|
|
3.743250775619095*^9, 3.74325080592728*^9}, {3.7432508434027357`*^9,
|
|
3.743250846975026*^9}, {3.743252083575445*^9, 3.743252083836508*^9},
|
|
3.7432521471107607`*^9, {3.743252199341425*^9, 3.743252228836989*^9}, {
|
|
3.743252277211143*^9, 3.743252285418354*^9}, {3.743252322389007*^9,
|
|
3.743252458849464*^9}, {3.743252502110982*^9,
|
|
3.743252502254023*^9}},ExpressionUUID->"2016af84-5098-4a00-a783-\
|
|
f0d93f8c9ba3"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
"1.`", ",", "0.6666666666666666`", ",", "0.23379769131419442`", ",",
|
|
"0.0580297869675747`", ",", "0.0115338105847618`", ",",
|
|
"0.001964066241684534`", ",", "0.00029881196177178093`", ",",
|
|
"0.0000417646114165144`", ",", "5.467974643583115`*^-6", ",",
|
|
"6.800336860330669`*^-7", ",", "8.117295909053398`*^-8", ",",
|
|
"9.172017060115108`*^-9", ",", "9.674590814152652`*^-10", ",",
|
|
"9.536315676229365`*^-11", ",", "8.851338979896362`*^-12", ",",
|
|
"7.783450438494016`*^-13", ",", "6.491954529766903`*^-14", ",",
|
|
"5.103921918620108`*^-15", ",", "3.710688560792493`*^-16", ",",
|
|
"2.3732207780114273`*^-17", ",", "1.1293028521778305`*^-18"}],
|
|
"}"}]], "Output",
|
|
CellChangeTimes->{{3.743249817817011*^9, 3.743249846809401*^9}, {
|
|
3.743249876864678*^9, 3.743249889626586*^9}, {3.7432501972877703`*^9,
|
|
3.7432502020302258`*^9}, 3.7432503335088663`*^9, 3.743250378877767*^9,
|
|
3.743250421241411*^9, {3.743250482612504*^9, 3.74325048942947*^9}, {
|
|
3.743250554983243*^9, 3.743250589229115*^9}, 3.743250677082205*^9, {
|
|
3.7432507765056057`*^9, 3.7432508061787043`*^9}, {3.743250843973938*^9,
|
|
3.743250847293895*^9}, {3.7432520845834312`*^9, 3.743252091222343*^9},
|
|
3.743252149197568*^9, {3.743252201340808*^9, 3.743252229471403*^9},
|
|
3.7432522861359997`*^9, {3.743252320366165*^9, 3.743252446848074*^9}, {
|
|
3.743252478524061*^9,
|
|
3.743252502778899*^9}},ExpressionUUID->"bd9eb2f7-582b-4a68-9544-\
|
|
172d9b5d206c"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{", "}"}]], "Output",
|
|
CellChangeTimes->{{3.743249817817011*^9, 3.743249846809401*^9}, {
|
|
3.743249876864678*^9, 3.743249889626586*^9}, {3.7432501972877703`*^9,
|
|
3.7432502020302258`*^9}, 3.7432503335088663`*^9, 3.743250378877767*^9,
|
|
3.743250421241411*^9, {3.743250482612504*^9, 3.74325048942947*^9}, {
|
|
3.743250554983243*^9, 3.743250589229115*^9}, 3.743250677082205*^9, {
|
|
3.7432507765056057`*^9, 3.7432508061787043`*^9}, {3.743250843973938*^9,
|
|
3.743250847293895*^9}, {3.7432520845834312`*^9, 3.743252091222343*^9},
|
|
3.743252149197568*^9, {3.743252201340808*^9, 3.743252229471403*^9},
|
|
3.7432522861359997`*^9, {3.743252320366165*^9, 3.743252446848074*^9}, {
|
|
3.743252478524061*^9,
|
|
3.7432525027935467`*^9}},ExpressionUUID->"202780ab-b52d-489c-a92e-\
|
|
1b0fd0915e99"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"a", "=",
|
|
RowBox[{
|
|
RowBox[{"CoefficientList", "[",
|
|
RowBox[{
|
|
RowBox[{"1.`", "\[VeryThinSpace]", "+",
|
|
RowBox[{"0.6666467666189491`", " ", "u"}], "+",
|
|
RowBox[{"0.233711497250696`", " ",
|
|
SuperscriptBox["u", "2"]}], "+",
|
|
RowBox[{"0.057892269462279114`", " ",
|
|
SuperscriptBox["u", "3"]}], "+",
|
|
RowBox[{"0.011416060718727025`", " ",
|
|
SuperscriptBox["u", "4"]}], "+",
|
|
RowBox[{"0.0019001512003665785`", " ",
|
|
SuperscriptBox["u", "5"]}], "+",
|
|
RowBox[{"0.00027454051463773074`", " ",
|
|
SuperscriptBox["u", "6"]}], "+",
|
|
RowBox[{"0.00003485368552570877`", " ",
|
|
SuperscriptBox["u", "7"]}], "+",
|
|
RowBox[{"3.909550758995941`*^-6", " ",
|
|
SuperscriptBox["u", "8"]}], "+",
|
|
RowBox[{"3.886613919337475`*^-7", " ",
|
|
SuperscriptBox["u", "9"]}], "+",
|
|
RowBox[{"3.423932142765105`*^-8", " ",
|
|
SuperscriptBox["u", "10"]}], "+",
|
|
RowBox[{"2.6560194575496133`*^-9", " ",
|
|
SuperscriptBox["u", "11"]}], "+",
|
|
RowBox[{"1.7871244353862165`*^-10", " ",
|
|
SuperscriptBox["u", "12"]}], "+",
|
|
RowBox[{"1.017581390449739`*^-11", " ",
|
|
SuperscriptBox["u", "13"]}], "+",
|
|
RowBox[{"4.734306593585661`*^-13", " ",
|
|
SuperscriptBox["u", "14"]}], "+",
|
|
RowBox[{"1.714745687814212`*^-14", " ",
|
|
SuperscriptBox["u", "15"]}], "+",
|
|
RowBox[{"4.501929931069031`*^-16", " ",
|
|
SuperscriptBox["u", "16"]}], "+",
|
|
RowBox[{"7.574161874717616`*^-18", " ",
|
|
SuperscriptBox["u", "17"]}], "+",
|
|
RowBox[{"6.100436598427603`*^-20", " ",
|
|
SuperscriptBox["u", "18"]}]}], ",", "u"}], "]"}], "//",
|
|
"N"}]}]], "Input",
|
|
CellChangeTimes->{{3.743252002666154*^9,
|
|
3.743252003628837*^9}},ExpressionUUID->"30e5f6ef-f847-4642-bbeb-\
|
|
30c280b77e0b"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
"1.`", ",", "0.6666467666189491`", ",", "0.233711497250696`", ",",
|
|
"0.057892269462279114`", ",", "0.011416060718727025`", ",",
|
|
"0.0019001512003665785`", ",", "0.00027454051463773074`", ",",
|
|
"0.00003485368552570877`", ",", "3.909550758995941`*^-6", ",",
|
|
"3.886613919337475`*^-7", ",", "3.423932142765105`*^-8", ",",
|
|
"2.6560194575496133`*^-9", ",", "1.7871244353862165`*^-10", ",",
|
|
"1.017581390449739`*^-11", ",", "4.734306593585661`*^-13", ",",
|
|
"1.714745687814212`*^-14", ",", "4.501929931069031`*^-16", ",",
|
|
"7.574161874717616`*^-18", ",", "6.100436598427603`*^-20"}],
|
|
"}"}]], "Output",
|
|
CellChangeTimes->{
|
|
3.7432520041573753`*^9},ExpressionUUID->"5e69b9d6-c0fe-4adf-b5a6-\
|
|
d354021c664b"]
|
|
}, Open ]]
|
|
}, Closed]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell["Triplet P state", "Subsection",
|
|
CellChangeTimes->{{3.742903401180684*^9, 3.742903403606084*^9}, {
|
|
3.742918347228277*^9,
|
|
3.742918347362217*^9}},ExpressionUUID->"c866a966-62d2-4aaa-be30-\
|
|
188e454b7735"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "-",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}]], "Input",ExpressionUUID->\
|
|
"c4a884e6-15b7-471a-9826-860d9af553cf"],
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Rho]", "\[CapitalLambda]"], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "=",
|
|
RowBox[{"2",
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "2"],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}]}]}], "\[IndentingNewLine]",
|
|
RowBox[{"\t",
|
|
RowBox[{"=",
|
|
RowBox[{"2",
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "-",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}], ")"}],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]",
|
|
"2"]}]}]}]}]}]}], "\[IndentingNewLine]",
|
|
RowBox[{"\t",
|
|
RowBox[{"=",
|
|
RowBox[{"2",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]",
|
|
RowBox[{"3", "/", "2"}]]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]",
|
|
RowBox[{"3", "/", "2"}]]}], "3"]}]}],
|
|
")"}]}]}]}], "\[IndentingNewLine]",
|
|
RowBox[{"\t",
|
|
RowBox[{"=",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"512", " ",
|
|
SuperscriptBox["\[Pi]",
|
|
RowBox[{"5", "/", "2"}]]}], "9"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}]}], ")"}]}]}]}]}], "Input",
|
|
CellChangeTimes->{{3.825573468131763*^9, 3.825573483409993*^9}, {
|
|
3.8255735297534857`*^9, 3.825573547708323*^9}, {3.8255736418172197`*^9,
|
|
3.825573733995967*^9}},ExpressionUUID->"ee948f7b-d70d-4f37-b367-\
|
|
09ca445c478b"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Rho]", "\[Psi]"], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "2"],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}]}], "=",
|
|
RowBox[{"2",
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}], "\[Infinity]"],
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"],
|
|
FractionBox[
|
|
RowBox[{"4", "\[Pi]"}],
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]"}], "+", "1"}]],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"m", "=",
|
|
RowBox[{"-", "\[ScriptL]"}]}], "\[ScriptL]"],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}], "*"], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}]}]}]}]}]}]}]}]], "Input",\
|
|
|
|
CellChangeTimes->{
|
|
3.8255734696027603`*^9, {3.825573792746961*^9,
|
|
3.8255737998234253`*^9}},ExpressionUUID->"141f30e2-0cbb-4f96-a17a-\
|
|
38662c6cc740"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"\[CapitalPhi]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}],
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "\t",
|
|
SuperscriptBox[
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "2"]}], "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}], "\[Infinity]"],
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"],
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Gamma]", "]"}], "]"}], "\t",
|
|
SubscriptBox["c", "\[ScriptL]"]}]}], "=",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]"}], "+", "1"}], "2"],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0", "\[Pi]"],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Gamma]", "]"}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "2"],
|
|
RowBox[{"Sin", "[", "\[Gamma]", "]"}],
|
|
RowBox[{"\[DifferentialD]", "\[Gamma]"}]}]}]}]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.742897993868801*^9, 3.7428981067548847`*^9}, {
|
|
3.742898182660631*^9,
|
|
3.742898271183833*^9}},ExpressionUUID->"5f15e614-bd85-47be-b20b-\
|
|
e346fe08a2c7"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"\[Rho]", "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "2"],
|
|
SuperscriptBox[
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "2"],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}]}], "=",
|
|
RowBox[{"2",
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}], "\[Infinity]"],
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"],
|
|
FractionBox[
|
|
RowBox[{"4", "\[Pi]"}],
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]"}], "+", "1"}]],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"m", "=",
|
|
RowBox[{"-", "\[ScriptL]"}]}], "\[ScriptL]"],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}], "*"], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "2"],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}]}]}]}]}]}]}]}]], "Input",\
|
|
|
|
CellChangeTimes->{{3.742898286664424*^9,
|
|
3.7428983914044456`*^9}},ExpressionUUID->"95762630-81b3-4910-890e-\
|
|
f8cbb4b3594c"],
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "2"],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}], "=",
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"4", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}]}], "-",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"4", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}]}]}], ")"}],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}]}], "\[IndentingNewLine]",
|
|
RowBox[{"\t\t\t\t\t ",
|
|
RowBox[{"=",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"\[ScriptL]", ",", "0"}]],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"m", ",", "0"}]]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"4", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"\[ScriptL]", ",", "0"}]],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"m", ",", "0"}]]}], "-",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"\[ScriptL]", ",", "1"}]],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"m", ",", "0"}]]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"\[ScriptL]", ",", "2"}]],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"m", ",", "0"}]]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"4", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"\[ScriptL]", ",", "0"}]],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"m", ",", "0"}]]}]}]}]}]}], "Input",
|
|
CellChangeTimes->{{3.742898559305214*^9, 3.7428985732593737`*^9}, {
|
|
3.7428986183390417`*^9, 3.742898668556341*^9}, {3.742898891156012*^9,
|
|
3.7428989301880617`*^9}, {3.7428993174640627`*^9, 3.742899416229143*^9}, {
|
|
3.7428994864779387`*^9,
|
|
3.742899491064481*^9}},ExpressionUUID->"d65bd25c-ca2f-407d-9b79-\
|
|
7092dc14020a"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{"Simplify", "[",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "-",
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], ")"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "-",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}]}],
|
|
"]"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "\[Equal]",
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
SqrtBox["5"], "2"]}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}]}], "//",
|
|
"Simplify"}]}], "Input",
|
|
CellChangeTimes->{{3.742880368692409*^9, 3.7428804029481373`*^9}, {
|
|
3.742880525109131*^9, 3.7428805458700542`*^9}, {3.742898467130229*^9,
|
|
3.7428985242579517`*^9}, {3.7428992114127827`*^9, 3.742899287783554*^9}, {
|
|
3.7429000811947393`*^9, 3.742900096336309*^9}, {3.7429001529365797`*^9,
|
|
3.742900153845666*^9}, {3.7429004278822927`*^9,
|
|
3.742900428277691*^9}},ExpressionUUID->"86c4c204-12d5-4cc4-91f3-\
|
|
4ef38f2f1176"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.742880543408547*^9, 3.742880546332151*^9}, {
|
|
3.7428984748725023`*^9, 3.742898524985319*^9}, 3.742899228848856*^9, {
|
|
3.7428992728911753`*^9, 3.742899296001245*^9}, {3.742900084424329*^9,
|
|
3.74290010643225*^9}, 3.7429001543651667`*^9, 3.7429004286643667`*^9,
|
|
3.742903530777356*^9},ExpressionUUID->"a2be3453-5dee-4d23-b728-\
|
|
7cbc223eac21"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.742880543408547*^9, 3.742880546332151*^9}, {
|
|
3.7428984748725023`*^9, 3.742898524985319*^9}, 3.742899228848856*^9, {
|
|
3.7428992728911753`*^9, 3.742899296001245*^9}, {3.742900084424329*^9,
|
|
3.74290010643225*^9}, 3.7429001543651667`*^9, 3.7429004286643667`*^9,
|
|
3.7429035307907057`*^9},ExpressionUUID->"f9680827-b5a0-43a4-8fce-\
|
|
6d063ed22fc4"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{"\[Rho]", "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}], "-",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "9"],
|
|
SubscriptBox["c", "1"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"15", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "2"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
"2"]}]}]}], "\[IndentingNewLine]",
|
|
RowBox[{"\t ",
|
|
RowBox[{"=",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}]}],
|
|
")"}]}]}]}]}], "Input",ExpressionUUID->"ffcbeb9c-6e95-4df6-bb5b-\
|
|
328b41b21992"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"Solve", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0", "\[Pi]"],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0",
|
|
RowBox[{"2", "\[Pi]"}]], " ",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], ")"}],
|
|
RowBox[{"Sin", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[Phi]", "1"]}],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[Theta]", "1"]}]}]}]}], "\[Equal]", "2"}], "//",
|
|
"Simplify"}], ",",
|
|
SubscriptBox["c", "0"]}], "]"}], "//", "Expand"}]], "Input",
|
|
CellChangeTimes->{{3.819446495654708*^9, 3.819446561481535*^9}, {
|
|
3.81944724019627*^9, 3.819447254727998*^9}, 3.8194477371302137`*^9,
|
|
3.8194478701360197`*^9},
|
|
CellLabel->
|
|
"In[164]:=",ExpressionUUID->"61ee86cb-074d-4ac7-9f61-c1c6b64052ea"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "\[Rule]",
|
|
RowBox[{"1", "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"]}]}], "}"}], "}"}]], "Output",
|
|
CellChangeTimes->{{3.819446505179634*^9, 3.8194465617697144`*^9}, {
|
|
3.819447239126412*^9, 3.819447255055852*^9}, 3.819447737776888*^9,
|
|
3.8194478707360773`*^9},
|
|
CellLabel->
|
|
"Out[164]=",ExpressionUUID->"c480bc7f-ce40-4eee-b55d-3f73c76d3e72"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ",",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}]}], "}"}], "/.",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "\[Rule]",
|
|
RowBox[{"1", "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"]}]}]}], "//", "Expand"}]], "Input",
|
|
CellChangeTimes->{{3.8194472635719957`*^9, 3.819447281067357*^9}, {
|
|
3.819447733328557*^9, 3.819447750959692*^9}, 3.819447876940724*^9},
|
|
CellLabel->
|
|
"In[165]:=",ExpressionUUID->"b6e55c8f-0333-4b09-aed9-bd0241fab7b8"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"1", "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"], "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], ",",
|
|
RowBox[{"1", "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}]}], "}"}]], "Output",
|
|
CellChangeTimes->{{3.81944726401453*^9, 3.81944728132707*^9}, {
|
|
3.819447747220999*^9, 3.819447751318356*^9}, 3.819447877777974*^9},
|
|
CellLabel->
|
|
"Out[165]=",ExpressionUUID->"dacdb030-75e3-4580-b198-bc005365a6e5"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{"\[Rho]", "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "1"]}]}]}], "=",
|
|
RowBox[{
|
|
RowBox[{"2", "\t", "\[Implies]", "\t",
|
|
SubscriptBox["c", "0"]}], "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"1", "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"]}], "\t", "\[Implies]", "\t",
|
|
RowBox[{"\[Rho]", "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}]}], "=",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"1", "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"], "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"1", "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}]}],
|
|
")"}]}]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.74290046592192*^9, 3.742900508615451*^9}, {
|
|
3.7429008186008587`*^9, 3.742900822411848*^9}, {3.742901066474793*^9,
|
|
3.7429010697015457`*^9}, {3.819447915116123*^9,
|
|
3.81944792204714*^9}},ExpressionUUID->"db51f6a7-4690-40c2-af32-\
|
|
a6f7eab9b126"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"2", "-",
|
|
SubscriptBox["c", "0"], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], "=",
|
|
RowBox[{"0", "\t", "\[Implies]", "\t",
|
|
RowBox[{
|
|
SubscriptBox["c", "2"], "\[Equal]",
|
|
RowBox[{
|
|
RowBox[{"5",
|
|
SubscriptBox["c", "0"]}], "-", "10"}]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.74290109712473*^9,
|
|
3.742901159497686*^9}},ExpressionUUID->"67e833cb-794e-46bf-aaaa-\
|
|
f7fedec74084"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"Solve", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], "\[Equal]", "0"}], ",",
|
|
SubscriptBox["c", "2"]}], "]"}]], "Input",
|
|
CellChangeTimes->{{3.7430170306628857`*^9,
|
|
3.743017043403906*^9}},ExpressionUUID->"3ade0751-2e40-483d-aa9f-\
|
|
7c6decd096ba"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["c", "2"], "\[Rule]",
|
|
RowBox[{"5", " ",
|
|
SubscriptBox["c", "0"]}]}], "}"}], "}"}]], "Output",
|
|
CellChangeTimes->{{3.743017034124732*^9,
|
|
3.743017043739946*^9}},ExpressionUUID->"e43011ca-1485-4c14-8ef5-\
|
|
e3e5c2853e54"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"Solve", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], "\[Equal]", "0"}], "/.",
|
|
RowBox[{
|
|
SubscriptBox["c", "2"], "\[Rule]",
|
|
RowBox[{"5", " ",
|
|
SubscriptBox["c", "0"]}]}]}], ",",
|
|
SubscriptBox["c", "1"]}], "]"}]], "Input",
|
|
CellChangeTimes->{{3.743017049528429*^9,
|
|
3.743017086151045*^9}},ExpressionUUID->"1f77c8a4-02f2-4a43-9353-\
|
|
2c6dc0e607c1"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["c", "1"], "\[Rule]",
|
|
RowBox[{"3", " ",
|
|
SubscriptBox["c", "0"]}]}], "}"}], "}"}]], "Output",
|
|
CellChangeTimes->{{3.7430170526953163`*^9,
|
|
3.743017086756802*^9}},ExpressionUUID->"8b84c089-d48f-4520-a0df-\
|
|
2c902ca82399"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "n_"], "[", "u_", "]"}], "=",
|
|
SuperscriptBox["u",
|
|
RowBox[{"n", "-", "1"}]]}], ";"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"M", "=", "10"}], ",",
|
|
RowBox[{"d", "=", "2"}]}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"H", "[", "R_", "]"}], "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0",
|
|
RowBox[{"2", "R"}]],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "i"], "[", "u", "]"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox[
|
|
SuperscriptBox["u", "2"],
|
|
RowBox[{"4",
|
|
SuperscriptBox["R", "2"]}]], "-", "1"}], ")"}],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Psi]", "j", "\[DoublePrime]"], "[", "u",
|
|
"]"}]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "d"}], "+", "1"}], ")"}], "u"}],
|
|
RowBox[{"4",
|
|
SuperscriptBox["R", "2"]}]], "-",
|
|
FractionBox[
|
|
RowBox[{"d", "+", "1"}], "u"]}], ")"}], " ",
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Psi]", "j", "\[Prime]"], "[", "u", "]"}]}],
|
|
"+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox["1", "u"], "+",
|
|
FractionBox["d",
|
|
RowBox[{"2",
|
|
SuperscriptBox["R", "2"]}]]}], ")"}],
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "j"], "[", "u", "]"}]}]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
FractionBox["u", "R"], ")"}],
|
|
RowBox[{"d", "-", "1"}]],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"1", "-",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
FractionBox["u",
|
|
RowBox[{"2", "R"}]], ")"}], "2"]}], ")"}],
|
|
FractionBox[
|
|
RowBox[{"d", "-", "2"}], "2"]],
|
|
RowBox[{"\[DifferentialD]", "u"}]}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"i", ",", "M"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"j", ",", "M"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"S", "[", "R_", "]"}], "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0",
|
|
RowBox[{"2", "R"}]],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "i"], "[", "u", "]"}],
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "j"], "[", "u", "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
FractionBox["u", "R"], ")"}],
|
|
RowBox[{"d", "-", "1"}]],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"1", "-",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
FractionBox["u",
|
|
RowBox[{"2", "R"}]], ")"}], "2"]}], ")"}],
|
|
FractionBox[
|
|
RowBox[{"d", "-", "2"}], "2"]],
|
|
RowBox[{"\[DifferentialD]", "u"}]}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"i", ",", "M"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"j", ",", "M"}], "}"}]}], "]"}]}], ";"}]}],
|
|
"\[IndentingNewLine]", "]"}], ";"}]}], "Input",
|
|
CellLabel->
|
|
"In[185]:=",ExpressionUUID->"fc6fe6fa-c5e9-41cb-966e-1e14dcc26ff6"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "10"}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{"tab3P3", "=",
|
|
RowBox[{"Table", "[", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"\[Epsilon]", ",", "c"}], "}"}], "=",
|
|
RowBox[{"SortEigensystem", "[",
|
|
RowBox[{"Eigensystem", "[",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"N", "[",
|
|
RowBox[{
|
|
RowBox[{"H", "[", "R", "]"}], ",", "100"}], "]"}], ",",
|
|
RowBox[{"N", "[",
|
|
RowBox[{
|
|
RowBox[{"S", "[", "R", "]"}], ",", "100"}], "]"}]}], "}"}],
|
|
"]"}], "]"}]}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"f", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "n"], "[",
|
|
RowBox[{"2", " ", "R", " ",
|
|
RowBox[{"Sin", "[",
|
|
RowBox[{"\[Theta]", "/", "2"}], "]"}]}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"n", ",", "M"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"\[Rho]", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"\[ScriptL]", "+",
|
|
FractionBox["1", "2"]}], ")"}],
|
|
RowBox[{"NIntegrate", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
"c", "\[LeftDoubleBracket]", "3", "\[RightDoubleBracket]"}],
|
|
".", "f"}], ")"}], "2"],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}], ",",
|
|
RowBox[{"WorkingPrecision", "->", "30"}]}], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",", "2"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"n", "[", "\[Theta]_", "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "1",
|
|
"\[RightDoubleBracket]"}], "-",
|
|
FractionBox[
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "3",
|
|
"\[RightDoubleBracket]"}], "5"]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{"\[Theta]", ",", "0"}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "1",
|
|
"\[RightDoubleBracket]"}], "-",
|
|
RowBox[{"2",
|
|
FractionBox[
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "2",
|
|
"\[RightDoubleBracket]"}], "3"]}], "+",
|
|
FractionBox[
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "3",
|
|
"\[RightDoubleBracket]"}], "5"]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{"\[Theta]", ",", "0"}], "]"}], "2"]}]}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"NIntegrate", "[",
|
|
RowBox[{
|
|
RowBox[{"4", "\[Pi]", " ",
|
|
RowBox[{"n", "[", "\[Theta]", "]"}],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}]}], "]"}],
|
|
"]"}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"NIntegrate", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",", "0"}], "]"}], "-",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",", "0"}], "]"}]}], ")"}],
|
|
"2"],
|
|
RowBox[{"Sin", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}],
|
|
RowBox[{"Sin", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",", "0", ",", "\[Pi]"}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",", "0", ",", "\[Pi]"}],
|
|
"}"}]}], "]"}], "]"}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"Plot", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{"\[Theta]", ",", "0"}], "]"}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{"\[Theta]", ",", "0"}], "]"}]}]}], ")"}], ",",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{"\[Theta]", ",", "0"}], "]"}], ")"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}]}], "]"}],
|
|
"]"}], ";"}], "*)"}], "\[IndentingNewLine]",
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
|
|
"-",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "2",
|
|
"\[RightDoubleBracket]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "3",
|
|
"\[RightDoubleBracket]"}]}]}]}], "}"}]}], ",",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",", "\[IndentingNewLine]",
|
|
RowBox[{"-", "40"}], ",",
|
|
RowBox[{"-", "5"}], ",",
|
|
FractionBox["5", "10"]}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]",
|
|
"]"}], ";"}]], "Input",
|
|
CellLabel->
|
|
"In[197]:=",ExpressionUUID->"a06ef68f-50cc-4e7f-bfb8-5863cadce9e2"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"Show", "[",
|
|
RowBox[{"{", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"ListPlot", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"tab3P1", ",", "tab3P2", ",", "tab3P3"}], "}"}], ",",
|
|
RowBox[{"ImageSize", "\[Rule]", "500"}], ",",
|
|
RowBox[{"Joined", "\[Rule]", "True"}], ",",
|
|
RowBox[{"InterpolationOrder", "\[Rule]", "2"}], ",",
|
|
RowBox[{"PlotRange", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{"All", ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "0.00135"}], ",", "0.001"}], "}"}]}], "}"}]}], ",",
|
|
RowBox[{"PlotTheme", "\[Rule]", "\"\<Scientific\>\""}], ",",
|
|
RowBox[{"AxesStyle", "\[Rule]", "Thick"}], ",",
|
|
RowBox[{"BaseStyle", "\[Rule]", "18"}], ",",
|
|
RowBox[{"GridLines", "\[Rule]", "Automatic"}], ",",
|
|
RowBox[{"AxesStyle", "\[Rule]",
|
|
RowBox[{"Directive", "[",
|
|
RowBox[{"Black", ",", "Thick"}], "]"}]}], ",",
|
|
RowBox[{"FrameStyle", "\[Rule]",
|
|
RowBox[{"Directive", "[",
|
|
RowBox[{"Black", ",", "Thick"}], "]"}]}], ",",
|
|
RowBox[{"FrameLabel", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"Style", "[",
|
|
RowBox[{"\"\<\[Mu]\>\"", ",",
|
|
RowBox[{"FontSize", "\[Rule]", "18"}]}], "]"}], ",",
|
|
RowBox[{"Style", "[",
|
|
RowBox[{
|
|
"\"\<\!\(\*SubscriptBox[\(c\), \(0\)]\)-\!\(\*FractionBox[\(2 \
|
|
\*SubscriptBox[\(c\), \(1\)]\), \
|
|
\(3\)]\)+\!\(\*FractionBox[SubscriptBox[\(c\), \(2\)], \(5\)]\)\>\"", ",",
|
|
RowBox[{"FontSize", "\[Rule]", "18"}]}], "]"}]}], "}"}]}], ",",
|
|
RowBox[{"PlotLegends", "\[Rule]",
|
|
RowBox[{"Placed", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"Style", "[",
|
|
RowBox[{
|
|
"\"\<\!\(\*SuperscriptBox[\(\[InvisiblePrefixScriptBase]\), \
|
|
\(3\)]\)P ground state\>\"", ",",
|
|
RowBox[{"FontSize", "\[Rule]", "18"}]}], "]"}], ",",
|
|
RowBox[{"Style", "[",
|
|
RowBox[{
|
|
"\"\<\!\(\*SuperscriptBox[\(\[InvisiblePrefixScriptBase]\), \
|
|
\(3\)]\)P first excited state\>\"", ",",
|
|
RowBox[{"FontSize", "\[Rule]", "18"}]}], "]"}], ",",
|
|
RowBox[{"Style", "[",
|
|
RowBox[{
|
|
"\"\<\!\(\*SuperscriptBox[\(\[InvisiblePrefixScriptBase]\), \
|
|
\(3\)]\)P second excited state\>\"", ",",
|
|
RowBox[{"FontSize", "\[Rule]", "18"}]}], "]"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"Left", ",", "Bottom"}], "}"}]}], "]"}]}]}], "]"}],
|
|
"\[IndentingNewLine]", ",", "\[IndentingNewLine]",
|
|
RowBox[{"ListPlot", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "5.3257"}], ",", "0"}], "}"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "15.9"}], ",", "0"}], "}"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "30.9"}], ",", "0"}], "}"}], "}"}]}], "}"}], ",",
|
|
RowBox[{"PlotTheme", "\[Rule]", "\"\<Scientific\>\""}], ",",
|
|
RowBox[{"PlotMarkers", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{"Automatic", ",", "Medium"}], "}"}]}]}], "]"}]}],
|
|
"\[IndentingNewLine]", "}"}], "]"}]], "Input",
|
|
CellLabel->
|
|
"In[198]:=",ExpressionUUID->"6619aa61-41df-4561-afa2-5b697e931325"],
|
|
|
|
Cell[BoxData[
|
|
TagBox[
|
|
GraphicsBox[{{{{}, {{}, {},
|
|
{RGBColor[0.9, 0.36, 0.054], PointSize[0.009166666666666668],
|
|
AbsoluteThickness[1.6], CapForm["Butt"], LineBox[CompressedData["
|
|
1:eJwsm3dcjX8Ux5saKg0l0k573FvdUbd7u8PKyMjIKkL2CGWFUD+yZaWFpIQ2
|
|
SfjeI0kZadAuDe29I+n3dJ+vf7zu6z73eb6f7znv8znne2/6XvuWb5UQExOb
|
|
LiMmNvH/uOifAKIc99rQZqZx6LKZTwL+CSDwdp5h3Ugqp2zf8p5ffwWwIYFj
|
|
3l2Uymmi5xVYjgrA7NRXvueTVM7GDTqL3H8LoH2y3x7qqVTO3IZlXtuGBXDf
|
|
jflk67JUTljuZrW1gwJYuGrq71G9VI674gpPSr8A2tTk1w50pnACUwzmtvUI
|
|
4MSl6V9dM1I4Wi++fTzXJQAp4C+fHJDC0dVc90u2QwABiUGtZnNSOFcqssP3
|
|
tAqgb3V9yBOZFM7uvwpdL5oEsPqNu+vlj8mc5yfsKusaBJBc2aJVFJjM6Rzc
|
|
KC1RJ4DTFlMX/uUmc+7+fatkUiOAW/yMVTqjSZzX1xcML60UgPqx00fVfZM4
|
|
y15MEp4qE8DFsbP/qrsTOWu39W1N+0E874uw8fCuRE5pnGJHe5EA5rfY2zQ0
|
|
J3A++7kvMysQwI0lDRW6WxM41O9Ft3Z9FUC+xOcWq4ZnHAXwf5X6SQCj4h3u
|
|
il7POOscV73591EAMxbPtUB1Tzk6As+oJR8EYPqr3JPr9ZSzsuKO56MsYn8/
|
|
xg7daHjCEZv4B8T1Q8+6M7Y+4eg/v3PK860AxHw6FiS1xHOeD3nUvM8UQAlj
|
|
q+zh3fGctx9XzrTKEEDEgmmmyr2POQ4m/g7hLwSwIl7iyTG/xxxz9SKaUpoA
|
|
/rmZXEn/G8e5dn21yn/JE9cHfX9/No6zPULhi0QisZ7LM09ET47jpNN6twY+
|
|
FcAjrc5zy2/Gcg5vkP4pHy8AjaGhgWLtWM4zNRfG7VgBHJvpmG38+BFntfub
|
|
vcYxAvhyJX1wgd0jjp+FZ9DrBwJQXrw7mCuM4cheph5feY/Yv9XrTsksiuG8
|
|
q4j07Y0QwLtug+rp5Q85qw4ohV0KE0Cpu9fj3q0POR/czrYYhwrgfMj0uit9
|
|
0RzFU383wi1ifyPmn+s9Gc2hDhyVXHODiPfh7rDpk6M51mmj33quCcDcUGmm
|
|
zJ0HnElvTuecuyIA7r0Y+UyDB5wMJYVm7UsC6GxP9bZNvM+Z/TSMmhYsAHs5
|
|
B8p+h/uchOtWsfPOEfq79uQ3nb/H6XyXPbsyUADau9ZMOxIVxZFz2qi494wA
|
|
5gbbs26mRZLxCRBAwvxxB1ZuBKdAMWbm9RMCcI5/pbanKpzjv3XRZv3jAhh/
|
|
sjnXrCeMIyHzuzj5iAB6Fo+t9pEM42zsi9/r7CeAqSH/ZQk07nLCTTztvh4U
|
|
wLbD4zIPTEM5ibGaBmt9BDA4ts002PEOJ2pfiWPTXgE8nwWGfxfe5mw7E3rC
|
|
Z7cAYrtk/vxef4sj/9OjbXSHAPLcnZ+e2XOTcz7I7HTQNgEYbfFm3D5xg1Pr
|
|
O8JT2iqAJOUTUfaXQzhqyZ8tb3sJYLfH2doNEdc5evYPedobBbBu8dExlafX
|
|
OMuYZWMPNxC8qqeMjRy4yunpe19jvk4A84JpVdevXuaMbvb+leJOxGvg1O2u
|
|
pxc5fheFSg6rBPDA/ZrllNxgjseObxvATQC3n3tH9Tec46SM3Sqct0wASFay
|
|
I3w8iHNovtrOb64C0Fy5VV1WK5DzyGWeyepFAoi5e3kGk36Gwxe3lfvpIgCv
|
|
kuOjFssCOIv3FU/ZNk8AWRob938s9efk3LBgdc8WgKzPigdI4SgnYa/jxcN8
|
|
Yn9efw9m83zJ+HAFcGGo1my2rw/n/Tz/u+fZAhgT9Ek8WraL0zsnabUKi6hf
|
|
xx31C19u5lz5E+oYxhRAkSltw3RHd07oVge+IV0AGfQFzzyk+Rzlc9f2PrMj
|
|
8jmrY8G+CiYa8IgS0qgCKMjcpZ3rsxLN7/SiCa0F8IE3lL1ztReSs635Nt9S
|
|
AGs+6CjUD+1AdCvlq0VmxOefT+uL+bwfFdeMHFhvQsR36k3jZRGHUM3c0ONN
|
|
RgIICQp86LvnCFqxtevxfgMB5Eq3bld19kdMx9E/f3QJvj5tfH1DNgBpG7DX
|
|
B2kLIKz/aFlX72l056jtyylaAthUkjqWWHkWPeJWTg7TFIDhwckW3z8EoXmH
|
|
GWuNNARQmHd2o0fyOXRCe150opoAgiu0ohaHB6N5dvK/mCoCcHxU3PDgv4so
|
|
NiNA972SAJrMnlLXHbiM7iQ8WbFYgdjP7dHnjnpcRTqq58+WyhHxTa46cPLR
|
|
NeTQpPlsk4wAfsmNPOoLv45azDbkt0sRPHENN9wNCUFm1SvafCUEsM/NI/RA
|
|
8A0kLgoQsd+C+NUnA26i3SEeUy6M8UFDRSr8zeFbaNfN/ZpTR/ng+nqvl9W+
|
|
2+ifNF0raoQPF/mtCQXed9Cs5sRppkN8yI49eCLWIxTVMSoVU/v58LdZsTBx
|
|
1V1EGckcY/XygTIp43Graxiaaura/KGLD1vED0itnheOLn28+WlJBx9Cylm/
|
|
hpwjUGjJlbjyVj5kXFGfn8eMRMyVTic3N/OhXm/cJp8ahfYIIl07f/FB/tpI
|
|
uLTFPUR7kKJ5uJ5Yb5dYDkP1Prq292iVWC0f4s4oik26eh9luzyKvFDNhzvG
|
|
K027Jj9AKoWNnlMr+fDhj3x7z/kH6LAUyzCqjA9249bzlSZFo5GGmGaTEj5U
|
|
271znns2Gt3YZ5iQUsyHz6HvCkPFHqL5cekHWYV8GLKi/JM++RBNvejB+pDP
|
|
h039Ch8ujz5EozO0pJZ8IdbXutqYcjQG/V3V8bUsjw+DSioGnUMxSNO5KNTr
|
|
Ix90tjIzsg89QouKv2zpyObD2favLel9j1CoWhXVL4sPptGFae/3x5LxAeL6
|
|
YMH09q5YdCaU+S34LR+c7xtOt9oTh7Srg+6pvebDo2aftOD2OFT0tXl/ZAYf
|
|
XDytW8R2Pkb3d3oITNL5YCWz5mVIy2N0Pq1VIyWNiOfPXj3nbfEo+HFwu2MK
|
|
H5KbR4wmNcWjWBfOu+xEPizX2/u+ecsTVHlbJtT1GR+owcv+NjQ8QebXGveV
|
|
xROfN3j47Y/XUxRCK5vvFceHZ+1ebMv6p0j93E+Djhg+LGi8NufIpmcoOXB0
|
|
zDeaDyZTrFpqap8hb2vLivF7fODvYMzauDEBqR74lh4cyYdJhg8jxn4moCts
|
|
wQ21cD5837W5K8MzEVVfO7cvMpS4v+DIjJCfiejfroiFJrf5cPtJnV6wZxLq
|
|
yT9tknKDD5fu3xOP+pmEXrxiSLKu8+Gj6hqPFptktMAS1WRf4cO3CIV45f3J
|
|
KMVYPdP1Eh827G2rnZecjDoeO90qC+bDgXN90ld6ktFQqv1+r3N8UGgx0myg
|
|
pKCi2WMLOgL5YHnt9LR5PikowOP2LL8zfCg+JSuVmZKCRO3bKT7IvnxVzepL
|
|
QcvMHCuCT/DhNe1WzBfbVORXMfu52nEiX0bD3HcfTEU71fSuRB7hw0u5z79n
|
|
PE9Ftt8/bzPx44OY56zzZQOpKHfmfF7KQT58GY2XfERLQ3adN2ewfPhgUOu+
|
|
O8AvDe2fk9qfvZfga7Jt1s6XaejErPtfXHfzYf0pmvSWkTS0/rLHo7IdfJjt
|
|
uJm22+E5UjzRecJrGx9SnV4vP3vsObo2sGhVxxY+xP7H3hD/+jn61e9v7efF
|
|
Bz3NthU1f58j+eMnJolt5INhLzgYcF6g2+47a4I38EGx422d76kXSG+dZ7ra
|
|
OiK/GqoMKuAFij2z/kqkOx+KSrTHXCXSkcm3Td4mq/jwJCdg/3dBOorh7uOk
|
|
uPGhMFX6xM6gdKRdGqjBWsaHeeHPDFQ+pqMbIdFd2a7Efgf4bsqVfYkkD+bm
|
|
uC4i1rNpo8O1BS+Rz5GhqDIXPgRy9jzZfuklqoy2POw1j+BVM+L5svyXiNe3
|
|
c0nHbD7Yd3WsXqicgaK9U4jtJHgCz5srl2cg0n/4YHF1YMf+mxloDVpVFszm
|
|
g+rap2XhJRko+cGLZDUWH9z0A2tLNV8hiSczgyOZfKj4dfK00bpXaEnpxU0m
|
|
dKIexYS/Ph35CoWZSTqm2BH1YWPFle6fr9DP+2dUWVQ+uE9nje4xyEQGbPn2
|
|
bGs+zMh/Kza2JRNt/Hf3vaslH2xPed2LiMtE4b+oEWVmRP5ampUuastEhd2F
|
|
h7xMCF5KVB4rWr1GknrHFncYEa/9Z6r+3Pca2fqaG/sZ8OGejov6u9TXaF13
|
|
/b9xXT6w3t5JSRt8jUzyokqDtflwRPN9+UvmG8Rkr0lW0+LDzZ6ggPzjb9DV
|
|
harBkZp8iJ5T+2gYvUFWA3mbTDSI+j2tyMVO4i2awghwTFHjg7f3ut2n57xF
|
|
DlNpaiwVPmjb+ivWn3+LHl9sac9W4sP7Y/ZWK7+8RR6RYdmuCkT8uYGfK6Yg
|
|
tMZlYWSZHB/entnVcsANofCrf3y9ZPigxm87q30HIf39j107pIj9PSkWVVGB
|
|
UGfbChM/CT74MhLpT3SEZHzEiPXs6V98yUuI3JPiy4LHeHBMr6AhIFaIhkeW
|
|
paiN8mDV0tkj59qEqKpqJDhyhAcX/sV9WDoNkMy6KC+TIR6sv3E039sB0OGD
|
|
fFZKPw9imm5r/LcOkLVxoxqrl3h/ZDwy8QQg84P/dWR3EZ/Pfb6l9h6g3WuN
|
|
P7h28MB89YudWlmABiqzI8taeeAcI57s+QtQ1vAmP69mHnxIumufMOkdKkkY
|
|
c+34xQN09MSIpNk7RPl3x8SvngfWEgmjmxe+Q4UtFDGxWh4ouZhyvu55hwTO
|
|
eWXB1TxInLx6HvfaO6RZvClFrZLQI/Mg6m3qO7Qw5k9wZBkPZJ0mzZ7z4x2q
|
|
Sb3hZVLCg6z4/xilw+9Q0T9LVkoxD4KWGhw9OCMLmZzPUWMV8mAZpVx2BjsL
|
|
Vbtu7MjO58Esl6dNnzyzUN/yP9muX3ggGR6q+t+ZLLTt5s3IsjwetM56cGnh
|
|
oyzEUbPx8/rIg4rW7BVauVno4Lc8145sHhQ1Se4abMtC8nlbTPyyePB9pse3
|
|
csX32H94UH+x+HQu5T1afSi8LPgtD/rstpx55/YeTTFmpKi95oGKunJhtt97
|
|
ZKJeHByZwQM7m9I9RXffo3u8fV4m6TzwOvPKve3Ne3T46WRWShoP7ii9vK5Q
|
|
+x6lLH+sxkoh1lP8TdNBMhu5MOZ0ZCfyQK9IsmufcTbir6nPdn3Gg4Nybiop
|
|
LtkoPONUZFk8D74cfXvm7+5stGqltp9XHA9sDQX85dey0X6b164dMTyIkP61
|
|
JDUtG7XNXWPiF80DNf37T2eWZqPs8OHx8Xs8uOR7eOX1P9losvztsuBIHoQN
|
|
Cn8p63xAX/bYp6iF8+DFjW894bwPSPJjUXBkKA+alsQetd36AaWp+3iZ3OaB
|
|
ofnsU9/Pf0CVa6awUm7wwM8gXvzMsw/o+I0ENdZ1HpQxf4ixCj6gkKyFHdlX
|
|
eLB4T67/eP8HZNjcmu16idhv4Rnfb9NykIX4+ciyYB7spEi1P2HloGfKxn5e
|
|
53igKlxUfd0zBz1Sz3btCOTB113rFwWezUHTlL1M/M4Q66XbMc/E5ZD8BPDA
|
|
X7fw/sXPOcirkbjdCR7sMKb/d787B7GAlaJ2nLj/Qq8WUPuILl8rD448Qlx/
|
|
ZeXHDsZH5L7qMHFDHkR1TzE0Wv8Rhamos1IOEvHfe33UO+AjWpGVqsby4cF0
|
|
hYqlL2I+ovPbl3Zk7yXi8bHVYEreR2QrRZTv3TyovA8+hzo/olW3LkaW7eCB
|
|
e6gHu1ElF/Vomfl5bSPyJ+F90CZ6LpIKzXHt2MKDgLruBa1rc9E1OSLfvHhA
|
|
sWu45H8qF93cT2TcRiK/oiMXasXkIlZxVFnwBiJeM4woObm5KIXhlKK2jgfv
|
|
zx5vONGZiwYjCT3uPAivebiVr5qHZCcRelYR+WgRma7GyEOt+6ayUtwIPnZs
|
|
K+ldl4fCKlPUWMt4UBUq8aEqIA9Nd1nSke3KA5vMvWe+P8pDWzKIl4t4YPD1
|
|
qVL5pzx02uxCZJkLD9IKX+1o685DOyOI5c7jQcPH0Buy6p+QoQpRPmYT7yfN
|
|
v2Tn+Ak9OUdsJ58H+sF5brs8P5H8cHlgv0KrLSnwEzI6RsSHzYNaZc4S8Sef
|
|
0LQhovyyiPohpJ71/PYJlR0k0pHJg2meQ0GfBj6h7f2+XiZ0HtzvubiaP+Mz
|
|
yjlE4GJH5P/BvuEc589oYJiwLyoPQlrMtrlv/Yy6/AmcrXnwx9X20dCFz+iV
|
|
JKHHkgfjsZNTHyR/RksvEeXGjAexPS8uryn5jDI0CD0mPGizoDJ1/n5GndFE
|
|
vhkR93c/kdKt/wX1Ugg9BjxYejjs99d5X9B7IPodXR7sO3de+dWeL2jlMkKP
|
|
Ng94vnJpKTe+oNA6Qo8WD35Y/ozMePUFXfIh9GjywDJRrvDrzy+IIk48ToO4
|
|
/vf5Rb3SX1HQNUKPGpFfShuUDS2/ogu6xHaoEPx1BM3cvPwr4iYSepSIeN6S
|
|
9Ek58hXFOhF6FHhAlSlRVLr3Fb39ROiRI+qtYKzvyAfifu6EHhkepMw/qtfX
|
|
/hX9ayT0SPFgquaC20dV85HpQUKPBA8cUvatmOKQj/2HB8ZT29ameeaji5cI
|
|
PWNc+Mp9Fb/1v3yUo0ksb5QLdEY11zghH6XGEHpGuLBleKXeYHE+cqUQeoa4
|
|
sPy04fyiP/ko/DWhp58Lkj/mZLzV/4ZC5xJ6erlwoO/N/pfzv6F5hYSeLi48
|
|
Lj/vI9z3DcWuI/R0cCHiQnzmj9vf0ItGQk8rF1ZI6y768/Yb8t1H6GnmwmeX
|
|
1llWjd9Q0whx+S8uSFhKGTEmFSDZM4Seei6Ia3LKa6YXoAp5Qk4tF2q3R6de
|
|
tipAl24Qeqq5kJR8d/psXgFaMJPQU8mFY6cvHZZYWYA0HhF6yrjArzz2JXd7
|
|
AeqxIvSUcEEWbdG841+AytIJPcVc+GS2YN2eawUo35nQU8iFSzoWtxbGFKCC
|
|
XEJPPhdcImRyqBkFqG4ZoecLF6Qe/uzU/VKAxCqJ2+dx4Y1tmoJGbQEyn8D9
|
|
I7EfC88YTB0oQFs7CT3ZXDDqXGQzQ7YQPSUe75fFhe/T1OxMZxaS8QEuBH7+
|
|
bsWhFCIv4nbBb7lgLRuiu352ISpSJfS85kLJ1wWyZ9wL0ZIIQk8GF47PHG9O
|
|
2l2IKmcRN0zngvZAImoMKESHkgg9aVxAK9ZeMrxViGY4EHpSuLCWI75sR3wh
|
|
+ppFLCeRCwPJDxVevi1E1xYRep4Rep/xhApFhcijhFhAPBd0qZXbdzYVIqeN
|
|
hJ44LqRx9ssV/ClEs9oIPTFc4P0Qe8CeUoR0iO7OL5oL+QOXbNIMi5DBP4Kf
|
|
e1xYFTn1BYVZhKwnyn8kFzJq18SlLypCjAk94cR+F+j4z9lUhNgTekK5cG3P
|
|
Zrtq3yLEJ+zB5DYXJr00+XriQhGaTeCfcoMLlgm7XEzuFSHBRDm5Try/1OZx
|
|
eVoR4k1s7xXi8/cOtN7MLUJOxEvXS8R6wmmKa6qLkP1E+IO58Hr2ETXjviJk
|
|
TizX6xwX1oU5/h2dVIx0JtIzkAtPI/w/VmgVI5WJ+JzhQvJCjm8WpRj7Dxe2
|
|
xp2STptTjDombneCWH8S98iztcWodALv41yo23L6a+K+YgQTco8Q98vhSWcG
|
|
FqPYifLjxwWTH6d18+8Wo/MT4ThI8HSNN7M9sRjtJD7O8iHiPRIwqpxdjOYT
|
|
5TZ7LxdAgfvWubwYzZoo37sJHvJPbjrcVYzGJ/TsIOLHYre8lPyOSif0bOPC
|
|
7VXHl4lP/44SJvRs4UKntkOkm/V3FDDxeC8uDF33+5wo+I6WTejZyIXEVLsq
|
|
1TXfkQFR/oM3cKE/QMEtYO931DuhZx0XwsYi0obPfkdZE3rcuRBr2jh25O53
|
|
dHNCzyouTJVopEolfUdbJ/S4caE5OGLJ3ezviDGhZxkXdGDyambFdyQ3oceV
|
|
iH+M7fy67u+ocuLlIi6kM1QMb0r/QEkTely4oHE0rnmp1g80gbvXPC5Ubx+8
|
|
NY36A62e0DObCzIyo1Ytc38giwk9fC7ccMtIylr/A88/XDjvaqUVd+AH+jER
|
|
Hzbx+eE1+2+d/4GeTOhhEdcv4SRdjvqBAib0MAn9KytKrz7/gVZN6KET+y9v
|
|
3Rb+6QeymtBjR+jb49CUUvsDSU18nErwc/Lv58KhH6hqIt+siXhwDoePKpSg
|
|
5xN6LLmg+ix+hY1hCbo0oceM4Dn3xvBuhxLkPaHHhEv077TA50tKEGdCjxEX
|
|
QhSu/pH2LkGaE3oMuGBrf3/tJv8S1Dsxb+tywV5+R0xOSAmaKP/B2kT+XVff
|
|
RY8vQbETerS4EPqlkJciLCH1aBL183WkKaOkBK2deJwGl5i3j+rmdpQg+wk9
|
|
asT907cYb5EsRYoTelSI+73zZE+eUYqaJ/QoEfcL2LnlLaUUvZvQo8CFL/2B
|
|
4cfmlaKwCT1yXBifkVTP9yhFE7h7yRD3G2px0PAtRYsn9EhxwTvI9sHAxVI0
|
|
ga+fBJE/uRc1a6JLsf9woUA4cK/oVSlKnVjOqDOI79rDKCooRRPl0mTIGRif
|
|
BmuqmkuRxsT6ep1hZ/Xl233/StGnifV0OMO9GJqHmkYZOj7x/GZnKNLtpDlb
|
|
lSHLiefVO4PskufafrPLUM3EflU7g6PtRfWMdWXoysT+lDnD3jwfbemDZYg7
|
|
sR/FzhA9dTttw4Uy1DehP98ZStT2boAHZWjC/srynEH+49lb1q/KkNvE47Od
|
|
gWMdXx1XUIakRPXaGfa71NAsW8rQiwk9r52hRqOY/2a8DHlP6El3huc3GfHu
|
|
08rRtAk9Kc4wmDV5h7hNOZqwE9dnxPMfLDmTPrccHZnQE+cMQork4GGPcmQ2
|
|
oSfaGXj7jd/N8StHFRN6Ip2BtvFVk+6VcjSBa2SoM1wXe7N1Umw5miiHKTec
|
|
YcMya87vt+VItNwrznB1ufL+kR/lKEpU/5zBTsprVLKrHC0R1Ttn4Hob1mpN
|
|
qsDnO87w+sgKHa5OBUoW1TNnuM8afLGfXoE2ieqXM/QnSscluFagqaJ65QwJ
|
|
RUG9Q94VaOJxrrudoSzW99aiUxXIV1SPnGGPxY+QxDsVaJao/jjDvo0xrTOT
|
|
K1DpxHI2ENfPabh7J7cCiezB3RnSKq8/1KmrIPW4OcOQfvKk1N8VpB5XZ4jT
|
|
5LxfplqJROF0cYYsIat8zLwSidJjtjMsnhY/P11QiSRE6eYMfN3/VI6vryTz
|
|
jeUMxjv5HYt8K9FmEe/OcPzC4uuWVypJPVTi+oA4sRlxleijiGdn8F+41FEd
|
|
KtFhEb/OYNExj6NTXolMRbw6w3yvKwq0vkoyPtqEngTDR2smV6FLIh6doTJf
|
|
RvaSURVii/hzhuUfHGlf2FWoS8Qbke/X31jOWF2F7ov4coYrtpe7fPdXoWUi
|
|
npxhffyzYz+Dq/D5tTNEDM4oXPWwCj0X8cOBhdPKeivfVJH5NsSBnUq/qvaW
|
|
VGF+OCBWyQmZ0lNF6unggPyJFhUkV03mWzMHAgZq1x0zrEbmIn6Iz/NM989m
|
|
V6MqET8c+LQZuc5cXU3qKePA3XUPh8V9qhFHxA8HKkxLdw5eqCb15HPg8uc1
|
|
j4diqtE9ET8cSBdYJEsLq9FyUQA54HqdaIjKq8n4AAfcn2fqLO6vRmkifjig
|
|
cZq+4j/FGrIepHPg62f/3nyTGqQu4ocDR29eHjLm15B6nnFAq3L75ivra9BR
|
|
ET8cSLunxJQ+XEPGJ5oDzvUnD128XoP54UBu9CtN/Wc16KKIHw7MrkNGOTk1
|
|
yEnED7HeyCuhx+pqMD8cmFlmeojztwbzw4GT1y6/VJn2Ey0V8cOB4pw3XgPU
|
|
n7g/4IDe8XTfpkU/kSjcxznglXCsp3nbT1KPHweiNsgVj5z5ifnhwMeLXtrT
|
|
o36iHBE/HOhh/Pdt/qufZL5t48Bkr0Ot577/JOupFwd05K12lXT/RKLlbOCA
|
|
iqa7eZh0LVkP3Dmg1vavaKlaLanHjQOKoxdspujXkvFx5YDEwr/OP6xrST0u
|
|
HOgrXy710KmWrAezOVAbd8X/yIJa7KccyHme9Hiley3mhwOxKWl/Hb1rST10
|
|
DhxfEtpheqgW88OBuVc2HNE9U0vqseSA1F7J+zrXasl8M+FAZlfwZuOoWswP
|
|
B7Yo92bRn9WichE/HJAuZqIlmbVkfDQ5EErftNIntxaJwq/GASPWzvPhJViP
|
|
Egdiat1W5//CeuQ4oGmikyXXX0vGR4oDZ5XycheL12F+ONB4e8WusCl12H/Y
|
|
4AAQ361dh0TLG2JD0AXFwMWWdaSeXjZkDzr+SXOsI+tbBxv+iLsoGLrUkfFp
|
|
ZoNREiMzbHUdqaeeDXPHJklpedeReqrZsLYjvfXhoTokSr8yNmzxn7eLdraO
|
|
jE8xG7YmZJz/dr2OzLd84vpT8vwD9+tIPXnE/fqc7mgn1ZF6stkwa9LS84Vv
|
|
6/C8QKwnU6B+5UsdmW+v2SB7dgu4VWI96WwILvg32bAN60lhw+mHqiOjI3VI
|
|
1I49Y0PP6L3AGpl6JEqvODaUlMemfNKox/ywgcI2OQWz6kk9kWyQNtbvFNrX
|
|
k3pC2bD45s3RXEE99h82KJw//aRyeT3mhw188Zbfw5vqyXodzIbe8Y+t2j71
|
|
mB82TA3UP7Y4oB7zw4akywNP/rtaj/2HDcKZPP+8qHpSjx8b5lFlutQT6zE/
|
|
xP0/zxXb/bYe88OGjLbx1M9fsJ5tbIi+ajuJVoX1eLFBIrPmd1x7PeaHDRU7
|
|
pK4YjWI97mwwu/cw64l8A5lvbmzoWvPmjuOMBuw/bDANc1X8btaA+WFDueda
|
|
w8MODZgfNkg+/Vlu6NKA/Yd4/vEaSoV7A+aHeH5lQ2bY9gbMDxsOFfnLex9p
|
|
IOsblQ2Dm+J1nc43YH7YcDZ4x5+ZoQ3Yf9hg4PI2TPZxA9kfGLCh8H6M2PjL
|
|
BswPG65d07UUy23A/sOG9ZrW2gplDdh/2ODILCg2aGlA3SJ+iHzqkV46e6QB
|
|
+w8b9Ljfru+X/YX9hw3mppZ34zR/4f6N2P/HM71bTX9hfpxgL9wfoTn8Iv10
|
|
yAni92csvezyi9TT6wS9GZv3dq/5hf3HCRbcjV62fucv7D9OkKji+6f42C/M
|
|
jxMYG1RuX3XxF1mvq53g2afvEQ3hv7D/OAF3stft489+YX6c4FfDmZU6b39h
|
|
/3GCsBWMis9ff2F+nGD9hlNGgTVYT7YTWP9baz+v+xf2HydQZnySUxdrxP7j
|
|
BOGp5S5dyo2knnQn8NS6fbdYvxH7jxNs9RkfybZtxP7jBI+fq2/PEjTi/s0J
|
|
LBrLmj6vaESidI12giYJF9+6rY3Yf4jXit5qkocbsf84gcEkyjvK+UYyPjec
|
|
IKI99uTOu42YHydYjj4tTH7SiP2H2L+T4aYSbxoxP05wwmK6+savjZgfYr8/
|
|
CFQ+1TSS8TnuBNGLtbS5PViPnxOEZN1jZok3YX6c4I1R4ealak2YHycwP5QU
|
|
1WbUhP3HCYqSHVuv0ZtIPV5OkFFxQCCY34T5cYKq3tUJ4mubsP84AX+o1fjL
|
|
ribsP07Q0GyaHH2iCfuPE7zPmeoSdLUJ8+MEP0MSeg8+aCL1zHYCzqL++L1p
|
|
Tdh/nKC0r9HH90MT5scJxqOeSgaXNmF+nEBux87pT1qbMD9OMLjUIK1sFOux
|
|
JPStKi6YqtSM/ccJdh47ccBDrxn7jxMMvNYLfWHbjPu3iXi/5c2Y04z9xwme
|
|
hi7fd2l1M6lHzQnK7er0FHY2I9FxjpITNHZsX3XXvxn7D7Ff71un2F9txv7j
|
|
BPczNi+uetCM/ccJln4uUQp53kzWt1EW1IzyV6z82Iz5YcHiBY+1jSuasf+w
|
|
ICp90i6pzmbsPyz4zPVw6hlvJutbMwsqWxKvt6q2YH6I9xNHdvbMaiHjU82C
|
|
iBBWrpRDCxmfMhYsuHk43nhRC+aHeH7aM6VVni3Yf1iwpLdiOORAC+aHBdGL
|
|
JLZWB7Vg/2FB0QeDVbS7Ldh/WNC03ulz2LMWUs9rFvzedOO2ErRg/2GB+azd
|
|
F64Xt2D/YcHx2JxYw+YW7D8s6GyMbs/+00LOC3HE+w1ia3yVWjE/LKIe13bZ
|
|
G7Ri/2HBkCY/QZLeSs4LoSz4tXTWzTqXVrJe32BB19wLD/M3tJLxucKCmaP7
|
|
Kz/5tGL/YcGWPeWskqBWzA8L8iPfZ/fcbcX8sMD9ko3fjMRW3L+xQNJBe6lb
|
|
VivmhwWfHl5aHl7SivlhQfKXEyf62lpJPbtZkJ7WU+A+3or9h4iPe+OifLU2
|
|
7D8s0H6zrne5aRuef1gQUO2GmpzaMD8skHj7NS14WRuef1gQuzavkOXdhv2H
|
|
WH/6XM2xY214/mHB3II5575ebcP+Q7x+nKOTENOG/Ye4npNXE/6qDfPDgoyN
|
|
di/C8tvw/MOCDdVtV580tGF+WOD6vHvv55E2zA8Lrjbylo8ptmN+WKDlU+fA
|
|
NWzH/kPEe1X+rJvMdlQp4ocF+ndkNX4vbsf8EPlHvSa/b3M79h8WeBlvlRw6
|
|
0o75YcER33NiV660Y/9hQbnOsDgjph37DwsuGzyX6X3Vjv2HeB2AVN58a8f+
|
|
4wiVTA290MZ2zI8j+C18bRs02o75cYTNGQkuZ1U6sP84Qtipzi0hJh3YfxxB
|
|
/8GxwFR2B+bHEYZmrnzc4NaB+XEEzX7/glk7OzA/jhBs2Pf3SEAH5scRFiQ+
|
|
t6q+3YH9xxFW3cj2Wp7QgflxhNQi/Yiy9x2YH0fYsPtL+b6KDswPcf3GbC3N
|
|
3g5Sz2tHeEp/sq9IphPz4wjbD+s03NPpxPw4wk0Dfb8AWifmxxHMmammhxZ1
|
|
4v7NEUwzCv8c29xJzgvRjnA9+lTHzWOdpJ5IR/Aefj327non7t8cIT79P2uJ
|
|
+E48/zjCktqfJ1dCJ2oX8UNcf+hj1+vSThQhuoEj/DrAPknr7iTn7UBHyK/k
|
|
WWVN6sL8OIJh0vfRTTpdmB/i+o7B1qn0Lty/OYLCrUfDFYu7kCgbfBzhflyD
|
|
0fOtXZgfR4g2Sva5f6IL8+MIigqTa+7d6sLzjyP83DCwIzWhC/PjCDozdquX
|
|
fejC/DhCLvdArXJNF+bHEWoKJ31eP9SF+XGE9V/NfrxW6ib1uDjCPLvKf1Ym
|
|
3fj8wBEiJLXmpzl34++zHGEtpzV5oXs3qYflCCnJu3eN7O/G/DhCscmX+Mzg
|
|
blIP1RFePpTZHRLdjflxhC1GuqmnXneTekwcoSRe1f/M926yvhk4gpp9fV5Y
|
|
Zzfu3xzhQl3O4i2SPZgfR9j79MKItHIPnn8c4cVhp62pM3tIPUqOsGlu1Y0d
|
|
Zj3kvC1HXD9tZ6AFvYesB1KOUNfWSB/h92B+iPXBkqfflvSQ/c6oA3SHxtWl
|
|
rO/B/DjAxYOd5VE7ekg9vQ5waan+zdt+Pdh/HKDLRqB892wPnn8c4LmKm2vs
|
|
tR7MjwPUDC51RZE9mB8H2FPlpFz3pAfz4wDrP2jcVMrowfw4EPtZUz73A9aT
|
|
7wDbo27WBRf1YH4cIPAK82npzx7MjwOIn/5Ep3T2kOdVQgdo8F0QeONPD+bH
|
|
AR4o/uRJyPbi8wMHSG1J1D6h3ov5cQANmcxpUoa9pJ5nDlCwXYxyh9KL/ccB
|
|
KhXPeNM5vdh/HMBxiPO6bmEv7t8I/foM67trejE/DjB4badw/bZe7D8OsERQ
|
|
vtfStxfz4wD/mGedZM/2Yv9xALED2017rvXi8zcHWN113vZXVC/mh3g/8dfa
|
|
X8968fxDfD75+IOezF7MD3H/4cWT5PKwHh8HGAhYF2xVivXsdoC2xTHmHo29
|
|
mB8HYHqYtoX1Yz1eDlCa0vyxQbyPzLcNDvBpfv17pnIf5scBlA01a+7q9OH+
|
|
zQGecYM1ZKz6cP/mAKEPaHsCWH24f3OAqjna9dIL+nD/5gA+VlzfO+59mB8H
|
|
WOseZUzb1kfmG8sBxurgzU/fPty/OUBWI+XfncA+8ryK6gCPN3e1bbjRR56P
|
|
WjpAwrrfZ6jRfeT5jokDFH9dlqOa0of9xwG0Moefi0Mf9h8iX/TaXf/l9+H5
|
|
xwEUxC1vytb0kedVag7wcl1moF5nH55/HOAM5bbe3L996IGIHwfYdUq47ejk
|
|
fvK8SsoBjs6nr82c0Y/7NweIv/hnWNa8H5+/MaF/vgJvq0M/Pr9mwraAXbRv
|
|
8/vx+RsTBqiaP+a695N6OpgQs0FV78u2fuw/TDgsuVbD83A/+X1GPfF5w+6X
|
|
4//1k3qqmXDsbaFU4u1+dFmUQExILBQf2xHbj8/fmCC28dR9u/R+7D/E9dsX
|
|
dMvn9OPzNyYotXu1dv/AerKZ8KE590p9Yz+ef5gQ5eH/s36wH/PDhIjUpahX
|
|
egDzw4Tvc6crKWsMkHpSmMDTKslnGw/g82sm/LQ5J3acPkDWgzgmvAy0fPhx
|
|
7gA+P2ACmp6Tbrh6APPDhH9dbqyr2wbw/MOEg1IlFPkjA3j+YYL62kV3bp4f
|
|
wP0bsb/d6Xut7w7g+YcJ0jnqL0vjB3D/xoT5Vdv3X8scIOMTwIQc2+Qw988D
|
|
eP5hgk9eO41SNYD7Nyasua/Fn9Y5gPlhwt6XzkLFfwPYf5jwRsk9QW3KIBmf
|
|
bUxwjt2iYKY3iPs3JnSf2Fq1mDqI5x8mVNxaq32GP4j5YcLfTsG3D26DmB8m
|
|
LP5Pv09z6yD2HyaUe/QHHfcbxPww4ebhVxc6zw1ifphwruCg2L67g3j+YcKz
|
|
HQbN408GMT/Eeuac4T94M4j5YcKprUs1VuQP4vM3Juz4dMlLs3YQn18zYegg
|
|
w6Srd5CsbyZMYHgt3fJDcgjPP0yYfqt0er76EJ5/mBCn8HVemckQqUeTCbW5
|
|
lK5+hyE8/xDxzJNQ1F80hP2HCQunCGI8PYbw/MOEgLu9aUn7h7D/EPu9XclJ
|
|
5ewQ9h8mNB+/6xR4a4j001EGaHwPeSH7eAjzw4Ce/X9iozKH8PkBA3yXFyjP
|
|
/TpExqeDAdFHpvb/+zmE5x8GHGvIWZzXh/XUM2AkpFnvkfQwPj9ggME5v90h
|
|
msPYfxgwJDxIuW4xTNbrYgYcYv/c/YAzjP2HAXfGM/TfLxvG/sMA70niS4a2
|
|
DGP/YUD9spcDjkeGcf/GgEn1larXLw7j8wMGnKCEFP+OGsb8EM9LH9volzqM
|
|
/Yd4nq/O60k5w7h/Y8DAroG6J+XDmB8G+ISd+uHVOYz5YUC/GNyyFh/B8w8D
|
|
jt57YaCkPoL9hwHifhv9xc1GcP/GgLOBEC3LHsHnBwxQ+vzjluGyEcwPAyJc
|
|
7q9cvnUE88MAMzG9+ptHR/D3PwzI7FrBar88gv2HAa7qzptWRo9g/2FAzcEa
|
|
t+L0EcwPAw7K26lt/TyC+WGAYrnTPfnaEfz9DwPifo4Ovx8YwfwwgK2zX/u6
|
|
3G/MDwMqb96dckDnNz5/Y4C/4Ei+t91v3L8xYKa5wtp983+T9cCVAW/mr0y9
|
|
uOE35ocBW+65lb4+8Bv3bwxQsJbJGz/3G/sPA54P7Du3OvI3nn8Y4FZ1f0d2
|
|
6m/cvzGg8euznHm5v/H8Q8Q770ZUXfVv3L8xoCx/Ze/1/t/4/I0BNMJL3OX+
|
|
YH4YEDS8U4au+wfzw4CcGeiTGe0P7t+I+M/rkLVf+AfPPwxQPTX4bsWmP3j+
|
|
IfITygcvHv6D+zcG6E6+G1N++Q8+P2CA8ka7fHbMH8wPA7rQ4wMZmX8wP3R4
|
|
Y/L7ukvhH9y/0cE3zMiyt/kP7t/oYDTNgpf07w+pp4MOEKlQeFZ9FPNDh0XW
|
|
eZV7LUcxP3TIyd24ab9gFPdvdLDdU7zp/NpRzA8drmjpV6f7jGJ+6FBR7FI8
|
|
en4U80MH5duLZ6++P4r5oYODlyUl7+Uo5ocOq5lNt5d9G8X80MFL8/iRnqZR
|
|
7D90OFX9emPcv1E8/9Chweto5WGNv6SeFDpcfJzWssn6L+aHDocSd57fOvcv
|
|
5ocOYYeiMs94/MX80EFi1PXUK7+/mB86pPD8S+Su/sX+Q4d7843hYNxfzA8d
|
|
Pk1Z7DQs/Iv9hw5Od3oW3Cz7i/mhQ1+NcseC3r+YHzo0NyXoasmP4f6NDrpJ
|
|
HxulDMew/9DhNsODI+s0hvmhw8oAH7NZK8cwP3SYHywet27vGD5/o8N/y5Ve
|
|
Pj03hs/f6CBXdWeN+oMxzA8dsmZFXQnNHMP80CHXRn8V7fsY9h86KPzRS27v
|
|
HMPn13S4FhgZ8VrmH2oT8UOHdd9uaz3S/4f5ocP6CgWrx6x/2H/o8PjReEH2
|
|
yn/Yf+jApO6TGd33D/NDB83Zc8IWXfiH/YcOBx7tcnsd8w/7Dx3mray3nSf8
|
|
R8bHkg4X3OKZPeX/8PxDB8F92JI+8A/zQ4f9LNOXd6eMk3q0ifyZVWsTZj6O
|
|
/YcOJhta8l/OGcf+Q8SvgXuzb+M4/v6HDskZracW+I9j/6GDWVX9deGdcbIe
|
|
SNFBxdXy07K0ccwPHfYq5ZiKfxvH/NCAo52c8LVtHPNDAz7b99k6STEheX5A
|
|
A90bjuqeKmJCkh8a0JVNVXx0xYQkPzT47zn7/nUrMSHJDw3UAo5nAUtMSH7/
|
|
Q4OqA3WH/7mICcnvf4jXl/bBAncxoai+FdNgWv6siEfeYkKSHxpcoktNnuIr
|
|
JiT5oQErR17x3FkxIckPDYxOOEQrhogJSX5oMG/dtU/R98WEpP/QYLFH8tV5
|
|
SWJCkh8aVJx1HP37FutJoUHnZ2vF91+wnmc0OEu//OFupZiQ5IcGse9XGp1u
|
|
w3qiifsdPG929DfWE0mDY3Nm/TgtKy4U9dehNKA4WpqETxMXkv0bDXYvi9T9
|
|
YCwuJPmhge3FI2icJk7qCaaBf/NbyYVzxEk9gTRw8d7THbtCXEj6Dw0eypw7
|
|
rbZFXEj6D7G/n+Uzrx0UJ/X40aAjZSRU56w4qceHBuWZS3XehoiTenYT621S
|
|
XbA7WpyMzzYazLV3nmmZKi4kzw9o8CXmx82/78SFJD80KGCUpFUXigtF9cCd
|
|
Bhs7uUe/1YkLSX4IvR/UGwt7sR5XGmjCiuFf4hJCUb12oQGzeixJVlVCSPoP
|
|
DZpmqkxhG0iQ8eHSYPqpK1PP2EoIyfMDGjw/eHGwjC8hJP2HBuE7tZv5bhJC
|
|
0n9o8Hnz7FbhZgmh6HGWNFjoKfZ3ySEJUo8JDVQ2LNPtD5QQkvMPDXQ2MNzi
|
|
b0kISf+hwUnP1DsHYiWEJD80mLUlq8P1pQQZHzUaaOzatpyTKyEk+aHB8kMP
|
|
crnlEmR85Ih8ObV/yao2CTI+UjR4evl708lRrEeMWF/k1yuZCpJkvo3ag03y
|
|
unlyOpKkniF7aMo+qbzLRpLU02sPDZX0tp9cSSHZv9mD+eDZ79uWS5L51mwP
|
|
SNn7m8QWSVJPvT2EWVdXJPtKknqq7SHLtXXI55wkqafMHhx9LhjOvSspJM8P
|
|
7GHgFmy0eipJ6sm3h79vLiaavJXE/NiDW1O7Au2bJObHHvpU6o6vrJMUkvOP
|
|
PZQ47xo93y8pJP3HHlQWuQwUSEuRetKJ9ag6frPWlML82IPvDfalaHMpzI89
|
|
3M93s7BkS5HxibMH7Wz/Z5+XSGF+7KH/YMaU015SmB97UK2ZtHKRrxSpJ9Qe
|
|
Tkls97c6L0XquWEP8+sqg4zCpTA/9uB5zMuHmihF5luwPeR8HeWseCeF+SE+
|
|
XxnXdem7FObHHi4/9A6obJbC/NhD6yzmgPOoFObHHiK8Zi7IVJLG/NjD7TVq
|
|
ZxYYSGN+7KFZXjuihyaN+bGHK34Ooc9cpIXk+YE9nInY7ndygzQZnw32kOv/
|
|
hO7tI03qcSfWO228bHOQNOaH0LPbe8Phu9JkfXMlPn+89v39BGkyPi72oDRn
|
|
j0LtO2kheX5tDx25CgxaiTTmxx70ZISC+23SmB97SEiqLzMYl8b82MOdAyUR
|
|
SG2SkDx/I/JhSdjVg6aTyHyztIfUedYpPPYkMt9M7OHHmhBxs+WTyPgY2IPH
|
|
fzkBZtsmkfHRtofFXz9ZC/wnkfVA0x5irO9N9rs+idSjZg9bngimZcVOwvwQ
|
|
ergZy0zeTBKK0lPOHhR6/2Y+KpyE+SHy8bWKG7t5EubHHlwfDE3v+juJ1DNq
|
|
B7IPnk7JUJXB/NiB6WuKfbipDPYfO0juDjp3hyOD+bGDB5yncgkrZDA/dtAZ
|
|
dz+zcqcM5scOYi28wwxPy5D1rdoOcvNGHwfekcH82MHiM5ua/iXIYH7sgLny
|
|
zvKQbBnsP3Zwnh/ZyamUwfzYgfOCgy+l+mTI+pZtBxt3T09ukJUVkn8vYwc1
|
|
j6+WVurKYn7soHv/kHY3XVYo+r1Yuh28pe09qOsqS8YnxQ44w0Olu7fKknqe
|
|
2cHBF9cWlvrLCsnzNzvYsZ+V73FTlsy3aDtQMR32lHwmi/khrq96L/bhvSwZ
|
|
n1A7uHj5QfLDSlkyPjfsYB3r2r57/bKYHzv41XiVnTFZjoxPsB1YXL4/o8tQ
|
|
DvNjBzOpWZN4TnKYHzsoKhwQT1khh/mxA+4+pgJnjxzmxw485S7PagmSI/X4
|
|
2AHjft/ipCg5sl7vtoMcux1BN17KYX7sQDG75/PNAjnsP3aguixYP61VTkie
|
|
X9tBXoXtf10S8pgfO7Dd1Pl77kx5sj9wswOPXxn+b2jymB87cNpyS2nJEnlS
|
|
jwux3tozSf+2y2P/sQODtac9P5+Rx/zYgUnBNZ0XEfKYHztwr9tKQ+nyZHzo
|
|
dmBt+aKjpUCezDeqHdxJPjmb1i6P+bGD+L1ZTg+lJ2N+7MDNO+CHrd5kMj4G
|
|
dhBxJ0Ppl+NkzI8dBErsaklfORn7jx3Ix93xerp/MplvasTzgjgn3l2cTMZH
|
|
yQ5GIjyZv2Mnk/VNzg6Wdf25sTxrMuaHeH1U+drX6smYHzsYYt+33Pl7MubH
|
|
FqhOT3aYqisIyfMDW5A6ZD1PlqqA/ccWghotP8gtVsD9my1EXHvUYLlDAfNj
|
|
C8t9Q6N9ghRw/2YLj25IS5Q9UMD9my3cbu8Q34gUMD+2QDnhGi1XqUDmW7Et
|
|
bJxv3vB9WIHUk28LxosDst9NVSTjk2cLoReXzi2gKpL1LdsWHkqGbxdbooj7
|
|
N1tY+MLTYvluRcyPLWizVfi5wYqknnRbeMAw2Lg1TpHUk2ILP2JCgsw+KJL5
|
|
9swWsgO9Uqc2KOL+zRZWlV5vMhZXIvMt2hbiIvQMNuoqYX5sIfa70lZgK2H/
|
|
Ia4/tT5p3nolzI8tvIyQEx86poT5sYVPlhprP99VwvzYwjWbM5kfM5TIfAu0
|
|
hSmPFhu0lyqRegKIeFw+cp02rETqOW4LSi0SsnEaU8h887OF6BcdQc70Kdh/
|
|
bOHXIG3y+MopZL7ttoWSxzV3Gn2nYH5s4Vh+k0X/rSlkfLxsocDb9aNJ+hRS
|
|
zwZbKPNR33m2ZArmxxZudrOmThqeQuabmy2I9dTWl05WxvzYQsgDN2fuTGUh
|
|
+f0PcX8FP903lspkvs22hVeU+WcXspUxP7awWunTzq7FymQ9YNmC+Rr2/lgP
|
|
Zew/tjDtQ4OV7z5lzI8t6Cx/+3BtgDKZb5a24Cz2qXDVdWXMjy0c+SaXsSNa
|
|
GfsPoUfov+pGmjLu32zBodAgoThbGfNjC+8l/742L1HG/NjC5tWyZ0OblbH/
|
|
2MLML/MktH8rY35soXtTpkOGvArmxxaqNDea7ZypgvmxhcYeZqGttQrmhwpy
|
|
bbOpqlwV7D9UYEsFusguV8H+Q4WrzkPT1beokPnWQQWxiPBopp8Knn+oEDT9
|
|
UMOB8yqYHyroZpyqeh+mgvs3KlQfRpctElQwP1RIdKcMxwtVsP9QIWztD03n
|
|
IhXMDxWiTiT0tf1Swf5DhbfvMgIThrGebCoMGg/n/yevivmhwsKE7YV+2qp4
|
|
/iHuXx166BRFFfsPFYx5ag+iBaqYHyo8LS1dVbtKFfdvVHB+0HSLuVNVSP5+
|
|
hwoNkc4eT0+o4v6NCre/1icxr6tifqiwhlJwoTZGFfNDBUqOTHd0hiqef6ig
|
|
dDW46tQXVTI+V6gwfmGl2+FaVTz/UEEqc5db8IAqWQ8CqTB15peqF7JqmB8q
|
|
2KX4df+dqYb5ocLmo7suelDVyHrgR4UHh54kV8xRw/wQ+xFt5+mzVg33b1RY
|
|
LCVzx2CfGqlnGxUyQ43cu86qkf2BFxWcNl6K/h6qhvmhwse1HL8fCWrkPOdO
|
|
BY/zjsU9WWqYH0JPa8Ar4zI1PP9QiX5Pxexwpxqef6gQIujQr5eYivmhwm62
|
|
Ssw2zalkf82lwoqdAUky1lNJPSwqbN2ueClbMJXUQ6fCkx8XT99fM1Uo+n08
|
|
lQp6qaNXw/dNxfxQoXRs/csXQVNJPSZUgIyk4a7wqULR75UNqFBX3790XupU
|
|
Ifn9DxUc/c3eo9yppB5NKuQFLnVd+XOqkPz+hwrX/27vkx+aivmhws2GA0k/
|
|
FdSF5Pc/VMhx2BtUbKguJH9/QAXq+NpDTY7qmB8q1No5+GsuVyf1jFLgbals
|
|
5I4d6th/KPCpLa+kPEAd+w8FtPb4m+0IVcf+Q4FID71b05LVST3NFFglfDG9
|
|
8aM65ocC8646vSz8qY75ocDe/Od7qofVMT8U+O6vw5ZV1sD+Q4GdYUdnLTfV
|
|
wPMPBWxNcoxfczWw/1CAbSjFE6zRwPxQ4NgVu0NtPhqYHwp0bV8ByRc0yPr2
|
|
mgKXxi7UhT7UwOcHFFh4Z/TGozcauH+jgAk9trTkhwb2HwqYVlx4Ztmtgecf
|
|
CrDOxqvGyU7D/RsFjlMl5OcaTCP7nUgKFPy6GSLnNI08DwmlwNzITc96V04j
|
|
+50bFKhYu331v33ThOT3p8R6tONv2FyYhv2HAhsbDTcFxUwTiv7eJJACK1LL
|
|
hONoGuaHAh6BH5Oiyqfh/o0CF9b1ULwGpuH+jQI1DDfBgimaQlURPxSYP72n
|
|
aZW5JvYfIn7jOVrn52iS/eg2ChxpL62r3qiJ+zcKcKoMHNz9NTE/FJhVFKc/
|
|
fEcT+w+xH1+9wzPTNDE/FFj01TM2+psm9h8KhBSF8JPaNfH8Q4G+qvF9tTLT
|
|
8fxDxLMj1ppuNB37DwUUxc+fTOZOJ+sbiwIHNpk9Wb5hOuaHArwVKn91j03H
|
|
5wcUOFnufEjzznTMD7Ge3ueqTs+nY/8h8iF8f+mFwunYfwi9pQeypLqnY34o
|
|
8Dz2dXG8wgw8/1BghuzCycfMZ2D/oUDjqN4O3/kzMD8U0D7D7gz3noH9hwLv
|
|
wu7f6Qycgfkh8nXOgu07H87A/FBg7VlHT9WsGdhvbGCum49/Y+0M7C82EPei
|
|
S9gwPoPku94GvJ+kminqauH8t4GH1LevNnG0sF/YAH+h0v66DVo4v21g6fCj
|
|
RZdOaOF+ygY+0QKXeEVq4fpvA6mT4o9sfquF670NyO6cmnu1WouclyJtoNAz
|
|
h908pkXWixs28LsZle/QmSkU/T4p2AZuSvwLn+Y8U/hPNC/YQHTS2cAez5k4
|
|
v2zArvn8pZGAmXgesIFND+Ym2EXPxPljA7Y1b5oevJ+Jz5uIz0e2MwWNM4Xk
|
|
+awNvPpZ9HCajDaZ37NtwDPmgImumTbu320guf3T+zULtfG8awOPX1Qe+bhH
|
|
m8xXExtgSjyau/2aNu4niM8XGls5pWnj+dUGHAw3WQpKtIXhonjZQOyw2+wT
|
|
v7XJ+WfcGl66jh9qm6lD+ueQNWwz3YwucHXw/Em8H3hKz2OLjtBIFB9rSNq8
|
|
InzLeR2h6Pd4ZdbA+VBnHfVMB8fHGrzjTSrlC3Xw/GgNzsrG958M6giTRPGx
|
|
hsTfVSdOzNDF9cUa0NZFh8466+J6Yg37Vxw6+2aLLo6PNbz9sOKp6QVdXC+s
|
|
IeFVZ/vHJF2ynwu2hvkU5zlhP3RxPbCGvWYuL++N6pL55mcN3zlj57uU9XB8
|
|
iPVLPAixMNLD8SHWX3t15D+GHubZGs6V5mWKLdTD/mcNwS2u5aEeephXa5ij
|
|
prtiyQE9HB9rgNWOFkb/6WEeraH1xX2PaWF6QvL3C9ZQYLW8yzRRD89L1nBY
|
|
6FrhnqWH+bKGwp23DeJK9Mh8k7OGOhuzj2rtepgfa8hQksmNGtcj823ICjgy
|
|
lFnzp+pjf7GCgOkxNVPM9Mn6W28FR+ZsHhhk65P5VmYFlhf3eP9Zro/jYwWh
|
|
bVn22tv1yXzLtoKszZs9PU7oY36sIGLIteltiD4+/7ICx4dBeazH+jg+VnBp
|
|
h4xc2Vt9HB8ruOPyPSakWB/PE1awXtARsatVH59fWUHFqiW9XuP65PlBgBWo
|
|
Bo49OKJugPmxgrypv8OSLAyEot8X7LaCpOWzc+X5BkLR7yO8rOA7+6fZBXcD
|
|
zI8VOJTkCa32GZD1yNUKirSkLgwGGQhFf6832woeKF05XxdhIBT9XoNlBc8T
|
|
t73uTTPA/YYVjI1eMzD+bIDjYwUnh+TQyXoDoejvn7StgBVVdHn0twHuH6yA
|
|
2t92PULFEJ+XWoH34PJPm8wMcXysoDBGnrGQZygk/x7LEvaLq5a5rzHE8bGE
|
|
FZN3JFzwMcTnNZawN2vKy9pgQ7JfKbMEMJ40uDbaEPu5JSxmLtr2O9NQSP5+
|
|
wxLUh+sU3xQbknpeE683f2yJ7jDE8bGE1f5/hxOkjUg9cZbwkX+aVa1jhONj
|
|
Cf7pK9MoTCN83mgJ3qVHPR8vM8L1zRIuPOp0nr3LiOzfAiyhRS9lhVSQEebH
|
|
EuaPqVp2RBnhftMS/Lo2rRjPMML8WILvQORXdrER7ictgTbl4524TiMcH2I9
|
|
nOpUJ9lZmB9LsDpbqzNmMAv3h8T6qwoqW9iz8DxlCa4LElvH3Wdh/7IEla9H
|
|
5vMPzcL8WMKDLZSRpKuz8Pm2JYwp/xiZ/3QW5seS8GfvBYofZ+H4WIL+48aO
|
|
v/WzMD8WUBuyrHba+CzsPxbgF/LEyEPLGPdjFpAb2/PqG8MYf39jAQPfDO/v
|
|
XmGMz8ssoElxdqm9jzGe7y0gZuMyT9MrxrifsgB67kLmvKfGOD4WEDTbzut6
|
|
rjH2Hwt4/EOmelKTMY6PBUQdz3scJ2mC/ccCVtCPfDiob0L2p8EWUCU91W6X
|
|
swmOjwUw2iJ6L28wEW4VxYe4nuW6qva4CY6PBdCWbU73DjMh/dTLAqotqlT0
|
|
X5kIRX8P624BLp8ztk8pM8H1zQLO2PzOpA6bkPk22wIOukfKntcwxfxYgPXc
|
|
R8tU6aZC8vdaFpAxony7YKUp5scCiG7mR5avKe4nLED+mZpK6y1THB9i/c+e
|
|
zBOkm+J+wQIOHHh0tLDElKwHYhbw5a9k3I1hU9xPm0P3wpxvwZpmmB9z+O7Z
|
|
0Z/mYIbjYw4BTD811XVmOD7mMPJjs3WMvxnZP+abgzXzxeydUWbYf8zB1HPn
|
|
qi1gJkwUxcccWhac3RxSbyZUFsXHHPaOju8akDIXHhDFxxwy9tfuu2BiLiwW
|
|
PcAccp8Y7VuxwFxIF8XHHKLiv+xYvsdceFMUH3Nw3lPmGXjNXDgk6g+I9wfn
|
|
LWtLMxeuE8XHHCqqYoKCS82FmaL4mIPF2yOzt42aC7VF8TEHv9vvL5/VtRCe
|
|
EsXHHN5vD9pUI7AQ1oviYw4a9kh4eLuFcLYoPuawe2TP4yWXLYSivwdnmUPB
|
|
i5ta3qkWQnlRfMzBcrft9NelFsL9oviYQ6DWvAeuYxakHm1z6HtflKZnaClk
|
|
iOJjDmu3/lhKdbHE9c0c3oy7HgnYZ4n5MQf7G87mSrctyXwbMoPHunHeFW8s
|
|
hV9EG2wGOo+CrBobLIVUUXzM4KFh5UnryVbCUFF8zEAzPG5tuq2VcEwUHzOI
|
|
ntwO/muthFtE8TEDU99HKafPWAm/iOJjBsS0YfnhiZWQKoqPGTjZnbKdV2wl
|
|
DBPFxwzyz0Vlyfy1EkqIDNsMNv2w/7+GO4+Hsv3+AK48thaVfZlh9qVk3wdj
|
|
GTvTMKNFihQJpSSVemiXKJW0EqX0tKOFoucca0U80UYolfaptFlav/c9v35/
|
|
zsttbte873PO53q9zNWryjaHWIUPH0dRPDeIxObQofDhY97spnJcaQ4CRf3w
|
|
0WpPbcKaI+ZwROHDR1H+MuM1LeagoThvgY965jpmTV/NYYnCh4+1c08WRtAs
|
|
4D+FDx8DuFZL3QItwFIRkPh4MPN0SUKqBexW+PARMwwc+49YwIDCh48VE1ZN
|
|
/afVAoIUPnxc5dC8sXLEAkoVPnzcsSaTqqFtCaPI9VD56MYt4UfwLSFc4cPH
|
|
bhPHF3eFlnBW4cPHuGgf6fLpln98+NjzsXWpw2JLkCp8eGjX2uZG32QJxxU+
|
|
PEz94nfN8pAlfCUD41MeHlnoIo+psASRwoeHFzknW/CmJexQ+PDwslXubI8n
|
|
ltCtKCge5m99f+jlsCWwFT48XDDles6FiVYQrwhkPKQZGZof51lBGRkgT/AQ
|
|
Zf0ZNe5W8EUREHno383bMDLTChwV53nw8OrZF7YRy6wgTbFB5KHeLer+/iwr
|
|
uEIG7AwezrJvO737qBX8VHyBnIcnnNNC4qutIIAMLIk8pHKPxSfdtYLDigMJ
|
|
eFj/PXDoyDsr+EUG3Jk83FG1bGiUmjUsqic/AB6unaObkEuzhi4ycIt4WPzG
|
|
PjTA2RrCFBtCHr6OvH/GWmYND8nzUqx4OPva5zS/JcTvKwIxDwdH59Zkb7WG
|
|
UYr64WGN5T/Lfhy1hqOKhs/D0z7CgwevWUOAwoeHLSKZfWyn9R8fHqpOeekd
|
|
+dkarip8uJg2MnRjs6YNbFAMEC5OKtsCXXwbkJID7ykXO8R5/NneNmCmaJhc
|
|
rLlHVRszzwY0yX/wa+Niu4gz88VaG/imGLBcnFBwhjKw3wbkZIOu5uLf3WUy
|
|
7iUb+KAYKFxUV7ZRymm3gWEyoJzgYoOWjanJextQySV9uFg2pry8d4wtMCpJ
|
|
Hy7imzOVzVxb8H5MLpiLwxUcq+ciW0hWI+uHixHzTUymRttClgXpw8WeGV2M
|
|
Exm2EEse2JHIxeXygmczCm1BO0PxgONE+qIoYbUtZJaSPlxs/Op6YE6XLdS2
|
|
kj5c3BVvvKNiyBZufCF9uLgwY5TQTc8ODhqTPlz0tx04rWRnB9aepA8XA7Je
|
|
3h2R2sGeOPLtuRiW/vIKf7kd1JEDjsrFZdoD4Tt320GVYoBxsdhvVNXUCjtY
|
|
RW6QNLj4mGrcPqrD7s/+h4P2ea6l4z7ZwTTyeRvkYNE/cQ5iLXtICiB9ODh2
|
|
bsGmJmt7kCWRPhzMvdC5fYXUHkYrBgAHzU5SpbNT7GFtFenDwTtuCXdX5tvD
|
|
/x0YwsHslNpJLZft4YYS6cNBWQBtbFinPRSxSB8OWmIm6n6zBxc/0oeDjPtD
|
|
VuMpDlCaQPpw0CBnaaTAzQE6d5A+HOQ8/ehXHOUAHeWkDwenda55L9joAPvu
|
|
kvXDwXVLNCWapQ7wbIgseA6WhH7updx0gIUU0oeDNdYp6ovlDjDZk/ThYLnm
|
|
rv9+TXCEKYtIHw5ue+Fv02HjCPG7SB8Oel89bPNyhiM8v0r6cPBFVu5t17WO
|
|
UPicbAAcTAmjjLlf7Ah7JpE+HHxE8e473+gIzW6kD7GePg1pyxtHcF5M+nBw
|
|
TlF8NG+iE7wqIH04uCx8oeZ1Oye410r6cDBxktKME7Od/viw0a/B1uXmeidY
|
|
aEP6sHHscpV/zf5xgrFxpA8by6jJPe1tTiAvJH3YKGpI21f11Qk075E+bPwn
|
|
1vRDH8UZEscTBdfGxp9/RT0LEDnDaF+ygbNRUOSSMpjgDN3rSR82htldOvIs
|
|
zxk+XiN92Ci7fjNBq8YZRN9JHzY6hqV1bOh3hrtO5MRk469HTfdsxwugaDWR
|
|
+PLYeHHB+RU8ewGcu0o2dOL9X9hUzIkUwOAPsn7YeG6+LPvuVgEIXciCZ+PM
|
|
KGNGXoUAJClEIktk45LIvH1FPQLgHicTOBvfR9W8HVF1gdo28jw4Ng4u2Gty
|
|
1MoFmB/JBsLGxAS65f4IFwgcRyQmERunp8yh9WS6gBONTPxsvJQR8GHxBReQ
|
|
mxGJ24qNWdtfFQQ/doEF1mSiYmN3oQN/zVhXKLEk1kNl4/4yhz2DDq5wkksm
|
|
WDZi46teWOAKy/WJ9WiwMaU3QPXBLtc/+Y2NB4fmjHcBV5j5hHjeBlk4VYfx
|
|
+b3cFVKqyQHCQmubfZUfjNxg5g6ioT5lYZnsWribvxsohZMDgIXFq/b0PFzp
|
|
BokmRINvY+GkIoprY6kbFHeTB1axUH49bO3Pe25QsMuR8CHe77Pw4EYVIYS7
|
|
k4mOhaPp3Xtn2Amh7yWT8GGhSwg3eXWMEKZsPUD4sPDNRpbZ63whuNDJ8wxZ
|
|
OOFKR0NpkxB0LmwifFh4asDKpWJICBWu34j6YWGELv3mZh13wC6y4Fl4dLzv
|
|
noip7jBQ9JzwYaGWQFIW5eMOLjvJhMfC64Uu1N2R7nDqVDvhw8IzduO6B1a5
|
|
g8MHX8KHhTdGw+u1u92hf86/hA8LqSph/vZn3OHcIHlCDwtPuLSNUJrc4cCV
|
|
04QPCxednPzdss8diksZhA8L4wLjg5O/ucOta8R6qCzczdg+0KfjATq/yQTL
|
|
whHzvP61Fh6wOp4YuBosLFy6lu8T4PFn/rBw+Us/cInxgOPkjmqQiRl5w8ej
|
|
1nlAwknyGxFMrE/J7i0/5AHTri0kfJjolj0q1rLSAyTfyQHAxMH74cKeDg9Y
|
|
MX8m4cPEzhn7Fl167wGVX28TPkwcHl/ZXz3GE/Qr/AkfJs4YuVL2geMJ+/bX
|
|
ET5M7DcsbpV4eYLTSQHhw8RjSYsEjyM9YfDZRcKHiaXfdL8dXOsJd/3MCR8m
|
|
Prx6XGPTAU/oeHCC8GGid5lB/MHLnvB+J52oHya+eLjE+NEdT5jdTyZCJn5S
|
|
P9gZ8tETRJ7ajeJEJuap50QMa3rBmVPbCB8m3u8SnWg384J8KpGwZjLx6NqG
|
|
qt4AL/h2MJXwYaLBxzG7KIu8oI/xlvBhIsXBwHJHphd4XZpL+DCxWizPty71
|
|
Am5oO+HDxC8OmXUajV6QNeJJ+DCx4dOrS9r9XhB3+gLhw8SpGZOWSpRF0LSQ
|
|
Sfgw0b5X6SMwRHDCfDfhw8Sb4yodoz1Ff3yYqKxp6+sQLYKH3YmEDwM7+1ZS
|
|
hBtEYFvXSfgw0G3zhqrVR0Uw4YIX4cNAu+9S45d1Iog5d5bwYeBdT7ko85kI
|
|
BBf1CB8Gjo4ItAv/yxt2NaQTPgy85bNMHsn2hpjHz8u0qxlopjw3fr+PN1T9
|
|
FUT4MJCza9J55ThvyLQtXxF9goF1A9lXj2R5Q+cSXcKHge/prTnJp73h5IVV
|
|
zuV5DDzFusdObfWGL6O7CzqzGDhhpGTzmQ/eUBvhQtQPA1WLnM7oavmAu1ox
|
|
UfAMpCX/2lBh6wOn/TSI+mGgvDX888YZPvCNtoqTGs3ABRXin1lpPmC7U761
|
|
cCYDd5g+LG4o9AHp3liigTAwSfdnr02tD8y1eREsFzHwQ17lxQf9PiBZmEAk
|
|
MAZyD2mwy9R9gWM9qCWwYqDBlM/m18x84U3eFqIhMbDMK6Xjl8QX8nIohA8D
|
|
h/pzJqxYQVxPqSIGGLE+TdcXpgd9odhzFuHDwPzaTdN//+v7x4eBH3/Mj9Lu
|
|
94VpsjOEDx0H8KFyhIYfbBbOJQYIHQvGv3bvMveDglpdXupTOuo826GfLfOD
|
|
ww87iIZJRyuPW5nL0vwgd1v+u4Y2Oj7jHtmVU+wH89rnSOQNdIzaN96up8kP
|
|
jM5PuaBdTcec3EnJUe/8oI75W1dQTsfpE8/6Ger4wzSLzlXRJ+jYZdhXpSrw
|
|
h7r2y8SWm7jfmVN1vGh/MB17yK08j46DTeNiM7L8Ia5705HOLDpmxKuWjCn3
|
|
hz2eKX8praNj8959q5s7/cF1ynSi4OnYcNj161WlAPieod8sTqTj3/dW0Dt5
|
|
AVDrXmWWGk3HcQL3X/SQADi02DG3cCYdZ/5XkL1/dQBsVt3/sUFMx8jd2TcF
|
|
RwMgfewDqVxER+GmcVVjWwJg3dqvl7QFdJQfM52h/iUAimd91hdY0dH8S0Op
|
|
FTUQGo7eXh3NpWNc8o/STJ9AGJmxvTuLSse5pk0zxiwNBNFqvmu5Nh1VvtOv
|
|
XDkQCIdUjx/u1KBjmsrElvz6wD8+dPzXbef2w+8CYUWM8zzuIA1vlh5Vuqsf
|
|
BL/sZcQAoeEmV1+WvWcQ7EkJZqY+paGmcvpwQ2IQOJlwiAFAw4VDPn+v2xcE
|
|
H2we9Te00TDd6GhFXF0QXL60wlveQMOgxNz9f78LguwS+XHtahoOyzUtwCAY
|
|
lv70VBWU03B2AS11qigY4upXxUafoOHatIbFN5KCIf7r9qasQhquyPymu/NQ
|
|
MGTkbeCU59Fwcn3dkk3Xg6G0cPqWziwa7p9KXXX8czA80B7z4ncGDZ82aVh/
|
|
NhVDouU4H24qDTtvXzw2N0gMTVNvlYoTaai/PaCzc5UYWsYGqKdG01DtR/Ot
|
|
ecfFsL15c3zhTBomUO03jLSLYXx8RmuDmIaOH7OHi36JQfTG3kouomHOylsW
|
|
YVOmgVXgmXxtAXF92RDXcOY06M15/M3ZiobnD41/8nbTNHA7fzsqmkusx0lz
|
|
dmv5NJhZkXE9i0rDO1kj+dceTQPzvXLzcm0a+jW99HukIoGacP19nRo0lNP8
|
|
uDEUyR8fGnbcpcZ+tiZejwu+I5ab4ucncSpZ/hJY0qX7T2GnKc7y46twoiQw
|
|
My48Xd5gip/UImOaUyVwrspouqDcFP+jjeGkbpdASvN0i22Fpvhx92Rf/jEJ
|
|
XCzUHNOVZYq+c/HGs6sSmGft+YKbaop9G1pOHW+XwNqtH+tTo03xX6Wgd0te
|
|
SUCnmFLSKDbF9gceO4W/JTBxdf1GHYEpWqmfzdPXC4Ec7Rcx87mmWLdr+9Cg
|
|
WQikJW3yr9A2xZ0pz6p7vUKgJeew+SglUzxTdq6vJTwEMh4yJ0rkJlh096zG
|
|
2WUhEHld+fXhThOkJxU9TNwaAkukblfeNZig/bqN0rFFIXAl/c46l3ITbFYL
|
|
T9l6KQTM/OuF2YUm+FWF6drfEgL3K8YPdmWZ4LG0R2dNnhLXV1eU8FJNsCcm
|
|
p8lhOARwfoXfymgTPHvdLNNCMxRUTo973ig2wW9F8EGFFQoZu2pX6QhM8M57
|
|
kVK1UyiY6Lcrz+eaoM/FmirxtFD4JhBsKdc2QbsBjmHtgtA/+c0Erx7dSNdK
|
|
CwXhfNNlYjkVG1o62j1yQ+FCzIGugk4qhiXoTJYcC4VQtSVObxuouHa932TX
|
|
K6HA9Svc6VRORZ5mUod6WyjY87iPMwupGDFpK+PC01CIPTGWfT+LivzsPCOX
|
|
oVDobAyIZqVScfmaXVdLxkoheWP/3uRoKoY+XT/6jakURH2ddSimYiUs+KRp
|
|
K4WgHu4LTQEVS7Sdt2n5SSF9ZbvSHC4VGY9GNX+ZLYVX5fe0TmtTcYppTfml
|
|
JClsybaljPymYNX9OI+wjVJYOJjs7CunoENKC+PkXimc6tfNzu+k4OfYE7+3
|
|
nJSC73SqZn8DBQfP/XjwvloK4sCseutyCtoFtZzua5XC2fpZp9cXUrDSTXtN
|
|
xGMpxMGOxttZFNy45a539ABxPzeeFi2VgjuYE8Z9UpKBugdnV1I0Be/r1reO
|
|
nSSDJ01bPUFMwYQ5A9vO02RAuT2NM0FAQddve716LWRQEbHGJZJLwTD55aE9
|
|
bjI4nzh283ltCp60kZy4HyT7Uz8UDLgdHXo0XAY1erPOSuTGyKp7Pzy0UAb/
|
|
leltP9JpjL4aXw4+SJGBqM2x6FODMZ46nuzosZ64XxI88yo3xqB98e2222UQ
|
|
nHcqPL/QGB0edcdU7JfBI+dvyi+zjHFeWtPXKyUyuBVz7rFjqjG2J0xeH3hO
|
|
Bgyd6++2RRtjRoWa+sIqGXR4i8x7xcaYLJ67bVydDLq/sY9YCIj7Cc3VXVpk
|
|
EGCT6LOBa4yMLSvXf70jA+oHPZN72sbYQ3cedOyRgZc5h8dTMsZurdRY1X4Z
|
|
LLqXU5UmN8Jka5+rb97IwOSmK/NWpxEOz2rsSh6QwRINpzhKoxHGZX1uOPyF
|
|
+Pv3pmcmlBvhTby9ZskQ8Xkkaa6/UmiE+kpzfj0ZlkFT/iuZ6jYjDPPdHzRC
|
|
vI5UH68cmmqEGXs3xF4krs+8via7INoI974zDtL+KoPAO7bvn4uN8HDQgp+6
|
|
H2WwZ4rjFHOBEbG/n51W81YG625v9lzBNcLljNH1qs9l8K2WalutbYSiAzMe
|
|
fOn5fx8j/K0fUbmFWG/pNrNSL7khnjs8YX7NDRk8nFfC2dJpiH5Tkx/m18ig
|
|
YPOC9dcbDLGtfiNV+7wMfnxNuqxWTvw8WmRmWyyDvorGRp9CQzyuflF1JFcG
|
|
sTUx5zdlGeL3yx1n5qXL4G8tyfLaFYYoXFxssiSB8L20adLPeYa4YAo1wmSG
|
|
DMKPKW9zEBvi5o9+MckeMuD33epZ6myIucB0jp8sgy1xfRonOYa4If/sQxUt
|
|
Yn2ubpP6tAxxyfIXPt7DUlCOfPFJ97cBusxqS+f1SiEh4+gB8VsDfGDwfl0Y
|
|
SkElxGVg+wMDpGxqC0w+IoV/71wYvFNvgG8OJj1OXyeFCjWNs7QyA1w6p12w
|
|
Zo4U7soF2ikFBriv5XPUQkcp6G4M4rdtNUDR8/tir0lSyG12/mC+wgDPnkpT
|
|
mfAqFMzrVWP2zjPAY8aPNzXXhMLvxLJtf4kN0Nvxr9YVRD8adcMharWzAe5W
|
|
etM7MSoU+HcLnn/hGOCilJ2Vh8xDYd2ux0YrtQ3wXd7QLL3vIX/6mwEqR5o2
|
|
rmsMgUrTX3ty5fp4757ayMPtIZA70NXF7tJH2nDZV5YsBIqS89rqGvXRusmo
|
|
eq5BCHQen7w8tkIfO4Xe/lsfSkCwrej6xCJ9nBRjWXzkoATumH5qqc3WR3X7
|
|
Hjg1UwK7YhnrVq/Sx3UVfv+U6Eggfa5lv0OMPoZeelthUDgNDqtRhn+EENfP
|
|
uV56c9w06Jn3vPqGmz7unc0yCyfm+fTFORaHpujjf+WjvZofB8MP/iRpioE+
|
|
BkVGvzX0CoaGfcs5MhV9PDjfi+1/NAjmHlO9x/ykh8kPWl0OfA2EAFfqtluP
|
|
9PBZOz890C4QCqIrvcUterhMOuN15LwACNG5p3ayUg95EdPT76/2h9mhqbd7
|
|
SvRw7luO6/l0P2ikHCp6nauH1aNust8k+cKe5V4r/lujh6FFLo6ZwT5wcXpS
|
|
yI6Fevi7bn3KFn1vcG8yseVI9XD1kv0PX7Z6gUldCHWfmx56Fa+LP73UE+YF
|
|
qI9/wtfDabOcWe2/3UEt0lP5L13itU32hIpBtz/1o4eLUDR5S5MAIqd6KN97
|
|
o4v0iCP7TZIcweSlyviN93Rxh+qR8DUDtmA7VUwdg7podc1raUGAFZz5bWgb
|
|
f0oXdVS0Lyh/nwxr5y4KKdmji0dP9pvN0GLCZX+XFZfSdXFV9/Ch2Mu64Fe7
|
|
u6g4ThfXzemowDOf/rVpTLy9IFQXb3xSffV6REO4IaxZbbSLLhaILZrUPU2F
|
|
tsSmZxVbF18tf3lMRYsvdDaeuO26pi6W7KkyhTgr4THJ8N0PQzooiQo3rEyy
|
|
F8ZoLeB87NPBMNNZ8KZQICyj7M+VNOvgbw2LsHfR7sI9U7roeRd18JlX1hXl
|
|
Xk/hRCG3t6pIB31cq3McXb2FNjM21NZm6+DGLw1t2Rt9hR+Wv2k7u0oH3RNK
|
|
M36e9xf65Eeq/B2rg3FHIou21wUKhdVPFliE6aDy3oGpLtXBwo7nS981iHRw
|
|
VMCsKRoHpwnP2zyYvtVZB3+c/NgRHC0R/g9dCfcl
|
|
"]]},
|
|
{RGBColor[0.365248, 0.427802, 0.758297], PointSize[
|
|
0.009166666666666668], AbsoluteThickness[1.6], CapForm["Butt"],
|
|
LineBox[CompressedData["
|
|
1:eJw8nHdcje8bx9t7H5KRTdqd6ux9TiQj38xIoYwkFMrISIoiiUIiI9kZGaG4
|
|
zyXZFGWktKeW9h6/p/Pc/fzzfZ1X5zznfj+f63ON+7nPd5Ln1oXrFOTk5JKV
|
|
5eSG/jso+yeBV9qxKh0xfxBdLe128IAEXn5fvfDujT8ob+vCpoo+CSzoKNyX
|
|
/+IPqqJ/+GrRK4Gd2zQj9uX+Qavdx89z7ZYA3env9jN1f9CschfPDZ0SiNqz
|
|
kz9NuRDFv/eirGiXwF6V1BrTiYXIVXvxKptWCSg2JG1L4hai0JTJs2qbJDDe
|
|
yuFP7IpCNPZJ9rsjjRL4/iFmWu/uQjTByK1CrV4CEyDG+Vd8IYrKzzy/+a8E
|
|
5PUdlpm+LES+fVqNT6qI679IEjSXFKLH++wKSsslcDzjiaq1ShFqaF+trFAq
|
|
gZmXfizUtChC5/pe6pgUSeBRlmfmPZcilH5yTud/BRLI+8995eidRcjliYr0
|
|
QJ4EUqa9GTP3QhFasaFl3aMfEhDPjx+UvCpCv25o19flSCD83R8Npaoi9CnQ
|
|
1cX0qwTCYiO5xzSKEfV7zulNXyTAeHwr9rdVMdKCvc8ffpTApen2lH8Li5Eb
|
|
e+mLgXcSkNaZP/sUWIzGS1ZdXPBGAqcUTx7aGl+MluSfXXUtQwLGW7wC8l8W
|
|
I7mhfyABD/Orx7VKi9Gkx2cPrHopgTvGM6oUFErQ4w6PotdpxP1Y8MTIi1KC
|
|
Xr5bMs7yGcFnurvo+tQSxDLZyzr/hPi+u9sZWbQSZDYyh6bzSAImBUlTfs8q
|
|
QdEnl+kffiCB2hStq++WlSDvC1qfFe5JQNX2zpNz3iUolda8LvSOBILdgt0W
|
|
7C5BO92VizVuSWCxVWRsTUQJSqY4Mc5cl0DI7azV6+JL0DLXF1umJ0lA66sj
|
|
vLldggLNV4WlX5FAy8XOh+rpJUjtODVoySUJUEcVMamfStCr/ISA5gsScJbv
|
|
lFtQUIKWbtOJj4yXwOdp/LSAuhL0ZtGhmulxErgZ+mjttd4SpH2gbzWclkC5
|
|
8TK5Is1SRG3brbg8RgIHmmccnzCuFFk96s1uipbAnsEZmj4WpUjlxcG3R6Ik
|
|
8MNx2Z6X3FL0TEer2jhSAtEfH+WPnl+KHO7EUx9FSODWEb7FAfdSdPek5XXH
|
|
IxKYeqBzS8PmUtTwKtOhIFQCfQ+KEtfuL0Xq3NXaW0IkQDNue1cRVUrqEyyB
|
|
L68ZRZsvlaKv2knjTu6TQGbSrcrB+6Vo77p5XpOCJDAOnIrioRQpqHbnPthF
|
|
xPdIo/f8b6VodcutLYJA4v5fG3G1rrQUnTdZZfdluwQ8/QRbr7SUonvXjSav
|
|
8Cf8FRBnsVqxDF3c+pNdtUUCmx9PKDAZUYY2hMTt8/eVgILVjz1dU8uQRrFH
|
|
be9GCXSWPtPMoZWh8DDTg2EbJDD368fjj2eVoZKALpHOOgkMdmnIX15WhigP
|
|
Plmc8ZSAwcrd62K9y9BE+6si49USONw9Mv3k7jLkwszrv+ougcSfPNXTR8tQ
|
|
U8vrIjM3Cdzrmr/g/Pky1Ou1viLFVQLJq2bFJCWXocBjUh3WUglc0DTJffCy
|
|
DHlszHaHRRLY1/dPB7LKUEr/6W+OLhL4z/bKrJziMrRjNsUn21kClLvsPdVN
|
|
Zeiak6PJsnkS+OD74tagfDkSy9uqFztJYKv/9B9jKOVo/tZc3Q2OElBJ39XH
|
|
nFqO3saYc/45SOCE06MJK2jl6O4W9rGdYgmoG//k759VTuojlEAgrXT5tWXl
|
|
6LXj3nPhPOL+n/rul+1djppn3l+mz5HAJNqDQ327y1FUTxw7nimBNeN2nLI4
|
|
Vo7i1rHEU+gSODl7YsKqC+VI70j0lmQ7CTx+/vjq6bvlqM3jopRGlcC7rdTr
|
|
WagczW7wpEmtiHjwOZOk8bUcqdsWZc+2kMDr2+UXnUrLEd1S70SOqQRuW48+
|
|
faylHOUWdW1baSKBQ930I18VK1DRrLigqqmEH9R4AUYjK9DidY03/SYTPCvN
|
|
V3lNr0BMdm9PzwQJpLbJz0xhVCDjybyVYcbE+ysO1Sg4VaCzu22f6o4l7h93
|
|
h+byFRXomrBAM95IAmYDOXcfbapAjjsZK6YaSmDLjMvZBvsq0D5jx8R7FAmc
|
|
SS/wC4wi/m6nUcHUl0DS07CTRZcq0PVnwRNe60ggdtxF6twU4vp3by+eryWB
|
|
jbVTXV5kVKDxBuGHfqlLYMqkMU3U7xWIVWWUvEaVqCewTye5sgLVmLpn1SkR
|
|
+fPDgmSzzgpkWri4NkBBAjfY0R/uqlUieZlAEmgbIVhPG1OJfE956B7tF8MU
|
|
15Uhr8wr0aZYP6MRvWKwV6oxXsirRAPK9LEXu8RgPrqMWe1ciaZV3xs1o0MM
|
|
ymfn5AavrkSljALth61iyNw3qWH8tkpk05XWz2kWw4Yv6w+/OlSJRsxwrn7T
|
|
KIZ/YWMueZ+uRJHvYj8uqBfDihtcxogblSjuZ9SN33/FcJv6xTnzWSViLuHu
|
|
96oWQ9HUz5W7PlaizZIE54YKMXQGs/qofyoR7UqK0c4yMbTOHHnqX0Mlit6y
|
|
+49ciRhyt6+6kTJYiTKdriUcLRRDV36Xxy79KqT/rXLViAIxZMzNKJBMqUI7
|
|
lThTLuaJgfo23XgErQp1lSdVm/wUw6w5lVP/zqpCMVun3E3JFYNcHr85w7UK
|
|
zb6Rup3zTQyrtr4PueJThUYc8+C8yRKDp17I79C9Vah3zFilBZ/FoJ6+qd03
|
|
qgr1La3/kvdBDK5bw34uv1yFjAQ5cZ7vxDDXMnvv3IdVaF7u57X1mWIob5td
|
|
I8qsQnGUP9TADDFMeNtixPtZReoDYlC88lmHV1OFQuKY2REvxRAR9vODqKcK
|
|
GReGXaKki+Hpdr05c7WqUc6Xar+EZ2II37TnxPLx1eiyj4fEJFUMA74j4n1t
|
|
qlH4o7+GKY/EMHpX0cZQcTWKuBlRx04RQ35k3sDlxdXouhP/VeY9MQjuKCzP
|
|
WF+NCs6oxjkni2FO7spdNbuqkVl05da8W2LoVqpeSTlWjU7R8mZ73hCDs/CK
|
|
iiShGo08Ujy5PkkMs8OOBey8X40ehPb2BySKoTr32q0Hr6rReiuL/MFLYjCz
|
|
aEpszK1GBtuyUyMSxFDsrnONWlWNoniSGMp5MWQzk1p3d1WjwugjWxPixND3
|
|
IiXqnUYNGth0Ya7JGTGsq6UHjjGuQU1ZB01SYsSg8cru9jbrGvTkOUORc1IM
|
|
tcKbZl9FNWiOBSrKjBKDmk9sp+3iGpQyfWSac6QY1nC79M6vr0H1N7mn8yKI
|
|
eHqaG6i2uwZ1PLT38zwihvd/ppsGHatBOQ79c+pDxfDjdrNJa0INCvY4My0w
|
|
RAzGk+23+z2oQbL27YAYksSNGq0ZNcjFlJ0fsU8M67Um/tvzowYF5js8pgQR
|
|
6z3wYYJaTQ3yoUyMStglhoTztRfie2qQ7fdPG0wCxTBizaH1ttp/0ftxs0Up
|
|
28XwJjtmb/aEv8iuIXYMx18Mj6rHFvvb/kV+Mx+2Zm4h/HBzbNTomX/RvmmX
|
|
Pzv7isGBEhPxdtlftPK4x7W8jWKomh7ybZfPX6S9r2Gf5wYxvC6vWWez7y+K
|
|
bpu3tH4t8Xmnd7MaTvxFFa17rQI9CX8vN95xP/Ev0gjapyK3muDXr2sIfPIX
|
|
nXH1KYpwF8OkcfJdkvd/0US3VakUN0KfiTY/DQv+oushK6MSXMWQM2FX+L+G
|
|
v8gke816k6VimDH6t06WXC1KEm7lpywSw1etRRsfUmqR8a9QQ46LGLJ6Ks9e
|
|
mF6LYk4lNmY6i2Fi+cn4SFYtUtz+/q3zPIL/zVL/kHm1yH9Xx8U8JzFIE+3H
|
|
7V9ViwoSLXZ6OhJ67zE/f2BbLRK1+CyodxDDnbmcxsNhtShxfQpxO8VwadTa
|
|
kbFxtbj+EPFQeE3vxp1atBwtzYvgiSH0olyJFNWiB1eePKBwxBC4fMehom+1
|
|
SOH2uIgEphjSdOR7FSpr0YJfx9aY0MWwEF2fZdlVi+JNFdkpdmLgeq9b765Z
|
|
h4ovhxhwqGII0uKtiBlfhybzNOoyrcSgc8dycja1Dq0eOPfa2UIMHRIG0ptZ
|
|
h85XUC/kmYrB5tdyK1fXOvTt37cdniYE39rT265tqkOKE/fMr58qhsv1f492
|
|
7a9DtgFm0wMniyFvy7KdLqfqkNu/soHBCWJYXVfIeHCtDpl8uPgrwpjILwdX
|
|
Go58XoeYvOUPKGOJ+73g4crgz3XoxFyDiAQjQp+lxRotxXXIsu3DGhNDMSw5
|
|
Uz7Rp7UO6TKC2SkU4no60os1KvWINYJG4eiLoQ75h24eU49uHqupy9QRw+CN
|
|
3m9dlvXIIyE+01lLDLEfVh45KqpHy53mJuSpiyFlyumkyUvq0fkTPQGeqsT9
|
|
Sk0yfeVdjyb53XSuVyLu78Fjhuv31qOG2sUmgQqE3mFOm/Sj60l95Ij3vyoy
|
|
eX21Hrnev5UX0S8CRfrceUFP61Fnl0sKpVcE3PKoPNanevTnT1dEQpcIut7f
|
|
+jxQVI9U3S56mnSIgFV9fsbHlnq0c7uYk9IqgkHeuvrzKg3IanolhdMsAqcv
|
|
ykY7xjQgs+2H6zMbRWB0et+dhVYNyHfF9DfO9SLwOf35OkPcgNoKMhPy/orA
|
|
IatFfcrSBpTRuSbQs1oEVwRN30f4NKCfd/ud6ytEEPI3U1V7fwOyGThrElgm
|
|
gtpPfomapxrQtxobObkSEXyvak3Su96AJIIPeRGFItAtCPYYl9aAjHLXpFAK
|
|
RODpNGe8dVYDmpvUE5GQJ4Js6n8Vs8saUNHDGE+TnyJYHHvqwcaOBpQzYMFJ
|
|
yRVBq5/+oZMajcgk/C2F800Ed959doPxjajQeXV9ZpYI9sZlsjtsG1HLwp5M
|
|
588iWFfeNcHOsRFtiI1NyPsggo03N2rudGtEfIp1oOc7ERyuNux/tbURbc/+
|
|
4FyfKYL0y3LtlNBGpPFhrUlghgg0vk9v9Y1rxPVHROgX0fk5uREt23E+L+Kl
|
|
CNpuzlCwf9WIdKczUijpIjg5R4mS+INY38jciIRnIhCvH2c2qrYRXRJt9TRJ
|
|
FYFen59jzEAj2nlHk5PyiPi8psImQ8o/lLLwJoWTIoKO09mxl03+ISfGzPrM
|
|
eyLQiv+dSeX+Q+LlZZnOySIQGk3s/fDfP3T+2YGEvFsiCNe7yti47h9ausQ4
|
|
0POGCBpDPPfo7vmH/KzTneuTCN6tHq9fRP1DtbOWmwQmikDu5xkD/6v/UOb5
|
|
zsHBS8T9S9X0tnj2D2lqnMmLSBCB+uxrRv8+/0OfN9unUM6L4CbM3f289B9S
|
|
fJcTkRAngiMTByOOdfxDj0b6e5qcEUHuo1XXHio3oYLlupyUGBEozX3rPkWv
|
|
CQXF3KVwTorgxxK7xrNjmtCpjLn1mVEicPx+fanetCY0pfpvpnOkCFa8nXg2
|
|
0roJmcuHJ+RFiEDb4sp9LXYTStabHuh5RARrlGdcjnZoQtdGZjrXh4pg6cIn
|
|
3kYLmtAoPU+TwBAR1Bs4qSctb8LzjwimOJYftFvbhDwricvtE0F346Gct1ua
|
|
EAc4KZQgEfhrmPe6725Cx6N/RyTsIu7fubzerkNNyHXpTuKCIhBdiPx+NqoJ
|
|
xeuP5KRsF0G8gWMY+1wTWpzxkMLxF0Fsn6pO6dUmFO79X33mFhFYr8jecuxe
|
|
E7JVItK3L3G/zRNusJ43oaWnjyXkbRTBLD//Z3Wvm1DTWNNAzw0iyJgx78qV
|
|
rCakFPfWuX6tCIoXW3q6/W5C0epEvHmK4ELbiF6jiiYU60dE3GoR9Koq+uY3
|
|
EuvPvZgX4U7E87cVZZe6m1AKg5tCcSP8GXPg2EalZtSeQPC4Euud77+BoduM
|
|
1FQInqXE++VsAtXHNKO/W0dwUhaJ4Pqd9KfFU5tRfEEKheMiAvcFIyzSrJvR
|
|
aKcF9ZnOIjhax8qNYzejtc+Il/NEYBlscTdoZjM6aHo0Ic+J4NGuf+75XzPy
|
|
uUAs15Hw96ld3fPdmtEUfSJ9OIjgt17OJt76ZnT7CHE7xSJYdKRLj+rfTPpH
|
|
SHy+o65mxt5mNHUPoQ+PiD/35NapR5rRqA4i/XKI+HrJok471YzythPhyCSu
|
|
NzL2imlCM/JuDfA0oRP5Z326g+3NZvR2B2EXO+L+3b8/RvCoGbV1EuWLKoKY
|
|
Zr8p/6Fm1LiXsLOVCF6YD3qs+9CMnisSPBYiWOmx4sv+783ov0gi3ZiKwC8i
|
|
ZMuF4mb0zJDgMRFBf/JOMaptRg2JRLxNJV6/ZzlVtDejZhuCZ7IIdhS+D9GR
|
|
b0Gvgeh3Johgde3Uf1ytFrTEheAxFoHHpkdo66gWFFdK8IwVgdqf35NuTG5B
|
|
kf4EjxFxv7lxRuWWLchGnvg6Q+L9kY2JU1gtKCya4KEQ/vv8B7wdWtDRCcTt
|
|
0CfyY6/ntocLWpDwHsGjI4K1Yw4+lXNrQde5BI+WCEaYMqIXrW9BLz8SPOoi
|
|
2GIS1nfbn7ieK8GjKoKAkZv6VPa1oIFKgkdJBNNba05sCG9BM7YTPAoiCIWB
|
|
1M8xLbj+iODEvmR/+qUWdCyS4OkXgsSsRZp0uwW9NSKW1yuEpLfZV0altqCH
|
|
SQRPlxAeLJw56sSrFuRsQ/B0CGFj1sKJml9a0Pl0gqdVCJ9ZXS+O5RH3YxbB
|
|
0yyE/Fhag15FC3L8RvA0CuFMsUZK/D+Cx43gqRdC3+hdaqa9LehJJcHzVwja
|
|
Dvta01VaUcBWgqdaCB/dx2xbZNCKqrqIt1cIwX7DgtB/xq1ILYTgKROC0+px
|
|
ZtGmrShfg8ApEYKG00EvGq0VRcYQPIXE51c1eRULW9GccQRPgRBKygo8oua1
|
|
IsNrBE8e8fkcyWKxaytqsiR4fgpB3WqGQ69XK8pLJXhyhTC2I9zq+dZWlCUg
|
|
eL4JIcxsPWVvUCv6+p7gyRKC6JO0RXKkFZW6EDyfhbAo7/RnvZhWJFdAXP6D
|
|
ENJcai6XXWxFZkN2fyeEAMbTrc9vt6J1DQRPJnG9CAXW6dRWdIf4+sAMIfx1
|
|
/NgXkNGK99+EcG2bTrpbVivyJC4X8VIID9Wzt8/Kb0U5BgRPuhBGamuZ0Kta
|
|
0YILBM8zIXzZ++a7WUsrKphGXDBVCL9de/dOHWhFO+4TPI+EwLlyd8IUjTY0
|
|
hkXwpAihecmfF9MN29CXDGI594TQE3hksfXkNhQ9j+BJFoKb0v0qrlUb8vhJ
|
|
LOCWEHQGFm5fwG5D3NUEzw0hGK3d3rN+VhuaVkvwJAlhB11v76GFbWg80d0F
|
|
JgphRoBpV5JHG5o8QPjnkhAsJ0q3fPJpQ1ZD6T9BCE/t/zPsDGxDjCGe80Jo
|
|
v+82bcahNsQb4okTQsXJ0vMeJ9qQmCgPJmeEcDi/dHf8+TbkQNg/JYbgi1gp
|
|
LbjRhiRD6eQkoe8lF9/Jj9uQaOj2Rgnh7LhXwVuAWC/x0jlSCApyd/qkn9uQ
|
|
/ZD8EUKYMEe3xPB3GzIjlut5RAj/ehrMtlcS6x8Kz1Ah+Bk4Fn5vbkP6Q/qE
|
|
EHpEj+nkDLTh+iOEyADvXTc12lH90OX2CWHqK5s1Y0a1o19D9g4Swpbt21NO
|
|
TmlHMIS7Swi+kTYbdWza0fWh9BMohHFa3uHR3HYUPiTHdiHsaxmta+TUjnyI
|
|
j3P8hRAtmNWftKQdzSbSbeYWIbi21i9keLajaUPp21cIX7V19LK3tKPBIZ6N
|
|
QuiNumXvG0R8/xDPBiHkBUpBJ7wd3R3iWSsE7zcLHqfGtqPgoa/3FMLtPSt0
|
|
115pRy5DPKuFcPFM8TfDe+1oMpH+I9wJf2xZSctOa0fNQzxuQkhe6rz9+Lt2
|
|
lDHE40r4a8GTYy7f21HsEM9SIVxefnL/2NJ2tG6IZ5EQqDvK5tY1tCPGEI+L
|
|
EIIu3WyFnnakPsTjLIQDBeUBF1Q7UMHQy3lC4M6Izdk3ogPdH+JxEkJK2HP1
|
|
dZM60JDdPR2FUN66aOxCqw60bIjHQQhZ27xUZ3I6kPkQj1gI2xRqvvBmd+D5
|
|
RwjfEku3cJd0oB9D+vCEULPov1qhZwe6PcTDEULqSHvh3K0dKHiIhykEYU2k
|
|
n9veDrR0iIcuhNBPK4L8IzqQ5RCPnRBCpAmrj5/pQEpDH6cKgZW5ZOL9qx3o
|
|
z1C8WQnh5u+QtJ8POtDjIR4LIeQOTrVWQh0ocojHlPg+Onc/41MHWj/EYyKE
|
|
xfvf3/DL60D8IZ6pxOd/frhzv7IDGQ3xTCbyh0B4tK2lAzUPzdsTiPU8N5cI
|
|
5DrRUPqPMBZCzLYqg2jtTnR9iGesEHad+0irHtNJ8hgJwcYq747DjE60Yujr
|
|
DIXw0kY34CatE9kP8VCI+Luy9aSBpBNpD/HoC2HBgW65Q/91ouohHh0hLP2U
|
|
/LrbvRO9GuLREoJtWMTvwE2dKH6IR53wW/IJcc+uTjRkd09VIXiKpQOHDnei
|
|
+UM8SkJ4NtNIZ0RsJxqyb6AC4efUeL/bVzpx/RFC2elZ0x3vd6KHQ8vpFcDj
|
|
srHWtS860VC6NOkQwPKEMcdiPnYiw6H1NQvg2xsxW5JH8A+tp14AE1fGcrsr
|
|
O1HQ0PdXC0CwWvfUk9ZOZDH0fWUCoOU8Yu+S70JFQ/erUAC9KQfpIt0uFDV0
|
|
f/IEEDe4K0zPuAsJh+5HrgBU0s+ZVJl1oZYh/iwBzKsoH5fB7EJD5S/vgwA8
|
|
g5atS5rVhRYNfX2mAJyD2+SOL+5CSrJ8LQCN1rR/QZ5d6MkQT7oAYuxu+Pn7
|
|
daH1QzypAvhx5UnG5v1daNQQTwrBw6uq9IvsQkPlxDlZABGqrPw98V1o1xDP
|
|
DQEMDNy9dOxmFzId4kkUgNnUmfSrqV0of4gnQQAjdw4kvMrsQkN2TYgTwPPO
|
|
3z+rcrrQUDpMiRHAuOu/SgxKu5BsuVHE/QjpTJ/5rwtdlOU/AehEsrwP9Heh
|
|
BbJ8J4DLrxMqpZrdeH9HAI0zptqrjulGD2T5TAAd6Z8XLZnRjdbI8pcA0vee
|
|
dbhN70YjZPlKAMxNoSoqM7vR0Nc5+wog4EjMOe9F3ShAlo8EsPFbZv+3Nd1o
|
|
miz/CGCsk5Gd2K8b/RpajrsAwhqPs57v70ay8uAqgHuvpukzjneTPIsEcDKj
|
|
+Hn6+W6Sx1kAVs3pdo63u5FMTicBHJmftv/3s24kCw8HAST8yo/f9q4bKcjC
|
|
TQBbThiHG/zsJuONIwC9jW+OPK/oRl4yvwvgguvIgg2tmIcqgBEe2iHGCj3o
|
|
nczPAgjcfXdvvl4P2inzrwAybrd/vDihB82Q+VUAXc2Vvj5WPaQ+xgIYvWC/
|
|
J4/XgyJlfhTAtAx0Z9S8HsST+Y/gn3tjdveKHtQo85sA+v4yWGUbe9Blmb8E
|
|
kHnRb1/Orh7kIvOTAII2uoz8eKQH718Tn5+TL/fhTA96LPMPH5KEmsLsaz1k
|
|
vHXwwWh+Rc6fxz3YP3wI3LruefNrzFPPh4wbUa3auT1kvFXzoaV91UFqWQ8y
|
|
k/mHD3orfnuubO5Bf2T+4cOY7z1no+R6SZ48PmitzZz4XrcX8WX+4cNfdXq/
|
|
2oRekieLDw/eLLB0sepFl2T+4cPas/opl3m9aKFMQD7IHQgK75zXS+oDfDi8
|
|
9/ijJSt70SOZf/hgc2BOQPqmXjIfpPKBHfhEzzSoF42U+YcPV9ZkhV082kvy
|
|
JPPBS3T6+9j4XrRb5h8+hI7U6L98q5fUJ5EPg4UWg5bPe7F/+FAY35+f8b4X
|
|
HZP5hw+G8/ZGr8rrRVyZf/hwr/nmBKWaXuwfPlw+dij8QWcv9g8f2kZrfVqr
|
|
2of+k/mHD4kXxNUTR/Xh/oDgp5gUVkzvQzK5g4j7d+B58gN6H8kTyIfyou4l
|
|
obP6sH/4oGJXk7dqaR96K/MPH44FhdIk6/vIeNvAB59nWZusAvvIfOrJh5t/
|
|
3wZNOtyHZMtx54NQd/O6cWf6yHzgygeu6asZE673kTyL+HCS8fqNaWofqY8z
|
|
H2axt3O5b/tIHic+LKZ+i1z6s4/MBw58eDOuMHVXFeYR8uFE35m0xI4+7B8+
|
|
qHIV/3xX6Sd56HzYP2v6Kt1R/dg/fGgaK+ew0KSf5LHgg8eL6KMJjH4y3kz4
|
|
8MEkz7bZsR/7hw/WHj+581370W+Zf/gQs+rYzRTvflIfIz60mncGjN/dj2Ty
|
|
U/jw3+vR12Ii+rF/+HBrWitNP76f5FHnw8DCQzPO3u4n9VEi3j/3495p6f3Y
|
|
P4ReOu9tX3zqx/WHB3UX9s5x+9OPZMvr4IF9R/VrhQbM08yDnWM0Lj3s7yfz
|
|
Wz0PnqmXF/joDJD6VPOg7fW2PeYTBkieMh5YOT3f02Y9QPIU8sDzXOqfN8IB
|
|
JAu/PB7EPva5fMllgNQnlwdv4n+8Oeg5QMZbFg+a5nbO890+QPJ84MHo99m0
|
|
VaEDJE8mD7i6q4JXnB7A8wIPVky6ZuFxfYCMt3Qe1Py4vN/n6QDJk8qD+Uou
|
|
aQfeD5A8KTyITH5SnPB7AMnasWQeXMvKasysHUCy8LrBg3M+F6rbejFPIrH+
|
|
4PEfLbUHSZ4EHqjrLTmzdfwgyRPHgyOjhfPSrAdx/eFB8YXiOm3RIPYPDwzi
|
|
7QJ8Fg6S+TqCBxP0uTXZXoPYPzxQVuh24AcMYv/w4K2vz7Enhwdx/eGBh0t0
|
|
Oi1ukOQJ5MH3+z4/0K1B7B8ejAvvzvsvfRD7hwcO+dy3dZ8HSZ4NPJBct084
|
|
UTRI8njyYGx9iTu3aRD7hwfVPyYqdcvJSWU8rjy4t83cOU9dTiq7XYt4sGae
|
|
nvYLAzkpWX94IOeVLUwaKycl/cOD46nef6OnyklJ//BA1fGPSoilnJSsPzzY
|
|
MsLs3E66nJT0Dw+sTS+88hfISUn/8CDtxN4rfrPlpLL8RuWB7uxPzB0uclLS
|
|
PzywXBh+ZO8KOSlZf3hgeO/R8QgvOamsP5jMg/du8+ee95WTkv4h+N2WQEqA
|
|
nJSsPzwIT/5U/3m/nJSsPzyIW/Dga/0ROek/mX944Oeg6Kt/Uk5K1h9Cr2OZ
|
|
iB0vJyXrDw/2TWl7731VTkr2bzx4rH3q6PlkzNPLhYdOFxVzn8hJZfW0gwtB
|
|
v4zsdaWYp5kL2k/lx/33Xk5K1h8ubKpxTT/9TU5K1h8unNg03qAkX05K+ocL
|
|
B4QLJ1pXyEll+bqQC8wNbZUhDZgnjwtpxUpeBR1yUtI/XFC5fegsU05eStYf
|
|
Lhi/9TsUry5P6vOBC312n6fLU+RJnkwuXG89fdB3nDypD3DBSDkr5s80eSlZ
|
|
f7iQs230PhdreZInlQvzHI3dPzHlSZ4ULhwL+W03RyxP8iQTr6c6y2fNlSd5
|
|
bnBhgWXQm6VL5KWycE3kQu6F1cEVHvIkTwKxvu0D1J3e8lKy/nDB5MHifJ1t
|
|
8qQ+MVxoX+S1+06QPBlvUVwI9TDTnR+GeSK48Cv71vnWKHkp6R8u1N8oHX8p
|
|
Tp7UJ5gLmVXf4hYkypP6BHHBI3KPunIy5gnkwou4Aj/pE3kp6R8u/NZsz9ov
|
|
lSfjzZf4e+XbKZIP8mS8beDC6ukuW7VyMY8nF95+iUnJ/yMvJf3DhcaCqNq7
|
|
VfJSsv5w4c9/4jGHm+RJfRZx4ajFPaFXD9bHmdBjS477TCUF7B8uWBnd97fQ
|
|
USB5HLgwbYbDXiMjBZJHyIXCiyf3qU9WwP7hgkaa66lBcwXsH2J9T1f86qEp
|
|
YP8Q33/m7LxegQL2Dxf2u+q2yM1RIPUx4YJT36t3mosVyHibzAVOyP0vYz0U
|
|
SH2MubC49pci1VuB1MeIC6ftOT5ztymQPBRi/at/y23aqyCVbefocCFy68N3
|
|
Jw5jHnUuiFe/Rc+jMY8SFybYjayqiVeQkvWHC9NrLvKMrylIZfmtlwMLD3i9
|
|
WXpfAfuHA9e6PPedfq5A6tPMgcmLE9b9fq0gJesPBzJOGuyfnKUglclRzYHI
|
|
lIy3fnmYp4wD+x7dFWSWKZD6FHLg9NncmnENCqQ+eRzIcbfP2NOJeXI5wFb5
|
|
+qlQXpGMtywOvI++rjxLSxH7h7he/9OtjwwVSZ5MDiyfp6QxfZIiqQ9wYOW+
|
|
Y98TzBVJnnQOPPAIqx5DV5SS9YcD+5GpW4JQkeRJ4cDrC7usp81VlJL1hwOH
|
|
uv3XPlyiKJXNCzc4kP59ZI/DakXsHw5sslrb9MdHkcxvCRw4o+LuuCdAUSqb
|
|
F+KI9bvLDY4LViTzdQwHltg6j3pzVJHUJ4oD9WGzoredVpSS9YcDPcv+bpx2
|
|
GfOEciDkJj2p8DbmCeZA6E4rwfknilKyf+PAQOZXtgcoYv9woCXa+Oz0T5jH
|
|
nwMeBSMWt/3APL4ckCSl+r8rUST12cCBxDqFpkt1iqQ+nhzYmdKdta9DUUrO
|
|
P8T9bo/XWSOvhP3DgVPPqu45aSlJyfmHAz+7/9xnjFLC9YcD0c/36ZtPViJ5
|
|
nDjwpvN97hRLJVx/OLDjMeqYxFTC9YcD5/957JkmUcL+4UBCooWflbMSyUPn
|
|
QOHb23+5y5WwfzjgtvJ31X9rlbB/ODDK69kGn61K2D8c0Ctw9I3Yo4TrDwdm
|
|
Zx5puxumJC2Q+YcDL8fvksuLVsL+4YBfrVG06gUlXH84sMbE5yr3hhL2DwdO
|
|
/NjE3vlQCdcfQp824yVPXyrh+kP4ISy4te+9Eq4/HIg6EjNy9nfM08uGRz1L
|
|
0+OKMU8HG0YWf6xorFXC/mHDU/t/J+d0KOH6w4bY3tcZd+SVcf1hw0M7p50G
|
|
2srYP2zQKtx/f7+RMvYPG5I6125qmqKM/cOG3Yd6b2+wVsb+YUNUsHhLBVsZ
|
|
1x82FDWynqyfpYz9w4bNWaUHGl2UsX/YwJ7AzgpyV8b+YcOsUvFlnY3KJE86
|
|
G8TBTf3Xdyhj/7ChcgPjn0OwMvYPG2ziRu2oOaaM/cOGKfonI0+eVSbj7QYb
|
|
0nOuMoVXlaWyeSGRDT1/Fuxqu4d5EthQZn167r00ZbLfiWOD/6ftDze/xTwx
|
|
BO/9umTbHGVpncw/bAj+08fuL1SWXpBdgA0KC2+s/PJXWSq7naFssNCr07/a
|
|
jnmC2dBr+H7FfnkV7B82BKznM1Zpq5A8gWyIGZh/Y+ZoFaksGvzZsKy44zZ1
|
|
mgr2Dxsy1VjiKVQV7B82/N4zYvMYngrJ48mGU7QI81FOKtg/bGhhnt03eokK
|
|
9g8b+kL5XpPWqGD/sCF59IE/VptVsH/YINfp+le0W4XkcWLDwLjPESvCVEge
|
|
BzYkHst7ueukCpmvhWxoEO8Pu5CAeThsmH5rXcGbWyrYP2yIn8pIa3uCeahs
|
|
cHjSMsk0QwX7hw3T3OIMvLIwjwkbeIYzIhPzVcj8NpkN0VVXoqqrVHD/xobR
|
|
n5XH2LaqYP+wIe/tIquQQRUyv1HY8PXnsU+/NFVJHh2Cp+9us62RqlQ2b6uz
|
|
YT097XLMVFUyHyixQe3wg7xuG1XsHzYU10afW8dTJfudXhY0rHUr/+mkiv3D
|
|
Avs23dT5S1VJnmYWPIy7p//RUxXXHxZ4L2R0zN2qSvYH1SxYOum2V26QKvYP
|
|
C/Yoq65YHa6K/cOCvIH5v1tiVbF/WLBJ+0Dp0Suq2D8sYFHjt824h3myWMDx
|
|
uRT5KU0V+4e43rMo6x3vVLF/WFA31ttt8ndVqWy/SsqCM7Hmej9LVLF/WCC8
|
|
M59+okGV7A9SWXC/Rpw6v0cV+4cFpfM0o/VV1UieZBYU/Lr+Op+ihusPC+Ii
|
|
RrrcmqiG6w8LxnguY+6zVMP9Gws81/juXspWw/5hgd+RxSNojmq4/rBA8F1X
|
|
ffRiNewfFvxyvLhMYY0arj8ssC0bHGzarEbqE8qCxVftFSr3qGH/sIB9jOtR
|
|
dESNrKdBLKg6N2pEYawa9g/x/uw3U0qvqOH6w4Kj5o7Ha+9hHl8WHLp3/r/u
|
|
dDXsHxaIXV9v1v6AeTxZ8HYGqpj+U42MN3cW6E6MfDKzXA37hwXGfMuSjU1q
|
|
uH9jQUvIlbUx/Wq4f2NBeGONOENDHfdvxPqCFYM6Rqnj/o0FGuxmLZtp6tg/
|
|
LGga/bBri606GW8cFix5a6jzSKCO+zcWtFX8G9c3T10q26+isuBdAG/anBXq
|
|
Utn+qAULfuwanJ6wQV0q298xYYFRI21y+w51XH9YcPpHieHCEHVcf1jgZC2n
|
|
/PiEOp5/iHjujakfk6Aule1XUVjgyrrw5fBtdTz/sODRX6ObnU/VpVdk/mGB
|
|
g5bG3s1v1KWy/SolFuhc2epUk4N55FhAuemk512iLiX335gwZ1Lc1/oGzNPB
|
|
BKTldjSwF/M0M2G9zymesroGyVPPBEc2vzbOUAPXHyas3usRTZ2qIZU9zyhj
|
|
wn2bVutsqgbJU8gE5rK+9/4CDelxWQAxofPfbrfR8zVInlwm1Pdsqn6zQgPX
|
|
HyZM2JXju9Nbg8wHH5gQuuFunWWgBsmTyYTJH/q8/h7SwPMPE7ovwI9bJzWw
|
|
f5igPPfBvy2XNLB/mDCbc2g1864GyZPChMzNrBkq6ZgnmQkBZTmz8t5rkPng
|
|
BhPWnFvw4t5PDTIfJDJh36n74REVGtg/TPj5peWOd4sGnn+YsG7u6Onz5DTx
|
|
/MOEaZpTOu10NHH/xoRJ2noTJo7TxPMPE5a6lCTomWni/o24379itiszNUl9
|
|
gpmw6rLZ5YGZmnj+YYL9naQpfYs0cf/GhFld8gP9azSxf5gQfkRsreSniesP
|
|
E1SWr3+qs1+T1GcDE9J8N58xjtTE/RsTLmUs+2wTr4nnHybAimnLZ9/UxP5h
|
|
whjaT+7aVE3sHyZcd/HZGZqpiesPE7Y8KFW7lYN5nJiwwYXb/K0E8zgw4YL9
|
|
HpvBRk08/zBBacX5tzb9mtg/TBi/dSx9vaYW9g8RX5MC5S+N1iJ5qEzI87sz
|
|
o8BEi+x3LJjg555+Zwxdi8xvJkzgVF876u6ghecfJljobHpzdaEWnn+Y4JSj
|
|
sbJhtRbJY8SEGLswZ/ZWLTz/EOuxzb9wdJ8Wrj9MuPZF3bHomBaef5iwVWXE
|
|
fFq8Fq4/TPD803XvxE0tXH+YcGTBM9+GVC2ynvYyIGfVwsPObzBPBwNma7/r
|
|
fZirhfcPGFC7zPDLmDItUp96BqQKhD1hTVp4/mFASqbDobYBzFNGXK9qivd6
|
|
bW28f8CASdcLbxaM1cb1hwHnFLbNXGymTebrXAYI+0p4X5nauP4wQCfG7NQC
|
|
R21cfxig9s5ZnLNEG9cfBtF/zXd2XauN+zcGhKiYpJZu08b7BwwwW7Dx1eaD
|
|
2tg/DHC9n/i094Q2rj8M0DLJjTt2URv3bwxwTO1Za3xXG/uHAXLuo8elpGtj
|
|
/zBANNYazfqojecfBmg0c+YW5Wnj+sOApUWC1zurtXH/xoAp5ezplA7ME8WA
|
|
PYMWOx4o6WD/EO+3M7y7gKKD/cOAJ/s7vjZN0iHr6QEGxJd+KY6x0cH1hwGK
|
|
Ky/8Zgp0cP1hQFPDGlQ8Xwf7hwFeZ8dHha/Uwf5hgIdrzmy7TTpkvG1gQIHN
|
|
vsbi3TrYPwz4PXHCgahwHewfBqye8ayHf1YH778xwNdx9prmazq4f2NA377s
|
|
h9ce65D5wJkBep/n/3N7jXmcGJBMfW04IkcH928M+HzP2jSrRAfXHwb4S2Km
|
|
H/2ng+cfBtx5OFbNcUAH928MiJV2vFXU1sXzD6Gfz1QvGKuL+zdiPQ+T/uw1
|
|
08X7b4SecTvtWCxd7B8GtI5N2NDuqIv9wwAmb+TulKW6uH9jgEVf8YbN63Tx
|
|
/MOAj679dqY7dPH8w4ARizYXVoTo4v6NAZp11msvn9TF+wcMuD9x5nu3y7rY
|
|
PwwYbE1WH3VfF/uHDr1rN8zIeamL+zc6XNm+Y+rxz7q4f6NDx4Tv/Y4FmKee
|
|
Dp0bDz9WqNXF/qFDksux2S+7ME8ZHfZvav6TrqiH+zc6yO2bpTRaUw/7hw7L
|
|
Cx3GBBroYf/QITyyfnzuaD3sHzocO8ozsJmkh/1Dh/W/GG2RM/Swf+hgtL0g
|
|
86+1HvYPHS67zwidxdDD9YcODmXxexL5enj+oYPzvPtNfTP1SJ4UOsD5dVVL
|
|
5uth/9Dh7NeXbncX62H/0CGn9ul/iiv1sH/osKN20ZtlXnrYP3TYm33y+W0f
|
|
PVx/6FB7zt+yz18P+4cOL5xaJ87brYfrDx3aigxj44MxTwQdYpf/OVx9BPOE
|
|
0uHcc0m37QnME0wHxcF5dXvPYJ4gOuSadq18k4B5AulEfzTTWeuaHvYPHa5a
|
|
20tdkvXw/hsdrmm8uX/6EebZQAetT50T8tIwjyedyO+fdUdnYH3c6aDZJz7g
|
|
+gHr40pcz9dty5mvWJ9FxP3NGFmY80tPWivzDx2UB/w/aRdjHic6fB7vx3Ks
|
|
wjwOdOibqmdyoAHzCOlwSm9h7JM2zMOhQ7Hp6tC/vXq4/tCB8Xxtz2hFfVx/
|
|
6HAJreqYpaFP6mNBBwO2yy4/fX08/9DhhDkr+IyRPvYPHcbGjNJ5PkGf5DGm
|
|
Q4pf/aS86fq4/tBhSebT9FZLfVx/6KAUtbtAk6ZP9js6RDx8oR6cyNXH9YcO
|
|
EYdKkqkSfTIfKNFh5f0wD8EcfewfOnBdJp1xctHH/qHBjI2PFv3nqo/9Q4PJ
|
|
nZyzi1ZhnmYaTOtNW71ovT72Dw3oATYPFmzGPNU0WLTuQtjsHZinjAb7Pg2U
|
|
8IL0yXgrpMHjG8syrEP0yfyWR4OO7uum4yP0yfyWSwOHjHpD9Wh97B8aXJQz
|
|
Pdp0BvN8oIHSE7dD3xP0sX9osLM4VOFJEuYB4noHklRP3dHH9YcGiroRLJ+H
|
|
+tg/NBirLC/gPsc8KTSQeGoZqQHmSaZBwPQ7mV/e6mP/0OCZS6HD8S+YJ5EG
|
|
ahWJcbO+Y54EGqwt7JV25+uT/XUcDbJ5NWnXS/Vx/0aDWcreEfNr9LF/aPDF
|
|
Lsi8sRHzRNBg1YdJV8LbMU8oDQbeuNWO69PH9YcGyaamqncUDHD9oYFPW0Sn
|
|
rboB9g8NbKfvT3+sa4D9Q6xPqrzIxtAA+4cG9WgiujbOAM8/NPgzLbtvxBQD
|
|
vH9Ag8JWPd39pgbYPzSomlHVVmJtQOYDVxrIv3G+x6MbYP/QwOz9HE4s1wDX
|
|
Hxp42OafrxAbkPnaidBLsT/byskA1x8a/OM8+rVtgQH2Dw3mFfQ9fLDEAO8f
|
|
0EDkvuJ4lZsBrj80cOPNO2XgaYDrDw3OBuW8svc2IOc5Cxp0jWoYO38L5jGh
|
|
QZDBhctuOwzw/EODiZuKF6zeY4DrD8E/6ampW7AB9g8N8uhTrOYdNsD1hwZ/
|
|
b01xt4s0wP6hgXHQs1S9UwbYPzTYfruUXXHWANcfGjQyLv29m4B55GhwfEpz
|
|
xuarBnj/wB7mb/71dsotzNNhD/YjF7Zn38M8zfbAHbvGedtjA9y/2YP3AaUc
|
|
jTQDvH9gD6kibvA5KeYpswdTT7Xl499gnkJ7QCXeK899xDx59rD7pftRja8G
|
|
eP/AHhZ3VZX5/8A8WcTrk0rrs/Mxzwd72BmeSplSgnkyiesV9tX5Vhrg+cce
|
|
pp/81Zhca4DrD7GefRmJJf8wT6o9bN3PilJux/GWYg8LYrgpY3twvCXbg+uL
|
|
T5pTBrE+N+whvLsqYawSBfvHHsrnRG1QVqdg/9iD14NX3iXaFJInzh40zA5e
|
|
STag4PpjD4VPP+v7jKJg/9jDr+VJz43GUch4i7CHbl21c88mUrB/7EGS33nf
|
|
aRoF+4dY/7PtA59MKdg/9uByJyhUYEXB/rGHkQ91xUm2FOwfexj8bM3ooVOw
|
|
f+zBoK/AS8ShYP/Yg7NgxPvdAgreP7CHh2fyvK5KKKQ+7vbAVzBlIEfM42oP
|
|
zQeVxR/nUrB/7OHLyC2h7xZQ8PxjDzkvPQeeLKLg+mMPA7vL759eRsH714R+
|
|
c5ri1rtRsH/s4ZtVxPMZqyjYP0R8jc5Iy/OkYP/YA6f33szt6yl4/80eKr8v
|
|
WNG1kYLrjz3Qrid1bdhMwf2bPczYendihh/WZzIRD9Y+OSo7sD7G9tBVna9N
|
|
30nB/Zs95J0dzFmwB/NQ7GGFIG/S4n0U7B97CC5a2yMOppD7O+r2MCfg2spx
|
|
h7A+SvaQphg/uyQM88jZw8cIMYoKxzy9dhCseumlyTHM02EHBXvvz7pzHOvT
|
|
bAd5f7cvHx2NeertIMi5vt3/FOaptgO4bTTuSSwF+8cObg90fSo7Q8H9mx0w
|
|
5hxX7o3D+uTZgffxH+/743G85doB//23kXUXsD5ZdpDac7A+4yLW54MdfJ9a
|
|
NS/sMoXMb5l2cGbWAN02kUL212AHPas+3v5wlYL9YweTFsSbOF6jSGXnxVLt
|
|
YErLS4vr17E+KXag7ERLq7qBeZLt4O0iua9qtyh4/80O1hpM2KJ1G8dboh2U
|
|
hJ6Mbb497B87YN9ZJnl2B+sTZwfbw/z3rE7G+sTYQTilmFWbPOwfO9i/5PLB
|
|
JXexPhF24DL3iUvi3WH/2IF8u/Htr3eH/WMH0Qvzj5bcHfaPHfR71bZ+uzvs
|
|
HzuYbepcmXQX8/jbgV+i8qrlxGty/80OdmbrrfmXPOwfO1j5YGvdeuI1WX/s
|
|
YMLMyQNSYv3k/rUdSI/PONdze9g/diA4GvLCkHhNzj92cIFt4z3i1rB/iHi4
|
|
SL3QegPzONlBc+ph18fXsT4OdlATYp2w9Nqwf+wAKVj45F8d9g/xfS3n77IS
|
|
sT50O+DqXlqy5TKON6od0FxpnrsuDvvHDm5+8chddmHYP3ZwduvYW1rxWJ/J
|
|
djDI21R+5uywf+ygkukc0hGLeYzsQLI6M8z8FI43ih2Mf/ylgXYC66ND6Gfv
|
|
kzYyEuc3dTtwKD1X9zF82D+EHmkrDy75v3/sYCk8DHpycNg/tnC25Xx+LeFH
|
|
cv/AFpa4GF1s303B9ccWIv+YvP0RgPNbvS0IYz8uPOY/7B9b2LJLzsFwM84H
|
|
ZbZgGPHhXKA35im0BfbbaYuTvYb9Ywu/rUduf+qB4y3XFlrfnO04uxzzZNlC
|
|
RPjdovmLsT4fbCFu51Lz3844v2XawtSYU39YTpgHbMGsYE3LVsmwf2whRKmR
|
|
t52HeVJtQT5zdTSHgXlSbOHm6LS/721wvCXbQoByj9NYM8xzwxY2HZmYYjsF
|
|
x1uiLRy+ZDlBd9ywf2zh0/xJsQ9GDNcfW2Cc6tUdpT3sH1v46PvilFh52D+2
|
|
EFboNc6u3wD7xxa8K5qTa9pwvxNK3L+D6x286nF/EGwLiY9flSWW43oaZAs9
|
|
+xTDbxD1mDw/agu7Cs3t/b8N92+2MDGXXT34DvcHvrbwz8PmyiI03L/ZQkWw
|
|
lqcv0T+Q848tKLKyTefcNsD717Yw+8iurvpLuD9wtYXHm9SyFp/G/cEi4u9V
|
|
+28fPGqA/WMLcp0Fx7cfMMDPf2yhPGHCLrMduD9wsIWWfKeN172H+zdiffdW
|
|
rKleiftRDrG+S5ddy/4b7t9s4RvTxzHSAfNQbeH9rqeWlQzcH1jYwvdV4ZoN
|
|
ZrjfMbGFpoY/JVeNMc9k4vpTntxV1xvu32xhw6DetvEKw/2bLbwMabIsax2e
|
|
f2xhxt1FpYsrh+cfIh72syMDf+pj/9gCtzPJyvEd7q+VCD7DmPdvnw7PP7Zw
|
|
rlBpRfuN4fmHCl5ze8pyzg7PP1SYvXq716ojw/MPFfjj/AriA/Xx8x8qiA80
|
|
zQlbNzz/UGFVRFvK+MXD8w8VYth79TaI9XH/RoXcU0fWe9jgeS6PCmanDB8r
|
|
jcc8uVSIZZp2L9fE80IWFSiHpTSPruH9Aypc2/N7o37l8P4BFeYa7jy9/dvw
|
|
/gEVBl3jnoW+1MPzDxWMnA930W7p4fpDhbdyR/fsitXD/qHCWP+r/HkH8Lyd
|
|
TAX9SzkOKRv18PkdKtw8Our4jUXD+wdUKLbbNsqaN7x/QIVn8WXljtPxvB1H
|
|
BQupd0uzjh6ef6gQJ1Y/vKJRl9QnigraIb53Wl/q4vmH+Dy3d/H9SF38/IcK
|
|
D7c9CTm+Au/vBFOhbsp5+ygTXewfKnj/l+yT0qpD5oNAKph01UztRMP7b1QY
|
|
M9bFa1WEDu7fiPc/r5hWu1AH719ToT7nqu/ZsTpkf+BJ3M8NUYwN5Xg/0Z0K
|
|
t3cmHV5+W5uc51ypIKdYtXyLH95PXESFveqLUq7RtPH8Q4VZx+oiB7u18PxD
|
|
haXh9+uDXmph/1AhSe7S1zHBWvj8ARXs254z/4i08P4BFcqPH2PFKQzvX1Mh
|
|
reti9fQMTansfDyVuD/2beLwYE3sHyrcEx2b+4KH9+NNqPBlwlr5190aUtl5
|
|
5clUUMrev/bCY/y8xJgKixcU7Ji9RQM//6FC+uXdtu+m4+clFCqwXy9PMCpS
|
|
x/6hwqvUoCfc2OHnP1QIDSreY+ekjs8fEPGmH9bQ14efz8lRQXmXr/a5+2r4
|
|
/IENDN4/na+6Rg3XHxuY/FxuiZO+Gq4/NsCMubvXHVRx/bGBPfwLLg5bVPHz
|
|
HxvITfuc2z9m+PmpDTioCRSPvlXB/rGB7OmtxTV++Pl2ng24G/7dOGYMfh6c
|
|
awOGvyZeGZ8xfP7ABga848PavZVx/SGu/2nJqEs6w+cPbCBvcOHSsY/weQqw
|
|
gRalU2KfpUr4/I4NBFVbb1vaNXx+xwY+PnIKuh2niPs3GyjaWOy+nqGI648N
|
|
XFJvHn30Oz6PdMMGFsXsvz/STwH3bzaQoBI+Xl1Dgex3EmzgtZf2hrWJ8nj/
|
|
2gbu3taJMGHJk/1ODMFXcCx0YZYcfn5qAzntocsr18jh+mMDI9tadaF6kPy9
|
|
SagN/Mn+MSFMbfj8qA2cPXC/bPT0AXx+1AaSFA667hfi872BNqC6fM7Bh8v6
|
|
kIHMPzZgckjTPXVTL3ke1tcGNA5m1kXs7cG/XyDevzDA0vJoNz5/bQOZHcaT
|
|
L8d2kedh3W1Aayv6UHa+E5+/JtaTtnRq+6UOfP7aBhj5VdRfl9vx7xdsoPDz
|
|
lpbwi234/LUNzI1pXKdxrhWfv7aBA5brI92i8e81hTYA8T/W7Q1tJs/Hc2zg
|
|
e3zrYNGOJnz+2gbkfzd8rX3VSJ6Pp9rA6QlS/oGT9fj8tQ14qLs5BbnW4t8v
|
|
2MDqM6+aigxr8PlrG9B522J/+3MlIv1jA+rxjSMLd5fj89c2MEXvSczO8aUk
|
|
D8UGehdFrmzdUYjPXxN/z5J8ens+jzzvr24Dz6Oit29MycW/X7CBveaVt1M3
|
|
fcG//7GBvte5pcyFr8nfX3RYw45fv0c9sniIz1dbg3Byh2/A/lA++XsE4u/c
|
|
jEjKyad8Mv6tYcvC9xnHN73lk/XCGpKCFK7vjvvKJ+PbGq4e0aS6a/3kk/2U
|
|
NVDnHwjxP1nAJ/O/NZhWWc0viCnhk/neGkJCFnHPbCjnk+djrMFl792ov5Iq
|
|
vixfxFhD9Deuw48Zf/my80kR1iAOlXdfbljPH5DNC9bgH9ubF6D1j0/GlzU4
|
|
26xW+E+lmU/OA9ZwJ2nbmemRLXwyfqxhkcmTm2hUG5/cb7IGyTMTltGtdj65
|
|
P2sN+cs+OtoJO/my+Hawhm6lhO+6hV1k+uJYw2u4VHz3QA+fTKfWwDyW4609
|
|
o49PPt+zhlgvmp/Vz34+2U9Yw1en9+16Rwf55PxqDTGX3uzNvyInOC/Tyxos
|
|
Jkl5xw/KC8j/P58V1N36+nLiWgWBrH52WEEWq6cv1klRQM6fVvDzK6f3L1VJ
|
|
MFWmjxWwtp5+NsFYWSA7j5dnBUdHqNLomioCUh8reAPRfpZ9KgJyfrSCuB22
|
|
m5SbVAX3ZfpYwWLr+qmoSk1A5hcroDe/TFhWoi4g84kV8NJu/Pj2R0NA6mMF
|
|
64/e+mzxR1NA5gsreLzmdYh3kZaAPJ9kBeuE7Z2h5doCMh9YgXSawCKkTkdA
|
|
Pv+1grIuX43fHboCUh8rGP/fNb78IT0BqY8VXNf2FR/Q0heQfraCGU+ORled
|
|
1Sd5nIm/z5I3ZUwzEJB+JT6fka3p/9hAQOpDrMekgxk7kyIg/WgFg4E7HlzO
|
|
owjI8wtWsOHBnG1nNo8QkPOSFTTm7tofoDRSQPrLCuaXDnznJYwUkOfhrCAk
|
|
70/AP4YhySNnBRPTDNYc/W4okF2uwxK2hF0+o7N9lICsL5aQzj5suJdiJJDh
|
|
llnCwO/XJTlPjASyeMuzBIHX8naDFaOxPpaw++esxVy5MQJZvGVawk+7yH7n
|
|
m2MEpH8soWiPafOchWMF5P6XJdgmj7e2GRiL9bGE5e82PR24Mw7rQ1zvs97R
|
|
VDdjATlPWEJsuvaNZdrjBeT+lSUkx3rqlMF4Afm83hJeLNOFJYETSJ5AS/D+
|
|
UpcxaDhRIDtf4GsJ53dLRxjumCiQnY/wJN7/IOTH5pyJJI+rJXzYRlNWtZ0k
|
|
IM+nWMJZ6a+rpacmCWS/13OwhKlnN6b0t00SyM5rcCzhaXetpZvrZAHZb1iC
|
|
erXb6J4Xk7E+BN+qF9vzJ08RyH7/ZGwJNp5avL6IKQLSgJag0jQ3YFXLFAG5
|
|
X2oJn9WCximtnIr1sYQFyedsa99OFZC/x7KAk/k3nurbTcP6WEBBzLU7ey5P
|
|
E5D7NRZQ8euUzjTd6QLyfLsFZFzfWqJ3YDrJk2UBO+W4k/hN0wXk+Q0LUKrs
|
|
/JrsaULypFvA+sVX/638aYL1sYAXzvx9znNnkDw3LOB+7vvdB1/NwPpYwMNy
|
|
cWU705SMtxgL8NufLL2TYkrGW4QFqCQpq181NxPI+rdg4u+LnV8VXDfD/iFe
|
|
W4g2hU0xJ3l8ifW+j4vIvmKO/WMBR0yXjEubZEHyuFrAaufAKTOvWmB9LOAO
|
|
o++i33RL7B8L2FRZFcW9Y0nGG8cCViyjt96kWpE8VAu4dLz205PnVgKyflmA
|
|
fbjiaC+JNfaPBUx0PJj/IMtaQO5vW4BVJTU829IG+8cCOsKXFBoG2GB9LKAr
|
|
6o6v1Usb7B9zMOi0oxuqUMl8UG8OG181srIWUAVkP2YOmQ0FO5fGUwXk8xtz
|
|
8N3b++9eJVVA7peZg9Xm+Ym/qLYkT6Y5GMG3qK/7bQVkP2UO/IDwJ+c+22J9
|
|
zME70t/QbqydgKw/5pClfDzlgo8d1scc/EvzD/9MsyPjLcYcRk1wO1OiaS+Q
|
|
9acR5tCDtEvS3O2xPuYw5lWL17oH9oJ1Mn3MIe/j+eg+RRrWh7j+wfjvF1xp
|
|
Alk99TQHuapG61n3aALZ72FdzcGnMy6xS4mO85s5TE6Ns3i8kk7Gm4M51E9q
|
|
/LLrCR37xxyUOOcOz9JlCMjzWsT9kI9fauzDwP4xh64dTbz+NwwB2U+Yw4vT
|
|
F7hVk5lYH3NI87q4MC+YSeYDdXNoLWo/kFvMJPOBnDl4qV7N/CVgCch+2gz0
|
|
Cq9NrLzMwv4xg45VAzG9CmysjxmMiE4eP3Y9G+tjBqGbH4DkI1sg6x+zzMCw
|
|
S31PgDUH1x8zKLd+PufBaY7gnkwfM6gZgWzb+jgCPZk+ZjDjhpGtaB1XsE2m
|
|
jxlcrno/+2wWV5Ar+wIzWJybFdjB5AnoMn3MQLjZ7IVHEk8QK9PHDIIfFxh9
|
|
1eMLOmT9gRmU3CyLnLOfL3CT6WMGX+39nzTW8wVpMn3MQEfy3LpwpUBgLNPH
|
|
DObkpvWOzBIIDsj0Id7fkhY5b6JQUCbTxwzUeAEOdiuEAgeZPmYwb7bWNGms
|
|
UCD7PTjHDO6OCLZqyhYKNGT6mIFG4tfVbzVFAj+ZPmbg3dSfLpotInmMzaBx
|
|
UFXoGSYSMGT6mMG2r431Jq9FOL+ZQfuahxmn5MXYP2aQ+Hjhq0ShmIy3DlOY
|
|
/z67ZlmwWPBZdoNNQTnBlPUQxAKqTB9TyLdd/TBFXiKIk+ljChciti9eKpEI
|
|
+mX6mMLRK14TLodJBGv/18LdhjQVhQEcp1mCaFQ0VlrWwAbnBOWiJG3hE3q3
|
|
e7e7l0tbL0TZGOXszcCSykUFghVJi2iOXpBMvWVY+WWQJfYMLYJEwaxsBVoJ
|
|
C7+UYK03M+9DH++nw70/Dud/PtyHfDhW15gXhp+XQh/5cNylT+TnZQmwhnw4
|
|
Vh32V+9UBLhGPhxrL/R82hARQEcHNsdbFWmh7oQA5eTD8X260ZI0WmGQfDjO
|
|
Ls9eEQtawUL7h6NU96WAPbBCE/lw9EnFps0pK2TQvAWOzfVNqrDJBpXkwzHg
|
|
zX40fd4GA+TDMXKjdXftkA3MFEgcF1XYogPLRbhMPhynYr/9YwdE+Eo+HEvr
|
|
nnbFH4rgJB+O48PNd4PpEqjkwzHjfsPK1z4JZmnvkzuz3pzGjXNbJNhBPhzN
|
|
I52jWZMS3CMfjkcs44ZXgv2/D0dDTv7I3gY7eMmHYWboXNGTz3ZoJR+G/rLv
|
|
pg8WB3zTgvEjw8W9x1tehB0gkA9Dc/u82KkxB1wkH4ZoeLztV5EM72hDMTyb
|
|
FqovviSDiXwYPqvyeOWkDPspyBie3FPYbgQndGgBeXvmebgg2h11wiQFIsPR
|
|
flFvmnBCIc3zYKiKlXk+2QU1dEFk2F/S1iurLujUAvs0w634I5Wpc8MU/UDO
|
|
MHlodUQtc4NDC5aDDJf+XHJ0VZcbGmkgAcP5gfiVmzke+KsF7naGV+8sS02f
|
|
8MC+Hu0DMOzoW3tdTnjgrRbcAkMleAbjuQpsoQshwwVvSoZeuhU4ptOH161n
|
|
+KdtYtAVUOAfR1X61g==
|
|
"]]},
|
|
{RGBColor[0.945109, 0.593901, 0.], PointSize[0.009166666666666668],
|
|
AbsoluteThickness[1.6], CapForm["Butt"], LineBox[CompressedData["
|
|
1:eJwtmnlcTO8Xx5NokUiLSJbSRlHT7PtSWrWS7AnZsoUsyb6lflkifaMkEVmz
|
|
ZInHkUKkVCTty8ykFIUKhd8z3cc/39d9zXTv/Zxz3udzzjPfCSFr/Zeqq6mp
|
|
HdJQU1P991//Pxm03Ywx+enVhJhaDzN3/ZVBat31hiD/JlSx1r9D3ieDn7ee
|
|
XhwX1ISUzIK3dr0y+DEpb5nXgiYUPH+sV9AvGSS4Zk+sW9KEpjX5hSzrkUG1
|
|
VmLNh1VNKOnlYoM5XTJ4uWbFceaGJhQ0dMZCh+8yCNo6Sda7rQntyzKf1toh
|
|
gzibqq+We5uQ6d3iFwe/yGD59sjE7JgmNM5krlyrTQbNG4cIrp1oQnGVeadX
|
|
t8hgyIiYGu2UJhTWp/vlrlIG7wJ+by3MaEJ3opyqGppkIOXOHtGV1YTau4IH
|
|
qTfIgH3//EPxoyb0X99jPetaGSTC+wNhz5tQzjGPHt8qGYQEfI3Y8rYJ+d0d
|
|
/GRnhQxOres4vKSyCc1Z9m3p7fcyYJp8zHWQN6EPGUPbPpfKQORxeWxNexN6
|
|
HRHkZ/tWBncGL0pZ0dOEHN+Vnlz1RgbHpqtJy9XkSBe2P7j1SgYfxx7UttCR
|
|
o7ncwEd/X8ggZlvXDx8DORorW5jiky+DS8GeGvPHyNHMylMLL+TKYGrJIZaH
|
|
pRypqf6BDMYXXosbOUWOJtw5tXPhYxls93uonc+UozvdC2qfPZSBbNH1S/4i
|
|
OXr8YuYY+/sy2NgbvQpc5YhjvZ1z+q4M9MZP99fzlaNJRqUMvdsyMCjumccP
|
|
kqOjx2bpH7gpg71ah2M8guVo+RndQvXrMphXOLCWvVyOshmdS/ddwfUweukM
|
|
zXVytHn+oDqdyzLw+X7ty93NcnTVwJ2VcFEGoYG1V513ytGsoEdrrNJl0Crr
|
|
jrt9QI4iJi/cn3NOBhU5XSfU4+RI63+OkTPPYn2oGjmelKOnlcmbOs/IwKR4
|
|
ZLbnGTkKDNdLik2SwcNwg4lzz8tRfsDeT1aJMjC6XKwVnClHQ3f2BcNJGViF
|
|
ey2ZkyVHjj+2DpwdL4Nvb6KZHvflaMrt3uKOozLY9OjgzqlP5Gjwo93PD8bJ
|
|
4LZgmkjnuRzd19NtNovF8fbL31RZKEfOV5Icb0fLYOZPDYvUMjm6dsz+outB
|
|
GTx2HOQ6t1KO2p/mOVftw/X8J79hSIMcafODh67Zg+83z/V7VjPJzy4cf+/o
|
|
yOlf5Ojt0PQxx6JkEFsas632hxxtX+q1eEKkDP7X4t2xpFeO1DV/ld3cIgO3
|
|
+NLq+gEKFPzt8hpRhAweFBuL/bUU6LT1Qqc3G2SgTDEd/UBPga5fNDGfsx7z
|
|
o9aw0shIgVLWlnOVa3C8u0Jpy0wVaNmexKj1YTLI2X5t3fUJCqRTt6C1d4UM
|
|
ChLuWH62VqBD+21371+G+ZJt9zObokD1m35K9JbKYOhejR/OdAUyuPnaLiFE
|
|
Bs4zpw8N4SrQePp5iVmwDOgPA5M3ihXIj13x5/x8GexDx6q2TlOgjm/PaifN
|
|
xflcs/bfGi8F6l0cKs8KkoHj669aM/wVKCLmiR4nUAZHykb8tAlSoAUriudD
|
|
AO4XBysK2+crUNafkyWufjKY+0l8MG2xAm10M1hZ7I3f94entesKBbrg7mo9
|
|
y0sG/Gu/rlatUSDpAJp2nTuOt76HSfBGBZq+tmzYMlcZOJgLVrzbqkDP4yfz
|
|
vjrjz2tLz7J3KtC1NdyYzVIZcF2HPIrdp6DyI5bBi7nKx2+jFeiZ6/b/Dglk
|
|
MHvMkgsaRxSo0+XGLH2eDDoO7Qu3OaFAcb8TuUlsnL9zrpb8/xQocSlHasGU
|
|
gV3otceiFAUafvDomqtOMigrv8tzOq9APxakPGE4ymDH9+CzxpcUyK09hPFk
|
|
Cq7vR9c/tVxVIG1abbGbnQzkDmdHXstSIKb98COltpgnP5pdcLYCldX+DJ9n
|
|
LYPgscutBuYoUO20xEjlRFzfp8SDE54o0IylXy6tM5fBl5yc1yZ5CsTm9v7+
|
|
PU4GKPZjRMxLBTIzF8zbb4b1Roxc2l6oQKe20u4NM5WBjuLbd0EJjqe4akiS
|
|
CX6fj6ssot4rkOtm1pyJxrj+/fd8z/yoQFFmrmnXDWQQ4cdc8qIGf+6kI2fr
|
|
4/74/uCm0gYFunh/17hnerh/1EVYFyrw/a9lzpiuK4Py1QO33WlRoLEjDu39
|
|
oC2D7t32q2PaFYijNLm6SBP3b9MuNb9OBfpkO7/oswZ+PncOY1CXAtnWzGjd
|
|
pC4D99p5Opd+KtCA/gRh3jX/7OT0KVDY8QXDDv+Rwo5sbsKDfwq06sQ6E8Ne
|
|
KZxsNZpuM1CJ/g5imqb8lIJ6elz6/sFKZNl8faRNtxRyG9PPlGgrUQOrauit
|
|
71L4cDGIoTtUiRx+PvzD65SCqOPyGsZwJTK08W7O/yKFPyjRbbqBEsW+OPHK
|
|
p00KwwwsnwUYK1FieVzGxxYpbGzzrnUbpUTsmfwdi5ulMNXTOMlujBKtliV7
|
|
t8ulIJwa2f13rBIxzmWZbG6UQmpi1PcnE5To6Jqt1Wr1Ugg8aHZs7UQlynO/
|
|
kHy4RgrXfNJSdK2VSL9EsdCwSgqtLgGfT9oq0WYNnkVKhRT0VzpsHmKnRD+b
|
|
0puty6Vg/ogjXT1FieLXWlzLKpOCKX+tV46DErllZG/gleD3b3l7souG9cQs
|
|
4OUXSeFF/oKxYxhK1DvaVMOnUApbik2UU1hK1BfY9qaiQArGmv/a7DlKZCIq
|
|
TQx5IYXTYfpOo3hK5FVWuKQtTwraar73O/hYv0G1Y0SuFBY8fbj9jlBJ5Qek
|
|
kHzTb9cSsRLtSWQXRz+WQt4bw2dqUiUyq9l/1iBHCuUmGi7RMiUqfdO8Lvm+
|
|
FN4eGzf4r7MSpa5cILPOlsIt9rLBC6cp0aHbLcZZt3F+h1a5XHVVouhL0Z+5
|
|
WVJwGB6Zp3BToovuwqd516VQJHbdM8RDiaoSNBO9r0oh4Kxop5mnEk06qlhb
|
|
cRnne/KSHFMvJTrOqHALyZCCifIOc/B0JTI6WGfeli6FOUWOndX4+ua+3j+b
|
|
0qSwW17ZetZbiUKn2FX+OyuF4zY3LXx8lGhEeHF2dLIUKpZWeLTg6ziBLN7g
|
|
tBTOLNs2bLWvEtUcPbg2OVEKdfYJ6yvx9d9VZzytE6Rw/v7k9Y5+StRRtNs6
|
|
K14KCk2eXji+vvuANZB3TAoXTfPczuBrDztUmxcnhebvz8ffxNdZVkYPvWPx
|
|
50dlCdfwddsl/smKaCnIOzmXT+Dr7lv0dSEH8f1HZs5eiq9Lnf94tO2TQv2A
|
|
Exnj8PWuBQmWEXukkHSz5/gz/D7949tOKby3eG/qh6/9bLmV0VFSODrXTvoS
|
|
64modL5jECmF17P+DLLF1ysNxsclb8HxMHFbtgHHg/bu9TLrCCk8TNYNzcDx
|
|
ejnGTZK1QQrrmj3U83F8ndpPjOatl8KFLnV+IY7/Opdb3/PW4Pi+pBs8xvmJ
|
|
skwt9A6TQtzC+oOn3JVo3v8WXKhYIQVpzqCkuTifQ6Pao0KWSWFDVbq7Ns73
|
|
0R9egW1LpGAJjxNSXZRI/n37lIgQKcxY4bt7Aq4XnciowWrBUhj0YZ52LK6v
|
|
hKCVtdHzpWCTnp1ai+tv/NyF2QZzpXB3leODkSJcL3vmxSUHSeG6/Rt/lkCJ
|
|
rIsXhVoHSkGvNXq1ANd3unitMCsA5zd1mfYkXP9mH/YZ8/zw5/6hVn+YmK/j
|
|
aV/yvKVw5c/+vGy6Eg3c8PK5txeu1/PPmwIxX+u3dKdUuEvBwtlmX81UXI9p
|
|
dptDXKXwrzbzgoe9Ekm+rfRpc5aCbKO3W8okJUoLzcLhlELHQIOwCsw75T+Y
|
|
r7ifw3/hfjAbBVZEC6RwaMQ/ppo5rs9zd28a8KSw6ZhVbTvuJ+qZY6KT2VJ4
|
|
pbN2cK6pEvl8iFlkzZTCgR0VN7abKFGS7UBulpMUbraFVJoZKVFd6p4RPEcp
|
|
iGfqHbigr0TmAp3PeVOkwL9fectAT4mC//73zNsO9yejl8HLdZTotNzxTIUt
|
|
zu/q8iPncf8s+VqyMcRaCpeeDBLnq2P947dNb5soBTfdwPVv/ioQbdMkqwhz
|
|
nJ+AFxaPfivQ3K+Nf/+Nk8LLE7NnHetWIOuClA/RZlKYIvXmeH7D/iSYfdPA
|
|
VAo6b5TdzdgPjniOiE42kcI8hsXRZdgv7H8ULLI2loJV5MBBr+QKNIy1i5tl
|
|
IIWlKQdnDqvH/mHIMODpS8Hs7I3drCoFuhTz6XOenhQ8oiKjpeV4nkhOyvPW
|
|
lcJX9ucwB+xvs909kyu0cXxL/04egP3v9JHfm0I0Mb9u2c/vPFegCesuebdp
|
|
YJ7O6As8nypQe+sM6wh13F+Lhh/JyyHzgRruHzW3H43Hfhx043JF9B8J7C34
|
|
nb/wpgL1/PTLMuiVQGi8InN3pgJVV/+MTv4pgVzuxlUH0hVIc25KiHW3BI4/
|
|
uai5Bs8HmzdIeVnfJfBxQtROdqICTbFSGPA6JXBqUU+p4pgCTdpwoC3viwQK
|
|
dxipR8Rgv5tjle/dJoEtWz/otuB55UdVXnJFiwSS/ATfhTsUKLdnUURIswRo
|
|
mq53N29WoPJrf7zb5BKQJv3wj1+nQA5/T1lHNErgpc60wmN4fir55KCmVi+B
|
|
50G8CRtCFEgmKqiIrpFAw4TJ9oy5CmRStijLoEoCMDDs9fsABfJM/x2dXCGB
|
|
xX//9M7A81ztrfgQ63IJvNZvQLecFaj0rx0vq0wCPQIjw698nO9Dzw14JRL4
|
|
tCepV5uhQDXewW15RRJIrl+3aaC9An3z/53nXSgBo1mJu6sm4vn0xInkigIJ
|
|
BCiHjz8+RoGEBlMjQl7g67hKX2tDBdpQXODdlieB0T5dBqeH4Pm1YIl1RK4E
|
|
0m0WrWhXJ/MBSODb6LF+Y3/j/WLj6YroxxIYZGX32r5TjoZZsbIMciRQ7R7z
|
|
wfSTHFkblUUn35fA1gO8iE+1cnRWsjbEOlsCFVX8jPj3eH+5MoSXdVsCfe5H
|
|
Vprh+T/L/5IBL0sCyrc02J8rR+4sl7a86zif66wvFeJ9Qjq7Mc/7qgQ0bFeb
|
|
f7suR6fv70yuuCwB9u+BU7vT8b4y0ywiJEMCdPnnNxVJcrRuao53Wzp+X+XE
|
|
f/8dlaPWabOtI9IksFH9Ri4H70N5p3v+/TsrgYfMwyb3I+VoiE5CRXSyBDb1
|
|
aUWOWC9HhavpWQanJTC7MGrJtFA5GviiNDo5UQILL356FzBXjm4brQ+xTpBA
|
|
7GH3Qi7e56pmD+NlxUugbkuqR6+zHEXGXzPgHZNA4Pp2n5McOTqe69mWFyeB
|
|
7xscqrXw/mjR3JLnHSuBe7tWfJ1pLkeTBxxKrojG+TuVGL3dGO9zw60iQg5K
|
|
4Or9x5nb8b56wSjPu22fBOqbKvwD/zahkcNDrCP2SIA3qnW39rcmsv9IIDuo
|
|
k5WgaEIhCny7KAnMS/uysa+iCfGAl2UQKQHL7gY2v7AJ/e/ox+jkLbg+Zrze
|
|
O/NJEwoK3IxvKIHJjzJnut1qQkn6RrysDRJYOmXXdcMLTWhG7i0D3npcz5me
|
|
cQ9PNaFDy33b8tZIwMtxaBfncBOiaeD2HYbr82le4/HtTSjwZExyxQrMw7zw
|
|
WflrmlCHqW1EyDIJoAHGASXBTUgj8bl32xIJVN288T7bvwkd1cb1FiKBMStF
|
|
dZucm9CJdbjigiWw3z5/rR4Tv39ZSkX0fAkwO5bHRVk3oSwWP8tgrgRmZvjj
|
|
ptGEupKxniDMl/+emHLtJqQ1GOsJxPX4rWcF/G5ELWsNeVkBEnA5eLsm6nMj
|
|
SqrKMuD5ScB0+F2lXnUjGuXu05bnLYHg//Xt21DYiJbcx5deEhj+L/r+lUeN
|
|
aLft4eQKd8z/0vm7711tRCvP4Nd1xXqeRNQlnGlEFvq4fTjjetIrL3WPbUSZ
|
|
B3E4pRKY6B85921kI8WPWAK/o0O3TlrViCZuw/kRSECUfcouaE4jGtmN2y8P
|
|
12u53qbZ7o2oYgMuR7YERrS99p/CbkTLv28KsWZKIK2rKL/cqhE934hxcZJA
|
|
yveRRf5GjehHD7YvRwnoKC+uShvYiL5sxzhPwfVSGJmS39mAHgzEeuwkYHMp
|
|
IfRRXQPyjcXtxlYClZt7nh1404DuG2M91hL4y0vJnpjTgNrTcL1NlEDcj8PC
|
|
hEsNqNMB6zGXwOFzj+dWnWxAzwDPO+Mk0C1l6v3Y04Bm+mE9ZhKwvuz3rnpt
|
|
A0pswHpMJbAzPczu+LwGFLse6zHB36cfNDZ0b0AOA/DjjCVwbM654yGMBrT/
|
|
KNZjIAFvo5zUqAkN6PA4HA59CdgvfSdeOrQBia9jPXr42qM9fNSvenSRj/Xo
|
|
SsAvbxArSV6PHr/CerQlkFBm9r/m4nq0Pwjr0cR6NjM2DcipR38VWI+GBA5l
|
|
eX1tvlCPbDZgPeq4nnYt7k06Wk/8RwJq8q3/jY6sRzGxWM8fMXyrPlIQurQe
|
|
PTfBr9crhkGrLsTs9KlHt9Kxnp9i4MY9rFvCqUfeDlhPtxjipxXnG1vUo9M5
|
|
WM93MQw50SQ4qVuPEqdhPZ1i8Gv/cgQ+1yHXEqznixgKq41efn1chy7OxXra
|
|
xBDXzZt4/0gduqvAelrEcIK7KH3Uojq0aS3W0yyG2kv73QxpdUj5E39dLoY1
|
|
ksvDL6nXIa09WE+jGMQahX3vSmtRpQ6WUy+GOZ3tuqfTalFsPNZTI4aOntSf
|
|
netrkccYrKdKDDLNzZtLxLXI+ALWUyEGr3HrojnDalGHPdZTLgZDceyUSTU1
|
|
qCIb6ykTw8kVr0PPZ9agIhHWUyKGt6ftaRc216C3L7GeIjG8KL91dKpzDWrw
|
|
w3oKxbBh9Nw90uE1SK0K374Av3+olWZtVTWapML9hRjUHhmOU8+oRkvbsZ48
|
|
MdSPsnp1fX01uoIfH5Erhq275mjJedXk/E0MeV+zPp4bVI1C8O2iH4uhdJmd
|
|
8FNRFSodgfXkiOHMpwLGvVNVyOcM1nNfDKPDD4NecBWqssQ3zBZDkMaa2i/W
|
|
VWjjDaznNtZ7duORWV8r0WgO1pMlhr/SlDK37Er0Jhe/znUxhH5tzczdXomO
|
|
emE9V3F+0ucY5Usr0YJy/AKXxbA6pH2Er1Yl4gdjPRliGGx7/vziNx+RZSvW
|
|
k47j/zPyxb9jH9FYPN1FpOH7vd28Y2LgR2T+F/NzVgwOWQkvS0Z9RFNU7T8Z
|
|
v8/gT5V/qisQS6XntBhCeJGtKWcrkEClJ1EMy3x9e+4sqkBSbA/WCWJY7LJs
|
|
gNiiAjlj/LPixeA/GrTE8g9Ipmonx8RAK54z9G76ByRRhTdODDpLWMPOLvmA
|
|
+PjSOxbHr2Km3l+LD4iuSn+0GI7ZZ+uUNpajSfh1Qw7iegoJ0jA9V47Gqspz
|
|
nxiaI/i9FQvKkb4qP3vEsGdVyNchY8qJ/4hBU/yq/nbFe9Smul2UGA7/2FD8
|
|
9sR79EGFd6QY/h1amBPi+x6BSu4WHI8/sekrhrxHF1XtJ0IMyK/vsCL/HTqk
|
|
SscGMQw7cG1N+c53aCX+c956nL+kVB8+5x1yw+02b40YouPe24/8VoYsVe07
|
|
TAw3Q7y0l2WWoX8qPSvEUGI8qHFySBn6oNKzTAwtmf/uLR1Vhq6p9CwRQ/tY
|
|
fozh21K0S/X4EFx/4Q/nsg+UIj+VnmAxvLu4zbaEV4rMcfuPni+G1m7nBWUd
|
|
JahTpWeuGGaebVjsdKEE5ar0BInBNNWX2xlUgk6o9ASKQfTrWIOubglaqtIT
|
|
IIZHmRdmH0BvEUulx08MR+7EpM1f9xZpq/R448+NnR8dn/AWVakuvcQQm5Y8
|
|
3TO9GN1Q6XEXw4KXs/LsNIqRCvcQVzEUpGRXF4QUoVkqPc64X1k+TDCHN2iy
|
|
So9UDO/nh3xjjnlD9h/cf6bd+Dp4cyF6r8qPAPerutS4429fo0yVHh7mx5ZV
|
|
/NHmNdql0sMWg8/E8Kzqna9QoEoPUwxXi/0Yp98XIHuVHicc78nlc4wmFSAN
|
|
1Z874nyz/03wjHqJqlX1NgXXW3fhYX7xC3RHpcdODIwlopMt416gWJUeWzEY
|
|
7A2U+K99jkJVeqzFcMt/xJGIx/lIqNIzEffPsvAdgTr5yESlx1wMvwZuGfZt
|
|
Zh7qVO3b48RwUTFB6p76DKnaf7SZGC7kX88Qt+Siiyo9pmI42jmv5JFDLqXH
|
|
BPe7FXZPHkc8RXNUjzPG8bMzWy/LAURX6TEQQ+qWBUWn+56goSo9+jheU/Ol
|
|
D3ci1KzSo4f1R60RNf57hJ6q9OiKIXfxnDyDqByUpNKjjT9vOFTi3fMAqXAP
|
|
0RTDjJ5fofFr7qPpKj0aYjiXfm1fQ2M2UuEboY6/33J+EmfGXeI/Ypj3vDoo
|
|
Kfc2uqV6nV4RDOMFDRs05RZStUvrbhH4uhp7b024iYxV79cpgtfl9pO+9FxD
|
|
r1Tv0yYCmfedl32PMlGk6vnNIljc9WTz2O0ZyE71vEYRFL/2ZQUw0lGtKl41
|
|
ImgsCdU8/SkVxaniUyGCXXoabz9PPo3EqniUieBEhfOtF9tOoG8q/UUiCFMf
|
|
vyo+Mgap7K+iQATrrBKWvSiLRAGqx+eJQK3uXtqw8eORRn+/FsFLa0mL/YBI
|
|
4V2VnhwR/FQ/G7NibowwVKUnWwRbh9sl/Lt0QjhSpSdLBJd6ln6efOu0UGUn
|
|
3ldFcOg0ajyz5Jxwi0pPhgheNLOPG/akC21VetJE4Fk3QSPq6CVhpUpPsgjy
|
|
9m5llztcFapwTU4UQXuZaOr4ihtCVTvMiheB/3LuRvtnWf3llRcnAi++Lu1Z
|
|
8m1hSn//E0F+qJFfSeRdoU9/vxOBYfPMklnz7wmp8x0RXHn85lag9IHwZn8/
|
|
E4FJ6/auN5NyhIv6+5cI3oQt/u+x8WOhYX+/EoGZy+4Uy8FPhKrHeYdh/ZxV
|
|
6nu3g3BTfz/Cz9/uGHpj81OhZX//we+/Iv73qY25wg+q15kvAi31Y0/4G54J
|
|
++0hSARHXCbdTd6QR+kJwPGmL6x6uCmf0uMtgi1vptJObH0u7E+nuwi69c88
|
|
sN35QthfHs4iODMgfX3kgZdC9f5yE8HkM65zoo8UCPvrjSeCsetHNm1NeiVc
|
|
3M87zs+w9MgNGa8pPY4imLu53SIiu1D4op9nEeRe+l61+8Ub4eZ+fkVQdD77
|
|
fEJlkdCmn1cRSJYzI+98LabyY4bjEcnJWr33rTC2n0cR1FplXx00vEQo6OdP
|
|
BOtZ+g5pySXCL/28ieDeVQ+ezK5UmNrPlwhuHAgp+pRTKvTr50kEsflBLce9
|
|
yoTU+bUI7FbYx0pqy4R3+vkRwo719dk/1r2j6q1bCHtr16+4qvFeSPEjhLCb
|
|
DeeX//ee0tMmhNHNU0Ntp5ZT9dYshNA9825+yS8XTurnRwiH9izbc3/+B2F1
|
|
Pz/4/s2+1Qe6P1B6KoRglWWCZh+tEAr7+RHC0Tpk7Tj5I6WnSAgoXDZq6IuP
|
|
wrP9/Aghd+XF4+2LK4X+/QkUQsSL5vjSAVVUfkAI7Yc0zR6lVglv9/MjBJu0
|
|
sUoQVwv7+0G2EASDp2X0NFQLjfr5EYLm3ajg4H01lJ6rQjh1PV+/17pWuLWf
|
|
HyF8+WaW86KwlspPmhC09hyY9zy8jvAjhAHX/23r1a0XxvTzI4RAcd4zu0X1
|
|
Qn4/P0IY9vOoVs/desKPEGzfL3WfM6SB8COE2x+kBwIXNQh9+/kRQsI/6yef
|
|
7zUIqflACAovox+jhjX2h8cgUghHnuhYNoQ2UnoihHBxlpa/5Ekj4UcIQ4z0
|
|
IrkmTcLn/fwIoaXHNLVwfRNVb8uEMF6N9rTndZOwv5+GCCHP3rc2x0ou7H+d
|
|
+UK4uyuix2SPnOoHQUIw/5WuO6xWTukJEII8ocoshaug8uMtBN05oyc/P6Wg
|
|
9LgL4aR0Ef1gl4LqB874fX1vchoClJQesRDq9mry3t1SEn6EYMzIP7t6RDOl
|
|
hymE+49cix+GNxN+hPBm9JGCnLJmSo+dEFg+p+PWMT5R9WYthAlzwsZ+PPWJ
|
|
8COE5Tz1rV2/Pwk/9vMjhInf56XkL2ih8mMiBPru7XHuz1qE/ek3EMIzRbD7
|
|
bptWwo8Qbo3XKQ6La6X0aAtBh7ZlnG5XK5UfDSEUjrrCXTjvM+EH57cibXxo
|
|
3mdKT68AEsMWloy3bxP2v163ANI+1HsdSWij9HQKQGeUdXyWWjvV39oE8MmB
|
|
ln5wVTuVn2YBjBynvkv/Qzulp1EABU0JVj6yL5SeGgFU7Og4Jb75RdhffhUC
|
|
8O7Qe6cw+0rlp0wANPa3SmHsV6reigRwODDpqmfvV0pPgQBSL+ydeIDRQenJ
|
|
E8DUmDFBsLqDyg8I4HvVyPUzLnZQ9ZYjgDtB6v4edR2UnmwBWOQur7ls0knp
|
|
yRKAu4mnwQb/TmH/OHZVAJZzL3+/ENsp7C+vDAE8Prx3h/RFJ+FHAH8vfrzt
|
|
pv6N0pMsgIE3r8TfF3yj9CQKIPvCL7PjW78R/xHA+EPP/N/f/Ub4EYB4ljZt
|
|
z7dvVL+OFoCZweucxKnfCT8CyMzR6jBZ/Z3wg/X45hapX/lO/EcAn0t7ZgW2
|
|
fKf0ROB4SC7HGNj8IPwI4M+Z8hXcZT8IPwIYp9j57dXFH5SeZQL4MuqCZb7y
|
|
B6UnRACbeNMG2lp3EX4EkOW+OKZ7WRelJ0gAV5z7Httf7qLqLUAAM+z0Txe1
|
|
dhH/EcAttTTzj3bdhB8BPH96fcb0td2EH1xPa1mOk291E/8RwGgd/v3wrm7C
|
|
jwA017ywsuf0EH4EMGaL/MHiqB6qvzkKYKFN/Hrj3B7CD47vjrLpLpo/if8I
|
|
wCXygneH109qPjAXQKeZ9saR8T8JPwIoDP37+OHHn8R/BIBm7rerHP+L+I8A
|
|
FK3JTzYt/yX82s+PAGyt3Db/7+Yv4j8CiNfcFzDh1y/iPwKYeMRvhqP0N5Uf
|
|
NZyPRze3Po75TfjhAxw99yz//W/KT7v5UKgzkeYxvpfS08mHH5PY+R6reon/
|
|
8MG7s2b7i+xe4j98uD/faDao9xF++DB/Xe1shk8f1a9r+DDWlrPT6kwf8R8+
|
|
DD5kWRDf0kf44cOI/51nRbH+EP/hgw/79qvG/X8IP3y4FD1jT967P5SePD7Y
|
|
7D64wHziX+I/fHgz1mth34a/xH/4MOa+ntv8vL+Unmw+bEjjVfsY/SP+w4ff
|
|
NaWm70L/Ef/hw/GV7wa33v9H5jd8/4mpRS8HqYn6yzWND4d5MWuXTlUTUf7D
|
|
h/2Rk5Ues9VElP/wQUu+i7Z1r5qoPz/xfBi1KWZGxzU1EcUPH+5N8fS6WaEm
|
|
ovyHDy3DYdSDgQNEFD98OG/a+khn6gARxQ8fOrwLGBfmDBD15yeSD88z5+87
|
|
dGCAqF9PBB+mTs24dOfWABHFDx9GV19Is60bIKL44cPZrNnhzUPURZT/8OHK
|
|
jdyRX9jqlJ4QPriU1x8XhKqLKH74EGZ5p+l9vLqI8h+sP5mvc++puojyH/y5
|
|
YNvghq/qIsp/+CAcvLoiYOxASo87H870GO4aNn0gpceZD3H64X8Mtg+k9Ihx
|
|
fGbs8110ZSClh8eHT8r/3fpTOVBE8cOHgd/ezvuqoyGi+OFD8KbpPkyeBqXH
|
|
jg/t6wYeLl2lIaL8hw9P5d90885oiCj/4cPrt6YVOkUaVH7M+GDA2PH54j8N
|
|
Kj8mfDihP9o10XEQpceAD0GhX1trFw8S9R/n6PHB3+lv+baEQZQebT5Eb5k2
|
|
JKxgEKVHgw+9jJcHb/UNElH+w4c7q/Z6eTsMFvX3t14enBm1ZbZoyWAqP908
|
|
yBNdvL4/cTCVn04eTKod6jXhzWAR5T88eP7juuMIdU1RfzqaeZC6N3phEEuT
|
|
0tPIg+zDye+/h2lS+anhga7O53h5miaVnwoeHB8QnjTpoyalp4wHIetpLfnD
|
|
tKh6K+JB6Gy7XdnTtCg9BTzIeLBwYV+UFqUnjwfmxwsPnLqrReUHeFDfGN59
|
|
sF2L0pPDg+EvFxW/s9QWUf7Dg+75l2j7F2hTerJ4cCx92vj/TmmLKP/hwafT
|
|
/MThJdqi/n0hgwdtssNJn3V0CD/4+WemWk9y0RFR/sODkRfthIU7dUT9+0Ii
|
|
D6TBu+tKHuqI+m8fzwOD1/ZDeN06VH7ieJCpdHyqSRsiovwH3//W/waw1wwh
|
|
/PBAOVVS+DpzCOGHB0nzvSY8ax4iouY3Hgzi31Aba6lL+OHB2NcrVlaH6BJ+
|
|
8P10ti/4m6pL6QnjwZpeRfXeOl0qP8t4cO1MhiJs7FAqPyE4/l9gy4P5Q0XU
|
|
/sMDbqdjworkoYQf/Hn6b0FUzVARtf9g/Vqm636Y6VH58eZBsFm8XfECPUqP
|
|
Ow9qG0M2DE3VE1H+wwOd2YedbzToiSj/we+3Uzv1jsUwwg+Ot8WGU5ahwyg9
|
|
TB6s1Z/D17k8jPDDg/VuKC6kbRjhhwfb5D6uI02GE354sN39nxmLO1xE+Q8P
|
|
XAJWvz46b7ioqp8fHrwYkOQzcedwwg8PRszcn9l5bjjV3wx4MGr61OqfecMJ
|
|
Pzj+LafknE/DRZT/8GD15CfP7gzRF1H+w4NH+he2rpiqT+VHjQeFZ9wHBwXo
|
|
U3p6uXC68OqKXZv1CT9csD1XdL7xtD7hhws7Rt+4swP0RZT/cCGW7X1mhkKf
|
|
0tPMhZDeK3OW6Iwg/HChO+Tl12tTRxB+uOC99vxcx5kjCD9cWDRekPJl2wjC
|
|
DxcEESfvKVJHUP2tiAvl665mGL8YQfjhwtThe9bsbh9B+OGCxwxjXStDA8IP
|
|
FyYLVuzS4BlQenK4sODlJ48JIQaEHy5s+67+eVe0AeGHC/vQvWALvEhS/HAh
|
|
ylbzqtZHA6reMrgwn95Z6DDAUNS/L6Rxwbpu07PTtoaUnmQu1NqePOLubyii
|
|
5jcu7Df0ceRGGlJ64rkw9Oz5S6vTDUWf+/nhwuGC411NbwxFZ/pvwIX2+DEm
|
|
yT2Gov5w7uMC/694+H8TjAg/XIjQUqv94GlE+OFC6q3Zu2dHGFF6IriQ1Tf9
|
|
t9k5I1F/NaznwlVltZtloRHhhwsn1g1evbbHiPDDhbCkV6F95saUnhCc3yW2
|
|
zEJvY8IPF0rfmFfVbjMm/HBh+YfsmfQMY8IPF9p2KS4UlhkTfrjg/+r66wy1
|
|
kZQedy5cvz3iRb79SEqPMxc6+PqJVnNHUv1azIWxoZnCV4dGUnp4XGjNun/x
|
|
bvZIwg8X9M8bP2qXj6T0OHLhICdvR7iBCeGHC36bnn6RSU0oPdZcWBuopxuy
|
|
3oTqb+Zc+FSdWV6YakL1NzMu3NQ65b3vrQnhhwuFH0s3HFIbRfU3Ay7wfBdM
|
|
++gwitKjxwWtMM7ziEWjRP37tjYXxtgv+R58fBTVDzS4cCS+9s2pZ6MIP1wI
|
|
OntppmnXKFH/vNPLgXW+uYc/W40m/HCg8uLk1VqzR1N6OjmQmibvWx8zmvgP
|
|
B+7I2jk2aDQ1HzRzYMxhl4mTO0cTfvDfb2rP2TbRlPDDgW+DFWojg0wJPxwI
|
|
ENh9/xdjSvjhgOGoZ8cZYEr8hwPmSZfr7v0wJfxwIBbqPh6wHUP44YAodunu
|
|
tAVjRP3nVU844PuHW65zYgzhhwMXNreOzi8YQ80H2RxwXPj3WPm/MYQfDnTd
|
|
juCJmGaUnqsc6N0UMPJfmBnxHw7QLpywNE43I/7DgTQJN3RflRmZ3zjg7en8
|
|
0d1gLOGHA4zcWztCPccS/+GA58X9gZV7xxJ+OHCx51HwhUdjif/g72cHJb/o
|
|
GkvlZx8HNBqDdCVTxxF+ODAw8vE1/RXjKD+N5IBs94HdnPPjCD8cyP5x++D9
|
|
mnHEfziQ1Woe7Ko7ntITht9XP8Wo1nY84Qc/b63nklTX8WR+40DwwMlecUvH
|
|
U/U2nwM2Rfw3GXvHE35wvIt3NbedG0/mNw4c0+xJmg/jyfzGAbuIs82/aseT
|
|
+Y0DK0y3vXn6ZzyZ3zgg7jngdXfMBMIPB25rP1/yjjeBqjceB961o7cT5k4g
|
|
8xvWI/zlkbptgqj/vMqRAzP6Npb5JE0Q9Z+P2nHgphVtpcPDCaL+8x1rDrx6
|
|
7DBMWjmB+A8HMp6uy933ewLxH1wftG97f442F1H7DwdODLsbkMwzF1ELMgcu
|
|
z37guGGeuYjafziwc/g/s21R5qJz/fxwQJd+wORWirmo/7xKgwML87wnmII5
|
|
md84sPFpEPtug7mIOn9jA3dy+vxdAy0oPd1seDvA8dh2SwtKTycbjF3+lV52
|
|
taD0tLFhbJeehdZKC+I/bGjWD959KtZC1P97RiMblp/+1j7rhgWlp4YNN489
|
|
X+5eaiH6X38BsSHrR1Xnqi4LSk8ZG8LyaNFPTCYS/2FDj9rrKc78iVQ/KGCD
|
|
Q2Z646+FEyk9eWywgyfp9XsnUvMBsKFVOmbTz4yJhB82GGj26DoXTiT8sGFN
|
|
Q6zl846JlJ4sNvwqqUE7jCwpPVfZkFHRUrGaa0n1gww2/K/r5ob4hZZUP0hj
|
|
wzEbpyNf91kSfthQuH7d5D2ZlmT/YQOtZLmb51tLsv+wIXvaGKVHtyWZ39gQ
|
|
XnpYY/cYK7L/sGHexjvn26VWZH5jwzK7/54dXWFF5WcXG67+Zi9ZedSK7D9s
|
|
GFYXv3/bPSsyv7HhysfL1k9rrQg/bAht3eYhHGxN/IcNM/U1v3TaW1P5WcaG
|
|
9d7eI6pnWpP5jQ2Xz/ne64uyJvsPG0yH6NUEXLQm/LDh4eEDexuKrAk/bIgc
|
|
/zDzQo818R82RBRe8k8db0P4YUNcnH9kibsN4YcN1aH3JnI22JD9hw2+Mz94
|
|
fzhjQ/jB72tY/r/rz20IP2y4uODDpqcdNpQeRzZo0KsGDze1peYdOzZsPNEg
|
|
TnKxpfqbNRvMdrVaBK+zJfsPG0q6u24sOm1L9h8cn58DFSnPbSk9JmzI3G/4
|
|
bOQ3W7L/sOFRsrVHodkk4j9s6BMLtj1yn0T2HzbMWDsz4NOmScR/2PDSZt17
|
|
n7RJxH9wPFf/T+170STKT3tZYCO49q6kdxLhhwV9p4r92mwmU/NoJwt+R/3Y
|
|
LA2cTOWnjQUjvpq6vts7mew/LPD57PLkXNZk4j8sSAsPr8+sm0zpqWHBuP3n
|
|
Mr8OtSP+w4Js8zKzdXw7ql+XsWCTpybXbpUd8R8WTPsn+GeRZEf8hwV84ebV
|
|
swrsiP+wYK7W7X3Pf9qR+Y0FCfM7ndfb2FP5yWHBrpMTO2YH2RN+WPBAU/Ry
|
|
zyF74j8scL4jfvP5vj2Z31hgdtr234kWe8IPCxiPfs3fMXoK4YcFqSOzWjI8
|
|
p5D9hwULr/mk6UdNIf7DghVR7w/mXJ9C5jcW3DgoTbpQP4WcH7DArzDhY/GI
|
|
qYQfFkg9S124LlMJPyzYqtFVK988lfLTnSwY8PNvenHmVOI/LPhg2XHqd81U
|
|
4j8s6Jkmr7ql5UD4YcFkE+c9h8wdCD8siD4wUrSD70DV2zIW6B5fMOJEoAPh
|
|
hwXXuKP6CtY5EH5YELXLtW9cjAOlJ4gFGxa3jEi44EDmNxbENf0V2YED1Q+8
|
|
WfBK7dDexkoHwg8L6Dn7au53OZD5jQXPRnRNvzHckfgPCzZrfnyXP9mR7D8s
|
|
mBq+0OfPNEcyv7GgYvK9pMAQR7L/sGAVvT67JMqRzG8saIupPL/mP0cqP9Ys
|
|
8KddXGR/15Hww4LL1rKOoSWOhB8WtK7K8hne7kjmNxaY/OvYSdemkf2HBXYN
|
|
A3Zvs6SR/YcFjiPk/o0SGpnfWDD2+KmuVQto5PyABb3BY1aMjKQRfrC+HeHX
|
|
5KdohB8mbPj8X27ZHRqZ35igm3H8kryERuY3JpzMmrdw5FcapaeNCVpDfipX
|
|
6ToRfpiw/PYSUaOtE+GHCdcz05Zvc3Ui8xsTlB1ZIfSlToQfJgw+cNx++F4n
|
|
wg8TjFY6Fww950T4YYJm8guG/RMnwg8TWseO2bCmxonww4RHXyW7S3qdCD9M
|
|
2DKMExw4mk78hwnyvusxf9h0sv8w4SPTb+eLWXRKTxYTZj4ex7sTQSf8MCHw
|
|
6Ognz07SCT9MKLshGdJ9h074YcIH05PjPN/RCT9MWPzOsC/3O534DxPWfYTU
|
|
+QYMwg8Teif9N9TUiUH8hwmGBcnSXn8G4YcJN28Xif6GMwg/THjTOnnQxHgG
|
|
md+YsH7N3eNhtxnEf3D8has+fShjEH6Y4Dx3+uDQHwzCD45/3tw2YyMmOX9j
|
|
wqhtCUmtDCY5f2PCjO1/hjcEMgk/TNB4fdTn92Ym4YcJbqG+gcz/mMR/cH69
|
|
+ZYnHzKp/AQwwWvPjEfG1UxRaz8/TBg98D/TnD9Mwg8TFr7Vlu0ZxyL+w4Sp
|
|
rRdpYRIW8R8mHPZd17plMYvwwwRfy4yll/aziP8wIfZw7NnfGSziP0yQ7hqf
|
|
uPYVi8qPHb7/4MU+mu0ssv/gehgzI//pMDbhhwnNz77/SqGxKT1mTPDvlbSn
|
|
zGQT/2GC3TPh2adb2MR/mLDVtHWY5hk2Ne/oMcFJw1m09gmb+A8TlkZ52f9u
|
|
ZFP9QIMJfw8MrMwYzCH8MEF7wgqXLZM4hB8G7PGMWrvKm0P4YUDYYHHQ7nAO
|
|
OT9gwDO/rH8PEjiEHwbE2pcsNcrhEH7w5/+dPRxfxyH8MGBVwpg1dA0uVW81
|
|
+PsWbsN/2nCp/lbBgBES8/W107lUfytjgPbXzKPN4VzCDwPW2jeuMUjkEn4Y
|
|
4NL3YkjIYy7hhwExc+ctK2vkEn4YIPY8u3uZFo/4DwNKjV/dM5vCI/ww4Lq2
|
|
8bKuAB7xHwa8sth75MtWHqXnKgPMl+o7aqfyCD/479+Ap8tzHuGHAU/mH6tL
|
|
a+MRfhjw1XBv2wQDPjVfJzJgxfeT4bkcPpnfGGD9q2D9vmA+4YcBTlbjWpcd
|
|
5BN+GLBt28mqsOt8wg8DBnTbTYt/zyf+w4CaRIVtVR+f+A8D1BY/OeA8UUD4
|
|
YUDwjIfzij0FhB8GDF5dfiVyg4Dww4BvVw02up8WkP2HARMMw++ynwnI+QED
|
|
77Oda90/Cwg/DPAPOn4+0kBI9YMgBsxkzPAt5gkJPwy4yGFFOC8REv/Bepby
|
|
jKpihVS/dmdA371g+/i7QuI/DBhDy0BhtULCD9ZbplewTFNEzg8Y4CdP/bbH
|
|
QUT8hwHvr4Y2PJotIv7DAHX74JNGe0XUPmfHAMWS/+n976qI8IPjPeOLl0W5
|
|
iOw/DDjau8e34p+I+A8DeNcu6JYbigk/DNh5/3xAsa2Y+A8D/jvL+/NBKCb8
|
|
MOBgyGrtjgAx4YcB0wdwtoxcISb+w4BPkSnu3jvEhB8GzC9NjjoRLybnB3RI
|
|
0WAZtl4SE37o8HTEyqE+SEzmNzrc7mOueFYmJvMbHbblJlu7tojJ+QEdTJak
|
|
uFX+FVN6GukQ28Au3G4oIfMbHd5xV9+aMklC/IcOv9byer+KJOT8gA4tu85f
|
|
hJkSsv/g562+cCd1lYTwQ4cgpsTy6G4J4YcOxZURP+NOScj+QwfjudOmJF+T
|
|
EP+hg8a1o3cfPJNQerLpEPicGdX0UUL4ocOwDPb+0R0Swg8dpvokvFkwWErO
|
|
3+iQjXwCb46REn7ocKVrybhhTlLCDx3Ufry3iXSXUnoS6XDvQVr4j4VS4j90
|
|
aJj2um9bhJTwQ4ew0z4v9P4npeotmg4L700tvXFeSvihw4OkVWYLHkoJP3TY
|
|
6TLw8qgSKeGHDhn3ujc2NksJP3QQdLrsvv9XSvihg/23jjenjWSEHxz/hz1z
|
|
Yu1khB+s32OOzWGZjJwf0GHPORPmyTkyKj/z6TASaPuurZcR/6HD8IuXRpQd
|
|
khF+6LAhYFvDoFQZ2X/owH+Z0eFyT0b8B+vTcBTHF8nI+TWOv5bx23aFjPBD
|
|
B62ywNSZf2SEHzrcXz+aU2DoTPjB+e04aO5q50zO3+jQ6312XrHMmfgPHeL/
|
|
F9y8aK4zmd/oYH71de7fcGfiP3S4nFn/5cJhZ3L+Rgfr6LOrZqU5k/mNDqmu
|
|
WhyDh87k/I0ORsrRsz6WOBN+6BCx5EP+5RZn6nxHmw5VuYL9+wa4EH7oQBvg
|
|
fXLFKBfCD47fOK3uIEcX4j9OUGAWluHv7kL4cQLtvq2XAxe5EP9xAslDx74l
|
|
W10IP06wOSj+bNQxF8KPE/xXnhKfetmF8OMED+kzKt48dSHzmxN8CL+9elCl
|
|
C+HHCT4dfRTg+s2F8OMEHXFrD8frTCP+g6/DCvVbzacRfpygdVJZiwdvGtXf
|
|
8pyg/uXeEdkB06j5Gpwgb1ptzOSwaYQfJ/Doi9t+ed80Uf//L5btBCYS6ZAp
|
|
ydPI/OYE1kY/WQ/uTiPzmxNs2nJT3bNoGjl/cwL9VatWNSmnkfM3/Pw2m/A9
|
|
/6YRfpxA6+8nYxsTVzK/OcGqlCuz3zm4kvM3JxhWtI570N2V8OMEv2PZD8Qh
|
|
ruT8zQmmVKmXq0W6En6cIPF+8dEX8a6EHyeYYXm25cRVV8KPE/hPWF+/PN+V
|
|
8OMEcVddNslqXcn5tRMMfzHm0sQeV3L+5gTv1nVv0R3uRvhxgurLpc2/bdyI
|
|
/+Dnh2f9+CpxI+fXToAKjp/9PMeN8OMEsTcjPrVvcCP7jxNctppf3B3rRvhx
|
|
gkF202YMvuhGfv9xgnRw3DzmiRvxHyc4JB/H5lS4EX6c4Pqp4afmdboRfpxA
|
|
eLdp2T4ddyo/TCdYaLJ1x3ULdzK/OYHG07eVlXx3wg+uvxut27UD3Qk/TjCw
|
|
6fkS7lp3cn6N4zNv6fHVh9wJP04w1fT5oPPn3In/4Poc14IqH7qT+Q3Hb0XR
|
|
Y8N37mT/cYKRvzap+7W7k/3HCcyL6mKPDPYg/OD4fBoy/+04D8KPE3xx+x1u
|
|
wPEg/NDg/JfMoiB/D3J+QIOGj2brUld5EP+hwX2dgFmt+zzI/EYDo90e+5gp
|
|
HoQfGvzla/Tsu+dB5jcabBTuuvH+rQeZ32iwZT+6ZtPqQfihwbARTzqjBnqS
|
|
/YcGdvLdke/HeFJ6imjwtnew51SmJ5WfAhrozvYOjvHxpPpbHg1KemfltCz3
|
|
JPMbDSbILeZ57PEk/NDAp7C9OvO0Jzk/oEHmms4PWnc9KT1ZNHB4PWX6kiJP
|
|
cn5Ng9aGC/zHzZ5kfqPBs1uBFw0GeJHff2jwXiA5vGy0F+GHBsP3Lv1038mL
|
|
+A8NNu15BprTvQg/NNDmzzWYEepF+KHByxt29ck7vQg/NLhVw7JWJHqR33+w
|
|
nvztn2xveZH9B99/ea9F2Gsvsv/QYE/e7Y9X5F5UvUXQwLrqgnbLHy/iPzT4
|
|
dqXktsXI6eT8gAafmayKuQ7TCT800NteHnHMfTrZf2gQHHnjSF7IdHJ+TYNa
|
|
eq55V+R0wg8NDl3Sc7A4OZ2cv+Hvl5+45319OuGHBivRjAebX0wnv//QICnY
|
|
m5FSP53sPzTofLR7cu6v6YQfGuwu+3K6aYQ31Q94NEhO7dFRs/Mm/kODB+P/
|
|
9hm6eBN+aPAmQD3cfIE3OT/A78fRWGmz2Zvwg/WVDlRYHfUm/kOD3rEDmswu
|
|
e5P5jQY9Zn2Lh+Z6E35o0Ff8Y1lXpTfhB39O//zl/Xdv4j80+OJV9/O6rg/h
|
|
B9f/yJL9uyx9CD+4Hk/CSQ+hD+GHBuj5NZuhs3wIP46QmZkofLnWh/iPIxyQ
|
|
7P4QeciH+I8jLIpZ9t36nA/5/ccRRIc8jxc+8CH7jyMYsu3vrCj1Ifw4Qm2S
|
|
7ux/rT5kfnOEoIqN8HyAL+HHEXL4jUY6er7EfxzhzLaiq+6jfQk/jtB7jLN/
|
|
v5Uv8R9HqNhjcfYxzZfMb47gND32d6fQl/DjCHqdG06Ze/qS/ccRDj8skHnP
|
|
8hXNGKcTnZLtCH2XO0unh/iK/g8OBjzt
|
|
"]]}}, {{}, {}}}, {{}, {
|
|
{RGBColor[0.9, 0.36, 0.054], PointSize[0.012833333333333334`],
|
|
AbsoluteThickness[1.6], CapForm["Butt"],
|
|
GeometricTransformationBox[InsetBox[
|
|
FormBox[
|
|
StyleBox[
|
|
GraphicsBox[
|
|
{EdgeForm[None], DiskBox[{0, 0}]}],
|
|
StripOnInput->False,
|
|
GraphicsBoxOptions->{DefaultBaseStyle->Directive[
|
|
PointSize[0.012833333333333334`],
|
|
RGBColor[0.9, 0.36, 0.054],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]]}],
|
|
TraditionalForm], {0., 0.}, Automatic, Offset[10]], {{{-5.3257,
|
|
0.}}, {{-5.3257, 0.}}}]},
|
|
{RGBColor[0.365248, 0.427802, 0.758297], PointSize[
|
|
0.012833333333333334`], AbsoluteThickness[1.6], CapForm["Butt"],
|
|
GeometricTransformationBox[InsetBox[
|
|
FormBox[
|
|
StyleBox[
|
|
GraphicsBox[
|
|
{EdgeForm[None],
|
|
PolygonBox[{{-1, -1}, {1, -1}, {1, 1}, {-1, 1}}]}],
|
|
StripOnInput->False,
|
|
GraphicsBoxOptions->{DefaultBaseStyle->Directive[
|
|
PointSize[0.012833333333333334`],
|
|
RGBColor[0.365248, 0.427802, 0.758297],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]]}],
|
|
TraditionalForm], {0., 0.}, Automatic, Offset[10]], {{{-15.9,
|
|
0.}}, {{-15.9, 0.}}}]},
|
|
{RGBColor[0.945109, 0.593901, 0.], PointSize[0.012833333333333334`],
|
|
AbsoluteThickness[1.6], CapForm["Butt"],
|
|
GeometricTransformationBox[InsetBox[
|
|
FormBox[
|
|
StyleBox[
|
|
GraphicsBox[
|
|
{EdgeForm[None], PolygonBox[{{0, 1}, {1, 0}, {0, -1}, {-1, 0}}]}],
|
|
StripOnInput->False,
|
|
GraphicsBoxOptions->{DefaultBaseStyle->Directive[
|
|
PointSize[0.012833333333333334`],
|
|
RGBColor[0.945109, 0.593901, 0.],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]]}],
|
|
TraditionalForm], {0., 0.}, Automatic, Offset[10]], {{{-30.9,
|
|
0.}}, {{-30.9, 0.}}}]}}, {{}, {}}}}, InsetBox[
|
|
TemplateBox[{
|
|
StyleBox[
|
|
"\"\\!\\(\\*SuperscriptBox[\\(\[InvisiblePrefixScriptBase]\\), \
|
|
\\(3\\)]\\)P ground state\"", FontSize -> 18, StripOnInput -> False],
|
|
StyleBox[
|
|
"\"\\!\\(\\*SuperscriptBox[\\(\[InvisiblePrefixScriptBase]\\), \
|
|
\\(3\\)]\\)P first excited state\"", FontSize -> 18, StripOnInput -> False],
|
|
StyleBox[
|
|
"\"\\!\\(\\*SuperscriptBox[\\(\[InvisiblePrefixScriptBase]\\), \
|
|
\\(3\\)]\\)P second excited state\"", FontSize -> 18, StripOnInput -> False]},
|
|
|
|
"PointLegend",
|
|
DisplayFunction->(FormBox[
|
|
StyleBox[
|
|
StyleBox[
|
|
PaneBox[
|
|
TagBox[
|
|
GridBox[{{
|
|
TagBox[
|
|
GridBox[{{
|
|
GraphicsBox[{{
|
|
Directive[
|
|
EdgeForm[
|
|
Directive[
|
|
Opacity[0.3],
|
|
GrayLevel[0]]],
|
|
PointSize[0.5],
|
|
RGBColor[0.9, 0.36, 0.054],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]], {
|
|
LineBox[{{0, 10}, {20, 10}}]}}, {
|
|
Directive[
|
|
EdgeForm[
|
|
Directive[
|
|
Opacity[0.3],
|
|
GrayLevel[0]]],
|
|
PointSize[0.5],
|
|
RGBColor[0.9, 0.36, 0.054],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full,
|
|
ImageSize -> {20, 10}, PlotRangePadding -> None,
|
|
ImagePadding -> Automatic,
|
|
BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
|
|
GraphicsBox[{{
|
|
Directive[
|
|
EdgeForm[
|
|
Directive[
|
|
Opacity[0.3],
|
|
GrayLevel[0]]],
|
|
PointSize[0.5],
|
|
RGBColor[0.365248, 0.427802, 0.758297],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]], {
|
|
LineBox[{{0, 10}, {20, 10}}]}}, {
|
|
Directive[
|
|
EdgeForm[
|
|
Directive[
|
|
Opacity[0.3],
|
|
GrayLevel[0]]],
|
|
PointSize[0.5],
|
|
RGBColor[0.365248, 0.427802, 0.758297],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full,
|
|
ImageSize -> {20, 10}, PlotRangePadding -> None,
|
|
ImagePadding -> Automatic,
|
|
BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
|
|
GraphicsBox[{{
|
|
Directive[
|
|
EdgeForm[
|
|
Directive[
|
|
Opacity[0.3],
|
|
GrayLevel[0]]],
|
|
PointSize[0.5],
|
|
RGBColor[0.945109, 0.593901, 0.],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]], {
|
|
LineBox[{{0, 10}, {20, 10}}]}}, {
|
|
Directive[
|
|
EdgeForm[
|
|
Directive[
|
|
Opacity[0.3],
|
|
GrayLevel[0]]],
|
|
PointSize[0.5],
|
|
RGBColor[0.945109, 0.593901, 0.],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full,
|
|
ImageSize -> {20, 10}, PlotRangePadding -> None,
|
|
ImagePadding -> Automatic,
|
|
BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}},
|
|
GridBoxAlignment -> {
|
|
"Columns" -> {Center, Left}, "Rows" -> {{Baseline}}},
|
|
AutoDelete -> False,
|
|
GridBoxDividers -> {
|
|
"Columns" -> {{False}}, "Rows" -> {{False}}},
|
|
GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
|
|
GridBoxSpacings -> {
|
|
"Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}},
|
|
GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}},
|
|
AutoDelete -> False,
|
|
GridBoxItemSize -> {
|
|
"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
|
|
GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}],
|
|
"Grid"], Alignment -> Left, AppearanceElements -> None,
|
|
ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction ->
|
|
"ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
|
|
FontFamily -> "Times"}, Background -> Automatic, StripOnInput ->
|
|
False], TraditionalForm]& ),
|
|
Editable->True,
|
|
InterpretationFunction:>(RowBox[{"PointLegend", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"Directive", "[",
|
|
RowBox[{
|
|
RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}],
|
|
",",
|
|
|
|
TemplateBox[<|"color" -> RGBColor[0.9, 0.36, 0.054]|>,
|
|
"RGBColorSwatchTemplate"], ",",
|
|
RowBox[{"CapForm", "[", "\"Butt\"", "]"}], ",",
|
|
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
|
|
",",
|
|
RowBox[{"Directive", "[",
|
|
RowBox[{
|
|
RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}],
|
|
",",
|
|
|
|
TemplateBox[<|
|
|
"color" -> RGBColor[0.365248, 0.427802, 0.758297]|>,
|
|
"RGBColorSwatchTemplate"], ",",
|
|
RowBox[{"CapForm", "[", "\"Butt\"", "]"}], ",",
|
|
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
|
|
",",
|
|
RowBox[{"Directive", "[",
|
|
RowBox[{
|
|
RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}],
|
|
",",
|
|
|
|
TemplateBox[<|
|
|
"color" -> RGBColor[0.945109, 0.593901, 0.]|>,
|
|
"RGBColorSwatchTemplate"], ",",
|
|
RowBox[{"CapForm", "[", "\"Butt\"", "]"}], ",",
|
|
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}]}],
|
|
"}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{#, ",", #2, ",", #3}], "}"}], ",",
|
|
RowBox[{"LegendMarkers", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"False", ",", "Automatic"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"False", ",", "Automatic"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"False", ",", "Automatic"}], "}"}]}], "}"}]}], ",",
|
|
RowBox[{"Joined", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], ",",
|
|
RowBox[{"LabelStyle", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{"FontFamily", "\[Rule]", "\"Times\""}], "}"}]}], ",",
|
|
RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& )],
|
|
Scaled[{0.01, 0.01}], ImageScaled[{0, 0}],
|
|
BaseStyle->{FontSize -> Larger},
|
|
FormatType->StandardForm]},
|
|
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
|
|
Axes->{False, False},
|
|
AxesLabel->{None, None},
|
|
AxesOrigin->{-4.270833333333344, 0},
|
|
AxesStyle->Thickness[Large],
|
|
BaseStyle->18,
|
|
DisplayFunction->Identity,
|
|
Frame->{{True, True}, {True, True}},
|
|
FrameLabel->{{
|
|
FormBox[
|
|
StyleBox[
|
|
"\"\\!\\(\\*SubscriptBox[\\(c\\), \
|
|
\\(0\\)]\\)-\\!\\(\\*FractionBox[\\(2 \\*SubscriptBox[\\(c\\), \\(1\\)]\\), \
|
|
\\(3\\)]\\)+\\!\\(\\*FractionBox[SubscriptBox[\\(c\\), \\(2\\)], \
|
|
\\(5\\)]\\)\"", FontSize -> 18, StripOnInput -> False], TraditionalForm],
|
|
None}, {
|
|
FormBox[
|
|
StyleBox["\"\[Mu]\"", FontSize -> 18, StripOnInput -> False],
|
|
TraditionalForm], None}},
|
|
FrameStyle->Directive[
|
|
GrayLevel[0],
|
|
Thickness[Large]],
|
|
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
|
|
GridLines->{Automatic, Automatic},
|
|
GridLinesStyle->Directive[
|
|
GrayLevel[0.5, 0.4]],
|
|
ImageSize->500,
|
|
LabelStyle->{FontFamily -> "Times"},
|
|
Method->{
|
|
"OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> True,
|
|
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
|
|
Identity[
|
|
Part[#, 1]],
|
|
Identity[
|
|
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
|
|
Identity[
|
|
Part[#, 1]],
|
|
Identity[
|
|
Part[#, 2]]}& )}},
|
|
PlotRange->{All, {-0.00135, 0.001}},
|
|
PlotRangeClipping->True,
|
|
PlotRangePadding->{{
|
|
Scaled[0.02],
|
|
Scaled[0.02]}, {0, 0}},
|
|
Ticks->{Automatic, Automatic}],
|
|
InterpretTemplate[Legended[
|
|
Graphics[{{{}, {{{}, {}, {
|
|
Hue[0.67, 0.6, 0.6],
|
|
Directive[
|
|
PointSize[0.009166666666666668],
|
|
RGBColor[0.9, 0.36, 0.054],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]],
|
|
Line[CompressedData["
|
|
1:eJwsm3dcjX8Ux5saKg0l0k573FvdUbd7u8PKyMjIKkL2CGWFUD+yZaWFpIQ2
|
|
SfjeI0kZadAuDe29I+n3dJ+vf7zu6z73eb6f7znv8znne2/6XvuWb5UQExOb
|
|
LiMmNvH/uOifAKIc99rQZqZx6LKZTwL+CSDwdp5h3Ugqp2zf8p5ffwWwIYFj
|
|
3l2Uymmi5xVYjgrA7NRXvueTVM7GDTqL3H8LoH2y3x7qqVTO3IZlXtuGBXDf
|
|
jflk67JUTljuZrW1gwJYuGrq71G9VI674gpPSr8A2tTk1w50pnACUwzmtvUI
|
|
4MSl6V9dM1I4Wi++fTzXJQAp4C+fHJDC0dVc90u2QwABiUGtZnNSOFcqssP3
|
|
tAqgb3V9yBOZFM7uvwpdL5oEsPqNu+vlj8mc5yfsKusaBJBc2aJVFJjM6Rzc
|
|
KC1RJ4DTFlMX/uUmc+7+fatkUiOAW/yMVTqjSZzX1xcML60UgPqx00fVfZM4
|
|
y15MEp4qE8DFsbP/qrsTOWu39W1N+0E874uw8fCuRE5pnGJHe5EA5rfY2zQ0
|
|
J3A++7kvMysQwI0lDRW6WxM41O9Ft3Z9FUC+xOcWq4ZnHAXwf5X6SQCj4h3u
|
|
il7POOscV73591EAMxbPtUB1Tzk6As+oJR8EYPqr3JPr9ZSzsuKO56MsYn8/
|
|
xg7daHjCEZv4B8T1Q8+6M7Y+4eg/v3PK860AxHw6FiS1xHOeD3nUvM8UQAlj
|
|
q+zh3fGctx9XzrTKEEDEgmmmyr2POQ4m/g7hLwSwIl7iyTG/xxxz9SKaUpoA
|
|
/rmZXEn/G8e5dn21yn/JE9cHfX9/No6zPULhi0QisZ7LM09ET47jpNN6twY+
|
|
FcAjrc5zy2/Gcg5vkP4pHy8AjaGhgWLtWM4zNRfG7VgBHJvpmG38+BFntfub
|
|
vcYxAvhyJX1wgd0jjp+FZ9DrBwJQXrw7mCuM4cheph5feY/Yv9XrTsksiuG8
|
|
q4j07Y0QwLtug+rp5Q85qw4ohV0KE0Cpu9fj3q0POR/czrYYhwrgfMj0uit9
|
|
0RzFU383wi1ifyPmn+s9Gc2hDhyVXHODiPfh7rDpk6M51mmj33quCcDcUGmm
|
|
zJ0HnElvTuecuyIA7r0Y+UyDB5wMJYVm7UsC6GxP9bZNvM+Z/TSMmhYsAHs5
|
|
B8p+h/uchOtWsfPOEfq79uQ3nb/H6XyXPbsyUADau9ZMOxIVxZFz2qi494wA
|
|
5gbbs26mRZLxCRBAwvxxB1ZuBKdAMWbm9RMCcI5/pbanKpzjv3XRZv3jAhh/
|
|
sjnXrCeMIyHzuzj5iAB6Fo+t9pEM42zsi9/r7CeAqSH/ZQk07nLCTTztvh4U
|
|
wLbD4zIPTEM5ibGaBmt9BDA4ts002PEOJ2pfiWPTXgE8nwWGfxfe5mw7E3rC
|
|
Z7cAYrtk/vxef4sj/9OjbXSHAPLcnZ+e2XOTcz7I7HTQNgEYbfFm3D5xg1Pr
|
|
O8JT2iqAJOUTUfaXQzhqyZ8tb3sJYLfH2doNEdc5evYPedobBbBu8dExlafX
|
|
OMuYZWMPNxC8qqeMjRy4yunpe19jvk4A84JpVdevXuaMbvb+leJOxGvg1O2u
|
|
pxc5fheFSg6rBPDA/ZrllNxgjseObxvATQC3n3tH9Tec46SM3Sqct0wASFay
|
|
I3w8iHNovtrOb64C0Fy5VV1WK5DzyGWeyepFAoi5e3kGk36Gwxe3lfvpIgCv
|
|
kuOjFssCOIv3FU/ZNk8AWRob938s9efk3LBgdc8WgKzPigdI4SgnYa/jxcN8
|
|
Yn9efw9m83zJ+HAFcGGo1my2rw/n/Tz/u+fZAhgT9Ek8WraL0zsnabUKi6hf
|
|
xx31C19u5lz5E+oYxhRAkSltw3RHd07oVge+IV0AGfQFzzyk+Rzlc9f2PrMj
|
|
8jmrY8G+CiYa8IgS0qgCKMjcpZ3rsxLN7/SiCa0F8IE3lL1ztReSs635Nt9S
|
|
AGs+6CjUD+1AdCvlq0VmxOefT+uL+bwfFdeMHFhvQsR36k3jZRGHUM3c0ONN
|
|
RgIICQp86LvnCFqxtevxfgMB5Eq3bld19kdMx9E/f3QJvj5tfH1DNgBpG7DX
|
|
B2kLIKz/aFlX72l056jtyylaAthUkjqWWHkWPeJWTg7TFIDhwckW3z8EoXmH
|
|
GWuNNARQmHd2o0fyOXRCe150opoAgiu0ohaHB6N5dvK/mCoCcHxU3PDgv4so
|
|
NiNA972SAJrMnlLXHbiM7iQ8WbFYgdjP7dHnjnpcRTqq58+WyhHxTa46cPLR
|
|
NeTQpPlsk4wAfsmNPOoLv45azDbkt0sRPHENN9wNCUFm1SvafCUEsM/NI/RA
|
|
8A0kLgoQsd+C+NUnA26i3SEeUy6M8UFDRSr8zeFbaNfN/ZpTR/ng+nqvl9W+
|
|
2+ifNF0raoQPF/mtCQXed9Cs5sRppkN8yI49eCLWIxTVMSoVU/v58LdZsTBx
|
|
1V1EGckcY/XygTIp43Graxiaaura/KGLD1vED0itnheOLn28+WlJBx9Cylm/
|
|
hpwjUGjJlbjyVj5kXFGfn8eMRMyVTic3N/OhXm/cJp8ahfYIIl07f/FB/tpI
|
|
uLTFPUR7kKJ5uJ5Yb5dYDkP1Prq292iVWC0f4s4oik26eh9luzyKvFDNhzvG
|
|
K027Jj9AKoWNnlMr+fDhj3x7z/kH6LAUyzCqjA9249bzlSZFo5GGmGaTEj5U
|
|
271znns2Gt3YZ5iQUsyHz6HvCkPFHqL5cekHWYV8GLKi/JM++RBNvejB+pDP
|
|
h039Ch8ujz5EozO0pJZ8IdbXutqYcjQG/V3V8bUsjw+DSioGnUMxSNO5KNTr
|
|
Ix90tjIzsg89QouKv2zpyObD2favLel9j1CoWhXVL4sPptGFae/3x5LxAeL6
|
|
YMH09q5YdCaU+S34LR+c7xtOt9oTh7Srg+6pvebDo2aftOD2OFT0tXl/ZAYf
|
|
XDytW8R2Pkb3d3oITNL5YCWz5mVIy2N0Pq1VIyWNiOfPXj3nbfEo+HFwu2MK
|
|
H5KbR4wmNcWjWBfOu+xEPizX2/u+ecsTVHlbJtT1GR+owcv+NjQ8QebXGveV
|
|
xROfN3j47Y/XUxRCK5vvFceHZ+1ebMv6p0j93E+Djhg+LGi8NufIpmcoOXB0
|
|
zDeaDyZTrFpqap8hb2vLivF7fODvYMzauDEBqR74lh4cyYdJhg8jxn4moCts
|
|
wQ21cD5837W5K8MzEVVfO7cvMpS4v+DIjJCfiejfroiFJrf5cPtJnV6wZxLq
|
|
yT9tknKDD5fu3xOP+pmEXrxiSLKu8+Gj6hqPFptktMAS1WRf4cO3CIV45f3J
|
|
KMVYPdP1Eh827G2rnZecjDoeO90qC+bDgXN90ld6ktFQqv1+r3N8UGgx0myg
|
|
pKCi2WMLOgL5YHnt9LR5PikowOP2LL8zfCg+JSuVmZKCRO3bKT7IvnxVzepL
|
|
QcvMHCuCT/DhNe1WzBfbVORXMfu52nEiX0bD3HcfTEU71fSuRB7hw0u5z79n
|
|
PE9Ftt8/bzPx44OY56zzZQOpKHfmfF7KQT58GY2XfERLQ3adN2ewfPhgUOu+
|
|
O8AvDe2fk9qfvZfga7Jt1s6XaejErPtfXHfzYf0pmvSWkTS0/rLHo7IdfJjt
|
|
uJm22+E5UjzRecJrGx9SnV4vP3vsObo2sGhVxxY+xP7H3hD/+jn61e9v7efF
|
|
Bz3NthU1f58j+eMnJolt5INhLzgYcF6g2+47a4I38EGx422d76kXSG+dZ7ra
|
|
OiK/GqoMKuAFij2z/kqkOx+KSrTHXCXSkcm3Td4mq/jwJCdg/3dBOorh7uOk
|
|
uPGhMFX6xM6gdKRdGqjBWsaHeeHPDFQ+pqMbIdFd2a7Efgf4bsqVfYkkD+bm
|
|
uC4i1rNpo8O1BS+Rz5GhqDIXPgRy9jzZfuklqoy2POw1j+BVM+L5svyXiNe3
|
|
c0nHbD7Yd3WsXqicgaK9U4jtJHgCz5srl2cg0n/4YHF1YMf+mxloDVpVFszm
|
|
g+rap2XhJRko+cGLZDUWH9z0A2tLNV8hiSczgyOZfKj4dfK00bpXaEnpxU0m
|
|
dKIexYS/Ph35CoWZSTqm2BH1YWPFle6fr9DP+2dUWVQ+uE9nje4xyEQGbPn2
|
|
bGs+zMh/Kza2JRNt/Hf3vaslH2xPed2LiMtE4b+oEWVmRP5ampUuastEhd2F
|
|
h7xMCF5KVB4rWr1GknrHFncYEa/9Z6r+3Pca2fqaG/sZ8OGejov6u9TXaF13
|
|
/b9xXT6w3t5JSRt8jUzyokqDtflwRPN9+UvmG8Rkr0lW0+LDzZ6ggPzjb9DV
|
|
harBkZp8iJ5T+2gYvUFWA3mbTDSI+j2tyMVO4i2awghwTFHjg7f3ut2n57xF
|
|
DlNpaiwVPmjb+ivWn3+LHl9sac9W4sP7Y/ZWK7+8RR6RYdmuCkT8uYGfK6Yg
|
|
tMZlYWSZHB/entnVcsANofCrf3y9ZPigxm87q30HIf39j107pIj9PSkWVVGB
|
|
UGfbChM/CT74MhLpT3SEZHzEiPXs6V98yUuI3JPiy4LHeHBMr6AhIFaIhkeW
|
|
paiN8mDV0tkj59qEqKpqJDhyhAcX/sV9WDoNkMy6KC+TIR6sv3E039sB0OGD
|
|
fFZKPw9imm5r/LcOkLVxoxqrl3h/ZDwy8QQg84P/dWR3EZ/Pfb6l9h6g3WuN
|
|
P7h28MB89YudWlmABiqzI8taeeAcI57s+QtQ1vAmP69mHnxIumufMOkdKkkY
|
|
c+34xQN09MSIpNk7RPl3x8SvngfWEgmjmxe+Q4UtFDGxWh4ouZhyvu55hwTO
|
|
eWXB1TxInLx6HvfaO6RZvClFrZLQI/Mg6m3qO7Qw5k9wZBkPZJ0mzZ7z4x2q
|
|
Sb3hZVLCg6z4/xilw+9Q0T9LVkoxD4KWGhw9OCMLmZzPUWMV8mAZpVx2BjsL
|
|
Vbtu7MjO58Esl6dNnzyzUN/yP9muX3ggGR6q+t+ZLLTt5s3IsjwetM56cGnh
|
|
oyzEUbPx8/rIg4rW7BVauVno4Lc8145sHhQ1Se4abMtC8nlbTPyyePB9pse3
|
|
csX32H94UH+x+HQu5T1afSi8LPgtD/rstpx55/YeTTFmpKi95oGKunJhtt97
|
|
ZKJeHByZwQM7m9I9RXffo3u8fV4m6TzwOvPKve3Ne3T46WRWShoP7ii9vK5Q
|
|
+x6lLH+sxkoh1lP8TdNBMhu5MOZ0ZCfyQK9IsmufcTbir6nPdn3Gg4Nybiop
|
|
LtkoPONUZFk8D74cfXvm7+5stGqltp9XHA9sDQX85dey0X6b164dMTyIkP61
|
|
JDUtG7XNXWPiF80DNf37T2eWZqPs8OHx8Xs8uOR7eOX1P9losvztsuBIHoQN
|
|
Cn8p63xAX/bYp6iF8+DFjW894bwPSPJjUXBkKA+alsQetd36AaWp+3iZ3OaB
|
|
ofnsU9/Pf0CVa6awUm7wwM8gXvzMsw/o+I0ENdZ1HpQxf4ixCj6gkKyFHdlX
|
|
eLB4T67/eP8HZNjcmu16idhv4Rnfb9NykIX4+ciyYB7spEi1P2HloGfKxn5e
|
|
53igKlxUfd0zBz1Sz3btCOTB113rFwWezUHTlL1M/M4Q66XbMc/E5ZD8BPDA
|
|
X7fw/sXPOcirkbjdCR7sMKb/d787B7GAlaJ2nLj/Qq8WUPuILl8rD448Qlx/
|
|
ZeXHDsZH5L7qMHFDHkR1TzE0Wv8Rhamos1IOEvHfe33UO+AjWpGVqsby4cF0
|
|
hYqlL2I+ovPbl3Zk7yXi8bHVYEreR2QrRZTv3TyovA8+hzo/olW3LkaW7eCB
|
|
e6gHu1ElF/Vomfl5bSPyJ+F90CZ6LpIKzXHt2MKDgLruBa1rc9E1OSLfvHhA
|
|
sWu45H8qF93cT2TcRiK/oiMXasXkIlZxVFnwBiJeM4woObm5KIXhlKK2jgfv
|
|
zx5vONGZiwYjCT3uPAivebiVr5qHZCcRelYR+WgRma7GyEOt+6ayUtwIPnZs
|
|
K+ldl4fCKlPUWMt4UBUq8aEqIA9Nd1nSke3KA5vMvWe+P8pDWzKIl4t4YPD1
|
|
qVL5pzx02uxCZJkLD9IKX+1o685DOyOI5c7jQcPH0Buy6p+QoQpRPmYT7yfN
|
|
v2Tn+Ak9OUdsJ58H+sF5brs8P5H8cHlgv0KrLSnwEzI6RsSHzYNaZc4S8Sef
|
|
0LQhovyyiPohpJ71/PYJlR0k0pHJg2meQ0GfBj6h7f2+XiZ0HtzvubiaP+Mz
|
|
yjlE4GJH5P/BvuEc589oYJiwLyoPQlrMtrlv/Yy6/AmcrXnwx9X20dCFz+iV
|
|
JKHHkgfjsZNTHyR/RksvEeXGjAexPS8uryn5jDI0CD0mPGizoDJ1/n5GndFE
|
|
vhkR93c/kdKt/wX1Ugg9BjxYejjs99d5X9B7IPodXR7sO3de+dWeL2jlMkKP
|
|
Ng94vnJpKTe+oNA6Qo8WD35Y/ozMePUFXfIh9GjywDJRrvDrzy+IIk48ToO4
|
|
/vf5Rb3SX1HQNUKPGpFfShuUDS2/ogu6xHaoEPx1BM3cvPwr4iYSepSIeN6S
|
|
9Ek58hXFOhF6FHhAlSlRVLr3Fb39ROiRI+qtYKzvyAfifu6EHhkepMw/qtfX
|
|
/hX9ayT0SPFgquaC20dV85HpQUKPBA8cUvatmOKQj/2HB8ZT29ameeaji5cI
|
|
PWNc+Mp9Fb/1v3yUo0ksb5QLdEY11zghH6XGEHpGuLBleKXeYHE+cqUQeoa4
|
|
sPy04fyiP/ko/DWhp58Lkj/mZLzV/4ZC5xJ6erlwoO/N/pfzv6F5hYSeLi48
|
|
Lj/vI9z3DcWuI/R0cCHiQnzmj9vf0ItGQk8rF1ZI6y768/Yb8t1H6GnmwmeX
|
|
1llWjd9Q0whx+S8uSFhKGTEmFSDZM4Seei6Ia3LKa6YXoAp5Qk4tF2q3R6de
|
|
tipAl24Qeqq5kJR8d/psXgFaMJPQU8mFY6cvHZZYWYA0HhF6yrjArzz2JXd7
|
|
AeqxIvSUcEEWbdG841+AytIJPcVc+GS2YN2eawUo35nQU8iFSzoWtxbGFKCC
|
|
XEJPPhdcImRyqBkFqG4ZoecLF6Qe/uzU/VKAxCqJ2+dx4Y1tmoJGbQEyn8D9
|
|
I7EfC88YTB0oQFs7CT3ZXDDqXGQzQ7YQPSUe75fFhe/T1OxMZxaS8QEuBH7+
|
|
bsWhFCIv4nbBb7lgLRuiu352ISpSJfS85kLJ1wWyZ9wL0ZIIQk8GF47PHG9O
|
|
2l2IKmcRN0zngvZAImoMKESHkgg9aVxAK9ZeMrxViGY4EHpSuLCWI75sR3wh
|
|
+ppFLCeRCwPJDxVevi1E1xYRep4Rep/xhApFhcijhFhAPBd0qZXbdzYVIqeN
|
|
hJ44LqRx9ssV/ClEs9oIPTFc4P0Qe8CeUoR0iO7OL5oL+QOXbNIMi5DBP4Kf
|
|
e1xYFTn1BYVZhKwnyn8kFzJq18SlLypCjAk94cR+F+j4z9lUhNgTekK5cG3P
|
|
Zrtq3yLEJ+zB5DYXJr00+XriQhGaTeCfcoMLlgm7XEzuFSHBRDm5Try/1OZx
|
|
eVoR4k1s7xXi8/cOtN7MLUJOxEvXS8R6wmmKa6qLkP1E+IO58Hr2ETXjviJk
|
|
TizX6xwX1oU5/h2dVIx0JtIzkAtPI/w/VmgVI5WJ+JzhQvJCjm8WpRj7Dxe2
|
|
xp2STptTjDombneCWH8S98iztcWodALv41yo23L6a+K+YgQTco8Q98vhSWcG
|
|
FqPYifLjxwWTH6d18+8Wo/MT4ThI8HSNN7M9sRjtJD7O8iHiPRIwqpxdjOYT
|
|
5TZ7LxdAgfvWubwYzZoo37sJHvJPbjrcVYzGJ/TsIOLHYre8lPyOSif0bOPC
|
|
7VXHl4lP/44SJvRs4UKntkOkm/V3FDDxeC8uDF33+5wo+I6WTejZyIXEVLsq
|
|
1TXfkQFR/oM3cKE/QMEtYO931DuhZx0XwsYi0obPfkdZE3rcuRBr2jh25O53
|
|
dHNCzyouTJVopEolfUdbJ/S4caE5OGLJ3ezviDGhZxkXdGDyambFdyQ3oceV
|
|
iH+M7fy67u+ocuLlIi6kM1QMb0r/QEkTely4oHE0rnmp1g80gbvXPC5Ubx+8
|
|
NY36A62e0DObCzIyo1Ytc38giwk9fC7ccMtIylr/A88/XDjvaqUVd+AH+jER
|
|
Hzbx+eE1+2+d/4GeTOhhEdcv4SRdjvqBAib0MAn9KytKrz7/gVZN6KET+y9v
|
|
3Rb+6QeymtBjR+jb49CUUvsDSU18nErwc/Lv58KhH6hqIt+siXhwDoePKpSg
|
|
5xN6LLmg+ix+hY1hCbo0oceM4Dn3xvBuhxLkPaHHhEv077TA50tKEGdCjxEX
|
|
QhSu/pH2LkGaE3oMuGBrf3/tJv8S1Dsxb+tywV5+R0xOSAmaKP/B2kT+XVff
|
|
RY8vQbETerS4EPqlkJciLCH1aBL183WkKaOkBK2deJwGl5i3j+rmdpQg+wk9
|
|
asT907cYb5EsRYoTelSI+73zZE+eUYqaJ/QoEfcL2LnlLaUUvZvQo8CFL/2B
|
|
4cfmlaKwCT1yXBifkVTP9yhFE7h7yRD3G2px0PAtRYsn9EhxwTvI9sHAxVI0
|
|
ga+fBJE/uRc1a6JLsf9woUA4cK/oVSlKnVjOqDOI79rDKCooRRPl0mTIGRif
|
|
BmuqmkuRxsT6ep1hZ/Xl233/StGnifV0OMO9GJqHmkYZOj7x/GZnKNLtpDlb
|
|
lSHLiefVO4PskufafrPLUM3EflU7g6PtRfWMdWXoysT+lDnD3jwfbemDZYg7
|
|
sR/FzhA9dTttw4Uy1DehP98ZStT2boAHZWjC/srynEH+49lb1q/KkNvE47Od
|
|
gWMdXx1XUIakRPXaGfa71NAsW8rQiwk9r52hRqOY/2a8DHlP6El3huc3GfHu
|
|
08rRtAk9Kc4wmDV5h7hNOZqwE9dnxPMfLDmTPrccHZnQE+cMQork4GGPcmQ2
|
|
oSfaGXj7jd/N8StHFRN6Ip2BtvFVk+6VcjSBa2SoM1wXe7N1Umw5miiHKTec
|
|
YcMya87vt+VItNwrznB1ufL+kR/lKEpU/5zBTsprVLKrHC0R1Ttn4Hob1mpN
|
|
qsDnO87w+sgKHa5OBUoW1TNnuM8afLGfXoE2ieqXM/QnSscluFagqaJ65QwJ
|
|
RUG9Q94VaOJxrrudoSzW99aiUxXIV1SPnGGPxY+QxDsVaJao/jjDvo0xrTOT
|
|
K1DpxHI2ENfPabh7J7cCiezB3RnSKq8/1KmrIPW4OcOQfvKk1N8VpB5XZ4jT
|
|
5LxfplqJROF0cYYsIat8zLwSidJjtjMsnhY/P11QiSRE6eYMfN3/VI6vryTz
|
|
jeUMxjv5HYt8K9FmEe/OcPzC4uuWVypJPVTi+oA4sRlxleijiGdn8F+41FEd
|
|
KtFhEb/OYNExj6NTXolMRbw6w3yvKwq0vkoyPtqEngTDR2smV6FLIh6doTJf
|
|
RvaSURVii/hzhuUfHGlf2FWoS8Qbke/X31jOWF2F7ov4coYrtpe7fPdXoWUi
|
|
npxhffyzYz+Dq/D5tTNEDM4oXPWwCj0X8cOBhdPKeivfVJH5NsSBnUq/qvaW
|
|
VGF+OCBWyQmZ0lNF6unggPyJFhUkV03mWzMHAgZq1x0zrEbmIn6Iz/NM989m
|
|
V6MqET8c+LQZuc5cXU3qKePA3XUPh8V9qhFHxA8HKkxLdw5eqCb15HPg8uc1
|
|
j4diqtE9ET8cSBdYJEsLq9FyUQA54HqdaIjKq8n4AAfcn2fqLO6vRmkifjig
|
|
cZq+4j/FGrIepHPg62f/3nyTGqQu4ocDR29eHjLm15B6nnFAq3L75ivra9BR
|
|
ET8cSLunxJQ+XEPGJ5oDzvUnD128XoP54UBu9CtN/Wc16KKIHw7MrkNGOTk1
|
|
yEnED7HeyCuhx+pqMD8cmFlmeojztwbzw4GT1y6/VJn2Ey0V8cOB4pw3XgPU
|
|
n7g/4IDe8XTfpkU/kSjcxznglXCsp3nbT1KPHweiNsgVj5z5ifnhwMeLXtrT
|
|
o36iHBE/HOhh/Pdt/qufZL5t48Bkr0Ot577/JOupFwd05K12lXT/RKLlbOCA
|
|
iqa7eZh0LVkP3Dmg1vavaKlaLanHjQOKoxdspujXkvFx5YDEwr/OP6xrST0u
|
|
HOgrXy710KmWrAezOVAbd8X/yIJa7KccyHme9Hiley3mhwOxKWl/Hb1rST10
|
|
DhxfEtpheqgW88OBuVc2HNE9U0vqseSA1F7J+zrXasl8M+FAZlfwZuOoWswP
|
|
B7Yo92bRn9WichE/HJAuZqIlmbVkfDQ5EErftNIntxaJwq/GASPWzvPhJViP
|
|
Egdiat1W5//CeuQ4oGmikyXXX0vGR4oDZ5XycheL12F+ONB4e8WusCl12H/Y
|
|
4AAQ361dh0TLG2JD0AXFwMWWdaSeXjZkDzr+SXOsI+tbBxv+iLsoGLrUkfFp
|
|
ZoNREiMzbHUdqaeeDXPHJklpedeReqrZsLYjvfXhoTokSr8yNmzxn7eLdraO
|
|
jE8xG7YmZJz/dr2OzLd84vpT8vwD9+tIPXnE/fqc7mgn1ZF6stkwa9LS84Vv
|
|
6/C8QKwnU6B+5UsdmW+v2SB7dgu4VWI96WwILvg32bAN60lhw+mHqiOjI3VI
|
|
1I49Y0PP6L3AGpl6JEqvODaUlMemfNKox/ywgcI2OQWz6kk9kWyQNtbvFNrX
|
|
k3pC2bD45s3RXEE99h82KJw//aRyeT3mhw188Zbfw5vqyXodzIbe8Y+t2j71
|
|
mB82TA3UP7Y4oB7zw4akywNP/rtaj/2HDcKZPP+8qHpSjx8b5lFlutQT6zE/
|
|
xP0/zxXb/bYe88OGjLbx1M9fsJ5tbIi+ajuJVoX1eLFBIrPmd1x7PeaHDRU7
|
|
pK4YjWI97mwwu/cw64l8A5lvbmzoWvPmjuOMBuw/bDANc1X8btaA+WFDueda
|
|
w8MODZgfNkg+/Vlu6NKA/Yd4/vEaSoV7A+aHeH5lQ2bY9gbMDxsOFfnLex9p
|
|
IOsblQ2Dm+J1nc43YH7YcDZ4x5+ZoQ3Yf9hg4PI2TPZxA9kfGLCh8H6M2PjL
|
|
BswPG65d07UUy23A/sOG9ZrW2gplDdh/2ODILCg2aGlA3SJ+iHzqkV46e6QB
|
|
+w8b9Ljfru+X/YX9hw3mppZ34zR/4f6N2P/HM71bTX9hfpxgL9wfoTn8Iv10
|
|
yAni92csvezyi9TT6wS9GZv3dq/5hf3HCRbcjV62fucv7D9OkKji+6f42C/M
|
|
jxMYG1RuX3XxF1mvq53g2afvEQ3hv7D/OAF3stft489+YX6c4FfDmZU6b39h
|
|
/3GCsBWMis9ff2F+nGD9hlNGgTVYT7YTWP9baz+v+xf2HydQZnySUxdrxP7j
|
|
BOGp5S5dyo2knnQn8NS6fbdYvxH7jxNs9RkfybZtxP7jBI+fq2/PEjTi/s0J
|
|
LBrLmj6vaESidI12giYJF9+6rY3Yf4jXit5qkocbsf84gcEkyjvK+UYyPjec
|
|
IKI99uTOu42YHydYjj4tTH7SiP2H2L+T4aYSbxoxP05wwmK6+savjZgfYr8/
|
|
CFQ+1TSS8TnuBNGLtbS5PViPnxOEZN1jZok3YX6c4I1R4ealak2YHycwP5QU
|
|
1WbUhP3HCYqSHVuv0ZtIPV5OkFFxQCCY34T5cYKq3tUJ4mubsP84AX+o1fjL
|
|
ribsP07Q0GyaHH2iCfuPE7zPmeoSdLUJ8+MEP0MSeg8+aCL1zHYCzqL++L1p
|
|
Tdh/nKC0r9HH90MT5scJxqOeSgaXNmF+nEBux87pT1qbMD9OMLjUIK1sFOux
|
|
JPStKi6YqtSM/ccJdh47ccBDrxn7jxMMvNYLfWHbjPu3iXi/5c2Y04z9xwme
|
|
hi7fd2l1M6lHzQnK7er0FHY2I9FxjpITNHZsX3XXvxn7D7Ff71un2F9txv7j
|
|
BPczNi+uetCM/ccJln4uUQp53kzWt1EW1IzyV6z82Iz5YcHiBY+1jSuasf+w
|
|
ICp90i6pzmbsPyz4zPVw6hlvJutbMwsqWxKvt6q2YH6I9xNHdvbMaiHjU82C
|
|
iBBWrpRDCxmfMhYsuHk43nhRC+aHeH7aM6VVni3Yf1iwpLdiOORAC+aHBdGL
|
|
JLZWB7Vg/2FB0QeDVbS7Ldh/WNC03ulz2LMWUs9rFvzedOO2ErRg/2GB+azd
|
|
F64Xt2D/YcHx2JxYw+YW7D8s6GyMbs/+00LOC3HE+w1ia3yVWjE/LKIe13bZ
|
|
G7Ri/2HBkCY/QZLeSs4LoSz4tXTWzTqXVrJe32BB19wLD/M3tJLxucKCmaP7
|
|
Kz/5tGL/YcGWPeWskqBWzA8L8iPfZ/fcbcX8sMD9ko3fjMRW3L+xQNJBe6lb
|
|
VivmhwWfHl5aHl7SivlhQfKXEyf62lpJPbtZkJ7WU+A+3or9h4iPe+OifLU2
|
|
7D8s0H6zrne5aRuef1gQUO2GmpzaMD8skHj7NS14WRuef1gQuzavkOXdhv2H
|
|
WH/6XM2xY214/mHB3II5575ebcP+Q7x+nKOTENOG/Ye4npNXE/6qDfPDgoyN
|
|
di/C8tvw/MOCDdVtV580tGF+WOD6vHvv55E2zA8Lrjbylo8ptmN+WKDlU+fA
|
|
NWzH/kPEe1X+rJvMdlQp4ocF+ndkNX4vbsf8EPlHvSa/b3M79h8WeBlvlRw6
|
|
0o75YcER33NiV660Y/9hQbnOsDgjph37DwsuGzyX6X3Vjv2HeB2AVN58a8f+
|
|
4wiVTA290MZ2zI8j+C18bRs02o75cYTNGQkuZ1U6sP84Qtipzi0hJh3YfxxB
|
|
/8GxwFR2B+bHEYZmrnzc4NaB+XEEzX7/glk7OzA/jhBs2Pf3SEAH5scRFiQ+
|
|
t6q+3YH9xxFW3cj2Wp7QgflxhNQi/Yiy9x2YH0fYsPtL+b6KDswPcf3GbC3N
|
|
3g5Sz2tHeEp/sq9IphPz4wjbD+s03NPpxPw4wk0Dfb8AWifmxxHMmammhxZ1
|
|
4v7NEUwzCv8c29xJzgvRjnA9+lTHzWOdpJ5IR/Aefj327non7t8cIT79P2uJ
|
|
+E48/zjCktqfJ1dCJ2oX8UNcf+hj1+vSThQhuoEj/DrAPknr7iTn7UBHyK/k
|
|
WWVN6sL8OIJh0vfRTTpdmB/i+o7B1qn0Lty/OYLCrUfDFYu7kCgbfBzhflyD
|
|
0fOtXZgfR4g2Sva5f6IL8+MIigqTa+7d6sLzjyP83DCwIzWhC/PjCDozdquX
|
|
fejC/DhCLvdArXJNF+bHEWoKJ31eP9SF+XGE9V/NfrxW6ib1uDjCPLvKf1Ym
|
|
3fj8wBEiJLXmpzl34++zHGEtpzV5oXs3qYflCCnJu3eN7O/G/DhCscmX+Mzg
|
|
blIP1RFePpTZHRLdjflxhC1GuqmnXneTekwcoSRe1f/M926yvhk4gpp9fV5Y
|
|
Zzfu3xzhQl3O4i2SPZgfR9j79MKItHIPnn8c4cVhp62pM3tIPUqOsGlu1Y0d
|
|
Zj3kvC1HXD9tZ6AFvYesB1KOUNfWSB/h92B+iPXBkqfflvSQ/c6oA3SHxtWl
|
|
rO/B/DjAxYOd5VE7ekg9vQ5waan+zdt+Pdh/HKDLRqB892wPnn8c4LmKm2vs
|
|
tR7MjwPUDC51RZE9mB8H2FPlpFz3pAfz4wDrP2jcVMrowfw4EPtZUz73A9aT
|
|
7wDbo27WBRf1YH4cIPAK82npzx7MjwOIn/5Ep3T2kOdVQgdo8F0QeONPD+bH
|
|
AR4o/uRJyPbi8wMHSG1J1D6h3ov5cQANmcxpUoa9pJ5nDlCwXYxyh9KL/ccB
|
|
KhXPeNM5vdh/HMBxiPO6bmEv7t8I/foM67trejE/DjB4badw/bZe7D8OsERQ
|
|
vtfStxfz4wD/mGedZM/2Yv9xALED2017rvXi8zcHWN113vZXVC/mh3g/8dfa
|
|
X8968fxDfD75+IOezF7MD3H/4cWT5PKwHh8HGAhYF2xVivXsdoC2xTHmHo29
|
|
mB8HYHqYtoX1Yz1eDlCa0vyxQbyPzLcNDvBpfv17pnIf5scBlA01a+7q9OH+
|
|
zQGecYM1ZKz6cP/mAKEPaHsCWH24f3OAqjna9dIL+nD/5gA+VlzfO+59mB8H
|
|
WOseZUzb1kfmG8sBxurgzU/fPty/OUBWI+XfncA+8ryK6gCPN3e1bbjRR56P
|
|
WjpAwrrfZ6jRfeT5jokDFH9dlqOa0of9xwG0Moefi0Mf9h8iX/TaXf/l9+H5
|
|
xwEUxC1vytb0kedVag7wcl1moF5nH55/HOAM5bbe3L996IGIHwfYdUq47ejk
|
|
fvK8SsoBjs6nr82c0Y/7NweIv/hnWNa8H5+/MaF/vgJvq0M/Pr9mwraAXbRv
|
|
8/vx+RsTBqiaP+a695N6OpgQs0FV78u2fuw/TDgsuVbD83A/+X1GPfF5w+6X
|
|
4//1k3qqmXDsbaFU4u1+dFmUQExILBQf2xHbj8/fmCC28dR9u/R+7D/E9dsX
|
|
dMvn9OPzNyYotXu1dv/AerKZ8KE590p9Yz+ef5gQ5eH/s36wH/PDhIjUpahX
|
|
egDzw4Tvc6crKWsMkHpSmMDTKslnGw/g82sm/LQ5J3acPkDWgzgmvAy0fPhx
|
|
7gA+P2ACmp6Tbrh6APPDhH9dbqyr2wbw/MOEg1IlFPkjA3j+YYL62kV3bp4f
|
|
wP0bsb/d6Xut7w7g+YcJ0jnqL0vjB3D/xoT5Vdv3X8scIOMTwIQc2+Qw988D
|
|
eP5hgk9eO41SNYD7Nyasua/Fn9Y5gPlhwt6XzkLFfwPYf5jwRsk9QW3KIBmf
|
|
bUxwjt2iYKY3iPs3JnSf2Fq1mDqI5x8mVNxaq32GP4j5YcLfTsG3D26DmB8m
|
|
LP5Pv09z6yD2HyaUe/QHHfcbxPww4ebhVxc6zw1ifphwruCg2L67g3j+YcKz
|
|
HQbN408GMT/Eeuac4T94M4j5YcKprUs1VuQP4vM3Juz4dMlLs3YQn18zYegg
|
|
w6Srd5CsbyZMYHgt3fJDcgjPP0yYfqt0er76EJ5/mBCn8HVemckQqUeTCbW5
|
|
lK5+hyE8/xDxzJNQ1F80hP2HCQunCGI8PYbw/MOEgLu9aUn7h7D/EPu9XclJ
|
|
5ewQ9h8mNB+/6xR4a4j001EGaHwPeSH7eAjzw4Ce/X9iozKH8PkBA3yXFyjP
|
|
/TpExqeDAdFHpvb/+zmE5x8GHGvIWZzXh/XUM2AkpFnvkfQwPj9ggME5v90h
|
|
msPYfxgwJDxIuW4xTNbrYgYcYv/c/YAzjP2HAXfGM/TfLxvG/sMA70niS4a2
|
|
DGP/YUD9spcDjkeGcf/GgEn1larXLw7j8wMGnKCEFP+OGsb8EM9LH9volzqM
|
|
/Yd4nq/O60k5w7h/Y8DAroG6J+XDmB8G+ISd+uHVOYz5YUC/GNyyFh/B8w8D
|
|
jt57YaCkPoL9hwHifhv9xc1GcP/GgLOBEC3LHsHnBwxQ+vzjluGyEcwPAyJc
|
|
7q9cvnUE88MAMzG9+ptHR/D3PwzI7FrBar88gv2HAa7qzptWRo9g/2FAzcEa
|
|
t+L0EcwPAw7K26lt/TyC+WGAYrnTPfnaEfz9DwPifo4Ovx8YwfwwgK2zX/u6
|
|
3G/MDwMqb96dckDnNz5/Y4C/4Ei+t91v3L8xYKa5wtp983+T9cCVAW/mr0y9
|
|
uOE35ocBW+65lb4+8Bv3bwxQsJbJGz/3G/sPA54P7Du3OvI3nn8Y4FZ1f0d2
|
|
6m/cvzGg8euznHm5v/H8Q8Q770ZUXfVv3L8xoCx/Ze/1/t/4/I0BNMJL3OX+
|
|
YH4YEDS8U4au+wfzw4CcGeiTGe0P7t+I+M/rkLVf+AfPPwxQPTX4bsWmP3j+
|
|
IfITygcvHv6D+zcG6E6+G1N++Q8+P2CA8ka7fHbMH8wPA7rQ4wMZmX8wP3R4
|
|
Y/L7ukvhH9y/0cE3zMiyt/kP7t/oYDTNgpf07w+pp4MOEKlQeFZ9FPNDh0XW
|
|
eZV7LUcxP3TIyd24ab9gFPdvdLDdU7zp/NpRzA8drmjpV6f7jGJ+6FBR7FI8
|
|
en4U80MH5duLZ6++P4r5oYODlyUl7+Uo5ocOq5lNt5d9G8X80MFL8/iRnqZR
|
|
7D90OFX9emPcv1E8/9Chweto5WGNv6SeFDpcfJzWssn6L+aHDocSd57fOvcv
|
|
5ocOYYeiMs94/MX80EFi1PXUK7+/mB86pPD8S+Su/sX+Q4d7843hYNxfzA8d
|
|
Pk1Z7DQs/Iv9hw5Od3oW3Cz7i/mhQ1+NcseC3r+YHzo0NyXoasmP4f6NDrpJ
|
|
HxulDMew/9DhNsODI+s0hvmhw8oAH7NZK8cwP3SYHywet27vGD5/o8N/y5Ve
|
|
Pj03hs/f6CBXdWeN+oMxzA8dsmZFXQnNHMP80CHXRn8V7fsY9h86KPzRS27v
|
|
HMPn13S4FhgZ8VrmH2oT8UOHdd9uaz3S/4f5ocP6CgWrx6x/2H/o8PjReEH2
|
|
yn/Yf+jApO6TGd33D/NDB83Zc8IWXfiH/YcOBx7tcnsd8w/7Dx3mray3nSf8
|
|
R8bHkg4X3OKZPeX/8PxDB8F92JI+8A/zQ4f9LNOXd6eMk3q0ifyZVWsTZj6O
|
|
/YcOJhta8l/OGcf+Q8SvgXuzb+M4/v6HDskZracW+I9j/6GDWVX9deGdcbIe
|
|
SNFBxdXy07K0ccwPHfYq5ZiKfxvH/NCAo52c8LVtHPNDAz7b99k6STEheX5A
|
|
A90bjuqeKmJCkh8a0JVNVXx0xYQkPzT47zn7/nUrMSHJDw3UAo5nAUtMSH7/
|
|
Q4OqA3WH/7mICcnvf4jXl/bBAncxoai+FdNgWv6siEfeYkKSHxpcoktNnuIr
|
|
JiT5oQErR17x3FkxIckPDYxOOEQrhogJSX5oMG/dtU/R98WEpP/QYLFH8tV5
|
|
SWJCkh8aVJx1HP37FutJoUHnZ2vF91+wnmc0OEu//OFupZiQ5IcGse9XGp1u
|
|
w3qiifsdPG929DfWE0mDY3Nm/TgtKy4U9dehNKA4WpqETxMXkv0bDXYvi9T9
|
|
YCwuJPmhge3FI2icJk7qCaaBf/NbyYVzxEk9gTRw8d7THbtCXEj6Dw0eypw7
|
|
rbZFXEj6D7G/n+Uzrx0UJ/X40aAjZSRU56w4qceHBuWZS3XehoiTenYT621S
|
|
XbA7WpyMzzYazLV3nmmZKi4kzw9o8CXmx82/78SFJD80KGCUpFUXigtF9cCd
|
|
Bhs7uUe/1YkLSX4IvR/UGwt7sR5XGmjCiuFf4hJCUb12oQGzeixJVlVCSPoP
|
|
DZpmqkxhG0iQ8eHSYPqpK1PP2EoIyfMDGjw/eHGwjC8hJP2HBuE7tZv5bhJC
|
|
0n9o8Hnz7FbhZgmh6HGWNFjoKfZ3ySEJUo8JDVQ2LNPtD5QQkvMPDXQ2MNzi
|
|
b0kISf+hwUnP1DsHYiWEJD80mLUlq8P1pQQZHzUaaOzatpyTKyEk+aHB8kMP
|
|
crnlEmR85Ih8ObV/yao2CTI+UjR4evl708lRrEeMWF/k1yuZCpJkvo3ag03y
|
|
unlyOpKkniF7aMo+qbzLRpLU02sPDZX0tp9cSSHZv9mD+eDZ79uWS5L51mwP
|
|
SNn7m8QWSVJPvT2EWVdXJPtKknqq7SHLtXXI55wkqafMHhx9LhjOvSspJM8P
|
|
7GHgFmy0eipJ6sm3h79vLiaavJXE/NiDW1O7Au2bJObHHvpU6o6vrJMUkvOP
|
|
PZQ47xo93y8pJP3HHlQWuQwUSEuRetKJ9ag6frPWlML82IPvDfalaHMpzI89
|
|
3M93s7BkS5HxibMH7Wz/Z5+XSGF+7KH/YMaU015SmB97UK2ZtHKRrxSpJ9Qe
|
|
Tkls97c6L0XquWEP8+sqg4zCpTA/9uB5zMuHmihF5luwPeR8HeWseCeF+SE+
|
|
XxnXdem7FObHHi4/9A6obJbC/NhD6yzmgPOoFObHHiK8Zi7IVJLG/NjD7TVq
|
|
ZxYYSGN+7KFZXjuihyaN+bGHK34Ooc9cpIXk+YE9nInY7ndygzQZnw32kOv/
|
|
hO7tI03qcSfWO228bHOQNOaH0LPbe8Phu9JkfXMlPn+89v39BGkyPi72oDRn
|
|
j0LtO2kheX5tDx25CgxaiTTmxx70ZISC+23SmB97SEiqLzMYl8b82MOdAyUR
|
|
SG2SkDx/I/JhSdjVg6aTyHyztIfUedYpPPYkMt9M7OHHmhBxs+WTyPgY2IPH
|
|
fzkBZtsmkfHRtofFXz9ZC/wnkfVA0x5irO9N9rs+idSjZg9bngimZcVOwvwQ
|
|
ergZy0zeTBKK0lPOHhR6/2Y+KpyE+SHy8bWKG7t5EubHHlwfDE3v+juJ1DNq
|
|
B7IPnk7JUJXB/NiB6WuKfbipDPYfO0juDjp3hyOD+bGDB5yncgkrZDA/dtAZ
|
|
dz+zcqcM5scOYi28wwxPy5D1rdoOcvNGHwfekcH82MHiM5ua/iXIYH7sgLny
|
|
zvKQbBnsP3Zwnh/ZyamUwfzYgfOCgy+l+mTI+pZtBxt3T09ukJUVkn8vYwc1
|
|
j6+WVurKYn7soHv/kHY3XVYo+r1Yuh28pe09qOsqS8YnxQ44w0Olu7fKknqe
|
|
2cHBF9cWlvrLCsnzNzvYsZ+V73FTlsy3aDtQMR32lHwmi/khrq96L/bhvSwZ
|
|
n1A7uHj5QfLDSlkyPjfsYB3r2r57/bKYHzv41XiVnTFZjoxPsB1YXL4/o8tQ
|
|
DvNjBzOpWZN4TnKYHzsoKhwQT1khh/mxA+4+pgJnjxzmxw485S7PagmSI/X4
|
|
2AHjft/ipCg5sl7vtoMcux1BN17KYX7sQDG75/PNAjnsP3aguixYP61VTkie
|
|
X9tBXoXtf10S8pgfO7Dd1Pl77kx5sj9wswOPXxn+b2jymB87cNpyS2nJEnlS
|
|
jwux3tozSf+2y2P/sQODtac9P5+Rx/zYgUnBNZ0XEfKYHztwr9tKQ+nyZHzo
|
|
dmBt+aKjpUCezDeqHdxJPjmb1i6P+bGD+L1ZTg+lJ2N+7MDNO+CHrd5kMj4G
|
|
dhBxJ0Ppl+NkzI8dBErsaklfORn7jx3Ix93xerp/MplvasTzgjgn3l2cTMZH
|
|
yQ5GIjyZv2Mnk/VNzg6Wdf25sTxrMuaHeH1U+drX6smYHzsYYt+33Pl7MubH
|
|
FqhOT3aYqisIyfMDW5A6ZD1PlqqA/ccWghotP8gtVsD9my1EXHvUYLlDAfNj
|
|
C8t9Q6N9ghRw/2YLj25IS5Q9UMD9my3cbu8Q34gUMD+2QDnhGi1XqUDmW7Et
|
|
bJxv3vB9WIHUk28LxosDst9NVSTjk2cLoReXzi2gKpL1LdsWHkqGbxdbooj7
|
|
N1tY+MLTYvluRcyPLWizVfi5wYqknnRbeMAw2Lg1TpHUk2ILP2JCgsw+KJL5
|
|
9swWsgO9Uqc2KOL+zRZWlV5vMhZXIvMt2hbiIvQMNuoqYX5sIfa70lZgK2H/
|
|
Ia4/tT5p3nolzI8tvIyQEx86poT5sYVPlhprP99VwvzYwjWbM5kfM5TIfAu0
|
|
hSmPFhu0lyqRegKIeFw+cp02rETqOW4LSi0SsnEaU8h887OF6BcdQc70Kdh/
|
|
bOHXIG3y+MopZL7ttoWSxzV3Gn2nYH5s4Vh+k0X/rSlkfLxsocDb9aNJ+hRS
|
|
zwZbKPNR33m2ZArmxxZudrOmThqeQuabmy2I9dTWl05WxvzYQsgDN2fuTGUh
|
|
+f0PcX8FP903lspkvs22hVeU+WcXspUxP7awWunTzq7FymQ9YNmC+Rr2/lgP
|
|
Zew/tjDtQ4OV7z5lzI8t6Cx/+3BtgDKZb5a24Cz2qXDVdWXMjy0c+SaXsSNa
|
|
GfsPoUfov+pGmjLu32zBodAgoThbGfNjC+8l/742L1HG/NjC5tWyZ0OblbH/
|
|
2MLML/MktH8rY35soXtTpkOGvArmxxaqNDea7ZypgvmxhcYeZqGttQrmhwpy
|
|
bbOpqlwV7D9UYEsFusguV8H+Q4WrzkPT1beokPnWQQWxiPBopp8Knn+oEDT9
|
|
UMOB8yqYHyroZpyqeh+mgvs3KlQfRpctElQwP1RIdKcMxwtVsP9QIWztD03n
|
|
IhXMDxWiTiT0tf1Swf5DhbfvMgIThrGebCoMGg/n/yevivmhwsKE7YV+2qp4
|
|
/iHuXx166BRFFfsPFYx5ag+iBaqYHyo8LS1dVbtKFfdvVHB+0HSLuVNVSP5+
|
|
hwoNkc4eT0+o4v6NCre/1icxr6tifqiwhlJwoTZGFfNDBUqOTHd0hiqef6ig
|
|
dDW46tQXVTI+V6gwfmGl2+FaVTz/UEEqc5db8IAqWQ8CqTB15peqF7JqmB8q
|
|
2KX4df+dqYb5ocLmo7suelDVyHrgR4UHh54kV8xRw/wQ+xFt5+mzVg33b1RY
|
|
LCVzx2CfGqlnGxUyQ43cu86qkf2BFxWcNl6K/h6qhvmhwse1HL8fCWrkPOdO
|
|
BY/zjsU9WWqYH0JPa8Ar4zI1PP9QiX5Pxexwpxqef6gQIujQr5eYivmhwm62
|
|
Ssw2zalkf82lwoqdAUky1lNJPSwqbN2ueClbMJXUQ6fCkx8XT99fM1Uo+n08
|
|
lQp6qaNXw/dNxfxQoXRs/csXQVNJPSZUgIyk4a7wqULR75UNqFBX3790XupU
|
|
Ifn9DxUc/c3eo9yppB5NKuQFLnVd+XOqkPz+hwrX/27vkx+aivmhws2GA0k/
|
|
FdSF5Pc/VMhx2BtUbKguJH9/QAXq+NpDTY7qmB8q1No5+GsuVyf1jFLgbals
|
|
5I4d6th/KPCpLa+kPEAd+w8FtPb4m+0IVcf+Q4FID71b05LVST3NFFglfDG9
|
|
8aM65ocC8646vSz8qY75ocDe/Od7qofVMT8U+O6vw5ZV1sD+Q4GdYUdnLTfV
|
|
wPMPBWxNcoxfczWw/1CAbSjFE6zRwPxQ4NgVu0NtPhqYHwp0bV8ByRc0yPr2
|
|
mgKXxi7UhT7UwOcHFFh4Z/TGozcauH+jgAk9trTkhwb2HwqYVlx4Ztmtgecf
|
|
CrDOxqvGyU7D/RsFjlMl5OcaTCP7nUgKFPy6GSLnNI08DwmlwNzITc96V04j
|
|
+50bFKhYu331v33ThOT3p8R6tONv2FyYhv2HAhsbDTcFxUwTiv7eJJACK1LL
|
|
hONoGuaHAh6BH5Oiyqfh/o0CF9b1ULwGpuH+jQI1DDfBgimaQlURPxSYP72n
|
|
aZW5JvYfIn7jOVrn52iS/eg2ChxpL62r3qiJ+zcKcKoMHNz9NTE/FJhVFKc/
|
|
fEcT+w+xH1+9wzPTNDE/FFj01TM2+psm9h8KhBSF8JPaNfH8Q4G+qvF9tTLT
|
|
8fxDxLMj1ppuNB37DwUUxc+fTOZOJ+sbiwIHNpk9Wb5hOuaHArwVKn91j03H
|
|
5wcUOFnufEjzznTMD7Ge3ueqTs+nY/8h8iF8f+mFwunYfwi9pQeypLqnY34o
|
|
8Dz2dXG8wgw8/1BghuzCycfMZ2D/oUDjqN4O3/kzMD8U0D7D7gz3noH9hwLv
|
|
wu7f6Qycgfkh8nXOgu07H87A/FBg7VlHT9WsGdhvbGCum49/Y+0M7C82EPei
|
|
S9gwPoPku94GvJ+kminqauH8t4GH1LevNnG0sF/YAH+h0v66DVo4v21g6fCj
|
|
RZdOaOF+ygY+0QKXeEVq4fpvA6mT4o9sfquF670NyO6cmnu1WouclyJtoNAz
|
|
h908pkXWixs28LsZle/QmSkU/T4p2AZuSvwLn+Y8U/hPNC/YQHTS2cAez5k4
|
|
v2zArvn8pZGAmXgesIFND+Ym2EXPxPljA7Y1b5oevJ+Jz5uIz0e2MwWNM4Xk
|
|
+awNvPpZ9HCajDaZ37NtwDPmgImumTbu320guf3T+zULtfG8awOPX1Qe+bhH
|
|
m8xXExtgSjyau/2aNu4niM8XGls5pWnj+dUGHAw3WQpKtIXhonjZQOyw2+wT
|
|
v7XJ+WfcGl66jh9qm6lD+ueQNWwz3YwucHXw/Em8H3hKz2OLjtBIFB9rSNq8
|
|
InzLeR2h6Pd4ZdbA+VBnHfVMB8fHGrzjTSrlC3Xw/GgNzsrG958M6giTRPGx
|
|
hsTfVSdOzNDF9cUa0NZFh8466+J6Yg37Vxw6+2aLLo6PNbz9sOKp6QVdXC+s
|
|
IeFVZ/vHJF2ynwu2hvkU5zlhP3RxPbCGvWYuL++N6pL55mcN3zlj57uU9XB8
|
|
iPVLPAixMNLD8SHWX3t15D+GHubZGs6V5mWKLdTD/mcNwS2u5aEeephXa5ij
|
|
prtiyQE9HB9rgNWOFkb/6WEeraH1xX2PaWF6QvL3C9ZQYLW8yzRRD89L1nBY
|
|
6FrhnqWH+bKGwp23DeJK9Mh8k7OGOhuzj2rtepgfa8hQksmNGtcj823ICjgy
|
|
lFnzp+pjf7GCgOkxNVPM9Mn6W28FR+ZsHhhk65P5VmYFlhf3eP9Zro/jYwWh
|
|
bVn22tv1yXzLtoKszZs9PU7oY36sIGLIteltiD4+/7ICx4dBeazH+jg+VnBp
|
|
h4xc2Vt9HB8ruOPyPSakWB/PE1awXtARsatVH59fWUHFqiW9XuP65PlBgBWo
|
|
Bo49OKJugPmxgrypv8OSLAyEot8X7LaCpOWzc+X5BkLR7yO8rOA7+6fZBXcD
|
|
zI8VOJTkCa32GZD1yNUKirSkLgwGGQhFf6832woeKF05XxdhIBT9XoNlBc8T
|
|
t73uTTPA/YYVjI1eMzD+bIDjYwUnh+TQyXoDoejvn7StgBVVdHn0twHuH6yA
|
|
2t92PULFEJ+XWoH34PJPm8wMcXysoDBGnrGQZygk/x7LEvaLq5a5rzHE8bGE
|
|
FZN3JFzwMcTnNZawN2vKy9pgQ7JfKbMEMJ40uDbaEPu5JSxmLtr2O9NQSP5+
|
|
wxLUh+sU3xQbknpeE683f2yJ7jDE8bGE1f5/hxOkjUg9cZbwkX+aVa1jhONj
|
|
Cf7pK9MoTCN83mgJ3qVHPR8vM8L1zRIuPOp0nr3LiOzfAiyhRS9lhVSQEebH
|
|
EuaPqVp2RBnhftMS/Lo2rRjPMML8WILvQORXdrER7ictgTbl4524TiMcH2I9
|
|
nOpUJ9lZmB9LsDpbqzNmMAv3h8T6qwoqW9iz8DxlCa4LElvH3Wdh/7IEla9H
|
|
5vMPzcL8WMKDLZSRpKuz8Pm2JYwp/xiZ/3QW5seS8GfvBYofZ+H4WIL+48aO
|
|
v/WzMD8WUBuyrHba+CzsPxbgF/LEyEPLGPdjFpAb2/PqG8MYf39jAQPfDO/v
|
|
XmGMz8ssoElxdqm9jzGe7y0gZuMyT9MrxrifsgB67kLmvKfGOD4WEDTbzut6
|
|
rjH2Hwt4/EOmelKTMY6PBUQdz3scJ2mC/ccCVtCPfDiob0L2p8EWUCU91W6X
|
|
swmOjwUw2iJ6L28wEW4VxYe4nuW6qva4CY6PBdCWbU73DjMh/dTLAqotqlT0
|
|
X5kIRX8P624BLp8ztk8pM8H1zQLO2PzOpA6bkPk22wIOukfKntcwxfxYgPXc
|
|
R8tU6aZC8vdaFpAxony7YKUp5scCiG7mR5avKe4nLED+mZpK6y1THB9i/c+e
|
|
zBOkm+J+wQIOHHh0tLDElKwHYhbw5a9k3I1hU9xPm0P3wpxvwZpmmB9z+O7Z
|
|
0Z/mYIbjYw4BTD811XVmOD7mMPJjs3WMvxnZP+abgzXzxeydUWbYf8zB1HPn
|
|
qi1gJkwUxcccWhac3RxSbyZUFsXHHPaOju8akDIXHhDFxxwy9tfuu2BiLiwW
|
|
PcAccp8Y7VuxwFxIF8XHHKLiv+xYvsdceFMUH3Nw3lPmGXjNXDgk6g+I9wfn
|
|
LWtLMxeuE8XHHCqqYoKCS82FmaL4mIPF2yOzt42aC7VF8TEHv9vvL5/VtRCe
|
|
EsXHHN5vD9pUI7AQ1oviYw4a9kh4eLuFcLYoPuawe2TP4yWXLYSivwdnmUPB
|
|
i5ta3qkWQnlRfMzBcrft9NelFsL9oviYQ6DWvAeuYxakHm1z6HtflKZnaClk
|
|
iOJjDmu3/lhKdbHE9c0c3oy7HgnYZ4n5MQf7G87mSrctyXwbMoPHunHeFW8s
|
|
hV9EG2wGOo+CrBobLIVUUXzM4KFh5UnryVbCUFF8zEAzPG5tuq2VcEwUHzOI
|
|
ntwO/muthFtE8TEDU99HKafPWAm/iOJjBsS0YfnhiZWQKoqPGTjZnbKdV2wl
|
|
DBPFxwzyz0Vlyfy1EkqIDNsMNv2w/7+GO4+Hsv3+AK48thaVfZlh9qVk3wdj
|
|
GTvTMKNFihQJpSSVemiXKJW0EqX0tKOFoucca0U80UYolfaptFlav/c9v35/
|
|
zsttbte873PO53q9zNWryjaHWIUPH0dRPDeIxObQofDhY97spnJcaQ4CRf3w
|
|
0WpPbcKaI+ZwROHDR1H+MuM1LeagoThvgY965jpmTV/NYYnCh4+1c08WRtAs
|
|
4D+FDx8DuFZL3QItwFIRkPh4MPN0SUKqBexW+PARMwwc+49YwIDCh48VE1ZN
|
|
/afVAoIUPnxc5dC8sXLEAkoVPnzcsSaTqqFtCaPI9VD56MYt4UfwLSFc4cPH
|
|
bhPHF3eFlnBW4cPHuGgf6fLpln98+NjzsXWpw2JLkCp8eGjX2uZG32QJxxU+
|
|
PEz94nfN8pAlfCUD41MeHlnoIo+psASRwoeHFzknW/CmJexQ+PDwslXubI8n
|
|
ltCtKCge5m99f+jlsCWwFT48XDDles6FiVYQrwhkPKQZGZof51lBGRkgT/AQ
|
|
Zf0ZNe5W8EUREHno383bMDLTChwV53nw8OrZF7YRy6wgTbFB5KHeLer+/iwr
|
|
uEIG7AwezrJvO737qBX8VHyBnIcnnNNC4qutIIAMLIk8pHKPxSfdtYLDigMJ
|
|
eFj/PXDoyDsr+EUG3Jk83FG1bGiUmjUsqic/AB6unaObkEuzhi4ycIt4WPzG
|
|
PjTA2RrCFBtCHr6OvH/GWmYND8nzUqx4OPva5zS/JcTvKwIxDwdH59Zkb7WG
|
|
UYr64WGN5T/Lfhy1hqOKhs/D0z7CgwevWUOAwoeHLSKZfWyn9R8fHqpOeekd
|
|
+dkarip8uJg2MnRjs6YNbFAMEC5OKtsCXXwbkJID7ykXO8R5/NneNmCmaJhc
|
|
rLlHVRszzwY0yX/wa+Niu4gz88VaG/imGLBcnFBwhjKw3wbkZIOu5uLf3WUy
|
|
7iUb+KAYKFxUV7ZRymm3gWEyoJzgYoOWjanJextQySV9uFg2pry8d4wtMCpJ
|
|
Hy7imzOVzVxb8H5MLpiLwxUcq+ciW0hWI+uHixHzTUymRttClgXpw8WeGV2M
|
|
Exm2EEse2JHIxeXygmczCm1BO0PxgONE+qIoYbUtZJaSPlxs/Op6YE6XLdS2
|
|
kj5c3BVvvKNiyBZufCF9uLgwY5TQTc8ODhqTPlz0tx04rWRnB9aepA8XA7Je
|
|
3h2R2sGeOPLtuRiW/vIKf7kd1JEDjsrFZdoD4Tt320GVYoBxsdhvVNXUCjtY
|
|
RW6QNLj4mGrcPqrD7s/+h4P2ea6l4z7ZwTTyeRvkYNE/cQ5iLXtICiB9ODh2
|
|
bsGmJmt7kCWRPhzMvdC5fYXUHkYrBgAHzU5SpbNT7GFtFenDwTtuCXdX5tvD
|
|
/x0YwsHslNpJLZft4YYS6cNBWQBtbFinPRSxSB8OWmIm6n6zBxc/0oeDjPtD
|
|
VuMpDlCaQPpw0CBnaaTAzQE6d5A+HOQ8/ehXHOUAHeWkDwenda55L9joAPvu
|
|
kvXDwXVLNCWapQ7wbIgseA6WhH7updx0gIUU0oeDNdYp6ovlDjDZk/ThYLnm
|
|
rv9+TXCEKYtIHw5ue+Fv02HjCPG7SB8Oel89bPNyhiM8v0r6cPBFVu5t17WO
|
|
UPicbAAcTAmjjLlf7Ah7JpE+HHxE8e473+gIzW6kD7GePg1pyxtHcF5M+nBw
|
|
TlF8NG+iE7wqIH04uCx8oeZ1Oye410r6cDBxktKME7Od/viw0a/B1uXmeidY
|
|
aEP6sHHscpV/zf5xgrFxpA8by6jJPe1tTiAvJH3YKGpI21f11Qk075E+bPwn
|
|
1vRDH8UZEscTBdfGxp9/RT0LEDnDaF+ygbNRUOSSMpjgDN3rSR82htldOvIs
|
|
zxk+XiN92Ci7fjNBq8YZRN9JHzY6hqV1bOh3hrtO5MRk469HTfdsxwugaDWR
|
|
+PLYeHHB+RU8ewGcu0o2dOL9X9hUzIkUwOAPsn7YeG6+LPvuVgEIXciCZ+PM
|
|
KGNGXoUAJClEIktk45LIvH1FPQLgHicTOBvfR9W8HVF1gdo28jw4Ng4u2Gty
|
|
1MoFmB/JBsLGxAS65f4IFwgcRyQmERunp8yh9WS6gBONTPxsvJQR8GHxBReQ
|
|
mxGJ24qNWdtfFQQ/doEF1mSiYmN3oQN/zVhXKLEk1kNl4/4yhz2DDq5wkksm
|
|
WDZi46teWOAKy/WJ9WiwMaU3QPXBLtc/+Y2NB4fmjHcBV5j5hHjeBlk4VYfx
|
|
+b3cFVKqyQHCQmubfZUfjNxg5g6ioT5lYZnsWribvxsohZMDgIXFq/b0PFzp
|
|
BokmRINvY+GkIoprY6kbFHeTB1axUH49bO3Pe25QsMuR8CHe77Pw4EYVIYS7
|
|
k4mOhaPp3Xtn2Amh7yWT8GGhSwg3eXWMEKZsPUD4sPDNRpbZ63whuNDJ8wxZ
|
|
OOFKR0NpkxB0LmwifFh4asDKpWJICBWu34j6YWGELv3mZh13wC6y4Fl4dLzv
|
|
noip7jBQ9JzwYaGWQFIW5eMOLjvJhMfC64Uu1N2R7nDqVDvhw8IzduO6B1a5
|
|
g8MHX8KHhTdGw+u1u92hf86/hA8LqSph/vZn3OHcIHlCDwtPuLSNUJrc4cCV
|
|
04QPCxednPzdss8diksZhA8L4wLjg5O/ucOta8R6qCzczdg+0KfjATq/yQTL
|
|
whHzvP61Fh6wOp4YuBosLFy6lu8T4PFn/rBw+Us/cInxgOPkjmqQiRl5w8ej
|
|
1nlAwknyGxFMrE/J7i0/5AHTri0kfJjolj0q1rLSAyTfyQHAxMH74cKeDg9Y
|
|
MX8m4cPEzhn7Fl167wGVX28TPkwcHl/ZXz3GE/Qr/AkfJs4YuVL2geMJ+/bX
|
|
ET5M7DcsbpV4eYLTSQHhw8RjSYsEjyM9YfDZRcKHiaXfdL8dXOsJd/3MCR8m
|
|
Prx6XGPTAU/oeHCC8GGid5lB/MHLnvB+J52oHya+eLjE+NEdT5jdTyZCJn5S
|
|
P9gZ8tETRJ7ajeJEJuap50QMa3rBmVPbCB8m3u8SnWg384J8KpGwZjLx6NqG
|
|
qt4AL/h2MJXwYaLBxzG7KIu8oI/xlvBhIsXBwHJHphd4XZpL+DCxWizPty71
|
|
Am5oO+HDxC8OmXUajV6QNeJJ+DCx4dOrS9r9XhB3+gLhw8SpGZOWSpRF0LSQ
|
|
Sfgw0b5X6SMwRHDCfDfhw8Sb4yodoz1Ff3yYqKxp6+sQLYKH3YmEDwM7+1ZS
|
|
hBtEYFvXSfgw0G3zhqrVR0Uw4YIX4cNAu+9S45d1Iog5d5bwYeBdT7ko85kI
|
|
BBf1CB8Gjo4ItAv/yxt2NaQTPgy85bNMHsn2hpjHz8u0qxlopjw3fr+PN1T9
|
|
FUT4MJCza9J55ThvyLQtXxF9goF1A9lXj2R5Q+cSXcKHge/prTnJp73h5IVV
|
|
zuV5DDzFusdObfWGL6O7CzqzGDhhpGTzmQ/eUBvhQtQPA1WLnM7oavmAu1ox
|
|
UfAMpCX/2lBh6wOn/TSI+mGgvDX888YZPvCNtoqTGs3ABRXin1lpPmC7U761
|
|
cCYDd5g+LG4o9AHp3liigTAwSfdnr02tD8y1eREsFzHwQ17lxQf9PiBZmEAk
|
|
MAZyD2mwy9R9gWM9qCWwYqDBlM/m18x84U3eFqIhMbDMK6Xjl8QX8nIohA8D
|
|
h/pzJqxYQVxPqSIGGLE+TdcXpgd9odhzFuHDwPzaTdN//+v7x4eBH3/Mj9Lu
|
|
94VpsjOEDx0H8KFyhIYfbBbOJQYIHQvGv3bvMveDglpdXupTOuo826GfLfOD
|
|
ww87iIZJRyuPW5nL0vwgd1v+u4Y2Oj7jHtmVU+wH89rnSOQNdIzaN96up8kP
|
|
jM5PuaBdTcec3EnJUe/8oI75W1dQTsfpE8/6Ger4wzSLzlXRJ+jYZdhXpSrw
|
|
h7r2y8SWm7jfmVN1vGh/MB17yK08j46DTeNiM7L8Ia5705HOLDpmxKuWjCn3
|
|
hz2eKX8praNj8959q5s7/cF1ynSi4OnYcNj161WlAPieod8sTqTj3/dW0Dt5
|
|
AVDrXmWWGk3HcQL3X/SQADi02DG3cCYdZ/5XkL1/dQBsVt3/sUFMx8jd2TcF
|
|
RwMgfewDqVxER+GmcVVjWwJg3dqvl7QFdJQfM52h/iUAimd91hdY0dH8S0Op
|
|
FTUQGo7eXh3NpWNc8o/STJ9AGJmxvTuLSse5pk0zxiwNBNFqvmu5Nh1VvtOv
|
|
XDkQCIdUjx/u1KBjmsrElvz6wD8+dPzXbef2w+8CYUWM8zzuIA1vlh5Vuqsf
|
|
BL/sZcQAoeEmV1+WvWcQ7EkJZqY+paGmcvpwQ2IQOJlwiAFAw4VDPn+v2xcE
|
|
H2we9Te00TDd6GhFXF0QXL60wlveQMOgxNz9f78LguwS+XHtahoOyzUtwCAY
|
|
lv70VBWU03B2AS11qigY4upXxUafoOHatIbFN5KCIf7r9qasQhquyPymu/NQ
|
|
MGTkbeCU59Fwcn3dkk3Xg6G0cPqWziwa7p9KXXX8czA80B7z4ncGDZ82aVh/
|
|
NhVDouU4H24qDTtvXzw2N0gMTVNvlYoTaai/PaCzc5UYWsYGqKdG01DtR/Ot
|
|
ecfFsL15c3zhTBomUO03jLSLYXx8RmuDmIaOH7OHi36JQfTG3kouomHOylsW
|
|
YVOmgVXgmXxtAXF92RDXcOY06M15/M3ZiobnD41/8nbTNHA7fzsqmkusx0lz
|
|
dmv5NJhZkXE9i0rDO1kj+dceTQPzvXLzcm0a+jW99HukIoGacP19nRo0lNP8
|
|
uDEUyR8fGnbcpcZ+tiZejwu+I5ab4ucncSpZ/hJY0qX7T2GnKc7y46twoiQw
|
|
My48Xd5gip/UImOaUyVwrspouqDcFP+jjeGkbpdASvN0i22Fpvhx92Rf/jEJ
|
|
XCzUHNOVZYq+c/HGs6sSmGft+YKbaop9G1pOHW+XwNqtH+tTo03xX6Wgd0te
|
|
SUCnmFLSKDbF9gceO4W/JTBxdf1GHYEpWqmfzdPXC4Ec7Rcx87mmWLdr+9Cg
|
|
WQikJW3yr9A2xZ0pz6p7vUKgJeew+SglUzxTdq6vJTwEMh4yJ0rkJlh096zG
|
|
2WUhEHld+fXhThOkJxU9TNwaAkukblfeNZig/bqN0rFFIXAl/c46l3ITbFYL
|
|
T9l6KQTM/OuF2YUm+FWF6drfEgL3K8YPdmWZ4LG0R2dNnhLXV1eU8FJNsCcm
|
|
p8lhOARwfoXfymgTPHvdLNNCMxRUTo973ig2wW9F8EGFFQoZu2pX6QhM8M57
|
|
kVK1UyiY6Lcrz+eaoM/FmirxtFD4JhBsKdc2QbsBjmHtgtA/+c0Erx7dSNdK
|
|
CwXhfNNlYjkVG1o62j1yQ+FCzIGugk4qhiXoTJYcC4VQtSVObxuouHa932TX
|
|
K6HA9Svc6VRORZ5mUod6WyjY87iPMwupGDFpK+PC01CIPTGWfT+LivzsPCOX
|
|
oVDobAyIZqVScfmaXVdLxkoheWP/3uRoKoY+XT/6jakURH2ddSimYiUs+KRp
|
|
K4WgHu4LTQEVS7Sdt2n5SSF9ZbvSHC4VGY9GNX+ZLYVX5fe0TmtTcYppTfml
|
|
JClsybaljPymYNX9OI+wjVJYOJjs7CunoENKC+PkXimc6tfNzu+k4OfYE7+3
|
|
nJSC73SqZn8DBQfP/XjwvloK4sCseutyCtoFtZzua5XC2fpZp9cXUrDSTXtN
|
|
xGMpxMGOxttZFNy45a539ABxPzeeFi2VgjuYE8Z9UpKBugdnV1I0Be/r1reO
|
|
nSSDJ01bPUFMwYQ5A9vO02RAuT2NM0FAQddve716LWRQEbHGJZJLwTD55aE9
|
|
bjI4nzh283ltCp60kZy4HyT7Uz8UDLgdHXo0XAY1erPOSuTGyKp7Pzy0UAb/
|
|
leltP9JpjL4aXw4+SJGBqM2x6FODMZ46nuzosZ64XxI88yo3xqB98e2222UQ
|
|
nHcqPL/QGB0edcdU7JfBI+dvyi+zjHFeWtPXKyUyuBVz7rFjqjG2J0xeH3hO
|
|
Bgyd6++2RRtjRoWa+sIqGXR4i8x7xcaYLJ67bVydDLq/sY9YCIj7Cc3VXVpk
|
|
EGCT6LOBa4yMLSvXf70jA+oHPZN72sbYQ3cedOyRgZc5h8dTMsZurdRY1X4Z
|
|
LLqXU5UmN8Jka5+rb97IwOSmK/NWpxEOz2rsSh6QwRINpzhKoxHGZX1uOPyF
|
|
+Pv3pmcmlBvhTby9ZskQ8Xkkaa6/UmiE+kpzfj0ZlkFT/iuZ6jYjDPPdHzRC
|
|
vI5UH68cmmqEGXs3xF4krs+8via7INoI974zDtL+KoPAO7bvn4uN8HDQgp+6
|
|
H2WwZ4rjFHOBEbG/n51W81YG625v9lzBNcLljNH1qs9l8K2WalutbYSiAzMe
|
|
fOn5fx8j/K0fUbmFWG/pNrNSL7khnjs8YX7NDRk8nFfC2dJpiH5Tkx/m18ig
|
|
YPOC9dcbDLGtfiNV+7wMfnxNuqxWTvw8WmRmWyyDvorGRp9CQzyuflF1JFcG
|
|
sTUx5zdlGeL3yx1n5qXL4G8tyfLaFYYoXFxssiSB8L20adLPeYa4YAo1wmSG
|
|
DMKPKW9zEBvi5o9+MckeMuD33epZ6myIucB0jp8sgy1xfRonOYa4If/sQxUt
|
|
Yn2ubpP6tAxxyfIXPt7DUlCOfPFJ97cBusxqS+f1SiEh4+gB8VsDfGDwfl0Y
|
|
SkElxGVg+wMDpGxqC0w+IoV/71wYvFNvgG8OJj1OXyeFCjWNs7QyA1w6p12w
|
|
Zo4U7soF2ikFBriv5XPUQkcp6G4M4rdtNUDR8/tir0lSyG12/mC+wgDPnkpT
|
|
mfAqFMzrVWP2zjPAY8aPNzXXhMLvxLJtf4kN0Nvxr9YVRD8adcMharWzAe5W
|
|
etM7MSoU+HcLnn/hGOCilJ2Vh8xDYd2ux0YrtQ3wXd7QLL3vIX/6mwEqR5o2
|
|
rmsMgUrTX3ty5fp4757ayMPtIZA70NXF7tJH2nDZV5YsBIqS89rqGvXRusmo
|
|
eq5BCHQen7w8tkIfO4Xe/lsfSkCwrej6xCJ9nBRjWXzkoATumH5qqc3WR3X7
|
|
Hjg1UwK7YhnrVq/Sx3UVfv+U6Eggfa5lv0OMPoZeelthUDgNDqtRhn+EENfP
|
|
uV56c9w06Jn3vPqGmz7unc0yCyfm+fTFORaHpujjf+WjvZofB8MP/iRpioE+
|
|
BkVGvzX0CoaGfcs5MhV9PDjfi+1/NAjmHlO9x/ykh8kPWl0OfA2EAFfqtluP
|
|
9PBZOz890C4QCqIrvcUterhMOuN15LwACNG5p3ayUg95EdPT76/2h9mhqbd7
|
|
SvRw7luO6/l0P2ikHCp6nauH1aNust8k+cKe5V4r/lujh6FFLo6ZwT5wcXpS
|
|
yI6Fevi7bn3KFn1vcG8yseVI9XD1kv0PX7Z6gUldCHWfmx56Fa+LP73UE+YF
|
|
qI9/wtfDabOcWe2/3UEt0lP5L13itU32hIpBtz/1o4eLUDR5S5MAIqd6KN97
|
|
o4v0iCP7TZIcweSlyviN93Rxh+qR8DUDtmA7VUwdg7podc1raUGAFZz5bWgb
|
|
f0oXdVS0Lyh/nwxr5y4KKdmji0dP9pvN0GLCZX+XFZfSdXFV9/Ch2Mu64Fe7
|
|
u6g4ThfXzemowDOf/rVpTLy9IFQXb3xSffV6REO4IaxZbbSLLhaILZrUPU2F
|
|
tsSmZxVbF18tf3lMRYsvdDaeuO26pi6W7KkyhTgr4THJ8N0PQzooiQo3rEyy
|
|
F8ZoLeB87NPBMNNZ8KZQICyj7M+VNOvgbw2LsHfR7sI9U7roeRd18JlX1hXl
|
|
Xk/hRCG3t6pIB31cq3McXb2FNjM21NZm6+DGLw1t2Rt9hR+Wv2k7u0oH3RNK
|
|
M36e9xf65Eeq/B2rg3FHIou21wUKhdVPFliE6aDy3oGpLtXBwo7nS981iHRw
|
|
VMCsKRoHpwnP2zyYvtVZB3+c/NgRHC0R/g9dCfcl
|
|
"]]}, {
|
|
Hue[0.9060679774997897, 0.6, 0.6],
|
|
Directive[
|
|
PointSize[0.009166666666666668],
|
|
RGBColor[0.365248, 0.427802, 0.758297],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]],
|
|
Line[CompressedData["
|
|
1:eJw8nHdcje8bx9t7H5KRTdqd6ux9TiQj38xIoYwkFMrISIoiiUIiI9kZGaG4
|
|
zyXZFGWktKeW9h6/p/Pc/fzzfZ1X5zznfj+f63ON+7nPd5Ln1oXrFOTk5JKV
|
|
5eSG/jso+yeBV9qxKh0xfxBdLe128IAEXn5fvfDujT8ob+vCpoo+CSzoKNyX
|
|
/+IPqqJ/+GrRK4Gd2zQj9uX+Qavdx89z7ZYA3env9jN1f9CschfPDZ0SiNqz
|
|
kz9NuRDFv/eirGiXwF6V1BrTiYXIVXvxKptWCSg2JG1L4hai0JTJs2qbJDDe
|
|
yuFP7IpCNPZJ9rsjjRL4/iFmWu/uQjTByK1CrV4CEyDG+Vd8IYrKzzy/+a8E
|
|
5PUdlpm+LES+fVqNT6qI679IEjSXFKLH++wKSsslcDzjiaq1ShFqaF+trFAq
|
|
gZmXfizUtChC5/pe6pgUSeBRlmfmPZcilH5yTud/BRLI+8995eidRcjliYr0
|
|
QJ4EUqa9GTP3QhFasaFl3aMfEhDPjx+UvCpCv25o19flSCD83R8Npaoi9CnQ
|
|
1cX0qwTCYiO5xzSKEfV7zulNXyTAeHwr9rdVMdKCvc8ffpTApen2lH8Li5Eb
|
|
e+mLgXcSkNaZP/sUWIzGS1ZdXPBGAqcUTx7aGl+MluSfXXUtQwLGW7wC8l8W
|
|
I7mhfyABD/Orx7VKi9Gkx2cPrHopgTvGM6oUFErQ4w6PotdpxP1Y8MTIi1KC
|
|
Xr5bMs7yGcFnurvo+tQSxDLZyzr/hPi+u9sZWbQSZDYyh6bzSAImBUlTfs8q
|
|
QdEnl+kffiCB2hStq++WlSDvC1qfFe5JQNX2zpNz3iUolda8LvSOBILdgt0W
|
|
7C5BO92VizVuSWCxVWRsTUQJSqY4Mc5cl0DI7azV6+JL0DLXF1umJ0lA66sj
|
|
vLldggLNV4WlX5FAy8XOh+rpJUjtODVoySUJUEcVMamfStCr/ISA5gsScJbv
|
|
lFtQUIKWbtOJj4yXwOdp/LSAuhL0ZtGhmulxErgZ+mjttd4SpH2gbzWclkC5
|
|
8TK5Is1SRG3brbg8RgIHmmccnzCuFFk96s1uipbAnsEZmj4WpUjlxcG3R6Ik
|
|
8MNx2Z6X3FL0TEer2jhSAtEfH+WPnl+KHO7EUx9FSODWEb7FAfdSdPek5XXH
|
|
IxKYeqBzS8PmUtTwKtOhIFQCfQ+KEtfuL0Xq3NXaW0IkQDNue1cRVUrqEyyB
|
|
L68ZRZsvlaKv2knjTu6TQGbSrcrB+6Vo77p5XpOCJDAOnIrioRQpqHbnPthF
|
|
xPdIo/f8b6VodcutLYJA4v5fG3G1rrQUnTdZZfdluwQ8/QRbr7SUonvXjSav
|
|
8Cf8FRBnsVqxDF3c+pNdtUUCmx9PKDAZUYY2hMTt8/eVgILVjz1dU8uQRrFH
|
|
be9GCXSWPtPMoZWh8DDTg2EbJDD368fjj2eVoZKALpHOOgkMdmnIX15WhigP
|
|
Plmc8ZSAwcrd62K9y9BE+6si49USONw9Mv3k7jLkwszrv+ougcSfPNXTR8tQ
|
|
U8vrIjM3Cdzrmr/g/Pky1Ou1viLFVQLJq2bFJCWXocBjUh3WUglc0DTJffCy
|
|
DHlszHaHRRLY1/dPB7LKUEr/6W+OLhL4z/bKrJziMrRjNsUn21kClLvsPdVN
|
|
Zeiak6PJsnkS+OD74tagfDkSy9uqFztJYKv/9B9jKOVo/tZc3Q2OElBJ39XH
|
|
nFqO3saYc/45SOCE06MJK2jl6O4W9rGdYgmoG//k759VTuojlEAgrXT5tWXl
|
|
6LXj3nPhPOL+n/rul+1djppn3l+mz5HAJNqDQ327y1FUTxw7nimBNeN2nLI4
|
|
Vo7i1rHEU+gSODl7YsKqC+VI70j0lmQ7CTx+/vjq6bvlqM3jopRGlcC7rdTr
|
|
WagczW7wpEmtiHjwOZOk8bUcqdsWZc+2kMDr2+UXnUrLEd1S70SOqQRuW48+
|
|
faylHOUWdW1baSKBQ930I18VK1DRrLigqqmEH9R4AUYjK9DidY03/SYTPCvN
|
|
V3lNr0BMdm9PzwQJpLbJz0xhVCDjybyVYcbE+ysO1Sg4VaCzu22f6o4l7h93
|
|
h+byFRXomrBAM95IAmYDOXcfbapAjjsZK6YaSmDLjMvZBvsq0D5jx8R7FAmc
|
|
SS/wC4wi/m6nUcHUl0DS07CTRZcq0PVnwRNe60ggdtxF6twU4vp3by+eryWB
|
|
jbVTXV5kVKDxBuGHfqlLYMqkMU3U7xWIVWWUvEaVqCewTye5sgLVmLpn1SkR
|
|
+fPDgmSzzgpkWri4NkBBAjfY0R/uqlUieZlAEmgbIVhPG1OJfE956B7tF8MU
|
|
15Uhr8wr0aZYP6MRvWKwV6oxXsirRAPK9LEXu8RgPrqMWe1ciaZV3xs1o0MM
|
|
ymfn5AavrkSljALth61iyNw3qWH8tkpk05XWz2kWw4Yv6w+/OlSJRsxwrn7T
|
|
KIZ/YWMueZ+uRJHvYj8uqBfDihtcxogblSjuZ9SN33/FcJv6xTnzWSViLuHu
|
|
96oWQ9HUz5W7PlaizZIE54YKMXQGs/qofyoR7UqK0c4yMbTOHHnqX0Mlit6y
|
|
+49ciRhyt6+6kTJYiTKdriUcLRRDV36Xxy79KqT/rXLViAIxZMzNKJBMqUI7
|
|
lThTLuaJgfo23XgErQp1lSdVm/wUw6w5lVP/zqpCMVun3E3JFYNcHr85w7UK
|
|
zb6Rup3zTQyrtr4PueJThUYc8+C8yRKDp17I79C9Vah3zFilBZ/FoJ6+qd03
|
|
qgr1La3/kvdBDK5bw34uv1yFjAQ5cZ7vxDDXMnvv3IdVaF7u57X1mWIob5td
|
|
I8qsQnGUP9TADDFMeNtixPtZReoDYlC88lmHV1OFQuKY2REvxRAR9vODqKcK
|
|
GReGXaKki+Hpdr05c7WqUc6Xar+EZ2II37TnxPLx1eiyj4fEJFUMA74j4n1t
|
|
qlH4o7+GKY/EMHpX0cZQcTWKuBlRx04RQ35k3sDlxdXouhP/VeY9MQjuKCzP
|
|
WF+NCs6oxjkni2FO7spdNbuqkVl05da8W2LoVqpeSTlWjU7R8mZ73hCDs/CK
|
|
iiShGo08Ujy5PkkMs8OOBey8X40ehPb2BySKoTr32q0Hr6rReiuL/MFLYjCz
|
|
aEpszK1GBtuyUyMSxFDsrnONWlWNoniSGMp5MWQzk1p3d1WjwugjWxPixND3
|
|
IiXqnUYNGth0Ya7JGTGsq6UHjjGuQU1ZB01SYsSg8cru9jbrGvTkOUORc1IM
|
|
tcKbZl9FNWiOBSrKjBKDmk9sp+3iGpQyfWSac6QY1nC79M6vr0H1N7mn8yKI
|
|
eHqaG6i2uwZ1PLT38zwihvd/ppsGHatBOQ79c+pDxfDjdrNJa0INCvY4My0w
|
|
RAzGk+23+z2oQbL27YAYksSNGq0ZNcjFlJ0fsU8M67Um/tvzowYF5js8pgQR
|
|
6z3wYYJaTQ3yoUyMStglhoTztRfie2qQ7fdPG0wCxTBizaH1ttp/0ftxs0Up
|
|
28XwJjtmb/aEv8iuIXYMx18Mj6rHFvvb/kV+Mx+2Zm4h/HBzbNTomX/RvmmX
|
|
Pzv7isGBEhPxdtlftPK4x7W8jWKomh7ybZfPX6S9r2Gf5wYxvC6vWWez7y+K
|
|
bpu3tH4t8Xmnd7MaTvxFFa17rQI9CX8vN95xP/Ev0gjapyK3muDXr2sIfPIX
|
|
nXH1KYpwF8OkcfJdkvd/0US3VakUN0KfiTY/DQv+oushK6MSXMWQM2FX+L+G
|
|
v8gke816k6VimDH6t06WXC1KEm7lpywSw1etRRsfUmqR8a9QQ46LGLJ6Ks9e
|
|
mF6LYk4lNmY6i2Fi+cn4SFYtUtz+/q3zPIL/zVL/kHm1yH9Xx8U8JzFIE+3H
|
|
7V9ViwoSLXZ6OhJ67zE/f2BbLRK1+CyodxDDnbmcxsNhtShxfQpxO8VwadTa
|
|
kbFxtbj+EPFQeE3vxp1atBwtzYvgiSH0olyJFNWiB1eePKBwxBC4fMehom+1
|
|
SOH2uIgEphjSdOR7FSpr0YJfx9aY0MWwEF2fZdlVi+JNFdkpdmLgeq9b765Z
|
|
h4ovhxhwqGII0uKtiBlfhybzNOoyrcSgc8dycja1Dq0eOPfa2UIMHRIG0ptZ
|
|
h85XUC/kmYrB5tdyK1fXOvTt37cdniYE39rT265tqkOKE/fMr58qhsv1f492
|
|
7a9DtgFm0wMniyFvy7KdLqfqkNu/soHBCWJYXVfIeHCtDpl8uPgrwpjILwdX
|
|
Go58XoeYvOUPKGOJ+73g4crgz3XoxFyDiAQjQp+lxRotxXXIsu3DGhNDMSw5
|
|
Uz7Rp7UO6TKC2SkU4no60os1KvWINYJG4eiLoQ75h24eU49uHqupy9QRw+CN
|
|
3m9dlvXIIyE+01lLDLEfVh45KqpHy53mJuSpiyFlyumkyUvq0fkTPQGeqsT9
|
|
Sk0yfeVdjyb53XSuVyLu78Fjhuv31qOG2sUmgQqE3mFOm/Sj60l95Ij3vyoy
|
|
eX21Hrnev5UX0S8CRfrceUFP61Fnl0sKpVcE3PKoPNanevTnT1dEQpcIut7f
|
|
+jxQVI9U3S56mnSIgFV9fsbHlnq0c7uYk9IqgkHeuvrzKg3IanolhdMsAqcv
|
|
ykY7xjQgs+2H6zMbRWB0et+dhVYNyHfF9DfO9SLwOf35OkPcgNoKMhPy/orA
|
|
IatFfcrSBpTRuSbQs1oEVwRN30f4NKCfd/ud6ytEEPI3U1V7fwOyGThrElgm
|
|
gtpPfomapxrQtxobObkSEXyvak3Su96AJIIPeRGFItAtCPYYl9aAjHLXpFAK
|
|
RODpNGe8dVYDmpvUE5GQJ4Js6n8Vs8saUNHDGE+TnyJYHHvqwcaOBpQzYMFJ
|
|
yRVBq5/+oZMajcgk/C2F800Ed959doPxjajQeXV9ZpYI9sZlsjtsG1HLwp5M
|
|
588iWFfeNcHOsRFtiI1NyPsggo03N2rudGtEfIp1oOc7ERyuNux/tbURbc/+
|
|
4FyfKYL0y3LtlNBGpPFhrUlghgg0vk9v9Y1rxPVHROgX0fk5uREt23E+L+Kl
|
|
CNpuzlCwf9WIdKczUijpIjg5R4mS+INY38jciIRnIhCvH2c2qrYRXRJt9TRJ
|
|
FYFen59jzEAj2nlHk5PyiPi8psImQ8o/lLLwJoWTIoKO09mxl03+ISfGzPrM
|
|
eyLQiv+dSeX+Q+LlZZnOySIQGk3s/fDfP3T+2YGEvFsiCNe7yti47h9ausQ4
|
|
0POGCBpDPPfo7vmH/KzTneuTCN6tHq9fRP1DtbOWmwQmikDu5xkD/6v/UOb5
|
|
zsHBS8T9S9X0tnj2D2lqnMmLSBCB+uxrRv8+/0OfN9unUM6L4CbM3f289B9S
|
|
fJcTkRAngiMTByOOdfxDj0b6e5qcEUHuo1XXHio3oYLlupyUGBEozX3rPkWv
|
|
CQXF3KVwTorgxxK7xrNjmtCpjLn1mVEicPx+fanetCY0pfpvpnOkCFa8nXg2
|
|
0roJmcuHJ+RFiEDb4sp9LXYTStabHuh5RARrlGdcjnZoQtdGZjrXh4pg6cIn
|
|
3kYLmtAoPU+TwBAR1Bs4qSctb8LzjwimOJYftFvbhDwricvtE0F346Gct1ua
|
|
EAc4KZQgEfhrmPe6725Cx6N/RyTsIu7fubzerkNNyHXpTuKCIhBdiPx+NqoJ
|
|
xeuP5KRsF0G8gWMY+1wTWpzxkMLxF0Fsn6pO6dUmFO79X33mFhFYr8jecuxe
|
|
E7JVItK3L3G/zRNusJ43oaWnjyXkbRTBLD//Z3Wvm1DTWNNAzw0iyJgx78qV
|
|
rCakFPfWuX6tCIoXW3q6/W5C0epEvHmK4ELbiF6jiiYU60dE3GoR9Koq+uY3
|
|
EuvPvZgX4U7E87cVZZe6m1AKg5tCcSP8GXPg2EalZtSeQPC4Euud77+BoduM
|
|
1FQInqXE++VsAtXHNKO/W0dwUhaJ4Pqd9KfFU5tRfEEKheMiAvcFIyzSrJvR
|
|
aKcF9ZnOIjhax8qNYzejtc+Il/NEYBlscTdoZjM6aHo0Ic+J4NGuf+75XzPy
|
|
uUAs15Hw96ld3fPdmtEUfSJ9OIjgt17OJt76ZnT7CHE7xSJYdKRLj+rfTPpH
|
|
SHy+o65mxt5mNHUPoQ+PiD/35NapR5rRqA4i/XKI+HrJok471YzythPhyCSu
|
|
NzL2imlCM/JuDfA0oRP5Z326g+3NZvR2B2EXO+L+3b8/RvCoGbV1EuWLKoKY
|
|
Zr8p/6Fm1LiXsLOVCF6YD3qs+9CMnisSPBYiWOmx4sv+783ov0gi3ZiKwC8i
|
|
ZMuF4mb0zJDgMRFBf/JOMaptRg2JRLxNJV6/ZzlVtDejZhuCZ7IIdhS+D9GR
|
|
b0Gvgeh3Johgde3Uf1ytFrTEheAxFoHHpkdo66gWFFdK8IwVgdqf35NuTG5B
|
|
kf4EjxFxv7lxRuWWLchGnvg6Q+L9kY2JU1gtKCya4KEQ/vv8B7wdWtDRCcTt
|
|
0CfyY6/ntocLWpDwHsGjI4K1Yw4+lXNrQde5BI+WCEaYMqIXrW9BLz8SPOoi
|
|
2GIS1nfbn7ieK8GjKoKAkZv6VPa1oIFKgkdJBNNba05sCG9BM7YTPAoiCIWB
|
|
1M8xLbj+iODEvmR/+qUWdCyS4OkXgsSsRZp0uwW9NSKW1yuEpLfZV0altqCH
|
|
SQRPlxAeLJw56sSrFuRsQ/B0CGFj1sKJml9a0Pl0gqdVCJ9ZXS+O5RH3YxbB
|
|
0yyE/Fhag15FC3L8RvA0CuFMsUZK/D+Cx43gqRdC3+hdaqa9LehJJcHzVwja
|
|
Dvta01VaUcBWgqdaCB/dx2xbZNCKqrqIt1cIwX7DgtB/xq1ILYTgKROC0+px
|
|
ZtGmrShfg8ApEYKG00EvGq0VRcYQPIXE51c1eRULW9GccQRPgRBKygo8oua1
|
|
IsNrBE8e8fkcyWKxaytqsiR4fgpB3WqGQ69XK8pLJXhyhTC2I9zq+dZWlCUg
|
|
eL4JIcxsPWVvUCv6+p7gyRKC6JO0RXKkFZW6EDyfhbAo7/RnvZhWJFdAXP6D
|
|
ENJcai6XXWxFZkN2fyeEAMbTrc9vt6J1DQRPJnG9CAXW6dRWdIf4+sAMIfx1
|
|
/NgXkNGK99+EcG2bTrpbVivyJC4X8VIID9Wzt8/Kb0U5BgRPuhBGamuZ0Kta
|
|
0YILBM8zIXzZ++a7WUsrKphGXDBVCL9de/dOHWhFO+4TPI+EwLlyd8IUjTY0
|
|
hkXwpAihecmfF9MN29CXDGI594TQE3hksfXkNhQ9j+BJFoKb0v0qrlUb8vhJ
|
|
LOCWEHQGFm5fwG5D3NUEzw0hGK3d3rN+VhuaVkvwJAlhB11v76GFbWg80d0F
|
|
JgphRoBpV5JHG5o8QPjnkhAsJ0q3fPJpQ1ZD6T9BCE/t/zPsDGxDjCGe80Jo
|
|
v+82bcahNsQb4okTQsXJ0vMeJ9qQmCgPJmeEcDi/dHf8+TbkQNg/JYbgi1gp
|
|
LbjRhiRD6eQkoe8lF9/Jj9uQaOj2Rgnh7LhXwVuAWC/x0jlSCApyd/qkn9uQ
|
|
/ZD8EUKYMEe3xPB3GzIjlut5RAj/ehrMtlcS6x8Kz1Ah+Bk4Fn5vbkP6Q/qE
|
|
EHpEj+nkDLTh+iOEyADvXTc12lH90OX2CWHqK5s1Y0a1o19D9g4Swpbt21NO
|
|
TmlHMIS7Swi+kTYbdWza0fWh9BMohHFa3uHR3HYUPiTHdiHsaxmta+TUjnyI
|
|
j3P8hRAtmNWftKQdzSbSbeYWIbi21i9keLajaUPp21cIX7V19LK3tKPBIZ6N
|
|
QuiNumXvG0R8/xDPBiHkBUpBJ7wd3R3iWSsE7zcLHqfGtqPgoa/3FMLtPSt0
|
|
115pRy5DPKuFcPFM8TfDe+1oMpH+I9wJf2xZSctOa0fNQzxuQkhe6rz9+Lt2
|
|
lDHE40r4a8GTYy7f21HsEM9SIVxefnL/2NJ2tG6IZ5EQqDvK5tY1tCPGEI+L
|
|
EIIu3WyFnnakPsTjLIQDBeUBF1Q7UMHQy3lC4M6Izdk3ogPdH+JxEkJK2HP1
|
|
dZM60JDdPR2FUN66aOxCqw60bIjHQQhZ27xUZ3I6kPkQj1gI2xRqvvBmd+D5
|
|
RwjfEku3cJd0oB9D+vCEULPov1qhZwe6PcTDEULqSHvh3K0dKHiIhykEYU2k
|
|
n9veDrR0iIcuhNBPK4L8IzqQ5RCPnRBCpAmrj5/pQEpDH6cKgZW5ZOL9qx3o
|
|
z1C8WQnh5u+QtJ8POtDjIR4LIeQOTrVWQh0ocojHlPg+Onc/41MHWj/EYyKE
|
|
xfvf3/DL60D8IZ6pxOd/frhzv7IDGQ3xTCbyh0B4tK2lAzUPzdsTiPU8N5cI
|
|
5DrRUPqPMBZCzLYqg2jtTnR9iGesEHad+0irHtNJ8hgJwcYq747DjE60Yujr
|
|
DIXw0kY34CatE9kP8VCI+Luy9aSBpBNpD/HoC2HBgW65Q/91ouohHh0hLP2U
|
|
/LrbvRO9GuLREoJtWMTvwE2dKH6IR53wW/IJcc+uTjRkd09VIXiKpQOHDnei
|
|
+UM8SkJ4NtNIZ0RsJxqyb6AC4efUeL/bVzpx/RFC2elZ0x3vd6KHQ8vpFcDj
|
|
srHWtS860VC6NOkQwPKEMcdiPnYiw6H1NQvg2xsxW5JH8A+tp14AE1fGcrsr
|
|
O1HQ0PdXC0CwWvfUk9ZOZDH0fWUCoOU8Yu+S70JFQ/erUAC9KQfpIt0uFDV0
|
|
f/IEEDe4K0zPuAsJh+5HrgBU0s+ZVJl1oZYh/iwBzKsoH5fB7EJD5S/vgwA8
|
|
g5atS5rVhRYNfX2mAJyD2+SOL+5CSrJ8LQCN1rR/QZ5d6MkQT7oAYuxu+Pn7
|
|
daH1QzypAvhx5UnG5v1daNQQTwrBw6uq9IvsQkPlxDlZABGqrPw98V1o1xDP
|
|
DQEMDNy9dOxmFzId4kkUgNnUmfSrqV0of4gnQQAjdw4kvMrsQkN2TYgTwPPO
|
|
3z+rcrrQUDpMiRHAuOu/SgxKu5BsuVHE/QjpTJ/5rwtdlOU/AehEsrwP9Heh
|
|
BbJ8J4DLrxMqpZrdeH9HAI0zptqrjulGD2T5TAAd6Z8XLZnRjdbI8pcA0vee
|
|
dbhN70YjZPlKAMxNoSoqM7vR0Nc5+wog4EjMOe9F3ShAlo8EsPFbZv+3Nd1o
|
|
miz/CGCsk5Gd2K8b/RpajrsAwhqPs57v70ay8uAqgHuvpukzjneTPIsEcDKj
|
|
+Hn6+W6Sx1kAVs3pdo63u5FMTicBHJmftv/3s24kCw8HAST8yo/f9q4bKcjC
|
|
TQBbThiHG/zsJuONIwC9jW+OPK/oRl4yvwvgguvIgg2tmIcqgBEe2iHGCj3o
|
|
nczPAgjcfXdvvl4P2inzrwAybrd/vDihB82Q+VUAXc2Vvj5WPaQ+xgIYvWC/
|
|
J4/XgyJlfhTAtAx0Z9S8HsST+Y/gn3tjdveKHtQo85sA+v4yWGUbe9Blmb8E
|
|
kHnRb1/Orh7kIvOTAII2uoz8eKQH718Tn5+TL/fhTA96LPMPH5KEmsLsaz1k
|
|
vHXwwWh+Rc6fxz3YP3wI3LruefNrzFPPh4wbUa3auT1kvFXzoaV91UFqWQ8y
|
|
k/mHD3orfnuubO5Bf2T+4cOY7z1no+R6SZ48PmitzZz4XrcX8WX+4cNfdXq/
|
|
2oRekieLDw/eLLB0sepFl2T+4cPas/opl3m9aKFMQD7IHQgK75zXS+oDfDi8
|
|
9/ijJSt70SOZf/hgc2BOQPqmXjIfpPKBHfhEzzSoF42U+YcPV9ZkhV082kvy
|
|
JPPBS3T6+9j4XrRb5h8+hI7U6L98q5fUJ5EPg4UWg5bPe7F/+FAY35+f8b4X
|
|
HZP5hw+G8/ZGr8rrRVyZf/hwr/nmBKWaXuwfPlw+dij8QWcv9g8f2kZrfVqr
|
|
2of+k/mHD4kXxNUTR/Xh/oDgp5gUVkzvQzK5g4j7d+B58gN6H8kTyIfyou4l
|
|
obP6sH/4oGJXk7dqaR96K/MPH44FhdIk6/vIeNvAB59nWZusAvvIfOrJh5t/
|
|
3wZNOtyHZMtx54NQd/O6cWf6yHzgygeu6asZE673kTyL+HCS8fqNaWofqY8z
|
|
H2axt3O5b/tIHic+LKZ+i1z6s4/MBw58eDOuMHVXFeYR8uFE35m0xI4+7B8+
|
|
qHIV/3xX6Sd56HzYP2v6Kt1R/dg/fGgaK+ew0KSf5LHgg8eL6KMJjH4y3kz4
|
|
8MEkz7bZsR/7hw/WHj+581370W+Zf/gQs+rYzRTvflIfIz60mncGjN/dj2Ty
|
|
U/jw3+vR12Ii+rF/+HBrWitNP76f5FHnw8DCQzPO3u4n9VEi3j/3495p6f3Y
|
|
P4ReOu9tX3zqx/WHB3UX9s5x+9OPZMvr4IF9R/VrhQbM08yDnWM0Lj3s7yfz
|
|
Wz0PnqmXF/joDJD6VPOg7fW2PeYTBkieMh5YOT3f02Y9QPIU8sDzXOqfN8IB
|
|
JAu/PB7EPva5fMllgNQnlwdv4n+8Oeg5QMZbFg+a5nbO890+QPJ84MHo99m0
|
|
VaEDJE8mD7i6q4JXnB7A8wIPVky6ZuFxfYCMt3Qe1Py4vN/n6QDJk8qD+Uou
|
|
aQfeD5A8KTyITH5SnPB7AMnasWQeXMvKasysHUCy8LrBg3M+F6rbejFPIrH+
|
|
4PEfLbUHSZ4EHqjrLTmzdfwgyRPHgyOjhfPSrAdx/eFB8YXiOm3RIPYPDwzi
|
|
7QJ8Fg6S+TqCBxP0uTXZXoPYPzxQVuh24AcMYv/w4K2vz7Enhwdx/eGBh0t0
|
|
Oi1ukOQJ5MH3+z4/0K1B7B8ejAvvzvsvfRD7hwcO+dy3dZ8HSZ4NPJBct084
|
|
UTRI8njyYGx9iTu3aRD7hwfVPyYqdcvJSWU8rjy4t83cOU9dTiq7XYt4sGae
|
|
nvYLAzkpWX94IOeVLUwaKycl/cOD46nef6OnyklJ//BA1fGPSoilnJSsPzzY
|
|
MsLs3E66nJT0Dw+sTS+88hfISUn/8CDtxN4rfrPlpLL8RuWB7uxPzB0uclLS
|
|
PzywXBh+ZO8KOSlZf3hgeO/R8QgvOamsP5jMg/du8+ee95WTkv4h+N2WQEqA
|
|
nJSsPzwIT/5U/3m/nJSsPzyIW/Dga/0ROek/mX944Oeg6Kt/Uk5K1h9Cr2OZ
|
|
iB0vJyXrDw/2TWl7731VTkr2bzx4rH3q6PlkzNPLhYdOFxVzn8hJZfW0gwtB
|
|
v4zsdaWYp5kL2k/lx/33Xk5K1h8ubKpxTT/9TU5K1h8unNg03qAkX05K+ocL
|
|
B4QLJ1pXyEll+bqQC8wNbZUhDZgnjwtpxUpeBR1yUtI/XFC5fegsU05eStYf
|
|
Lhi/9TsUry5P6vOBC312n6fLU+RJnkwuXG89fdB3nDypD3DBSDkr5s80eSlZ
|
|
f7iQs230PhdreZInlQvzHI3dPzHlSZ4ULhwL+W03RyxP8iQTr6c6y2fNlSd5
|
|
bnBhgWXQm6VL5KWycE3kQu6F1cEVHvIkTwKxvu0D1J3e8lKy/nDB5MHifJ1t
|
|
8qQ+MVxoX+S1+06QPBlvUVwI9TDTnR+GeSK48Cv71vnWKHkp6R8u1N8oHX8p
|
|
Tp7UJ5gLmVXf4hYkypP6BHHBI3KPunIy5gnkwou4Aj/pE3kp6R8u/NZsz9ov
|
|
lSfjzZf4e+XbKZIP8mS8beDC6ukuW7VyMY8nF95+iUnJ/yMvJf3DhcaCqNq7
|
|
VfJSsv5w4c9/4jGHm+RJfRZx4ajFPaFXD9bHmdBjS477TCUF7B8uWBnd97fQ
|
|
USB5HLgwbYbDXiMjBZJHyIXCiyf3qU9WwP7hgkaa66lBcwXsH2J9T1f86qEp
|
|
YP8Q33/m7LxegQL2Dxf2u+q2yM1RIPUx4YJT36t3mosVyHibzAVOyP0vYz0U
|
|
SH2MubC49pci1VuB1MeIC6ftOT5ztymQPBRi/at/y23aqyCVbefocCFy68N3
|
|
Jw5jHnUuiFe/Rc+jMY8SFybYjayqiVeQkvWHC9NrLvKMrylIZfmtlwMLD3i9
|
|
WXpfAfuHA9e6PPedfq5A6tPMgcmLE9b9fq0gJesPBzJOGuyfnKUglclRzYHI
|
|
lIy3fnmYp4wD+x7dFWSWKZD6FHLg9NncmnENCqQ+eRzIcbfP2NOJeXI5wFb5
|
|
+qlQXpGMtywOvI++rjxLSxH7h7he/9OtjwwVSZ5MDiyfp6QxfZIiqQ9wYOW+
|
|
Y98TzBVJnnQOPPAIqx5DV5SS9YcD+5GpW4JQkeRJ4cDrC7usp81VlJL1hwOH
|
|
uv3XPlyiKJXNCzc4kP59ZI/DakXsHw5sslrb9MdHkcxvCRw4o+LuuCdAUSqb
|
|
F+KI9bvLDY4LViTzdQwHltg6j3pzVJHUJ4oD9WGzoredVpSS9YcDPcv+bpx2
|
|
GfOEciDkJj2p8DbmCeZA6E4rwfknilKyf+PAQOZXtgcoYv9woCXa+Oz0T5jH
|
|
nwMeBSMWt/3APL4ckCSl+r8rUST12cCBxDqFpkt1iqQ+nhzYmdKdta9DUUrO
|
|
P8T9bo/XWSOvhP3DgVPPqu45aSlJyfmHAz+7/9xnjFLC9YcD0c/36ZtPViJ5
|
|
nDjwpvN97hRLJVx/OLDjMeqYxFTC9YcD5/957JkmUcL+4UBCooWflbMSyUPn
|
|
QOHb23+5y5WwfzjgtvJ31X9rlbB/ODDK69kGn61K2D8c0Ctw9I3Yo4TrDwdm
|
|
Zx5puxumJC2Q+YcDL8fvksuLVsL+4YBfrVG06gUlXH84sMbE5yr3hhL2DwdO
|
|
/NjE3vlQCdcfQp824yVPXyrh+kP4ISy4te+9Eq4/HIg6EjNy9nfM08uGRz1L
|
|
0+OKMU8HG0YWf6xorFXC/mHDU/t/J+d0KOH6w4bY3tcZd+SVcf1hw0M7p50G
|
|
2srYP2zQKtx/f7+RMvYPG5I6125qmqKM/cOG3Yd6b2+wVsb+YUNUsHhLBVsZ
|
|
1x82FDWynqyfpYz9w4bNWaUHGl2UsX/YwJ7AzgpyV8b+YcOsUvFlnY3KJE86
|
|
G8TBTf3Xdyhj/7ChcgPjn0OwMvYPG2ziRu2oOaaM/cOGKfonI0+eVSbj7QYb
|
|
0nOuMoVXlaWyeSGRDT1/Fuxqu4d5EthQZn167r00ZbLfiWOD/6ftDze/xTwx
|
|
BO/9umTbHGVpncw/bAj+08fuL1SWXpBdgA0KC2+s/PJXWSq7naFssNCr07/a
|
|
jnmC2dBr+H7FfnkV7B82BKznM1Zpq5A8gWyIGZh/Y+ZoFaksGvzZsKy44zZ1
|
|
mgr2Dxsy1VjiKVQV7B82/N4zYvMYngrJ48mGU7QI81FOKtg/bGhhnt03eokK
|
|
9g8b+kL5XpPWqGD/sCF59IE/VptVsH/YINfp+le0W4XkcWLDwLjPESvCVEge
|
|
BzYkHst7ueukCpmvhWxoEO8Pu5CAeThsmH5rXcGbWyrYP2yIn8pIa3uCeahs
|
|
cHjSMsk0QwX7hw3T3OIMvLIwjwkbeIYzIhPzVcj8NpkN0VVXoqqrVHD/xobR
|
|
n5XH2LaqYP+wIe/tIquQQRUyv1HY8PXnsU+/NFVJHh2Cp+9us62RqlQ2b6uz
|
|
YT097XLMVFUyHyixQe3wg7xuG1XsHzYU10afW8dTJfudXhY0rHUr/+mkiv3D
|
|
Avs23dT5S1VJnmYWPIy7p//RUxXXHxZ4L2R0zN2qSvYH1SxYOum2V26QKvYP
|
|
C/Yoq65YHa6K/cOCvIH5v1tiVbF/WLBJ+0Dp0Suq2D8sYFHjt824h3myWMDx
|
|
uRT5KU0V+4e43rMo6x3vVLF/WFA31ttt8ndVqWy/SsqCM7Hmej9LVLF/WCC8
|
|
M59+okGV7A9SWXC/Rpw6v0cV+4cFpfM0o/VV1UieZBYU/Lr+Op+ihusPC+Ii
|
|
RrrcmqiG6w8LxnguY+6zVMP9Gws81/juXspWw/5hgd+RxSNojmq4/rBA8F1X
|
|
ffRiNewfFvxyvLhMYY0arj8ssC0bHGzarEbqE8qCxVftFSr3qGH/sIB9jOtR
|
|
dESNrKdBLKg6N2pEYawa9g/x/uw3U0qvqOH6w4Kj5o7Ha+9hHl8WHLp3/r/u
|
|
dDXsHxaIXV9v1v6AeTxZ8HYGqpj+U42MN3cW6E6MfDKzXA37hwXGfMuSjU1q
|
|
uH9jQUvIlbUx/Wq4f2NBeGONOENDHfdvxPqCFYM6Rqnj/o0FGuxmLZtp6tg/
|
|
LGga/bBri606GW8cFix5a6jzSKCO+zcWtFX8G9c3T10q26+isuBdAG/anBXq
|
|
Utn+qAULfuwanJ6wQV0q298xYYFRI21y+w51XH9YcPpHieHCEHVcf1jgZC2n
|
|
/PiEOp5/iHjujakfk6Aule1XUVjgyrrw5fBtdTz/sODRX6ObnU/VpVdk/mGB
|
|
g5bG3s1v1KWy/SolFuhc2epUk4N55FhAuemk512iLiX335gwZ1Lc1/oGzNPB
|
|
BKTldjSwF/M0M2G9zymesroGyVPPBEc2vzbOUAPXHyas3usRTZ2qIZU9zyhj
|
|
wn2bVutsqgbJU8gE5rK+9/4CDelxWQAxofPfbrfR8zVInlwm1Pdsqn6zQgPX
|
|
HyZM2JXju9Nbg8wHH5gQuuFunWWgBsmTyYTJH/q8/h7SwPMPE7ovwI9bJzWw
|
|
f5igPPfBvy2XNLB/mDCbc2g1864GyZPChMzNrBkq6ZgnmQkBZTmz8t5rkPng
|
|
BhPWnFvw4t5PDTIfJDJh36n74REVGtg/TPj5peWOd4sGnn+YsG7u6Onz5DTx
|
|
/MOEaZpTOu10NHH/xoRJ2noTJo7TxPMPE5a6lCTomWni/o24379itiszNUl9
|
|
gpmw6rLZ5YGZmnj+YYL9naQpfYs0cf/GhFld8gP9azSxf5gQfkRsreSniesP
|
|
E1SWr3+qs1+T1GcDE9J8N58xjtTE/RsTLmUs+2wTr4nnHybAimnLZ9/UxP5h
|
|
whjaT+7aVE3sHyZcd/HZGZqpiesPE7Y8KFW7lYN5nJiwwYXb/K0E8zgw4YL9
|
|
HpvBRk08/zBBacX5tzb9mtg/TBi/dSx9vaYW9g8RX5MC5S+N1iJ5qEzI87sz
|
|
o8BEi+x3LJjg555+Zwxdi8xvJkzgVF876u6ghecfJljobHpzdaEWnn+Y4JSj
|
|
sbJhtRbJY8SEGLswZ/ZWLTz/EOuxzb9wdJ8Wrj9MuPZF3bHomBaef5iwVWXE
|
|
fFq8Fq4/TPD803XvxE0tXH+YcGTBM9+GVC2ynvYyIGfVwsPObzBPBwNma7/r
|
|
fZirhfcPGFC7zPDLmDItUp96BqQKhD1hTVp4/mFASqbDobYBzFNGXK9qivd6
|
|
bW28f8CASdcLbxaM1cb1hwHnFLbNXGymTebrXAYI+0p4X5nauP4wQCfG7NQC
|
|
R21cfxig9s5ZnLNEG9cfBtF/zXd2XauN+zcGhKiYpJZu08b7BwwwW7Dx1eaD
|
|
2tg/DHC9n/i094Q2rj8M0DLJjTt2URv3bwxwTO1Za3xXG/uHAXLuo8elpGtj
|
|
/zBANNYazfqojecfBmg0c+YW5Wnj+sOApUWC1zurtXH/xoAp5ezplA7ME8WA
|
|
PYMWOx4o6WD/EO+3M7y7gKKD/cOAJ/s7vjZN0iHr6QEGxJd+KY6x0cH1hwGK
|
|
Ky/8Zgp0cP1hQFPDGlQ8Xwf7hwFeZ8dHha/Uwf5hgIdrzmy7TTpkvG1gQIHN
|
|
vsbi3TrYPwz4PXHCgahwHewfBqye8ayHf1YH778xwNdx9prmazq4f2NA377s
|
|
h9ce65D5wJkBep/n/3N7jXmcGJBMfW04IkcH928M+HzP2jSrRAfXHwb4S2Km
|
|
H/2ng+cfBtx5OFbNcUAH928MiJV2vFXU1sXzD6Gfz1QvGKuL+zdiPQ+T/uw1
|
|
08X7b4SecTvtWCxd7B8GtI5N2NDuqIv9wwAmb+TulKW6uH9jgEVf8YbN63Tx
|
|
/MOAj679dqY7dPH8w4ARizYXVoTo4v6NAZp11msvn9TF+wcMuD9x5nu3y7rY
|
|
PwwYbE1WH3VfF/uHDr1rN8zIeamL+zc6XNm+Y+rxz7q4f6NDx4Tv/Y4FmKee
|
|
Dp0bDz9WqNXF/qFDksux2S+7ME8ZHfZvav6TrqiH+zc6yO2bpTRaUw/7hw7L
|
|
Cx3GBBroYf/QITyyfnzuaD3sHzocO8ozsJmkh/1Dh/W/GG2RM/Swf+hgtL0g
|
|
86+1HvYPHS67zwidxdDD9YcODmXxexL5enj+oYPzvPtNfTP1SJ4UOsD5dVVL
|
|
5uth/9Dh7NeXbncX62H/0CGn9ul/iiv1sH/osKN20ZtlXnrYP3TYm33y+W0f
|
|
PVx/6FB7zt+yz18P+4cOL5xaJ87brYfrDx3aigxj44MxTwQdYpf/OVx9BPOE
|
|
0uHcc0m37QnME0wHxcF5dXvPYJ4gOuSadq18k4B5AulEfzTTWeuaHvYPHa5a
|
|
20tdkvXw/hsdrmm8uX/6EebZQAetT50T8tIwjyedyO+fdUdnYH3c6aDZJz7g
|
|
+gHr40pcz9dty5mvWJ9FxP3NGFmY80tPWivzDx2UB/w/aRdjHic6fB7vx3Ks
|
|
wjwOdOibqmdyoAHzCOlwSm9h7JM2zMOhQ7Hp6tC/vXq4/tCB8Xxtz2hFfVx/
|
|
6HAJreqYpaFP6mNBBwO2yy4/fX08/9DhhDkr+IyRPvYPHcbGjNJ5PkGf5DGm
|
|
Q4pf/aS86fq4/tBhSebT9FZLfVx/6KAUtbtAk6ZP9js6RDx8oR6cyNXH9YcO
|
|
EYdKkqkSfTIfKNFh5f0wD8EcfewfOnBdJp1xctHH/qHBjI2PFv3nqo/9Q4PJ
|
|
nZyzi1ZhnmYaTOtNW71ovT72Dw3oATYPFmzGPNU0WLTuQtjsHZinjAb7Pg2U
|
|
8IL0yXgrpMHjG8syrEP0yfyWR4OO7uum4yP0yfyWSwOHjHpD9Wh97B8aXJQz
|
|
Pdp0BvN8oIHSE7dD3xP0sX9osLM4VOFJEuYB4noHklRP3dHH9YcGiroRLJ+H
|
|
+tg/NBirLC/gPsc8KTSQeGoZqQHmSaZBwPQ7mV/e6mP/0OCZS6HD8S+YJ5EG
|
|
ahWJcbO+Y54EGqwt7JV25+uT/XUcDbJ5NWnXS/Vx/0aDWcreEfNr9LF/aPDF
|
|
Lsi8sRHzRNBg1YdJV8LbMU8oDQbeuNWO69PH9YcGyaamqncUDHD9oYFPW0Sn
|
|
rboB9g8NbKfvT3+sa4D9Q6xPqrzIxtAA+4cG9WgiujbOAM8/NPgzLbtvxBQD
|
|
vH9Ag8JWPd39pgbYPzSomlHVVmJtQOYDVxrIv3G+x6MbYP/QwOz9HE4s1wDX
|
|
Hxp42OafrxAbkPnaidBLsT/byskA1x8a/OM8+rVtgQH2Dw3mFfQ9fLDEAO8f
|
|
0EDkvuJ4lZsBrj80cOPNO2XgaYDrDw3OBuW8svc2IOc5Cxp0jWoYO38L5jGh
|
|
QZDBhctuOwzw/EODiZuKF6zeY4DrD8E/6ampW7AB9g8N8uhTrOYdNsD1hwZ/
|
|
b01xt4s0wP6hgXHQs1S9UwbYPzTYfruUXXHWANcfGjQyLv29m4B55GhwfEpz
|
|
xuarBnj/wB7mb/71dsotzNNhD/YjF7Zn38M8zfbAHbvGedtjA9y/2YP3AaUc
|
|
jTQDvH9gD6kibvA5KeYpswdTT7Xl499gnkJ7QCXeK899xDx59rD7pftRja8G
|
|
eP/AHhZ3VZX5/8A8WcTrk0rrs/Mxzwd72BmeSplSgnkyiesV9tX5Vhrg+cce
|
|
pp/81Zhca4DrD7GefRmJJf8wT6o9bN3PilJux/GWYg8LYrgpY3twvCXbg+uL
|
|
T5pTBrE+N+whvLsqYawSBfvHHsrnRG1QVqdg/9iD14NX3iXaFJInzh40zA5e
|
|
STag4PpjD4VPP+v7jKJg/9jDr+VJz43GUch4i7CHbl21c88mUrB/7EGS33nf
|
|
aRoF+4dY/7PtA59MKdg/9uByJyhUYEXB/rGHkQ91xUm2FOwfexj8bM3ooVOw
|
|
f+zBoK/AS8ShYP/Yg7NgxPvdAgreP7CHh2fyvK5KKKQ+7vbAVzBlIEfM42oP
|
|
zQeVxR/nUrB/7OHLyC2h7xZQ8PxjDzkvPQeeLKLg+mMPA7vL759eRsH714R+
|
|
c5ri1rtRsH/s4ZtVxPMZqyjYP0R8jc5Iy/OkYP/YA6f33szt6yl4/80eKr8v
|
|
WNG1kYLrjz3Qrid1bdhMwf2bPczYendihh/WZzIRD9Y+OSo7sD7G9tBVna9N
|
|
30nB/Zs95J0dzFmwB/NQ7GGFIG/S4n0U7B97CC5a2yMOppD7O+r2MCfg2spx
|
|
h7A+SvaQphg/uyQM88jZw8cIMYoKxzy9dhCseumlyTHM02EHBXvvz7pzHOvT
|
|
bAd5f7cvHx2NeertIMi5vt3/FOaptgO4bTTuSSwF+8cObg90fSo7Q8H9mx0w
|
|
5hxX7o3D+uTZgffxH+/743G85doB//23kXUXsD5ZdpDac7A+4yLW54MdfJ9a
|
|
NS/sMoXMb5l2cGbWAN02kUL212AHPas+3v5wlYL9YweTFsSbOF6jSGXnxVLt
|
|
YErLS4vr17E+KXag7ERLq7qBeZLt4O0iua9qtyh4/80O1hpM2KJ1G8dboh2U
|
|
hJ6Mbb497B87YN9ZJnl2B+sTZwfbw/z3rE7G+sTYQTilmFWbPOwfO9i/5PLB
|
|
JXexPhF24DL3iUvi3WH/2IF8u/Htr3eH/WMH0Qvzj5bcHfaPHfR71bZ+uzvs
|
|
HzuYbepcmXQX8/jbgV+i8qrlxGty/80OdmbrrfmXPOwfO1j5YGvdeuI1WX/s
|
|
YMLMyQNSYv3k/rUdSI/PONdze9g/diA4GvLCkHhNzj92cIFt4z3i1rB/iHi4
|
|
SL3QegPzONlBc+ph18fXsT4OdlATYp2w9Nqwf+wAKVj45F8d9g/xfS3n77IS
|
|
sT50O+DqXlqy5TKON6od0FxpnrsuDvvHDm5+8chddmHYP3ZwduvYW1rxWJ/J
|
|
djDI21R+5uywf+ygkukc0hGLeYzsQLI6M8z8FI43ih2Mf/ylgXYC66ND6Gfv
|
|
kzYyEuc3dTtwKD1X9zF82D+EHmkrDy75v3/sYCk8DHpycNg/tnC25Xx+LeFH
|
|
cv/AFpa4GF1s303B9ccWIv+YvP0RgPNbvS0IYz8uPOY/7B9b2LJLzsFwM84H
|
|
ZbZgGPHhXKA35im0BfbbaYuTvYb9Ywu/rUduf+qB4y3XFlrfnO04uxzzZNlC
|
|
RPjdovmLsT4fbCFu51Lz3844v2XawtSYU39YTpgHbMGsYE3LVsmwf2whRKmR
|
|
t52HeVJtQT5zdTSHgXlSbOHm6LS/721wvCXbQoByj9NYM8xzwxY2HZmYYjsF
|
|
x1uiLRy+ZDlBd9ywf2zh0/xJsQ9GDNcfW2Cc6tUdpT3sH1v46PvilFh52D+2
|
|
EFboNc6u3wD7xxa8K5qTa9pwvxNK3L+D6x286nF/EGwLiY9flSWW43oaZAs9
|
|
+xTDbxD1mDw/agu7Cs3t/b8N92+2MDGXXT34DvcHvrbwz8PmyiI03L/ZQkWw
|
|
lqcv0T+Q848tKLKyTefcNsD717Yw+8iurvpLuD9wtYXHm9SyFp/G/cEi4u9V
|
|
+28fPGqA/WMLcp0Fx7cfMMDPf2yhPGHCLrMduD9wsIWWfKeN172H+zdiffdW
|
|
rKleiftRDrG+S5ddy/4b7t9s4RvTxzHSAfNQbeH9rqeWlQzcH1jYwvdV4ZoN
|
|
ZrjfMbGFpoY/JVeNMc9k4vpTntxV1xvu32xhw6DetvEKw/2bLbwMabIsax2e
|
|
f2xhxt1FpYsrh+cfIh72syMDf+pj/9gCtzPJyvEd7q+VCD7DmPdvnw7PP7Zw
|
|
rlBpRfuN4fmHCl5ze8pyzg7PP1SYvXq716ojw/MPFfjj/AriA/Xx8x8qiA80
|
|
zQlbNzz/UGFVRFvK+MXD8w8VYth79TaI9XH/RoXcU0fWe9jgeS6PCmanDB8r
|
|
jcc8uVSIZZp2L9fE80IWFSiHpTSPruH9Aypc2/N7o37l8P4BFeYa7jy9/dvw
|
|
/gEVBl3jnoW+1MPzDxWMnA930W7p4fpDhbdyR/fsitXD/qHCWP+r/HkH8Lyd
|
|
TAX9SzkOKRv18PkdKtw8Our4jUXD+wdUKLbbNsqaN7x/QIVn8WXljtPxvB1H
|
|
BQupd0uzjh6ef6gQJ1Y/vKJRl9QnigraIb53Wl/q4vmH+Dy3d/H9SF38/IcK
|
|
D7c9CTm+Au/vBFOhbsp5+ygTXewfKnj/l+yT0qpD5oNAKph01UztRMP7b1QY
|
|
M9bFa1WEDu7fiPc/r5hWu1AH719ToT7nqu/ZsTpkf+BJ3M8NUYwN5Xg/0Z0K
|
|
t3cmHV5+W5uc51ypIKdYtXyLH95PXESFveqLUq7RtPH8Q4VZx+oiB7u18PxD
|
|
haXh9+uDXmph/1AhSe7S1zHBWvj8ARXs254z/4i08P4BFcqPH2PFKQzvX1Mh
|
|
reti9fQMTansfDyVuD/2beLwYE3sHyrcEx2b+4KH9+NNqPBlwlr5190aUtl5
|
|
5clUUMrev/bCY/y8xJgKixcU7Ji9RQM//6FC+uXdtu+m4+clFCqwXy9PMCpS
|
|
x/6hwqvUoCfc2OHnP1QIDSreY+ekjs8fEPGmH9bQ14efz8lRQXmXr/a5+2r4
|
|
/IENDN4/na+6Rg3XHxuY/FxuiZO+Gq4/NsCMubvXHVRx/bGBPfwLLg5bVPHz
|
|
HxvITfuc2z9m+PmpDTioCRSPvlXB/rGB7OmtxTV++Pl2ng24G/7dOGYMfh6c
|
|
awOGvyZeGZ8xfP7ABga848PavZVx/SGu/2nJqEs6w+cPbCBvcOHSsY/weQqw
|
|
gRalU2KfpUr4/I4NBFVbb1vaNXx+xwY+PnIKuh2niPs3GyjaWOy+nqGI648N
|
|
XFJvHn30Oz6PdMMGFsXsvz/STwH3bzaQoBI+Xl1Dgex3EmzgtZf2hrWJ8nj/
|
|
2gbu3taJMGHJk/1ODMFXcCx0YZYcfn5qAzntocsr18jh+mMDI9tadaF6kPy9
|
|
SagN/Mn+MSFMbfj8qA2cPXC/bPT0AXx+1AaSFA667hfi872BNqC6fM7Bh8v6
|
|
kIHMPzZgckjTPXVTL3ke1tcGNA5m1kXs7cG/XyDevzDA0vJoNz5/bQOZHcaT
|
|
L8d2kedh3W1Aayv6UHa+E5+/JtaTtnRq+6UOfP7aBhj5VdRfl9vx7xdsoPDz
|
|
lpbwi234/LUNzI1pXKdxrhWfv7aBA5brI92i8e81hTYA8T/W7Q1tJs/Hc2zg
|
|
e3zrYNGOJnz+2gbkfzd8rX3VSJ6Pp9rA6QlS/oGT9fj8tQ14qLs5BbnW4t8v
|
|
2MDqM6+aigxr8PlrG9B522J/+3MlIv1jA+rxjSMLd5fj89c2MEXvSczO8aUk
|
|
D8UGehdFrmzdUYjPXxN/z5J8ens+jzzvr24Dz6Oit29MycW/X7CBveaVt1M3
|
|
fcG//7GBvte5pcyFr8nfX3RYw45fv0c9sniIz1dbg3Byh2/A/lA++XsE4u/c
|
|
jEjKyad8Mv6tYcvC9xnHN73lk/XCGpKCFK7vjvvKJ+PbGq4e0aS6a/3kk/2U
|
|
NVDnHwjxP1nAJ/O/NZhWWc0viCnhk/neGkJCFnHPbCjnk+djrMFl792ov5Iq
|
|
vixfxFhD9Deuw48Zf/my80kR1iAOlXdfbljPH5DNC9bgH9ubF6D1j0/GlzU4
|
|
26xW+E+lmU/OA9ZwJ2nbmemRLXwyfqxhkcmTm2hUG5/cb7IGyTMTltGtdj65
|
|
P2sN+cs+OtoJO/my+Hawhm6lhO+6hV1k+uJYw2u4VHz3QA+fTKfWwDyW4609
|
|
o49PPt+zhlgvmp/Vz34+2U9Yw1en9+16Rwf55PxqDTGX3uzNvyInOC/Tyxos
|
|
Jkl5xw/KC8j/P58V1N36+nLiWgWBrH52WEEWq6cv1klRQM6fVvDzK6f3L1VJ
|
|
MFWmjxWwtp5+NsFYWSA7j5dnBUdHqNLomioCUh8reAPRfpZ9KgJyfrSCuB22
|
|
m5SbVAX3ZfpYwWLr+qmoSk1A5hcroDe/TFhWoi4g84kV8NJu/Pj2R0NA6mMF
|
|
64/e+mzxR1NA5gsreLzmdYh3kZaAPJ9kBeuE7Z2h5doCMh9YgXSawCKkTkdA
|
|
Pv+1grIuX43fHboCUh8rGP/fNb78IT0BqY8VXNf2FR/Q0heQfraCGU+ORled
|
|
1Sd5nIm/z5I3ZUwzEJB+JT6fka3p/9hAQOpDrMekgxk7kyIg/WgFg4E7HlzO
|
|
owjI8wtWsOHBnG1nNo8QkPOSFTTm7tofoDRSQPrLCuaXDnznJYwUkOfhrCAk
|
|
70/AP4YhySNnBRPTDNYc/W4okF2uwxK2hF0+o7N9lICsL5aQzj5suJdiJJDh
|
|
llnCwO/XJTlPjASyeMuzBIHX8naDFaOxPpaw++esxVy5MQJZvGVawk+7yH7n
|
|
m2MEpH8soWiPafOchWMF5P6XJdgmj7e2GRiL9bGE5e82PR24Mw7rQ1zvs97R
|
|
VDdjATlPWEJsuvaNZdrjBeT+lSUkx3rqlMF4Afm83hJeLNOFJYETSJ5AS/D+
|
|
UpcxaDhRIDtf4GsJ53dLRxjumCiQnY/wJN7/IOTH5pyJJI+rJXzYRlNWtZ0k
|
|
IM+nWMJZ6a+rpacmCWS/13OwhKlnN6b0t00SyM5rcCzhaXetpZvrZAHZb1iC
|
|
erXb6J4Xk7E+BN+qF9vzJ08RyH7/ZGwJNp5avL6IKQLSgJag0jQ3YFXLFAG5
|
|
X2oJn9WCximtnIr1sYQFyedsa99OFZC/x7KAk/k3nurbTcP6WEBBzLU7ey5P
|
|
E5D7NRZQ8euUzjTd6QLyfLsFZFzfWqJ3YDrJk2UBO+W4k/hN0wXk+Q0LUKrs
|
|
/JrsaULypFvA+sVX/638aYL1sYAXzvx9znNnkDw3LOB+7vvdB1/NwPpYwMNy
|
|
cWU705SMtxgL8NufLL2TYkrGW4QFqCQpq181NxPI+rdg4u+LnV8VXDfD/iFe
|
|
W4g2hU0xJ3l8ifW+j4vIvmKO/WMBR0yXjEubZEHyuFrAaufAKTOvWmB9LOAO
|
|
o++i33RL7B8L2FRZFcW9Y0nGG8cCViyjt96kWpE8VAu4dLz205PnVgKyflmA
|
|
fbjiaC+JNfaPBUx0PJj/IMtaQO5vW4BVJTU829IG+8cCOsKXFBoG2GB9LKAr
|
|
6o6v1Usb7B9zMOi0oxuqUMl8UG8OG181srIWUAVkP2YOmQ0FO5fGUwXk8xtz
|
|
8N3b++9eJVVA7peZg9Xm+Ym/qLYkT6Y5GMG3qK/7bQVkP2UO/IDwJ+c+22J9
|
|
zME70t/QbqydgKw/5pClfDzlgo8d1scc/EvzD/9MsyPjLcYcRk1wO1OiaS+Q
|
|
9acR5tCDtEvS3O2xPuYw5lWL17oH9oJ1Mn3MIe/j+eg+RRrWh7j+wfjvF1xp
|
|
Alk99TQHuapG61n3aALZ72FdzcGnMy6xS4mO85s5TE6Ns3i8kk7Gm4M51E9q
|
|
/LLrCR37xxyUOOcOz9JlCMjzWsT9kI9fauzDwP4xh64dTbz+NwwB2U+Yw4vT
|
|
F7hVk5lYH3NI87q4MC+YSeYDdXNoLWo/kFvMJPOBnDl4qV7N/CVgCch+2gz0
|
|
Cq9NrLzMwv4xg45VAzG9CmysjxmMiE4eP3Y9G+tjBqGbH4DkI1sg6x+zzMCw
|
|
S31PgDUH1x8zKLd+PufBaY7gnkwfM6gZgWzb+jgCPZk+ZjDjhpGtaB1XsE2m
|
|
jxlcrno/+2wWV5Ar+wIzWJybFdjB5AnoMn3MQLjZ7IVHEk8QK9PHDIIfFxh9
|
|
1eMLOmT9gRmU3CyLnLOfL3CT6WMGX+39nzTW8wVpMn3MQEfy3LpwpUBgLNPH
|
|
DObkpvWOzBIIDsj0Id7fkhY5b6JQUCbTxwzUeAEOdiuEAgeZPmYwb7bWNGms
|
|
UCD7PTjHDO6OCLZqyhYKNGT6mIFG4tfVbzVFAj+ZPmbg3dSfLpotInmMzaBx
|
|
UFXoGSYSMGT6mMG2r431Jq9FOL+ZQfuahxmn5MXYP2aQ+Hjhq0ShmIy3DlOY
|
|
/z67ZlmwWPBZdoNNQTnBlPUQxAKqTB9TyLdd/TBFXiKIk+ljChciti9eKpEI
|
|
+mX6mMLRK14TLodJBGv/18LdhjQVhQEcp1mCaFQ0VlrWwAbnBOWiJG3hE3q3
|
|
e7e7l0tbL0TZGOXszcCSykUFghVJi2iOXpBMvWVY+WWQJfYMLYJEwaxsBVoJ
|
|
C7+UYK03M+9DH++nw70/Dud/PtyHfDhW15gXhp+XQh/5cNylT+TnZQmwhnw4
|
|
Vh32V+9UBLhGPhxrL/R82hARQEcHNsdbFWmh7oQA5eTD8X260ZI0WmGQfDjO
|
|
Ls9eEQtawUL7h6NU96WAPbBCE/lw9EnFps0pK2TQvAWOzfVNqrDJBpXkwzHg
|
|
zX40fd4GA+TDMXKjdXftkA3MFEgcF1XYogPLRbhMPhynYr/9YwdE+Eo+HEvr
|
|
nnbFH4rgJB+O48PNd4PpEqjkwzHjfsPK1z4JZmnvkzuz3pzGjXNbJNhBPhzN
|
|
I52jWZMS3CMfjkcs44ZXgv2/D0dDTv7I3gY7eMmHYWboXNGTz3ZoJR+G/rLv
|
|
pg8WB3zTgvEjw8W9x1tehB0gkA9Dc/u82KkxB1wkH4ZoeLztV5EM72hDMTyb
|
|
FqovviSDiXwYPqvyeOWkDPspyBie3FPYbgQndGgBeXvmebgg2h11wiQFIsPR
|
|
flFvmnBCIc3zYKiKlXk+2QU1dEFk2F/S1iurLujUAvs0w634I5Wpc8MU/UDO
|
|
MHlodUQtc4NDC5aDDJf+XHJ0VZcbGmkgAcP5gfiVmzke+KsF7naGV+8sS02f
|
|
8MC+Hu0DMOzoW3tdTnjgrRbcAkMleAbjuQpsoQshwwVvSoZeuhU4ptOH161n
|
|
+KdtYtAVUOAfR1X61g==
|
|
"]]}, {
|
|
Hue[0.1421359549995791, 0.6, 0.6],
|
|
Directive[
|
|
PointSize[0.009166666666666668],
|
|
RGBColor[0.945109, 0.593901, 0.],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]],
|
|
Line[CompressedData["
|
|
1:eJwtmnlcTO8Xx5NokUiLSJbSRlHT7PtSWrWS7AnZsoUsyb6lflkifaMkEVmz
|
|
ZInHkUKkVCTty8ykFIUKhd8z3cc/39d9zXTv/Zxz3udzzjPfCSFr/Zeqq6mp
|
|
HdJQU1P991//Pxm03Ywx+enVhJhaDzN3/ZVBat31hiD/JlSx1r9D3ieDn7ee
|
|
XhwX1ISUzIK3dr0y+DEpb5nXgiYUPH+sV9AvGSS4Zk+sW9KEpjX5hSzrkUG1
|
|
VmLNh1VNKOnlYoM5XTJ4uWbFceaGJhQ0dMZCh+8yCNo6Sda7rQntyzKf1toh
|
|
gzibqq+We5uQ6d3iFwe/yGD59sjE7JgmNM5krlyrTQbNG4cIrp1oQnGVeadX
|
|
t8hgyIiYGu2UJhTWp/vlrlIG7wJ+by3MaEJ3opyqGppkIOXOHtGV1YTau4IH
|
|
qTfIgH3//EPxoyb0X99jPetaGSTC+wNhz5tQzjGPHt8qGYQEfI3Y8rYJ+d0d
|
|
/GRnhQxOres4vKSyCc1Z9m3p7fcyYJp8zHWQN6EPGUPbPpfKQORxeWxNexN6
|
|
HRHkZ/tWBncGL0pZ0dOEHN+Vnlz1RgbHpqtJy9XkSBe2P7j1SgYfxx7UttCR
|
|
o7ncwEd/X8ggZlvXDx8DORorW5jiky+DS8GeGvPHyNHMylMLL+TKYGrJIZaH
|
|
pRypqf6BDMYXXosbOUWOJtw5tXPhYxls93uonc+UozvdC2qfPZSBbNH1S/4i
|
|
OXr8YuYY+/sy2NgbvQpc5YhjvZ1z+q4M9MZP99fzlaNJRqUMvdsyMCjumccP
|
|
kqOjx2bpH7gpg71ah2M8guVo+RndQvXrMphXOLCWvVyOshmdS/ddwfUweukM
|
|
zXVytHn+oDqdyzLw+X7ty93NcnTVwJ2VcFEGoYG1V513ytGsoEdrrNJl0Crr
|
|
jrt9QI4iJi/cn3NOBhU5XSfU4+RI63+OkTPPYn2oGjmelKOnlcmbOs/IwKR4
|
|
ZLbnGTkKDNdLik2SwcNwg4lzz8tRfsDeT1aJMjC6XKwVnClHQ3f2BcNJGViF
|
|
ey2ZkyVHjj+2DpwdL4Nvb6KZHvflaMrt3uKOozLY9OjgzqlP5Gjwo93PD8bJ
|
|
4LZgmkjnuRzd19NtNovF8fbL31RZKEfOV5Icb0fLYOZPDYvUMjm6dsz+outB
|
|
GTx2HOQ6t1KO2p/mOVftw/X8J79hSIMcafODh67Zg+83z/V7VjPJzy4cf+/o
|
|
yOlf5Ojt0PQxx6JkEFsas632hxxtX+q1eEKkDP7X4t2xpFeO1DV/ld3cIgO3
|
|
+NLq+gEKFPzt8hpRhAweFBuL/bUU6LT1Qqc3G2SgTDEd/UBPga5fNDGfsx7z
|
|
o9aw0shIgVLWlnOVa3C8u0Jpy0wVaNmexKj1YTLI2X5t3fUJCqRTt6C1d4UM
|
|
ChLuWH62VqBD+21371+G+ZJt9zObokD1m35K9JbKYOhejR/OdAUyuPnaLiFE
|
|
Bs4zpw8N4SrQePp5iVmwDOgPA5M3ihXIj13x5/x8GexDx6q2TlOgjm/PaifN
|
|
xflcs/bfGi8F6l0cKs8KkoHj669aM/wVKCLmiR4nUAZHykb8tAlSoAUriudD
|
|
AO4XBysK2+crUNafkyWufjKY+0l8MG2xAm10M1hZ7I3f94entesKBbrg7mo9
|
|
y0sG/Gu/rlatUSDpAJp2nTuOt76HSfBGBZq+tmzYMlcZOJgLVrzbqkDP4yfz
|
|
vjrjz2tLz7J3KtC1NdyYzVIZcF2HPIrdp6DyI5bBi7nKx2+jFeiZ6/b/Dglk
|
|
MHvMkgsaRxSo0+XGLH2eDDoO7Qu3OaFAcb8TuUlsnL9zrpb8/xQocSlHasGU
|
|
gV3otceiFAUafvDomqtOMigrv8tzOq9APxakPGE4ymDH9+CzxpcUyK09hPFk
|
|
Cq7vR9c/tVxVIG1abbGbnQzkDmdHXstSIKb98COltpgnP5pdcLYCldX+DJ9n
|
|
LYPgscutBuYoUO20xEjlRFzfp8SDE54o0IylXy6tM5fBl5yc1yZ5CsTm9v7+
|
|
PU4GKPZjRMxLBTIzF8zbb4b1Roxc2l6oQKe20u4NM5WBjuLbd0EJjqe4akiS
|
|
CX6fj6ssot4rkOtm1pyJxrj+/fd8z/yoQFFmrmnXDWQQ4cdc8qIGf+6kI2fr
|
|
4/74/uCm0gYFunh/17hnerh/1EVYFyrw/a9lzpiuK4Py1QO33WlRoLEjDu39
|
|
oC2D7t32q2PaFYijNLm6SBP3b9MuNb9OBfpkO7/oswZ+PncOY1CXAtnWzGjd
|
|
pC4D99p5Opd+KtCA/gRh3jX/7OT0KVDY8QXDDv+Rwo5sbsKDfwq06sQ6E8Ne
|
|
KZxsNZpuM1CJ/g5imqb8lIJ6elz6/sFKZNl8faRNtxRyG9PPlGgrUQOrauit
|
|
71L4cDGIoTtUiRx+PvzD65SCqOPyGsZwJTK08W7O/yKFPyjRbbqBEsW+OPHK
|
|
p00KwwwsnwUYK1FieVzGxxYpbGzzrnUbpUTsmfwdi5ulMNXTOMlujBKtliV7
|
|
t8ulIJwa2f13rBIxzmWZbG6UQmpi1PcnE5To6Jqt1Wr1Ugg8aHZs7UQlynO/
|
|
kHy4RgrXfNJSdK2VSL9EsdCwSgqtLgGfT9oq0WYNnkVKhRT0VzpsHmKnRD+b
|
|
0puty6Vg/ogjXT1FieLXWlzLKpOCKX+tV46DErllZG/gleD3b3l7souG9cQs
|
|
4OUXSeFF/oKxYxhK1DvaVMOnUApbik2UU1hK1BfY9qaiQArGmv/a7DlKZCIq
|
|
TQx5IYXTYfpOo3hK5FVWuKQtTwraar73O/hYv0G1Y0SuFBY8fbj9jlBJ5Qek
|
|
kHzTb9cSsRLtSWQXRz+WQt4bw2dqUiUyq9l/1iBHCuUmGi7RMiUqfdO8Lvm+
|
|
FN4eGzf4r7MSpa5cILPOlsIt9rLBC6cp0aHbLcZZt3F+h1a5XHVVouhL0Z+5
|
|
WVJwGB6Zp3BToovuwqd516VQJHbdM8RDiaoSNBO9r0oh4Kxop5mnEk06qlhb
|
|
cRnne/KSHFMvJTrOqHALyZCCifIOc/B0JTI6WGfeli6FOUWOndX4+ua+3j+b
|
|
0qSwW17ZetZbiUKn2FX+OyuF4zY3LXx8lGhEeHF2dLIUKpZWeLTg6ziBLN7g
|
|
tBTOLNs2bLWvEtUcPbg2OVEKdfYJ6yvx9d9VZzytE6Rw/v7k9Y5+StRRtNs6
|
|
K14KCk2eXji+vvuANZB3TAoXTfPczuBrDztUmxcnhebvz8ffxNdZVkYPvWPx
|
|
50dlCdfwddsl/smKaCnIOzmXT+Dr7lv0dSEH8f1HZs5eiq9Lnf94tO2TQv2A
|
|
Exnj8PWuBQmWEXukkHSz5/gz/D7949tOKby3eG/qh6/9bLmV0VFSODrXTvoS
|
|
64modL5jECmF17P+DLLF1ysNxsclb8HxMHFbtgHHg/bu9TLrCCk8TNYNzcDx
|
|
ejnGTZK1QQrrmj3U83F8ndpPjOatl8KFLnV+IY7/Opdb3/PW4Pi+pBs8xvmJ
|
|
skwt9A6TQtzC+oOn3JVo3v8WXKhYIQVpzqCkuTifQ6Pao0KWSWFDVbq7Ns73
|
|
0R9egW1LpGAJjxNSXZRI/n37lIgQKcxY4bt7Aq4XnciowWrBUhj0YZ52LK6v
|
|
hKCVtdHzpWCTnp1ai+tv/NyF2QZzpXB3leODkSJcL3vmxSUHSeG6/Rt/lkCJ
|
|
rIsXhVoHSkGvNXq1ANd3unitMCsA5zd1mfYkXP9mH/YZ8/zw5/6hVn+YmK/j
|
|
aV/yvKVw5c/+vGy6Eg3c8PK5txeu1/PPmwIxX+u3dKdUuEvBwtlmX81UXI9p
|
|
dptDXKXwrzbzgoe9Ekm+rfRpc5aCbKO3W8okJUoLzcLhlELHQIOwCsw75T+Y
|
|
r7ifw3/hfjAbBVZEC6RwaMQ/ppo5rs9zd28a8KSw6ZhVbTvuJ+qZY6KT2VJ4
|
|
pbN2cK6pEvl8iFlkzZTCgR0VN7abKFGS7UBulpMUbraFVJoZKVFd6p4RPEcp
|
|
iGfqHbigr0TmAp3PeVOkwL9fectAT4mC//73zNsO9yejl8HLdZTotNzxTIUt
|
|
zu/q8iPncf8s+VqyMcRaCpeeDBLnq2P947dNb5soBTfdwPVv/ioQbdMkqwhz
|
|
nJ+AFxaPfivQ3K+Nf/+Nk8LLE7NnHetWIOuClA/RZlKYIvXmeH7D/iSYfdPA
|
|
VAo6b5TdzdgPjniOiE42kcI8hsXRZdgv7H8ULLI2loJV5MBBr+QKNIy1i5tl
|
|
IIWlKQdnDqvH/mHIMODpS8Hs7I3drCoFuhTz6XOenhQ8oiKjpeV4nkhOyvPW
|
|
lcJX9ucwB+xvs909kyu0cXxL/04egP3v9JHfm0I0Mb9u2c/vPFegCesuebdp
|
|
YJ7O6As8nypQe+sM6wh13F+Lhh/JyyHzgRruHzW3H43Hfhx043JF9B8J7C34
|
|
nb/wpgL1/PTLMuiVQGi8InN3pgJVV/+MTv4pgVzuxlUH0hVIc25KiHW3BI4/
|
|
uai5Bs8HmzdIeVnfJfBxQtROdqICTbFSGPA6JXBqUU+p4pgCTdpwoC3viwQK
|
|
dxipR8Rgv5tjle/dJoEtWz/otuB55UdVXnJFiwSS/ATfhTsUKLdnUURIswRo
|
|
mq53N29WoPJrf7zb5BKQJv3wj1+nQA5/T1lHNErgpc60wmN4fir55KCmVi+B
|
|
50G8CRtCFEgmKqiIrpFAw4TJ9oy5CmRStijLoEoCMDDs9fsABfJM/x2dXCGB
|
|
xX//9M7A81ztrfgQ63IJvNZvQLecFaj0rx0vq0wCPQIjw698nO9Dzw14JRL4
|
|
tCepV5uhQDXewW15RRJIrl+3aaC9An3z/53nXSgBo1mJu6sm4vn0xInkigIJ
|
|
BCiHjz8+RoGEBlMjQl7g67hKX2tDBdpQXODdlieB0T5dBqeH4Pm1YIl1RK4E
|
|
0m0WrWhXJ/MBSODb6LF+Y3/j/WLj6YroxxIYZGX32r5TjoZZsbIMciRQ7R7z
|
|
wfSTHFkblUUn35fA1gO8iE+1cnRWsjbEOlsCFVX8jPj3eH+5MoSXdVsCfe5H
|
|
Vprh+T/L/5IBL0sCyrc02J8rR+4sl7a86zif66wvFeJ9Qjq7Mc/7qgQ0bFeb
|
|
f7suR6fv70yuuCwB9u+BU7vT8b4y0ywiJEMCdPnnNxVJcrRuao53Wzp+X+XE
|
|
f/8dlaPWabOtI9IksFH9Ri4H70N5p3v+/TsrgYfMwyb3I+VoiE5CRXSyBDb1
|
|
aUWOWC9HhavpWQanJTC7MGrJtFA5GviiNDo5UQILL356FzBXjm4brQ+xTpBA
|
|
7GH3Qi7e56pmD+NlxUugbkuqR6+zHEXGXzPgHZNA4Pp2n5McOTqe69mWFyeB
|
|
7xscqrXw/mjR3JLnHSuBe7tWfJ1pLkeTBxxKrojG+TuVGL3dGO9zw60iQg5K
|
|
4Or9x5nb8b56wSjPu22fBOqbKvwD/zahkcNDrCP2SIA3qnW39rcmsv9IIDuo
|
|
k5WgaEIhCny7KAnMS/uysa+iCfGAl2UQKQHL7gY2v7AJ/e/ox+jkLbg+Zrze
|
|
O/NJEwoK3IxvKIHJjzJnut1qQkn6RrysDRJYOmXXdcMLTWhG7i0D3npcz5me
|
|
cQ9PNaFDy33b8tZIwMtxaBfncBOiaeD2HYbr82le4/HtTSjwZExyxQrMw7zw
|
|
WflrmlCHqW1EyDIJoAHGASXBTUgj8bl32xIJVN288T7bvwkd1cb1FiKBMStF
|
|
dZucm9CJdbjigiWw3z5/rR4Tv39ZSkX0fAkwO5bHRVk3oSwWP8tgrgRmZvjj
|
|
ptGEupKxniDMl/+emHLtJqQ1GOsJxPX4rWcF/G5ELWsNeVkBEnA5eLsm6nMj
|
|
SqrKMuD5ScB0+F2lXnUjGuXu05bnLYHg//Xt21DYiJbcx5deEhj+L/r+lUeN
|
|
aLft4eQKd8z/0vm7711tRCvP4Nd1xXqeRNQlnGlEFvq4fTjjetIrL3WPbUSZ
|
|
B3E4pRKY6B85921kI8WPWAK/o0O3TlrViCZuw/kRSECUfcouaE4jGtmN2y8P
|
|
12u53qbZ7o2oYgMuR7YERrS99p/CbkTLv28KsWZKIK2rKL/cqhE934hxcZJA
|
|
yveRRf5GjehHD7YvRwnoKC+uShvYiL5sxzhPwfVSGJmS39mAHgzEeuwkYHMp
|
|
IfRRXQPyjcXtxlYClZt7nh1404DuG2M91hL4y0vJnpjTgNrTcL1NlEDcj8PC
|
|
hEsNqNMB6zGXwOFzj+dWnWxAzwDPO+Mk0C1l6v3Y04Bm+mE9ZhKwvuz3rnpt
|
|
A0pswHpMJbAzPczu+LwGFLse6zHB36cfNDZ0b0AOA/DjjCVwbM654yGMBrT/
|
|
KNZjIAFvo5zUqAkN6PA4HA59CdgvfSdeOrQBia9jPXr42qM9fNSvenSRj/Xo
|
|
SsAvbxArSV6PHr/CerQlkFBm9r/m4nq0Pwjr0cR6NjM2DcipR38VWI+GBA5l
|
|
eX1tvlCPbDZgPeq4nnYt7k06Wk/8RwJq8q3/jY6sRzGxWM8fMXyrPlIQurQe
|
|
PTfBr9crhkGrLsTs9KlHt9Kxnp9i4MY9rFvCqUfeDlhPtxjipxXnG1vUo9M5
|
|
WM93MQw50SQ4qVuPEqdhPZ1i8Gv/cgQ+1yHXEqznixgKq41efn1chy7OxXra
|
|
xBDXzZt4/0gduqvAelrEcIK7KH3Uojq0aS3W0yyG2kv73QxpdUj5E39dLoY1
|
|
ksvDL6nXIa09WE+jGMQahX3vSmtRpQ6WUy+GOZ3tuqfTalFsPNZTI4aOntSf
|
|
netrkccYrKdKDDLNzZtLxLXI+ALWUyEGr3HrojnDalGHPdZTLgZDceyUSTU1
|
|
qCIb6ykTw8kVr0PPZ9agIhHWUyKGt6ftaRc216C3L7GeIjG8KL91dKpzDWrw
|
|
w3oKxbBh9Nw90uE1SK0K374Av3+olWZtVTWapML9hRjUHhmOU8+oRkvbsZ48
|
|
MdSPsnp1fX01uoIfH5Erhq275mjJedXk/E0MeV+zPp4bVI1C8O2iH4uhdJmd
|
|
8FNRFSodgfXkiOHMpwLGvVNVyOcM1nNfDKPDD4NecBWqssQ3zBZDkMaa2i/W
|
|
VWjjDaznNtZ7duORWV8r0WgO1pMlhr/SlDK37Er0Jhe/znUxhH5tzczdXomO
|
|
emE9V3F+0ucY5Usr0YJy/AKXxbA6pH2Er1Yl4gdjPRliGGx7/vziNx+RZSvW
|
|
k47j/zPyxb9jH9FYPN1FpOH7vd28Y2LgR2T+F/NzVgwOWQkvS0Z9RFNU7T8Z
|
|
v8/gT5V/qisQS6XntBhCeJGtKWcrkEClJ1EMy3x9e+4sqkBSbA/WCWJY7LJs
|
|
gNiiAjlj/LPixeA/GrTE8g9Ipmonx8RAK54z9G76ByRRhTdODDpLWMPOLvmA
|
|
+PjSOxbHr2Km3l+LD4iuSn+0GI7ZZ+uUNpajSfh1Qw7iegoJ0jA9V47Gqspz
|
|
nxiaI/i9FQvKkb4qP3vEsGdVyNchY8qJ/4hBU/yq/nbFe9Smul2UGA7/2FD8
|
|
9sR79EGFd6QY/h1amBPi+x6BSu4WHI8/sekrhrxHF1XtJ0IMyK/vsCL/HTqk
|
|
SscGMQw7cG1N+c53aCX+c956nL+kVB8+5x1yw+02b40YouPe24/8VoYsVe07
|
|
TAw3Q7y0l2WWoX8qPSvEUGI8qHFySBn6oNKzTAwtmf/uLR1Vhq6p9CwRQ/tY
|
|
fozh21K0S/X4EFx/4Q/nsg+UIj+VnmAxvLu4zbaEV4rMcfuPni+G1m7nBWUd
|
|
JahTpWeuGGaebVjsdKEE5ar0BInBNNWX2xlUgk6o9ASKQfTrWIOubglaqtIT
|
|
IIZHmRdmH0BvEUulx08MR+7EpM1f9xZpq/R448+NnR8dn/AWVakuvcQQm5Y8
|
|
3TO9GN1Q6XEXw4KXs/LsNIqRCvcQVzEUpGRXF4QUoVkqPc64X1k+TDCHN2iy
|
|
So9UDO/nh3xjjnlD9h/cf6bd+Dp4cyF6r8qPAPerutS4429fo0yVHh7mx5ZV
|
|
/NHmNdql0sMWg8/E8Kzqna9QoEoPUwxXi/0Yp98XIHuVHicc78nlc4wmFSAN
|
|
1Z874nyz/03wjHqJqlX1NgXXW3fhYX7xC3RHpcdODIwlopMt416gWJUeWzEY
|
|
7A2U+K99jkJVeqzFcMt/xJGIx/lIqNIzEffPsvAdgTr5yESlx1wMvwZuGfZt
|
|
Zh7qVO3b48RwUTFB6p76DKnaf7SZGC7kX88Qt+Siiyo9pmI42jmv5JFDLqXH
|
|
BPe7FXZPHkc8RXNUjzPG8bMzWy/LAURX6TEQQ+qWBUWn+56goSo9+jheU/Ol
|
|
D3ci1KzSo4f1R60RNf57hJ6q9OiKIXfxnDyDqByUpNKjjT9vOFTi3fMAqXAP
|
|
0RTDjJ5fofFr7qPpKj0aYjiXfm1fQ2M2UuEboY6/33J+EmfGXeI/Ypj3vDoo
|
|
Kfc2uqV6nV4RDOMFDRs05RZStUvrbhH4uhp7b024iYxV79cpgtfl9pO+9FxD
|
|
r1Tv0yYCmfedl32PMlGk6vnNIljc9WTz2O0ZyE71vEYRFL/2ZQUw0lGtKl41
|
|
ImgsCdU8/SkVxaniUyGCXXoabz9PPo3EqniUieBEhfOtF9tOoG8q/UUiCFMf
|
|
vyo+Mgap7K+iQATrrBKWvSiLRAGqx+eJQK3uXtqw8eORRn+/FsFLa0mL/YBI
|
|
4V2VnhwR/FQ/G7NibowwVKUnWwRbh9sl/Lt0QjhSpSdLBJd6ln6efOu0UGUn
|
|
3ldFcOg0ajyz5Jxwi0pPhgheNLOPG/akC21VetJE4Fk3QSPq6CVhpUpPsgjy
|
|
9m5llztcFapwTU4UQXuZaOr4ihtCVTvMiheB/3LuRvtnWf3llRcnAi++Lu1Z
|
|
8m1hSn//E0F+qJFfSeRdoU9/vxOBYfPMklnz7wmp8x0RXHn85lag9IHwZn8/
|
|
E4FJ6/auN5NyhIv6+5cI3oQt/u+x8WOhYX+/EoGZy+4Uy8FPhKrHeYdh/ZxV
|
|
6nu3g3BTfz/Cz9/uGHpj81OhZX//we+/Iv73qY25wg+q15kvAi31Y0/4G54J
|
|
++0hSARHXCbdTd6QR+kJwPGmL6x6uCmf0uMtgi1vptJObH0u7E+nuwi69c88
|
|
sN35QthfHs4iODMgfX3kgZdC9f5yE8HkM65zoo8UCPvrjSeCsetHNm1NeiVc
|
|
3M87zs+w9MgNGa8pPY4imLu53SIiu1D4op9nEeRe+l61+8Ub4eZ+fkVQdD77
|
|
fEJlkdCmn1cRSJYzI+98LabyY4bjEcnJWr33rTC2n0cR1FplXx00vEQo6OdP
|
|
BOtZ+g5pySXCL/28ieDeVQ+ezK5UmNrPlwhuHAgp+pRTKvTr50kEsflBLce9
|
|
yoTU+bUI7FbYx0pqy4R3+vkRwo719dk/1r2j6q1bCHtr16+4qvFeSPEjhLCb
|
|
DeeX//ee0tMmhNHNU0Ntp5ZT9dYshNA9825+yS8XTurnRwiH9izbc3/+B2F1
|
|
Pz/4/s2+1Qe6P1B6KoRglWWCZh+tEAr7+RHC0Tpk7Tj5I6WnSAgoXDZq6IuP
|
|
wrP9/Aghd+XF4+2LK4X+/QkUQsSL5vjSAVVUfkAI7Yc0zR6lVglv9/MjBJu0
|
|
sUoQVwv7+0G2EASDp2X0NFQLjfr5EYLm3ajg4H01lJ6rQjh1PV+/17pWuLWf
|
|
HyF8+WaW86KwlspPmhC09hyY9zy8jvAjhAHX/23r1a0XxvTzI4RAcd4zu0X1
|
|
Qn4/P0IY9vOoVs/desKPEGzfL3WfM6SB8COE2x+kBwIXNQh9+/kRQsI/6yef
|
|
7zUIqflACAovox+jhjX2h8cgUghHnuhYNoQ2UnoihHBxlpa/5Ekj4UcIQ4z0
|
|
IrkmTcLn/fwIoaXHNLVwfRNVb8uEMF6N9rTndZOwv5+GCCHP3rc2x0ou7H+d
|
|
+UK4uyuix2SPnOoHQUIw/5WuO6xWTukJEII8ocoshaug8uMtBN05oyc/P6Wg
|
|
9LgL4aR0Ef1gl4LqB874fX1vchoClJQesRDq9mry3t1SEn6EYMzIP7t6RDOl
|
|
hymE+49cix+GNxN+hPBm9JGCnLJmSo+dEFg+p+PWMT5R9WYthAlzwsZ+PPWJ
|
|
8COE5Tz1rV2/Pwk/9vMjhInf56XkL2ih8mMiBPru7XHuz1qE/ek3EMIzRbD7
|
|
bptWwo8Qbo3XKQ6La6X0aAtBh7ZlnG5XK5UfDSEUjrrCXTjvM+EH57cibXxo
|
|
3mdKT68AEsMWloy3bxP2v163ANI+1HsdSWij9HQKQGeUdXyWWjvV39oE8MmB
|
|
ln5wVTuVn2YBjBynvkv/Qzulp1EABU0JVj6yL5SeGgFU7Og4Jb75RdhffhUC
|
|
8O7Qe6cw+0rlp0wANPa3SmHsV6reigRwODDpqmfvV0pPgQBSL+ydeIDRQenJ
|
|
E8DUmDFBsLqDyg8I4HvVyPUzLnZQ9ZYjgDtB6v4edR2UnmwBWOQur7ls0knp
|
|
yRKAu4mnwQb/TmH/OHZVAJZzL3+/ENsp7C+vDAE8Prx3h/RFJ+FHAH8vfrzt
|
|
pv6N0pMsgIE3r8TfF3yj9CQKIPvCL7PjW78R/xHA+EPP/N/f/Ub4EYB4ljZt
|
|
z7dvVL+OFoCZweucxKnfCT8CyMzR6jBZ/Z3wg/X45hapX/lO/EcAn0t7ZgW2
|
|
fKf0ROB4SC7HGNj8IPwI4M+Z8hXcZT8IPwIYp9j57dXFH5SeZQL4MuqCZb7y
|
|
B6UnRACbeNMG2lp3EX4EkOW+OKZ7WRelJ0gAV5z7Httf7qLqLUAAM+z0Txe1
|
|
dhH/EcAttTTzj3bdhB8BPH96fcb0td2EH1xPa1mOk291E/8RwGgd/v3wrm7C
|
|
jwA017ywsuf0EH4EMGaL/MHiqB6qvzkKYKFN/Hrj3B7CD47vjrLpLpo/if8I
|
|
wCXygneH109qPjAXQKeZ9saR8T8JPwIoDP37+OHHn8R/BIBm7rerHP+L+I8A
|
|
FK3JTzYt/yX82s+PAGyt3Db/7+Yv4j8CiNfcFzDh1y/iPwKYeMRvhqP0N5Uf
|
|
NZyPRze3Po75TfjhAxw99yz//W/KT7v5UKgzkeYxvpfS08mHH5PY+R6reon/
|
|
8MG7s2b7i+xe4j98uD/faDao9xF++DB/Xe1shk8f1a9r+DDWlrPT6kwf8R8+
|
|
DD5kWRDf0kf44cOI/51nRbH+EP/hgw/79qvG/X8IP3y4FD1jT967P5SePD7Y
|
|
7D64wHziX+I/fHgz1mth34a/xH/4MOa+ntv8vL+Unmw+bEjjVfsY/SP+w4ff
|
|
NaWm70L/Ef/hw/GV7wa33v9H5jd8/4mpRS8HqYn6yzWND4d5MWuXTlUTUf7D
|
|
h/2Rk5Ues9VElP/wQUu+i7Z1r5qoPz/xfBi1KWZGxzU1EcUPH+5N8fS6WaEm
|
|
ovyHDy3DYdSDgQNEFD98OG/a+khn6gARxQ8fOrwLGBfmDBD15yeSD88z5+87
|
|
dGCAqF9PBB+mTs24dOfWABHFDx9GV19Is60bIKL44cPZrNnhzUPURZT/8OHK
|
|
jdyRX9jqlJ4QPriU1x8XhKqLKH74EGZ5p+l9vLqI8h+sP5mvc++puojyH/y5
|
|
YNvghq/qIsp/+CAcvLoiYOxASo87H870GO4aNn0gpceZD3H64X8Mtg+k9Ihx
|
|
fGbs8110ZSClh8eHT8r/3fpTOVBE8cOHgd/ezvuqoyGi+OFD8KbpPkyeBqXH
|
|
jg/t6wYeLl2lIaL8hw9P5d90885oiCj/4cPrt6YVOkUaVH7M+GDA2PH54j8N
|
|
Kj8mfDihP9o10XEQpceAD0GhX1trFw8S9R/n6PHB3+lv+baEQZQebT5Eb5k2
|
|
JKxgEKVHgw+9jJcHb/UNElH+w4c7q/Z6eTsMFvX3t14enBm1ZbZoyWAqP908
|
|
yBNdvL4/cTCVn04eTKod6jXhzWAR5T88eP7juuMIdU1RfzqaeZC6N3phEEuT
|
|
0tPIg+zDye+/h2lS+anhga7O53h5miaVnwoeHB8QnjTpoyalp4wHIetpLfnD
|
|
tKh6K+JB6Gy7XdnTtCg9BTzIeLBwYV+UFqUnjwfmxwsPnLqrReUHeFDfGN59
|
|
sF2L0pPDg+EvFxW/s9QWUf7Dg+75l2j7F2hTerJ4cCx92vj/TmmLKP/hwafT
|
|
/MThJdqi/n0hgwdtssNJn3V0CD/4+WemWk9y0RFR/sODkRfthIU7dUT9+0Ii
|
|
D6TBu+tKHuqI+m8fzwOD1/ZDeN06VH7ieJCpdHyqSRsiovwH3//W/waw1wwh
|
|
/PBAOVVS+DpzCOGHB0nzvSY8ax4iouY3Hgzi31Aba6lL+OHB2NcrVlaH6BJ+
|
|
8P10ti/4m6pL6QnjwZpeRfXeOl0qP8t4cO1MhiJs7FAqPyE4/l9gy4P5Q0XU
|
|
/sMDbqdjworkoYQf/Hn6b0FUzVARtf9g/Vqm636Y6VH58eZBsFm8XfECPUqP
|
|
Ow9qG0M2DE3VE1H+wwOd2YedbzToiSj/we+3Uzv1jsUwwg+Ot8WGU5ahwyg9
|
|
TB6s1Z/D17k8jPDDg/VuKC6kbRjhhwfb5D6uI02GE354sN39nxmLO1xE+Q8P
|
|
XAJWvz46b7ioqp8fHrwYkOQzcedwwg8PRszcn9l5bjjV3wx4MGr61OqfecMJ
|
|
Pzj+LafknE/DRZT/8GD15CfP7gzRF1H+w4NH+he2rpiqT+VHjQeFZ9wHBwXo
|
|
U3p6uXC68OqKXZv1CT9csD1XdL7xtD7hhws7Rt+4swP0RZT/cCGW7X1mhkKf
|
|
0tPMhZDeK3OW6Iwg/HChO+Tl12tTRxB+uOC99vxcx5kjCD9cWDRekPJl2wjC
|
|
DxcEESfvKVJHUP2tiAvl665mGL8YQfjhwtThe9bsbh9B+OGCxwxjXStDA8IP
|
|
FyYLVuzS4BlQenK4sODlJ48JIQaEHy5s+67+eVe0AeGHC/vQvWALvEhS/HAh
|
|
ylbzqtZHA6reMrgwn95Z6DDAUNS/L6Rxwbpu07PTtoaUnmQu1NqePOLubyii
|
|
5jcu7Df0ceRGGlJ64rkw9Oz5S6vTDUWf+/nhwuGC411NbwxFZ/pvwIX2+DEm
|
|
yT2Gov5w7uMC/694+H8TjAg/XIjQUqv94GlE+OFC6q3Zu2dHGFF6IriQ1Tf9
|
|
t9k5I1F/NaznwlVltZtloRHhhwsn1g1evbbHiPDDhbCkV6F95saUnhCc3yW2
|
|
zEJvY8IPF0rfmFfVbjMm/HBh+YfsmfQMY8IPF9p2KS4UlhkTfrjg/+r66wy1
|
|
kZQedy5cvz3iRb79SEqPMxc6+PqJVnNHUv1azIWxoZnCV4dGUnp4XGjNun/x
|
|
bvZIwg8X9M8bP2qXj6T0OHLhICdvR7iBCeGHC36bnn6RSU0oPdZcWBuopxuy
|
|
3oTqb+Zc+FSdWV6YakL1NzMu3NQ65b3vrQnhhwuFH0s3HFIbRfU3Ay7wfBdM
|
|
++gwitKjxwWtMM7ziEWjRP37tjYXxtgv+R58fBTVDzS4cCS+9s2pZ6MIP1wI
|
|
OntppmnXKFH/vNPLgXW+uYc/W40m/HCg8uLk1VqzR1N6OjmQmibvWx8zmvgP
|
|
B+7I2jk2aDQ1HzRzYMxhl4mTO0cTfvDfb2rP2TbRlPDDgW+DFWojg0wJPxwI
|
|
ENh9/xdjSvjhgOGoZ8cZYEr8hwPmSZfr7v0wJfxwIBbqPh6wHUP44YAodunu
|
|
tAVjRP3nVU844PuHW65zYgzhhwMXNreOzi8YQ80H2RxwXPj3WPm/MYQfDnTd
|
|
juCJmGaUnqsc6N0UMPJfmBnxHw7QLpywNE43I/7DgTQJN3RflRmZ3zjg7en8
|
|
0d1gLOGHA4zcWztCPccS/+GA58X9gZV7xxJ+OHCx51HwhUdjif/g72cHJb/o
|
|
GkvlZx8HNBqDdCVTxxF+ODAw8vE1/RXjKD+N5IBs94HdnPPjCD8cyP5x++D9
|
|
mnHEfziQ1Woe7Ko7ntITht9XP8Wo1nY84Qc/b63nklTX8WR+40DwwMlecUvH
|
|
U/U2nwM2Rfw3GXvHE35wvIt3NbedG0/mNw4c0+xJmg/jyfzGAbuIs82/aseT
|
|
+Y0DK0y3vXn6ZzyZ3zgg7jngdXfMBMIPB25rP1/yjjeBqjceB961o7cT5k4g
|
|
8xvWI/zlkbptgqj/vMqRAzP6Npb5JE0Q9Z+P2nHgphVtpcPDCaL+8x1rDrx6
|
|
7DBMWjmB+A8HMp6uy933ewLxH1wftG97f442F1H7DwdODLsbkMwzF1ELMgcu
|
|
z37guGGeuYjafziwc/g/s21R5qJz/fxwQJd+wORWirmo/7xKgwML87wnmII5
|
|
md84sPFpEPtug7mIOn9jA3dy+vxdAy0oPd1seDvA8dh2SwtKTycbjF3+lV52
|
|
taD0tLFhbJeehdZKC+I/bGjWD959KtZC1P97RiMblp/+1j7rhgWlp4YNN489
|
|
X+5eaiH6X38BsSHrR1Xnqi4LSk8ZG8LyaNFPTCYS/2FDj9rrKc78iVQ/KGCD
|
|
Q2Z646+FEyk9eWywgyfp9XsnUvMBsKFVOmbTz4yJhB82GGj26DoXTiT8sGFN
|
|
Q6zl846JlJ4sNvwqqUE7jCwpPVfZkFHRUrGaa0n1gww2/K/r5ob4hZZUP0hj
|
|
wzEbpyNf91kSfthQuH7d5D2ZlmT/YQOtZLmb51tLsv+wIXvaGKVHtyWZ39gQ
|
|
XnpYY/cYK7L/sGHexjvn26VWZH5jwzK7/54dXWFF5WcXG67+Zi9ZedSK7D9s
|
|
GFYXv3/bPSsyv7HhysfL1k9rrQg/bAht3eYhHGxN/IcNM/U1v3TaW1P5WcaG
|
|
9d7eI6pnWpP5jQ2Xz/ne64uyJvsPG0yH6NUEXLQm/LDh4eEDexuKrAk/bIgc
|
|
/zDzQo818R82RBRe8k8db0P4YUNcnH9kibsN4YcN1aH3JnI22JD9hw2+Mz94
|
|
fzhjQ/jB72tY/r/rz20IP2y4uODDpqcdNpQeRzZo0KsGDze1peYdOzZsPNEg
|
|
TnKxpfqbNRvMdrVaBK+zJfsPG0q6u24sOm1L9h8cn58DFSnPbSk9JmzI3G/4
|
|
bOQ3W7L/sOFRsrVHodkk4j9s6BMLtj1yn0T2HzbMWDsz4NOmScR/2PDSZt17
|
|
n7RJxH9wPFf/T+170STKT3tZYCO49q6kdxLhhwV9p4r92mwmU/NoJwt+R/3Y
|
|
LA2cTOWnjQUjvpq6vts7mew/LPD57PLkXNZk4j8sSAsPr8+sm0zpqWHBuP3n
|
|
Mr8OtSP+w4Js8zKzdXw7ql+XsWCTpybXbpUd8R8WTPsn+GeRZEf8hwV84ebV
|
|
swrsiP+wYK7W7X3Pf9qR+Y0FCfM7ndfb2FP5yWHBrpMTO2YH2RN+WPBAU/Ry
|
|
zyF74j8scL4jfvP5vj2Z31hgdtr234kWe8IPCxiPfs3fMXoK4YcFqSOzWjI8
|
|
p5D9hwULr/mk6UdNIf7DghVR7w/mXJ9C5jcW3DgoTbpQP4WcH7DArzDhY/GI
|
|
qYQfFkg9S124LlMJPyzYqtFVK988lfLTnSwY8PNvenHmVOI/LPhg2XHqd81U
|
|
4j8s6Jkmr7ql5UD4YcFkE+c9h8wdCD8siD4wUrSD70DV2zIW6B5fMOJEoAPh
|
|
hwXXuKP6CtY5EH5YELXLtW9cjAOlJ4gFGxa3jEi44EDmNxbENf0V2YED1Q+8
|
|
WfBK7dDexkoHwg8L6Dn7au53OZD5jQXPRnRNvzHckfgPCzZrfnyXP9mR7D8s
|
|
mBq+0OfPNEcyv7GgYvK9pMAQR7L/sGAVvT67JMqRzG8saIupPL/mP0cqP9Ys
|
|
8KddXGR/15Hww4LL1rKOoSWOhB8WtK7K8hne7kjmNxaY/OvYSdemkf2HBXYN
|
|
A3Zvs6SR/YcFjiPk/o0SGpnfWDD2+KmuVQto5PyABb3BY1aMjKQRfrC+HeHX
|
|
5KdohB8mbPj8X27ZHRqZ35igm3H8kryERuY3JpzMmrdw5FcapaeNCVpDfipX
|
|
6ToRfpiw/PYSUaOtE+GHCdcz05Zvc3Ui8xsTlB1ZIfSlToQfJgw+cNx++F4n
|
|
wg8TjFY6Fww950T4YYJm8guG/RMnwg8TWseO2bCmxonww4RHXyW7S3qdCD9M
|
|
2DKMExw4mk78hwnyvusxf9h0sv8w4SPTb+eLWXRKTxYTZj4ex7sTQSf8MCHw
|
|
6Ognz07SCT9MKLshGdJ9h074YcIH05PjPN/RCT9MWPzOsC/3O534DxPWfYTU
|
|
+QYMwg8Teif9N9TUiUH8hwmGBcnSXn8G4YcJN28Xif6GMwg/THjTOnnQxHgG
|
|
md+YsH7N3eNhtxnEf3D8has+fShjEH6Y4Dx3+uDQHwzCD45/3tw2YyMmOX9j
|
|
wqhtCUmtDCY5f2PCjO1/hjcEMgk/TNB4fdTn92Ym4YcJbqG+gcz/mMR/cH69
|
|
+ZYnHzKp/AQwwWvPjEfG1UxRaz8/TBg98D/TnD9Mwg8TFr7Vlu0ZxyL+w4Sp
|
|
rRdpYRIW8R8mHPZd17plMYvwwwRfy4yll/aziP8wIfZw7NnfGSziP0yQ7hqf
|
|
uPYVi8qPHb7/4MU+mu0ssv/gehgzI//pMDbhhwnNz77/SqGxKT1mTPDvlbSn
|
|
zGQT/2GC3TPh2adb2MR/mLDVtHWY5hk2Ne/oMcFJw1m09gmb+A8TlkZ52f9u
|
|
ZFP9QIMJfw8MrMwYzCH8MEF7wgqXLZM4hB8G7PGMWrvKm0P4YUDYYHHQ7nAO
|
|
OT9gwDO/rH8PEjiEHwbE2pcsNcrhEH7w5/+dPRxfxyH8MGBVwpg1dA0uVW81
|
|
+PsWbsN/2nCp/lbBgBES8/W107lUfytjgPbXzKPN4VzCDwPW2jeuMUjkEn4Y
|
|
4NL3YkjIYy7hhwExc+ctK2vkEn4YIPY8u3uZFo/4DwNKjV/dM5vCI/ww4Lq2
|
|
8bKuAB7xHwa8sth75MtWHqXnKgPMl+o7aqfyCD/479+Ap8tzHuGHAU/mH6tL
|
|
a+MRfhjw1XBv2wQDPjVfJzJgxfeT4bkcPpnfGGD9q2D9vmA+4YcBTlbjWpcd
|
|
5BN+GLBt28mqsOt8wg8DBnTbTYt/zyf+w4CaRIVtVR+f+A8D1BY/OeA8UUD4
|
|
YUDwjIfzij0FhB8GDF5dfiVyg4Dww4BvVw02up8WkP2HARMMw++ynwnI+QED
|
|
77Oda90/Cwg/DPAPOn4+0kBI9YMgBsxkzPAt5gkJPwy4yGFFOC8REv/Bepby
|
|
jKpihVS/dmdA371g+/i7QuI/DBhDy0BhtULCD9ZbplewTFNEzg8Y4CdP/bbH
|
|
QUT8hwHvr4Y2PJotIv7DAHX74JNGe0XUPmfHAMWS/+n976qI8IPjPeOLl0W5
|
|
iOw/DDjau8e34p+I+A8DeNcu6JYbigk/DNh5/3xAsa2Y+A8D/jvL+/NBKCb8
|
|
MOBgyGrtjgAx4YcB0wdwtoxcISb+w4BPkSnu3jvEhB8GzC9NjjoRLybnB3RI
|
|
0WAZtl4SE37o8HTEyqE+SEzmNzrc7mOueFYmJvMbHbblJlu7tojJ+QEdTJak
|
|
uFX+FVN6GukQ28Au3G4oIfMbHd5xV9+aMklC/IcOv9byer+KJOT8gA4tu85f
|
|
hJkSsv/g562+cCd1lYTwQ4cgpsTy6G4J4YcOxZURP+NOScj+QwfjudOmJF+T
|
|
EP+hg8a1o3cfPJNQerLpEPicGdX0UUL4ocOwDPb+0R0Swg8dpvokvFkwWErO
|
|
3+iQjXwCb46REn7ocKVrybhhTlLCDx3Ufry3iXSXUnoS6XDvQVr4j4VS4j90
|
|
aJj2um9bhJTwQ4ew0z4v9P4npeotmg4L700tvXFeSvihw4OkVWYLHkoJP3TY
|
|
6TLw8qgSKeGHDhn3ujc2NksJP3QQdLrsvv9XSvihg/23jjenjWSEHxz/hz1z
|
|
Yu1khB+s32OOzWGZjJwf0GHPORPmyTkyKj/z6TASaPuurZcR/6HD8IuXRpQd
|
|
khF+6LAhYFvDoFQZ2X/owH+Z0eFyT0b8B+vTcBTHF8nI+TWOv5bx23aFjPBD
|
|
B62ywNSZf2SEHzrcXz+aU2DoTPjB+e04aO5q50zO3+jQ6312XrHMmfgPHeL/
|
|
F9y8aK4zmd/oYH71de7fcGfiP3S4nFn/5cJhZ3L+Rgfr6LOrZqU5k/mNDqmu
|
|
WhyDh87k/I0ORsrRsz6WOBN+6BCx5EP+5RZn6nxHmw5VuYL9+wa4EH7oQBvg
|
|
fXLFKBfCD47fOK3uIEcX4j9OUGAWluHv7kL4cQLtvq2XAxe5EP9xAslDx74l
|
|
W10IP06wOSj+bNQxF8KPE/xXnhKfetmF8OMED+kzKt48dSHzmxN8CL+9elCl
|
|
C+HHCT4dfRTg+s2F8OMEHXFrD8frTCP+g6/DCvVbzacRfpygdVJZiwdvGtXf
|
|
8pyg/uXeEdkB06j5Gpwgb1ptzOSwaYQfJ/Doi9t+ed80Uf//L5btBCYS6ZAp
|
|
ydPI/OYE1kY/WQ/uTiPzmxNs2nJT3bNoGjl/cwL9VatWNSmnkfM3/Pw2m/A9
|
|
/6YRfpxA6+8nYxsTVzK/OcGqlCuz3zm4kvM3JxhWtI570N2V8OMEv2PZD8Qh
|
|
ruT8zQmmVKmXq0W6En6cIPF+8dEX8a6EHyeYYXm25cRVV8KPE/hPWF+/PN+V
|
|
8OMEcVddNslqXcn5tRMMfzHm0sQeV3L+5gTv1nVv0R3uRvhxgurLpc2/bdyI
|
|
/+Dnh2f9+CpxI+fXToAKjp/9PMeN8OMEsTcjPrVvcCP7jxNctppf3B3rRvhx
|
|
gkF202YMvuhGfv9xgnRw3DzmiRvxHyc4JB/H5lS4EX6c4Pqp4afmdboRfpxA
|
|
eLdp2T4ddyo/TCdYaLJ1x3ULdzK/OYHG07eVlXx3wg+uvxut27UD3Qk/TjCw
|
|
6fkS7lp3cn6N4zNv6fHVh9wJP04w1fT5oPPn3In/4Poc14IqH7qT+Q3Hb0XR
|
|
Y8N37mT/cYKRvzap+7W7k/3HCcyL6mKPDPYg/OD4fBoy/+04D8KPE3xx+x1u
|
|
wPEg/NDg/JfMoiB/D3J+QIOGj2brUld5EP+hwX2dgFmt+zzI/EYDo90e+5gp
|
|
HoQfGvzla/Tsu+dB5jcabBTuuvH+rQeZ32iwZT+6ZtPqQfihwbARTzqjBnqS
|
|
/YcGdvLdke/HeFJ6imjwtnew51SmJ5WfAhrozvYOjvHxpPpbHg1KemfltCz3
|
|
JPMbDSbILeZ57PEk/NDAp7C9OvO0Jzk/oEHmms4PWnc9KT1ZNHB4PWX6kiJP
|
|
cn5Ng9aGC/zHzZ5kfqPBs1uBFw0GeJHff2jwXiA5vGy0F+GHBsP3Lv1038mL
|
|
+A8NNu15BprTvQg/NNDmzzWYEepF+KHByxt29ck7vQg/NLhVw7JWJHqR33+w
|
|
nvztn2xveZH9B99/ea9F2Gsvsv/QYE/e7Y9X5F5UvUXQwLrqgnbLHy/iPzT4
|
|
dqXktsXI6eT8gAafmayKuQ7TCT800NteHnHMfTrZf2gQHHnjSF7IdHJ+TYNa
|
|
eq55V+R0wg8NDl3Sc7A4OZ2cv+Hvl5+45319OuGHBivRjAebX0wnv//QICnY
|
|
m5FSP53sPzTofLR7cu6v6YQfGuwu+3K6aYQ31Q94NEhO7dFRs/Mm/kODB+P/
|
|
9hm6eBN+aPAmQD3cfIE3OT/A78fRWGmz2Zvwg/WVDlRYHfUm/kOD3rEDmswu
|
|
e5P5jQY9Zn2Lh+Z6E35o0Ff8Y1lXpTfhB39O//zl/Xdv4j80+OJV9/O6rg/h
|
|
B9f/yJL9uyx9CD+4Hk/CSQ+hD+GHBuj5NZuhs3wIP46QmZkofLnWh/iPIxyQ
|
|
7P4QeciH+I8jLIpZ9t36nA/5/ccRRIc8jxc+8CH7jyMYsu3vrCj1Ifw4Qm2S
|
|
7ux/rT5kfnOEoIqN8HyAL+HHEXL4jUY6er7EfxzhzLaiq+6jfQk/jtB7jLN/
|
|
v5Uv8R9HqNhjcfYxzZfMb47gND32d6fQl/DjCHqdG06Ze/qS/ccRDj8skHnP
|
|
8hXNGKcTnZLtCH2XO0unh/iK/g8OBjzt
|
|
"]]}}}, {{}, {}}}, {{}, {{{
|
|
Directive[
|
|
PointSize[0.012833333333333334`],
|
|
RGBColor[0.9, 0.36, 0.054],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]],
|
|
GeometricTransformation[
|
|
Inset[
|
|
Style[
|
|
Graphics[{
|
|
EdgeForm[],
|
|
Disk[{0, 0}]}],
|
|
GraphicsBoxOptions -> {DefaultBaseStyle -> Directive[
|
|
PointSize[0.012833333333333334`],
|
|
RGBColor[0.9, 0.36, 0.054],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]]}], {0., 0.}, Automatic,
|
|
Offset[10]], {{{-5.3257, 0.}}, {{-5.3257, 0.}}}]}, {
|
|
Directive[
|
|
PointSize[0.012833333333333334`],
|
|
RGBColor[0.365248, 0.427802, 0.758297],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]],
|
|
GeometricTransformation[
|
|
Inset[
|
|
Style[
|
|
Graphics[{
|
|
EdgeForm[],
|
|
Polygon[{{-1, -1}, {1, -1}, {1, 1}, {-1, 1}}]}],
|
|
GraphicsBoxOptions -> {DefaultBaseStyle -> Directive[
|
|
PointSize[0.012833333333333334`],
|
|
RGBColor[0.365248, 0.427802, 0.758297],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]]}], {0., 0.}, Automatic,
|
|
Offset[10]], {{{-15.9, 0.}}, {{-15.9, 0.}}}]}, {
|
|
Directive[
|
|
PointSize[0.012833333333333334`],
|
|
RGBColor[0.945109, 0.593901, 0.],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]],
|
|
GeometricTransformation[
|
|
Inset[
|
|
Style[
|
|
Graphics[{
|
|
EdgeForm[],
|
|
Polygon[{{0, 1}, {1, 0}, {0, -1}, {-1, 0}}]}],
|
|
GraphicsBoxOptions -> {DefaultBaseStyle -> Directive[
|
|
PointSize[0.012833333333333334`],
|
|
RGBColor[0.945109, 0.593901, 0.],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]]}], {0., 0.}, Automatic,
|
|
Offset[10]], {{{-30.9, 0.}}, {{-30.9, 0.}}}]}}}, {{}, {}}}}, {
|
|
DisplayFunction -> Identity, DisplayFunction -> Identity, AspectRatio ->
|
|
GoldenRatio^(-1), Axes -> {False, False}, AxesLabel -> {None, None},
|
|
AxesOrigin -> {-4.270833333333344, 0}, AxesStyle -> Thickness[Large],
|
|
BaseStyle -> 18, DisplayFunction :> Identity,
|
|
Frame -> {{True, True}, {True, True}}, FrameLabel -> {{
|
|
Style[
|
|
"\!\(\*SubscriptBox[\(c\), \(0\)]\)-\!\(\*FractionBox[\(2 \
|
|
\*SubscriptBox[\(c\), \(1\)]\), \
|
|
\(3\)]\)+\!\(\*FractionBox[SubscriptBox[\(c\), \(2\)], \(5\)]\)", FontSize ->
|
|
18], None}, {
|
|
Style["\[Mu]", FontSize -> 18], None}}, FrameStyle -> Directive[
|
|
GrayLevel[0],
|
|
Thickness[Large]],
|
|
FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}},
|
|
GridLines -> {Automatic, Automatic}, GridLinesStyle -> Directive[
|
|
GrayLevel[0.5, 0.4]], ImageSize -> 500,
|
|
LabelStyle -> {FontFamily -> "Times"},
|
|
Method -> {
|
|
"OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> True,
|
|
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
|
|
Identity[
|
|
Part[#, 1]],
|
|
Identity[
|
|
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
|
|
Identity[
|
|
Part[#, 1]],
|
|
Identity[
|
|
Part[#, 2]]}& )}}, PlotRange -> {All, {-0.00135, 0.001}},
|
|
PlotRangeClipping -> True, PlotRangePadding -> {{
|
|
Scaled[0.02],
|
|
Scaled[0.02]}, {0, 0}}, Ticks -> {Automatic, Automatic}}],
|
|
Placed[
|
|
Unevaluated[
|
|
PointLegend[{
|
|
Directive[
|
|
PointSize[0.009166666666666668],
|
|
RGBColor[0.9, 0.36, 0.054],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]],
|
|
Directive[
|
|
PointSize[0.009166666666666668],
|
|
RGBColor[0.365248, 0.427802, 0.758297],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]],
|
|
Directive[
|
|
PointSize[0.009166666666666668],
|
|
RGBColor[0.945109, 0.593901, 0.],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6]]}, {
|
|
Style[
|
|
"\!\(\*SuperscriptBox[\(\[InvisiblePrefixScriptBase]\), \(3\)]\)P \
|
|
ground state", FontSize -> 18],
|
|
Style[
|
|
"\!\(\*SuperscriptBox[\(\[InvisiblePrefixScriptBase]\), \(3\)]\)P \
|
|
first excited state", FontSize -> 18],
|
|
Style[
|
|
"\!\(\*SuperscriptBox[\(\[InvisiblePrefixScriptBase]\), \(3\)]\)P \
|
|
second excited state", FontSize -> 18]},
|
|
LegendMarkers -> {{False, Automatic}, {False, Automatic}, {
|
|
False, Automatic}}, Joined -> {True, True, True},
|
|
LabelStyle -> {FontFamily -> "Times"}, LegendLayout -> "Column"]], {
|
|
Left, Bottom}, Identity]]& ],
|
|
AutoDelete->True,
|
|
Editable->True,
|
|
SelectWithContents->False,
|
|
Selectable->True]], "Output",
|
|
CellLabel->
|
|
"Out[198]=",ExpressionUUID->"826737d4-2b6e-4de9-b31d-fe96204e193e"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"\[Psi]c", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
|
|
".", "f"}]], "Input",
|
|
CellChangeTimes->{{3.8255671403095007`*^9,
|
|
3.8255671407645397`*^9}},ExpressionUUID->"b5b12c32-af87-4895-806f-\
|
|
bf157bb129aa"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{"2",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"]}], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{"\[Theta]", ",", "\[Phi]"}], "]"}], "2"]}]}]], "Input",
|
|
CellChangeTimes->{{3.82556704003997*^9, 3.825567086674712*^9}},
|
|
CellLabel->"In[16]:=",ExpressionUUID->"cc05efbd-961f-46db-b61a-58c996905985"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}],
|
|
RowBox[{"4", " ", "\[Pi]"}]], "+",
|
|
FractionBox[
|
|
RowBox[{"3", " ",
|
|
SuperscriptBox[
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
FractionBox[
|
|
RowBox[{"2", " ",
|
|
SubscriptBox["c", "1"]}], "3"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], ")"}]}],
|
|
RowBox[{"4", " ", "\[Pi]"}]]}]], "Output",
|
|
CellChangeTimes->{3.825567086983945*^9},
|
|
CellLabel->"Out[16]=",ExpressionUUID->"8fa408ca-cd50-43f5-b8e3-e8f3a0b3e9c1"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"\[CapitalGamma]", "[",
|
|
RowBox[{"1", ",", "2"}], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"\[Rho]", "[", "1", "]"}],
|
|
RowBox[{"\[Rho]", "[", "2", "]"}]}], "+",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalGamma]", "xc"], "[",
|
|
RowBox[{"1", ",", "2"}], "]"}]}]}]], "Input",
|
|
CellChangeTimes->{{3.8255726886967688`*^9,
|
|
3.825572727248165*^9}},ExpressionUUID->"98d3c666-fed4-4e94-8773-\
|
|
702f80e147f2"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox["\[Rho]", "hole"], "[",
|
|
RowBox[{"1", ",", "2"}], "]"}], "=",
|
|
FractionBox[
|
|
RowBox[{"\[CapitalGamma]", "[",
|
|
RowBox[{"1", ",", "2"}], "]"}],
|
|
RowBox[{"\[Rho]", "[", "1", "]"}]]}]], "Input",
|
|
CellChangeTimes->{{3.825572744179343*^9,
|
|
3.825572776821579*^9}},ExpressionUUID->"7760399b-0d77-4553-9ef6-\
|
|
998865cceadc"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell["Triplet P state at the HF level", "Subsection",
|
|
CellChangeTimes->{{3.826883274965623*^9,
|
|
3.826883280731924*^9}},ExpressionUUID->"77b56f7c-700c-4596-b77a-\
|
|
642cfae1f22b"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "5"}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"H", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"\[Mu]", ",", "\[Nu]"}]],
|
|
SuperscriptBox["R", "2"]],
|
|
FractionBox[
|
|
RowBox[{"\[Mu]",
|
|
RowBox[{"(",
|
|
RowBox[{"\[Mu]", "+", "1"}], ")"}]}], "2"]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Mu]", ",", "0", ",",
|
|
RowBox[{"M", "-", "1"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Nu]", ",", "0", ",",
|
|
RowBox[{"M", "-", "1"}]}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"ERI", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox["1", "R"],
|
|
SqrtBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "\[Mu]"}], "+", "1"}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "\[Nu]"}], "+", "1"}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "\[Lambda]"}], "+", "1"}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "\[Sigma]"}], "+", "1"}], ")"}]}]],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"L", "=",
|
|
RowBox[{"Max", "[",
|
|
RowBox[{
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{"\[Mu]", "-", "\[Nu]"}], "]"}], ",",
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{"\[Lambda]", "-", "\[Sigma]"}], "]"}]}], "]"}]}],
|
|
RowBox[{"Min", "[",
|
|
RowBox[{
|
|
RowBox[{"\[Mu]", "+", "\[Nu]"}], ",",
|
|
RowBox[{"\[Lambda]", "+", "\[Sigma]"}]}], "]"}]],
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"J3", "[",
|
|
RowBox[{"\[Mu]", ",", "\[Nu]", ",", "L"}], "]"}], "2"],
|
|
SuperscriptBox[
|
|
RowBox[{"J3", "[",
|
|
RowBox[{"\[Lambda]", ",", "\[Sigma]", ",", "L"}], "]"}],
|
|
"2"]}]}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Mu]", ",", "0", ",",
|
|
RowBox[{"M", "-", "1"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Nu]", ",", "0", ",",
|
|
RowBox[{"M", "-", "1"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Lambda]", ",", "0", ",",
|
|
RowBox[{"M", "-", "1"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Sigma]", ",", "0", ",",
|
|
RowBox[{"M", "-", "1"}]}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"P", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["c", "\[Mu]"],
|
|
SubscriptBox["c", "\[Nu]"]}], "+",
|
|
RowBox[{
|
|
SubscriptBox["d", "\[Mu]"],
|
|
SubscriptBox["d", "\[Nu]"]}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Mu]", ",", "0", ",",
|
|
RowBox[{"M", "-", "1"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Nu]", ",", "0", ",",
|
|
RowBox[{"M", "-", "1"}]}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"EHF", "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[Mu]", "=", "1"}], "M"],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[Nu]", "=", "1"}], "M"],
|
|
RowBox[{
|
|
RowBox[{"P", "\[LeftDoubleBracket]",
|
|
RowBox[{"\[Mu]", ",", "\[Nu]"}], "\[RightDoubleBracket]"}], " ",
|
|
RowBox[{"H", "\[LeftDoubleBracket]",
|
|
RowBox[{"\[Mu]", ",", "\[Nu]"}], "\[RightDoubleBracket]"}]}]}]}],
|
|
"+",
|
|
RowBox[{
|
|
FractionBox["1", "2"],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[Mu]", "=", "1"}], "M"],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[Nu]", "=", "1"}], "M"],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[Lambda]", "=", "1"}], "M"],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[Sigma]", "=", "1"}], "M"],
|
|
RowBox[{
|
|
RowBox[{"P", "\[LeftDoubleBracket]",
|
|
RowBox[{"\[Mu]", ",", "\[Nu]"}], "\[RightDoubleBracket]"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"ERI", "\[LeftDoubleBracket]",
|
|
RowBox[{
|
|
"\[Mu]", ",", "\[Nu]", ",", "\[Lambda]", ",", "\[Sigma]"}],
|
|
"\[RightDoubleBracket]"}], "-",
|
|
RowBox[{"ERI", "\[LeftDoubleBracket]",
|
|
RowBox[{
|
|
"\[Mu]", ",", "\[Sigma]", ",", "\[Lambda]", ",", "\[Nu]"}],
|
|
"\[RightDoubleBracket]"}]}], ")"}],
|
|
RowBox[{"P", "\[LeftDoubleBracket]",
|
|
RowBox[{"\[Lambda]", ",", "\[Sigma]"}],
|
|
"\[RightDoubleBracket]"}]}]}]}]}]}]}]}]}], ";"}]}],
|
|
"\[IndentingNewLine]", "]"}]], "Input",
|
|
CellChangeTimes->{{3.830473225525598*^9, 3.830473266650823*^9}, {
|
|
3.830473467880327*^9, 3.830473526937747*^9}, {3.830473567469343*^9,
|
|
3.8304737943835783`*^9}, {3.8304738507796183`*^9, 3.830473865402197*^9}, {
|
|
3.830474375921876*^9, 3.830474423491139*^9}, 3.830735504071245*^9, {
|
|
3.830735548008272*^9, 3.830735555839553*^9}, 3.830736428075189*^9,
|
|
3.8307365554896917`*^9, {3.830736622565399*^9, 3.830736632714836*^9}, {
|
|
3.830736684566133*^9, 3.830736684613557*^9}, {3.830736827507369*^9,
|
|
3.830736827619969*^9}, 3.83073685845255*^9},
|
|
CellLabel->"In[17]:=",ExpressionUUID->"0096765c-1955-4233-8b61-c68add30afd7"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "5"}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"t1", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox["R", "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox["1",
|
|
SuperscriptBox["R", "2"]], "+",
|
|
FractionBox["2",
|
|
RowBox[{"3", "R"}]]}], ")"}]}], "//", "Chop"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",", "0.5", ",", "5", ",", "0.5"}], "}"}]}], "]"}]}],
|
|
";", "\[IndentingNewLine]",
|
|
RowBox[{"t2", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox["R", "2"],
|
|
RowBox[{
|
|
RowBox[{"FindMinimum", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"EHF", ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
SubsuperscriptBox["c", "\[ScriptL]", "2"]}], "\[Equal]",
|
|
"1"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
SubsuperscriptBox["d", "\[ScriptL]", "2"]}], "\[Equal]",
|
|
"1"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"],
|
|
SubscriptBox["d", "\[ScriptL]"]}]}], "\[Equal]", "0"}]}],
|
|
"}"}], ",",
|
|
RowBox[{"Sequence", "[",
|
|
RowBox[{"Flatten", "[",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"], ",",
|
|
SubscriptBox["d", "\[ScriptL]"]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",",
|
|
RowBox[{"M", "-", "1"}]}], "}"}]}], "]"}], "]"}], "]"}],
|
|
",",
|
|
RowBox[{"MaxIterations", "\[Rule]", "1000"}]}], "]"}],
|
|
"\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "//",
|
|
"Chop"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",", "0.5", ",", "5", ",", "0.5"}], "}"}]}], "]"}]}],
|
|
";", "\[IndentingNewLine]",
|
|
RowBox[{"ListPlot", "[",
|
|
RowBox[{"{",
|
|
RowBox[{"t1", ",", "t2"}], "}"}], "]"}]}]}], "\[IndentingNewLine]",
|
|
"]"}]], "Input",
|
|
CellChangeTimes->{{3.830647960800611*^9, 3.830647984368167*^9}, {
|
|
3.830648066133828*^9, 3.830648116961814*^9}, {3.830735245706052*^9,
|
|
3.830735290795759*^9}, {3.830735326842476*^9, 3.8307353568877077`*^9}, {
|
|
3.830735487419773*^9, 3.8307354898285303`*^9}, {3.830735534745571*^9,
|
|
3.830735562582773*^9}, {3.830736430381339*^9, 3.83073643051947*^9}, {
|
|
3.830736557810408*^9, 3.830736580382964*^9}, {3.83074198769138*^9,
|
|
3.83074198801427*^9}},
|
|
CellLabel->
|
|
"In[126]:=",ExpressionUUID->"b5718ede-6400-4124-b4a6-2186a8843623"],
|
|
|
|
Cell[BoxData[
|
|
GraphicsBox[{{}, {{
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[
|
|
0.012833333333333334`], AbsoluteThickness[1.6],
|
|
PointBox[{{0.5, 1.3333333333333333`}, {1., 1.6666666666666665`}, {1.5,
|
|
2.}, {2., 2.333333333333333}, {2.5, 2.6666666666666665`}, {3., 3.}, {
|
|
3.5, 3.333333333333333}, {4., 3.6666666666666665`}, {4.5, 4.}, {5.,
|
|
4.333333333333334}}]},
|
|
{RGBColor[0.880722, 0.611041, 0.142051], PointSize[
|
|
0.012833333333333334`], AbsoluteThickness[1.6],
|
|
PointBox[{{0.5, 1.3321627506682057`}, {1., 1.662040362356781}, {1.5,
|
|
1.9897228095268746`}, {2., 2.3152998525246113`}, {2.5,
|
|
2.638860700178723}, {3., 2.96049497994671}, {3.5,
|
|
3.2802894335048958`}, {4., 3.5983285495217125`}, {4.5,
|
|
3.91469383988601}, {5., 4.229463906569754}}]}}, {
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[
|
|
0.012833333333333334`], AbsoluteThickness[1.6]},
|
|
{RGBColor[0.880722, 0.611041, 0.142051], PointSize[
|
|
0.012833333333333334`], AbsoluteThickness[1.6]}, {}, {}, {}}, {
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[
|
|
0.012833333333333334`], AbsoluteThickness[1.6]},
|
|
{RGBColor[0.880722, 0.611041, 0.142051], PointSize[
|
|
0.012833333333333334`], AbsoluteThickness[1.6]}, {}, {}, {}}}, {{}, {}}},
|
|
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, Automatic}, {Automatic, Automatic}},
|
|
GridLines->{None, None},
|
|
GridLinesStyle->Directive[
|
|
GrayLevel[0.5, 0.4]],
|
|
Method->{
|
|
"OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> True,
|
|
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
|
|
Identity[
|
|
Part[#, 1]],
|
|
Identity[
|
|
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
|
|
Identity[
|
|
Part[#, 1]],
|
|
Identity[
|
|
Part[#, 2]]}& )}},
|
|
PlotRange->{{0, 5.}, {0, 4.333333333333334}},
|
|
PlotRangeClipping->True,
|
|
PlotRangePadding->{{
|
|
Scaled[0.02],
|
|
Scaled[0.02]}, {
|
|
Scaled[0.02],
|
|
Scaled[0.05]}},
|
|
Ticks->{Automatic, Automatic}]], "Output",
|
|
CellChangeTimes->{
|
|
3.830735586848072*^9, 3.8307364447136497`*^9, {3.830736582842355*^9,
|
|
3.8307365838820467`*^9}, 3.830741989468062*^9},
|
|
CellLabel->
|
|
"Out[126]=",ExpressionUUID->"86990887-6b9b-4c25-928a-8a2d9a47fc30"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "3"}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"Integrate", "\[IndentingNewLine]", "[",
|
|
RowBox[{
|
|
RowBox[{"Evaluate", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
SubscriptBox["\[ScriptL]", "1"]], "[", "\[Theta]", "]"}],
|
|
RowBox[{"P", "\[LeftDoubleBracket]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], "+", "1"}], ",",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], "+", "1"}]}],
|
|
"\[RightDoubleBracket]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
SubscriptBox["\[ScriptL]", "2"]], "[", "\[Theta]", "]"}], "2",
|
|
"\[Pi]", " ",
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}]}], "/.",
|
|
RowBox[{
|
|
RowBox[{"FindMinimum", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"EHF", ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
SubsuperscriptBox["c", "\[ScriptL]", "2"]}], "\[Equal]",
|
|
"1"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
SubsuperscriptBox["d", "\[ScriptL]", "2"]}], "\[Equal]",
|
|
"1"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"],
|
|
SubscriptBox["d", "\[ScriptL]"]}]}], "\[Equal]", "0"}]}],
|
|
"}"}], ",",
|
|
RowBox[{"Sequence", "[",
|
|
RowBox[{"Flatten", "[",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"], ",",
|
|
SubscriptBox["d", "\[ScriptL]"]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",",
|
|
RowBox[{"M", "-", "1"}]}], "}"}]}], "]"}], "]"}], "]"}],
|
|
",",
|
|
RowBox[{"MaxIterations", "\[Rule]", "1000"}]}], "]"}],
|
|
"\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "//",
|
|
"Chop"}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}]}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",",
|
|
RowBox[{"-", "5"}], ",",
|
|
RowBox[{"-", "3"}], ",", "1"}], "}"}]}], "]"}]}],
|
|
"\[IndentingNewLine]", "]"}]], "Input",
|
|
CellChangeTimes->{{3.83073459034871*^9, 3.830734623615212*^9},
|
|
3.830735213633275*^9, {3.8307355774386806`*^9, 3.8307356308105373`*^9},
|
|
3.830735667895907*^9, 3.8307364645708838`*^9, {3.830736562947638*^9,
|
|
3.830736578184195*^9}},
|
|
CellLabel->"In[71]:=",ExpressionUUID->"e6212f5c-f61a-44bd-9741-ee94d91faa85"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
"2.0000004831758984`", ",", "2.000000000140928`", ",",
|
|
"2.0000000000015334`"}], "}"}]], "Output",
|
|
CellChangeTimes->{{3.830734611081441*^9, 3.83073462512887*^9},
|
|
3.83073521502177*^9, {3.83073561338946*^9, 3.8307356427160892`*^9},
|
|
3.830736102369392*^9, {3.830736461355761*^9, 3.830736465819791*^9},
|
|
3.8307365865744553`*^9},
|
|
CellLabel->"Out[71]=",ExpressionUUID->"9dd3881f-824b-4e31-8bf6-7abeadcfec2e"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "5"}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"Plot", "[",
|
|
RowBox[{
|
|
RowBox[{"Evaluate", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
SubscriptBox["\[ScriptL]", "1"]], "[", "\[Theta]", "]"}],
|
|
RowBox[{"P", "\[LeftDoubleBracket]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], "+", "1"}], ",",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], "+", "1"}]}],
|
|
"\[RightDoubleBracket]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
SubscriptBox["\[ScriptL]", "2"]], "[", "\[Theta]", "]"}], "2",
|
|
"\[Pi]", " ",
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}]}], "/.",
|
|
RowBox[{
|
|
RowBox[{"NMinimize", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"EHF", ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
SubsuperscriptBox["c", "\[ScriptL]", "2"]}], "\[Equal]",
|
|
"1"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
SubsuperscriptBox["d", "\[ScriptL]", "2"]}], "\[Equal]",
|
|
"1"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"],
|
|
SubscriptBox["d", "\[ScriptL]"]}]}], "\[Equal]", "0"}]}],
|
|
"}"}], ",",
|
|
RowBox[{"Sequence", "[",
|
|
RowBox[{"Flatten", "[",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"], ",",
|
|
SubscriptBox["d", "\[ScriptL]"]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",",
|
|
RowBox[{"M", "-", "1"}]}], "}"}]}], "]"}], "]"}], "]"}],
|
|
",",
|
|
RowBox[{"MaxIterations", "\[Rule]", "1000"}]}], "]"}],
|
|
"\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "//",
|
|
"Chop"}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}]}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",",
|
|
RowBox[{"-", "10"}], ",",
|
|
RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "]"}]}],
|
|
"\[IndentingNewLine]", "]"}], "\[IndentingNewLine]"}]], "Input",
|
|
CellChangeTimes->{{3.830473979645761*^9, 3.8304741285754957`*^9}, {
|
|
3.830474184490314*^9, 3.830474250565394*^9}, {3.830474964907248*^9,
|
|
3.83047497775926*^9}, {3.830475092729837*^9, 3.830475092989079*^9}, {
|
|
3.830647806409987*^9, 3.830647863050076*^9}, {3.830647924689271*^9,
|
|
3.8306479408892937`*^9}, {3.830734334994896*^9, 3.830734384620667*^9}, {
|
|
3.830734426509309*^9, 3.830734445275111*^9}, {3.830734477943736*^9,
|
|
3.830734499964684*^9}, {3.83073453133243*^9, 3.830734531450156*^9}, {
|
|
3.830734669552342*^9, 3.8307347330418987`*^9}, {3.830734784237891*^9,
|
|
3.830734787692189*^9}, {3.83073564655136*^9, 3.830735683307749*^9}, {
|
|
3.830735922031253*^9, 3.830735924268929*^9}, {3.830736054508175*^9,
|
|
3.8307360613608418`*^9}, {3.830736467744708*^9, 3.830736490036508*^9}, {
|
|
3.830736566411104*^9, 3.8307365665213213`*^9}, {3.830736600130419*^9,
|
|
3.830736601805414*^9}, 3.830736640645602*^9, {3.830736689957271*^9,
|
|
3.8307366899958887`*^9}, {3.83073686333617*^9, 3.8307369979494867`*^9}, {
|
|
3.83073703709055*^9, 3.830737037311466*^9}, {3.8307396998582363`*^9,
|
|
3.830739703621557*^9}, {3.8307400683106327`*^9, 3.830740070085244*^9}, {
|
|
3.830740453538498*^9, 3.830740464794182*^9}},
|
|
CellLabel->
|
|
"In[115]:=",ExpressionUUID->"b2ce964b-b1a4-4e17-b745-0e349e4a0a11"],
|
|
|
|
Cell[BoxData["$Aborted"], "Output",
|
|
CellChangeTimes->{{3.8307370310660143`*^9, 3.830737041883093*^9},
|
|
3.830739705899571*^9, 3.830740072472069*^9, 3.830740465312282*^9,
|
|
3.830740537631157*^9, 3.830741894590104*^9},
|
|
CellLabel->
|
|
"Out[115]=",ExpressionUUID->"b0ff418f-98de-4bad-842e-e06fcdb95ae7"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData["\[IndentingNewLine]"], "Input",
|
|
CellChangeTimes->{
|
|
3.8307418899456472`*^9},ExpressionUUID->"d55ebddf-dd3a-4100-b7d6-\
|
|
bf59fb20a73f"],
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{"\[Rho]", "=",
|
|
RowBox[{
|
|
UnderscriptBox["\[Sum]", "\[Mu]\[Nu]"],
|
|
RowBox[{
|
|
SubscriptBox["\[Phi]", "\[Mu]"],
|
|
SubscriptBox["P", "\[Mu]\[Nu]"],
|
|
SubscriptBox["\[Phi]", "\[Nu]"]}]}]}], "\[IndentingNewLine]",
|
|
RowBox[{"=",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "00"],
|
|
SubsuperscriptBox["Y", "0", "2"]}], "+",
|
|
RowBox[{
|
|
SubscriptBox["P", "11"],
|
|
SubsuperscriptBox["Y", "1", "2"]}], "+",
|
|
RowBox[{
|
|
SubscriptBox["P", "22"],
|
|
SubsuperscriptBox["Y", "2", "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["P", "01"], "+",
|
|
SubscriptBox["P", "10"]}], ")"}],
|
|
SubscriptBox["Y", "0"],
|
|
SubscriptBox["Y", "1"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["P", "02"], "+",
|
|
SubscriptBox["P", "20"]}], ")"}],
|
|
SubscriptBox["Y", "0"],
|
|
SubscriptBox["Y", "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["P", "12"], "+",
|
|
SubscriptBox["P", "21"]}], ")"}],
|
|
SubscriptBox["Y", "1"],
|
|
SubscriptBox["Y", "2"]}]}]}], "\[IndentingNewLine]",
|
|
RowBox[{"=",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "00"],
|
|
SubsuperscriptBox["Y", "0", "2"]}], "+",
|
|
RowBox[{
|
|
SubscriptBox["P", "11"],
|
|
SubsuperscriptBox["Y", "1", "2"]}], "+",
|
|
RowBox[{
|
|
SubscriptBox["P", "22"],
|
|
SubsuperscriptBox["Y", "2", "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["P", "01"], "+",
|
|
SubscriptBox["P", "10"]}], ")"}],
|
|
SubscriptBox["Y", "0"],
|
|
SubscriptBox["Y", "1"]}], "-",
|
|
RowBox[{
|
|
FractionBox[
|
|
SqrtBox["5"], "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["P", "02"], "+",
|
|
SubscriptBox["P", "20"]}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
SubscriptBox["Y", "0"], "2"], "-",
|
|
SuperscriptBox[
|
|
SubscriptBox["Y", "1"], "2"]}], ")"}]}], "-",
|
|
RowBox[{"2",
|
|
SqrtBox["5"], "\[Pi]",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["P", "12"], "+",
|
|
SubscriptBox["P", "21"]}], ")"}],
|
|
SubscriptBox["Y", "1"],
|
|
SubscriptBox["Y", "0"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
SubscriptBox["Y", "0"], "2"], "-",
|
|
SuperscriptBox[
|
|
SubscriptBox["Y", "1"], "2"]}], ")"}]}]}]}], "\[IndentingNewLine]",
|
|
RowBox[{"=",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["P", "00"], "-",
|
|
RowBox[{
|
|
FractionBox[
|
|
SqrtBox["5"], "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["P", "02"], "+",
|
|
SubscriptBox["P", "20"]}], ")"}]}]}], ")"}],
|
|
SubsuperscriptBox["Y", "0", "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["P", "11"], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
SqrtBox["5"], "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["P", "02"], "+",
|
|
SubscriptBox["P", "20"]}], ")"}]}]}], " ", ")"}],
|
|
SubsuperscriptBox["Y", "1", "2"]}], "+",
|
|
RowBox[{
|
|
SubscriptBox["P", "22"],
|
|
SubsuperscriptBox["Y", "2", "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["P", "01"], "+",
|
|
SubscriptBox["P", "10"]}], ")"}],
|
|
SubscriptBox["Y", "0"],
|
|
SubscriptBox["Y", "1"]}], "-",
|
|
RowBox[{"2",
|
|
SqrtBox["5"], "\[Pi]",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["P", "12"], "+",
|
|
SubscriptBox["P", "21"]}], ")"}],
|
|
SubscriptBox["Y", "1"],
|
|
SubscriptBox["Y", "0"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
SubscriptBox["Y", "0"], "2"], "-",
|
|
SuperscriptBox[
|
|
SubscriptBox["Y", "1"], "2"]}], ")"}]}]}]}]}], "Input",
|
|
CellChangeTimes->{{3.830474886698345*^9, 3.830474909278191*^9}, {
|
|
3.830474993211896*^9, 3.830475054281109*^9}, {3.8306487631162853`*^9,
|
|
3.8306488009431458`*^9}, {3.830648963104704*^9, 3.830649003248741*^9}, {
|
|
3.83065014611966*^9, 3.8306501515648203`*^9}, {3.8306502382792673`*^9,
|
|
3.830650281786264*^9}},ExpressionUUID->"20962513-a6c6-46ea-aebc-\
|
|
973a60c3f95f"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "5"}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"tabHF", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
SubscriptBox["\[ScriptL]", "1"]], "[", "\[Theta]", "]"}],
|
|
RowBox[{"P", "\[LeftDoubleBracket]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "1"], "+", "1"}], ",",
|
|
RowBox[{
|
|
SubscriptBox["\[ScriptL]", "2"], "+", "1"}]}],
|
|
"\[RightDoubleBracket]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
SubscriptBox["\[ScriptL]", "2"]], "[", "\[Theta]", "]"}], "2",
|
|
"\[Pi]", " ",
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}]}], "/.",
|
|
RowBox[{
|
|
RowBox[{"FindMinimum", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"EHF", ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
SubsuperscriptBox["c", "\[ScriptL]", "2"]}], "\[Equal]",
|
|
"1"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
SubsuperscriptBox["d", "\[ScriptL]", "2"]}], "\[Equal]",
|
|
"1"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}],
|
|
RowBox[{"M", "-", "1"}]],
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"],
|
|
SubscriptBox["d", "\[ScriptL]"]}]}], "\[Equal]", "0"}]}],
|
|
"}"}], ",",
|
|
RowBox[{"Sequence", "[",
|
|
RowBox[{"Flatten", "[",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"], ",",
|
|
SubscriptBox["d", "\[ScriptL]"]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",",
|
|
RowBox[{"M", "-", "1"}]}], "}"}]}], "]"}], "]"}], "]"}],
|
|
",",
|
|
RowBox[{"MaxIterations", "\[Rule]", "1000"}]}], "]"}],
|
|
"\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "//",
|
|
"Chop"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "8"}], ",",
|
|
RowBox[{"-", "7"}], ",",
|
|
RowBox[{"-", "6"}]}], "}"}]}], "}"}]}], "]"}]}], ";"}]}],
|
|
"\[IndentingNewLine]", "]"}], "\[IndentingNewLine]"}]], "Input",
|
|
CellChangeTimes->{{3.8307410481576357`*^9, 3.8307410734529753`*^9}, {
|
|
3.830741150283545*^9, 3.830741187675805*^9}, {3.830741932329652*^9,
|
|
3.830741935369385*^9}, {3.8307420158647823`*^9, 3.830742032583829*^9}, {
|
|
3.8307424050983667`*^9, 3.830742408854731*^9}},
|
|
CellLabel->"In[18]:=",ExpressionUUID->"d3a32aba-35d9-4b11-8965-8489f6e162bc"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"Plot", "[",
|
|
RowBox[{"tabHF", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}], ",",
|
|
RowBox[{"ImageSize", "\[Rule]", "400"}], ",",
|
|
RowBox[{"PlotRange", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{"All", ",", "All"}], "}"}]}], ",",
|
|
RowBox[{"PlotTheme", "\[Rule]", "\"\<Scientific\>\""}], ",",
|
|
RowBox[{"AxesStyle", "\[Rule]", "Thick"}], ",",
|
|
RowBox[{"BaseStyle", "\[Rule]", "18"}], ",",
|
|
RowBox[{"GridLines", "\[Rule]", "Automatic"}], ",",
|
|
RowBox[{"AxesStyle", "\[Rule]",
|
|
RowBox[{"Directive", "[",
|
|
RowBox[{"Black", ",", "Thick"}], "]"}]}], ",",
|
|
RowBox[{"FrameStyle", "\[Rule]",
|
|
RowBox[{"Directive", "[",
|
|
RowBox[{"Black", ",", "Thick"}], "]"}]}], ",",
|
|
RowBox[{"FrameTicks", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"Automatic", ",", "None"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"0", ",",
|
|
RowBox[{"\[Pi]", "/", "2"}], ",", "\[Pi]"}], "}"}], ",", "None"}],
|
|
"}"}]}], "}"}]}], ",",
|
|
RowBox[{"PlotStyle", "\[Rule]", "Thick"}], ",",
|
|
RowBox[{"FrameLabel", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"Style", "[",
|
|
RowBox[{"\"\<\[Theta]\>\"", ",",
|
|
RowBox[{"FontSize", "\[Rule]", "18"}]}], "]"}], ",",
|
|
RowBox[{"Style", "[",
|
|
RowBox[{
|
|
"\"\<\!\(\*SuperscriptBox[OverscriptBox[\(\[Rho]\), \(~\)], \
|
|
\(HF\)]\)(\[Theta])\>\"", ",",
|
|
RowBox[{"FontSize", "\[Rule]", "16"}]}], "]"}]}], "}"}]}], ",",
|
|
RowBox[{"PlotLegends", "\[Rule]",
|
|
RowBox[{"Placed", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"Style", "[",
|
|
RowBox[{"\"\<\[Mu] = -8\>\"", ",",
|
|
RowBox[{"FontSize", "\[Rule]", "18"}]}], "]"}], ",",
|
|
RowBox[{"Style", "[",
|
|
RowBox[{"\"\<\[Mu] = -7\>\"", ",",
|
|
RowBox[{"FontSize", "\[Rule]", "18"}]}], "]"}], ",",
|
|
RowBox[{"Style", "[",
|
|
RowBox[{"\"\<\[Mu] = -6\>\"", ",",
|
|
RowBox[{"FontSize", "\[Rule]", "18"}]}], "]"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"Center", ",", "Bottom"}], "}"}]}], "]"}]}]}], "]"}],
|
|
"\[IndentingNewLine]"}]], "Input",
|
|
CellLabel->"In[23]:=",ExpressionUUID->"0d9be6fe-c20c-4b13-b4c3-a4f6c73c3a1d"],
|
|
|
|
Cell[BoxData[
|
|
TagBox[
|
|
GraphicsBox[{{{{}, {},
|
|
TagBox[
|
|
{RGBColor[0.9, 0.36, 0.054], Thickness[Large], Opacity[1.], CapForm[
|
|
"Butt"], LineBox[CompressedData["
|
|
1:eJwV13k8VdsXAHDudblIMo898qK6lQYh4zrkSciUKRVSxhAqKooiQ3qFKBkr
|
|
GR9JMqSJIvI8L/OU4rruvQ5PCnckv/3763y+n8/+fM5e+6y91lmbfM46+RIE
|
|
BATcBAUE/v8kvhPrntINN60cqeDnOUWbas68Nfrtrj3kddkW6W44Crxnu06P
|
|
ZHhBXfyNTq5kIEzLBnDqM87C1w1L5Z8kL8GoZcL74oxY0En37QyQTIEBr4wt
|
|
+Rl3wJlB2y23/gE4BSuNZmcUwofR8Nlv5HJI/3m89l5GNVgdq9hBWWoEozZr
|
|
MfNzzWApl+q+/fEnCLtsd7I2rAM+3zXJWf+wF0IafW8Tfv8MAn6bI0snh6Cf
|
|
eUi01KcfTpICG+JXv8DNXSyB+qPDoNrzRacgYwIuRx3aTg8aBknulc1LORMQ
|
|
+C7PRT5mGEaVjT0siibAyv5ARWTBMAQ5fsnqq50AkbNpR/SnhiHrdJ5zVf8E
|
|
JDyllDQGj4CWm5+RndwkXN3pZfMqdhQwDg0OZUxC+PaOrObiL+DYWxx6JJoK
|
|
NF9a3MP6L/B9Wb5A7ToVXB8KBMe1f4HrKTtj6clUMJQzMMdmvoCgj+Xx0/eo
|
|
QFgrn3+3Yxz2DAhWqddQIaM39eC72nHwVOdI5E9T4fkle+6blq+gopo98sx6
|
|
CninzjwdD52AyvcBys9JNPCWWrz4OnICtHYmaY6K0aDt7eUDuVcnoMbfR/CX
|
|
JA3SlG4Ou9+egBVNEx0DZRps+beM0F81ATkWCQ1XtGngbEh37ZybgNfhpaJm
|
|
rjR4uuHkWn3QJDS3VF5595gGPm9cHdL8qJCsVbJVYfc07K1XlFY6S4W2T5XW
|
|
BfumgVA92vcoigoRjfpbNxlMw+OHnm61KE4xXFtD2XwaqPF+noMVVNCbsg4Y
|
|
OTINPtaRwarfqeBFOsu+E4k8lJVcFjUF+78sGCw2TsOpH/3Nzck0+G+L0GXL
|
|
vXTwvpzm1phGg+ehZ5Uf6NLhONF2vjqbBiGLk3XM/XRwlfugUlhGg56QO8yr
|
|
QAcrg5rIKx00ENdfSEqypYP2tT93GJKngVnQTVrnRwfOBsvs2qRpyI7wql66
|
|
R4dbuxvOliTSoXLsgeHIAh069w7RL9ymQ976coOIRTqQddkn/kDrtFJ3LZFZ
|
|
dEgw0LelFdNhQ5xt8S4+HaLNG7ZqtNFBBzc18iExIMi5YTKfyIDw0yw7TyUG
|
|
HLzYcCQrjgEn1C9XvgcGEJob9BMuM8Hlz+RrbxIZUCEhXbJ6nQl7nk5fIKUw
|
|
wOlYsGxUKhMMDAvP2KQyoIil/iMwjwnrJSX8eu4wwGLnzQr7t0xYk6+ktmUz
|
|
IDHn+EYVwgwkeO88cqSCAWIXBInPU2YgW7vXT7qLAVIUm+5v2Thss7VkVIox
|
|
gS5SKNXxEAe+durVwHVMaJr+6fysDIcat8PUzeuZcPpRzlhcIw4ERxf5bCkm
|
|
NCrizE3DOITu8zoZpsgET5EU4mmFWWDH5wnhmkyopH3cz8yaBfeakC0SGBOs
|
|
Cs2LFjLmQF2ulBoYzgSF712WsQ3zUG/ZSxnvYUJOe5MgMXABHOnbEyO0ZsB4
|
|
o9ma+ukfUOvy4mt/6Axsn9hAu3L+J7y8fUbVsGEGqsqkA+oiFtE5V+t3LKE4
|
|
B96ZEaMWYaeqFLN1eQaOE0JUHKMXIYI3qtjCmgGx4+3dc/GLQO+R5TVwZsBP
|
|
MkZ3c9YifD4l/qxwZQbUI6cJdxsWAZRJaa5COGQeaMwPW1mEYVtPEy8ZHGK+
|
|
nujbnrgE3cvVjq27cFg6aJLve3MJfi2ofnmwG4fgGlX/wttLUPyB0hO6B4dj
|
|
CWM86ftLYNMTxZXXwcGQclSDV7oEdjJret56OHAvOId3fFqC/BlBkUFjHCIl
|
|
bCR9JZZhxKBI2PYQDvORlJECqWUIXn0ns94aB78J0aJhuWXwyxG6+i+ya22H
|
|
nu1vy6guHgtwsMVB96ilp86uZRgwLUm2tkf7e2JWJei4DGcO2eaqueAQbrzf
|
|
piBzGaheIrusvXEQCM2MvZO9DDMFxddmkW8XLtTG5S1D/GFLo1sncagglKue
|
|
erIMNvGHqH/74EDtUJrf8mIZ3FejWQd8cXB24afV9KH14d4/5INw0At9O9gq
|
|
zQLvwV9iludwaC1UFq+XZ4GLvdGTPmSnnkgoVWbB67aGHO/z/8+bXWUpGixg
|
|
eloVXLyAQymv8JLdXhYcZ71mP4zCQTHpmuqwIwvmFGJe9EbjwCu08JlNY4Hv
|
|
nHtAYzwOpmyTjD1ZLFDe0GBmlIDDNTv991EPWOBKuuL4Bpm8uk1D6DEL6G4s
|
|
6Xc3cJDzkKSq1rJgw+Iz2ZdJOOyWHT1pN8CCh9UO/ySm4nDuTF965ggLTP4J
|
|
Yqwg17/vahkdZ4F+PmdvxC0cTMLfbfKns2CPv/kJjz9xsO5+MhnLZsGLZ6Es
|
|
9Ts4+CafPVmjxIb799/wEzNwKPsWkM7eyAbrgi6xBeQ5PZ8WEw02MIL7LN3v
|
|
4hAx7bypk8KGyIwmC61MHOLMDSepRmz4GF7h0JiFQ86K0ElZTzaE6d8Le4Hu
|
|
6eewHO+ox2woOo9vES/AgZK2gX++hA2zbpk6zsjx1YlZERVsmMjtistD1puP
|
|
6Ax5zoaXpAPfKIU45J+x2Xf6PRvSh0dKTdE9D/JbEXGksqH/xqM/zB+j73Uj
|
|
4rEdnQ0Pyp+5xSJvLGYa2+JsMMmdKXuF/HmqP/zgTzbkXrcj7y3CQf9k1ZgJ
|
|
gQMLF3Qa5J7gIHTcs5qiwQFFUeuXjcU4eEb3H9qqxQGd2odPZ5AbcqxpmhQO
|
|
nDuwbVKpBL1/RE9p014OHNU9uRqF3OMqGa9gzoGsuzGS20tRfJE3NspZcuBt
|
|
ztlZF+SELH6DtDUHlhXfE+OQ9/cz5iScOJB+Z/NMD3KBY7OrkA8HDqc4JgSj
|
|
usUJ0/sh6MeB98ersXRkp7TK1LVADmga1++vQyb9m93MC+eAiWXwGA852Dac
|
|
8uMaB7qO2s3ElOPw8Qyjdf4GB+atPsblIqulnvCaS+HANunDR14i9346lMlI
|
|
5wA3wbz8J7LBQY1f4484cFKCpHC8Aod9RZ3J7cUcMIg1XXceWXstQqamnAOR
|
|
Q/UHUpE1Gj5sTajhwKfJ3ZcakFVlgmtD6jhA/q4U1YUsf1bW1O0lBxQebGiY
|
|
QBbf4nuE0sIBFpG3IvwXDsLxEl9l2jhgETJEUEIW+FYXsNrBgYut960pyEv3
|
|
hK9+/syBu0q5hdbI8z+fkpv6OfD3+q7Ko8hMO7e7RcMcuDnxiu+PPC5cVhY5
|
|
wQGZe42e15GHfRx0vGkc0G6pj7iN3PuW8+YQkwMJbq4dD5C7lB9Z6cxxQEg4
|
|
3esJ8sfIQ32qCxxonfLe/xS5uffHCeElDpAimp0akJu0c5jf2Rwwy6t4+g75
|
|
xU3zcyN8DmxuVLZtR66m46vv1zjw+Ma67d3IFeZ3kyuJXJjVjrHpR35SYCRz
|
|
T4QLcVZ+VSPIBbyp/FhxLmzsaXf4ipztemtroCQXqHsKdKnIGc/31TrJcGGP
|
|
KePYNPKt9eMmxgpcaNF59IGBnBh0o0NThQtPmjqDZ5Cvfdx5RFKNCxbTPm44
|
|
cozG4DhHgwvHdwfG/9+RV68GULW4QIofX/j/+rBRrcW/KVyo1m4uZCIH6f17
|
|
pU6bC5u+S6XRkU9nRJEL93IhFu9rmUL2nFe7m6zHBaMaEd0JZHfrjo0RhlzY
|
|
bFo9M4Z8pCSs7JgpF1xZXd8Gke0ISjp/mHPBtPyUQg+ylWfLG21LLtxLi0zr
|
|
RDZvCrRStObCaQdRmw/IxvLSfYJ26LxYagdfIetFNJ2YdeTCm5W3Cc+Rd3f7
|
|
MPtduJBrMUssR9ZMrF0tPcGFh/sF2+8iq1OPJaef5ILdG5ZYMrKyqZBMtC+K
|
|
Vzc9LRp5Pct5q10IF5RMe7y9kclOq8/1w7kwzrnxlyMy4WmxyaYLXDjPXdU3
|
|
R2b7spyWYriwVukhvwn5Z0vB+HgcF4xHHAMkkec2HgxoT+BCp8melRWU3xMD
|
|
96/k3OJCm3bvzADypz8MyrA8dD7Wg+NXkS+2X9WOfYjia76j54u89VDrizdP
|
|
uCD1h8Aza+REW/sWwyouNOXYkmSQLY74ju57y4VE/3yjB+h+LvVXeJ97zwUb
|
|
Pfm8i8hFrgv0mo9cYG6b3OiGTPCIXtT+lwvEobYbUsjN3unrtk1wYeK080w0
|
|
qg9h1MEMfxoXumNors7IaqdVlUqYXBj4LZG+Hfmqf6nm7z+4MBoSEDyM6pFx
|
|
6BvTjQQeiFfXyG1BboieCZPazINPR8I5Oage+q1qs+238iBZ+XWmL7J87Pkr
|
|
t3fwIFaB6LIL+fz1tRRxXR6EjsmYN6P6ujdFrohkyQOFZPPeIVR/n94zG+D6
|
|
88BsvmZu/BHKL8WkY/uDeWAOt0ZzkCVyuiYjw3igIzU274ocnO82v3iRB5/d
|
|
k1K7UP2nPAkRmU/hgeL1DTlVqD8U1zwwoP7Fg3/Xu+kezEf5zD9GGa7mgV66
|
|
uuhKHsqfP35T6a7lgeM/0hrPkF8PP155+YoHdf2qm+WR+9b+epf+Nw/YP26F
|
|
jOTgIGj39g+zWR6cfepiYoL61wmc6viQwgej4Bz1aNQPNfYVm9/T5sOo/uii
|
|
IjLzir/Orb18mM32kK5PR/FLzcleNOSDii13z3waDqn7l4fsrflQo9Yh6Ir6
|
|
7ctEEc+1QD6MBZbICaH+LPf7jiDPcj40B1Y9G0P9Py0j1bW8ig9dz1/CUWQx
|
|
wqz5Ug0fijd7EAfR/4PAZLnKzSY+XJcv2/bPdZSPBVv+qfubDxGjrfyaONQP
|
|
lX/fLTHPhxeDPYKuMWg/0sqsV3tXYFkqQ1QM/c98v3aJKqy/AktcymBoBDqv
|
|
H8PdjkYrgA+WUnvDcfD+fL+UcWAFvp3seZ0dhoPtbbmjMi4rICh/N04lFIff
|
|
xaReB0WtwID7mbzVAFRfBcnXlV6vQGD7tlk9T1Svqx54OjSvgFntuqakEziI
|
|
emw3Smpdgckh8S9Dx3HAntstLXWtwMLNn8qRx1A++GT5fR5fAdmjF+9UuKPz
|
|
+qBhk7S2Avsf/FO56ITuww0T2WXzVTAqbvtT9CAOdeRzJZ8/rYKqwwvhYztx
|
|
2CG3Icin7RdcGpnVuciege+3WbI6g2vwq+fj1ui6Gfg9KWnX2SABTO1QMaU/
|
|
fAaoHmOj5gwB7Itx62Y1ygxYTfdx60IFMZ+QyECvASZcjPANkP9PEPPoeicX
|
|
dIUJyTbz/obfBbH/pOzc+qOZcH9zlL/nD0HsdLVBpQmae+oHk/1KlgWxvdld
|
|
KRJRTFg0rDyt90sQe2vVTn8UxoRQ4qK3qyQBO3wrtz73FBNOZcYdvbeHgE1Y
|
|
Jt1vt2KCXX2utXwkAVuUPSN8X5IJAYs+a3IXCdip4v0NQxJMiN9NeSF3mYCV
|
|
pVF2KaD5prGicaPcVQLm2LIzJIPMBI3CgQWZRAJGZGrOXxJkAitJ8r7UPQL2
|
|
F93wpPgiAwqOxk+tqydgDhIDdykDDJhfCYohsgiYec7WQGYmA46622zjsgmY
|
|
h/wx1kAGA1prtw/OcwmY156/h1vSGPAgaG7X6CoBIzEHMzNvoXltOGTqGYmI
|
|
7VQJrdJMYEBubZi1pxwRc5+4fnkpggFWQZGKL/cRMf0P98V17RnwaOjai9Bz
|
|
RKzdQm/je0EG0Nt2f7t9gYgtOvPf8H/RYceLb6LVUURsQrcMpSkd6tNMvL5H
|
|
EzFLI7uWbDSfdh3iioYlELG1D7kFFrNo3n0V5hWeRcTavFRoiv10sHvoJXa+
|
|
gYhV2ypfyS+iAy/AxPsSn4j5D+heOGVAB+tXFOzCKlqftfWFgh4dciUU1cPX
|
|
iFhmWtNSB5rHjZ///BZAFMLCvShhGjvocJVf6uUuLoQ58TDhmt/oQLwt7aWv
|
|
IoS11i95GRLpsK6WcWLZUAh7JL/oMftpGjauph8LvyyEbfNMOrPv8DRYUQ+/
|
|
vB8jhFmwpBZfWU3D+XZRhbdXhbCtwck6qElDZ/q1XrF4IYxhkdy732gaIrXC
|
|
Dz1JFcJG1T12c7ZOw2d7B/2hPCHM/aZy1RPiNFx/vF7G5J0QZhJxU7Wwjgb0
|
|
g6mdZCES1nfGvfy8OA18bLzVNYVJmIaQA/k/Eg3G7XQjzcgkLG3gTKa3AA36
|
|
Xb5turyOhKWonaIYLE/B+1M6l2ZlSVjoYwuxZ1+nID92bEu3Jgm75ryW+vzZ
|
|
FDg3bL9x9yAJaxLYM8JzmIIPWl3wWyoJ+5nwpFzrOhWsb3+zlv+ThJ36zS6j
|
|
O5oKn5d/uqy/Q8JkCu1Hwy9Q4WurUvCvDBIWtlAYXxFABY6Pf/bXHBJmpqCu
|
|
QrOjwo5Cwo+CChJ26cINvyhlKtxTMHis1knCqE3rzys8nYQgconQJlFhzLbz
|
|
55pU+wQ0PNxs8iFdGJu23+EC6uPQbWTc5iQlgp0a6Su55DkMnKDcI963RbB8
|
|
GbMlix190OFQ6CIhT8Yi5YgjnjKd4GNgXFqaScYCfO2LemmvIPC/f5a/3CNj
|
|
058y9wRHvoKwR14W0g/I2HfeUiFb5BXEisZPxuSTMcZwHp9GaYK8kU8qTiVk
|
|
TKvQ/pNaWCMMXnJLW2kgYyUpVwYtOS/AuinikuMYGWO7/enRLVgJjqFCHYnj
|
|
ZCxoKP37EY2/wF3jnvzrb2RM/+7hc3+bV4D/zZe1WjQy1vn5sGxGfBkkeAjM
|
|
8+fImNnjIs+bQsXwlvenT8kvtD9n+1ZF0Txoe6pWMyYgipmSXfS6rXKgy6dm
|
|
bQNRFAsTFRWMTM6Gsc7+vGgRUUxdZfOBhyJZwMlRGXLYIIppHLg7+UPsFqzZ
|
|
VWkmSotiTXWpxnUpySBMhPOvZEWxi5fnBs+Qb4DsGR8pLSVR7Mnres3z4jGg
|
|
orbkdUxFFPPgyz+vIF8Ajb4bT9M2imK7BFMKK8WDgZKksNqmJop1m524jYsf
|
|
hz1G5Tb8TaLYFnb2cIRTtOn/ANysuKY=
|
|
"]]},
|
|
Annotation[#, "Charting`Private`Tag$14372#1"]& ],
|
|
TagBox[
|
|
{RGBColor[0.365248, 0.427802, 0.758297], Thickness[Large], Opacity[1.],
|
|
CapForm["Butt"], LineBox[CompressedData["
|
|
1:eJwV2Hk4VF0YAPBZyFIqaylKik+yVFQS3ktFIbJEskUIUUhEspSyJCFr2ZK9
|
|
UGRJZctOKBKVnZk7kX2ZGeQ7/prn9zxzzr3nPee857x3j/UNfVsSgUCYIxII
|
|
67/kSs62kSOuKuHXOt1JSXdUxGgVJ3Y91YVfw7bn3Q1NgPlG1qY3yhI66J/l
|
|
FQwdYIzPnl4SdQNs1YO5OQy94Kd6YE1GlB9k6nsfyDMIge+WUf8lRT2BuJmh
|
|
RWf9BNB3EvwZH5UC0o936Ieey4HIWbOi2KgC6Cjfw9ym+B5O1Glyqt2sAuEd
|
|
84ys6SZw8daxKnJphGVvK1x38Bs4l9mGk/Z2gGnEBaiEHujCz3JkWXdBPzU5
|
|
yyegD0JlFwklJj1wTYE5MU8dBG/Pswcojj0gsBJ0NnV6EBwqEy8I+PRAccuv
|
|
v6cZg3BG92SuR3IPpBNdN/lzDgHbjQiDYyM9sDWrIb5AaggC8yUzy5x6of96
|
|
/4flG0PgK22p9cHvJ2RNXSvRmB0C1wONMVUZv8HKtFLk49gwjNqO+qeW/IYF
|
|
6TPaPRPDYJRKcPJv+A0jrT83TM0NgyL/cTWM9hvS07OlNpFGgLSWM1kp1Qda
|
|
ZZmGrLtGIOrbI43Koj4oUN0/O2c4AoVeuoxP1f2wWaRSuLliBJhXruX3XR+E
|
|
Ey0k1ox7o3CZe+72R49ByLq0h29j8CjUVXiffO47CLHwqMjp8ShECIb2XAwf
|
|
hAJJ+RzR+FH4rz2b1JU3COJDbM9M8kbBUJFi1DwxCIvaf//Md49C/lartRLH
|
|
IXga9vbRhPgY8FXgTTFuQxAWzFnYcGAMvK65RLt7D4FjaFZi8sExOFXvt/9w
|
|
6BC4vPhYB4pj8OtOskFezhCkbDiQoHtuDNipv7Je4kPw1e/Qz0y3MbD+ZHQ+
|
|
wm4YZBtK2rDyMThcsp1H8MYw6Jyfeb5QMQakgp+dLzyHofl3SnHG5zFIS7Uw
|
|
LgoeBsuoOz1LrWMwfN/Oojt3GIKqY/baDKD+ND2chKaGYY5Vh9uSTAHrHzHB
|
|
2Z4jUC29v3JagwKHO4w1D/mPgJAhYT+fNgVITYKbyoNHQNSfQ17uPAXSypOe
|
|
tCSMwEHvDwo2FykwnJQRO/lhBASXD2lG2aP+bIrT5QmjwApR/0SCKXBlpquq
|
|
CsX5cbbFbaFaClz2jjAuixgF2Wd2e30aKGBG1p4sQHEmCGA6Pc0UMOL/vDMl
|
|
exROcP6UeviVAmeOv/W42zgK2zb81S3rp4BMwGMpRfYxaFgOUb1NpwB9q3p8
|
|
UdAY2geSYZ77qTCfQJR99WQMXORa265JUWFG9FNdWtwYYGM1fWayVPgjLz8X
|
|
mTUGg8IXHY8coULfRVEdl4Yx4OGsC6jCqFCT+o8szUaB25onGzBjKoQdLL2R
|
|
+ZAC1cOFScwAKjQf/kG5FU4Bkdt3pP0DqcB+ZMn8dCwFirkH50hBVAg8fkx7
|
|
NIMCjnNx0oQwKtxRK5UQraPANa6b0b0xVHA0LB1KIlMheOC1FGcOFTRulxrE
|
|
+FNBwK3M0u0Lau/9o9kmmAopTMv/Xraj9/FZUpWPoMJ7z0Xnr1+poBJw7GBn
|
|
ChWeUIb8xbupcDS0dBN3JRWWXx1eKeynwr7E0rqwVSpM8m45YTxFBVJV6bFA
|
|
bxwW3+Xo/N6MQy4XT+bqPRxuFWSa/9mKg76pE5/nIxy23tr7ZYEHh5eLIjMO
|
|
iTjo/U3vYdmGwynp0FzdChxCLzVNknfj8PCZmfBOEg0+sor6BMvgwHmLSC4M
|
|
ocF/xi/IFVo4FNaYuh6IooEazw/bu+dwuLS1ZCD9GQ14nLN8FXVxePXK8WPc
|
|
Kxoc2R3cn6ePg/Zw5627X2hQCptTvUxwCNfNxM9w/wEvncZrWXY4cEtqtQ3E
|
|
/wGRHbZUZz8cKGwp3I2pfyC77Fh1uz8O5WOzhm+y/8DtwrARWTQumxfPfvmX
|
|
/YGN2Skc44E4lG3/g+/p+QNHtAx4zoXiYMEWQrbZNg6ZSwpN1dE4vB6tV8Bj
|
|
xiFnv7/YnWwcAmp2+HQkjQPnyYymnBwc5aPrlWUZ4/BcgjnbnYsDwUxAPaR4
|
|
HGzD3H5L5eFg0GlrIPl9HN485lJueIsDs5rluhPfBMiWsdSWluNwJkXt5XTU
|
|
BDya8tgR3YJDUGNH373nE0DteOP5uhWH+hmL7fzpE/Dq0laTz19wOH3qzuPj
|
|
xRPQx/X8zUQ7Dmq0Is97Pybg/fTEhHQXDkpyYtp8Qn9B7k6EjdNvHA42sC0c
|
|
y/gLBT+eHKeO43BjOka2Oe8vNHCEk7omcMgX3OdoVvIX9ol/Ca/8i4O0Ezbg
|
|
3/AXxlKd6VFTOEhyezU10f7Cfi/bkwfmcNhn+ifJVGYSwu1FtfYycdg21aru
|
|
VzoJyS/T9JTZaBAfWWlFq5yEN4lj6iR2GmyXL/QxaJyEJ+/4sPp1e8UV/teL
|
|
2iepndLipMEOsvWuDuYkPIWGT2e5aLBr29KCiMoUxHB1Vgjy0kAc9mTU1E4B
|
|
u8aDsS27aJA5xFsl9WUK3ud82FuGLB644Vfs9yngT2mJstyN1lnT+NZrlClQ
|
|
X0lmfy1Cg+j9phUcLNNQ2FflcWIvDWKLxCQLxabh1WiO+xEJGjxrKCeSHaZB
|
|
uLLwUvIhGkwPvvGacpqGo09xI7HDNNBgZs78cpkGn4dDla+Q56WeDr27PQ2M
|
|
ime/SuRooBN1rdoueBqufDTSrz9CA5K5UEBz1jTQpc8xm4/T4NrsXUIUZRos
|
|
NE4PuKjSoGaj+23fP6i/y21cVOTtYo7TjpPTQGIrrzFTo0G9sdHgycVp+Pw+
|
|
qUb9JA1EPslULbDOQHB7nAz/aRp0BQ34mYjNQDZvlkHiGRooCauuidjMQDuH
|
|
qvdFXRqcMetys7afgdXmTTFNyIbPr1JeOs3A+Meo44rn0fsIhn8RvzUDXAXN
|
|
ojv00Pj5fz2XejgDdsSQ0C59GtC5bikoZM/AbGmYrrwRDd79y3bVnZiBxVcJ
|
|
DulmNDgwuHX0rvssvMKvWNjbo/FTRWo8bs9C9ZPNXB+QXSYPpt7wmYXJhgu3
|
|
uBxQ+5XzZlaBs/CYQ9T9LbKSYGTXqehZKB4xk190pIG2Pnfdxnez4Le2lfOm
|
|
Mw2carkzE+Zm4bOx7DElNxrkZfPYF7vNQZ5DavzOOzQI/F6pSvacg0/JlvE2
|
|
yGYk5516d+bAXEvMJA+Z06yhbeL+HGwXfbVLxYcGdlt8juyLmQNKXH2l2V0U
|
|
T48x0tPSOcim48Hhfmh9nCxLclmZA+nu/gd192ng02/eeeDhPBBbKm+GPELz
|
|
raGcZBs6D+ejxZg1yE5vha6mhM+DfEyu9gqyaeAvJk/cPDj4GRldD6OBoqSJ
|
|
KDNrHnTx5VXdxzRg3DJ0bWyaB+FFvVccT2jgwaW1xZZrAdR7PTqMUB6c9JDs
|
|
TeZegI0E9fkQZLtBjpc9/AuwNSF+7COyUVHjUe1dC7Dfpu+g6FOUF03ULeRk
|
|
F0BQ28HxD/J8umoeUW8BLu8tcXKNoYGrkoJWcvQC5F9xfG8STwPC9Wi/J/EL
|
|
UF2AR95HDk+ZLvJPXIAFvXiVPORcUo7QlfQF2Dd0j4+QQIPhRsHJ/94tgNEg
|
|
FL5ENrywHPG2cwHOfysrHEZ5+uj1iu5ankV4PzDxCpJoUJuyY2OJwCLsL+ki
|
|
2yDrf/WArB2LsNnTQTYY+bq8bHaI6CJ8ItwjdiBnMVO8dA4vgkBAbYR5Mlr/
|
|
QQFCPXqLUK5Ov+CSQgNmyinr8YhF6LswoOn+ggYqS8pRh2IWYXjUMTUGOUDn
|
|
WI1nwiJ81vteVYLMvrpflCVtEZJZdlvTkfkvbRkWKlqEbnlnMa80Ghzk+2ml
|
|
830RFGp5Ml1e0uDmtc7I6N5FMDXoSA9HLqlprf7ZtwgafU3Or5GVXSv3XKUs
|
|
wklrDQsqsmZb+pDf0iJIwNmyS+k0sA2+YfVWcAm2zehoHMugQfaAfeSS8BK8
|
|
v/h3VA954qh1tbLoEiSn7tF2QnYbM9zTLLkEys9EPVOR/dUUh4ZPLIHwkJ3K
|
|
hky0/1ZYrPgslgBX4QtpQO5weXbZM20JgqVqm0SyaSAZsXXZPXMJOj+oH5dD
|
|
vl/wMMYtdwl+HtG8fRr56KRbs3PhEgxTSmwckJOuacnb1CyBDslyMR/Z0W6F
|
|
TW94CWLvfl88mIPm64Fbmg5lCbL8hUwxZOEMXEn7zxJI5XmE6yJ3jHS5aswu
|
|
wetdWtbOyMes8n4pk+iQrVD/KROZxcyiQFKUDqUqLSpbc2lgcafrrIQ4HX5X
|
|
OkcKIZc+0xwVk6SDekhdoQSyY+9RwT2H6RA74WeFIX812nJ/mxod1n5FXHdG
|
|
lvR4IMyvToefLDpHbyMHxiyX8mjSQcEwvvUeskIXdYJLnw489dU2ccjJelVG
|
|
LNZ0KJmiqVUg012OzhDt6MD+KdK3AVk/4vWjNQc69Hu9DO5AZm2Pr2K60qEu
|
|
Z55tGNlJ21VyJoAOIQ1DhSR0z6i/Rq2dfEAHMTsnK07k3Y/MLSdC6OA3qtbP
|
|
jfyt6Ww0NZIOLzbWq4kgH9cQ/df3gg5HH7WUKCLLv2wObsigw+6L7O8xZJk1
|
|
N963OXR4/J/9I3Vk0dLPEoFv6bCx4GGqHrIQr1ORczF6n1BsxAhZ4AafivF7
|
|
OoS+4V00Rd74H7ovVNNhlrz6yBZ5w32uft46OigzN29xRCYMFNuvNtKB3nLI
|
|
+jryfOwG344OOjR7pt32QJ6czWcv76KDXPXECW9kXMf46cseOrypxdrvIvdt
|
|
yM72GKSDfuWabSByj/V5ucujdGj7ctUhaH28FfRPZ3E6CNV1KoUit+54cUZu
|
|
gg7ltmqDYevx8jjbKTRNB8MHhQZPkKu+zZhvmEfj2bw3LhK5XOYZPrVEB2nS
|
|
09ynyO9C1W72LtOB4k4Mj0EuoPxZrVmjQ2qks+r6PS9X7WnwazIDzsZ318Yj
|
|
pyef4I1lY8DB/hPbnyEnM0eS/DYyYOpL4onnyPFGYRIOWxgQRqXLJCJHFcoX
|
|
6fMy4GKV7uy6wzb3KSttY8BW8osHScgPHR80iu1kQOeNCXzdAfXSBlt2M2Dv
|
|
70NCycg+ot19dFEG4Iddd6/bw9fXflicAS7uubPr/3f5KT7XIsmAmyV9Met2
|
|
PNp+t1iGARz7NnKs2ybKkz3lMAMKVw9rrz/fYnL30+CjDDBMuGC5/r4XNRuF
|
|
3RQZcNj6ptr6eAwyXbJNVRiw0BO2sD5eHZKg3Gk1BiQ8Tbu9Ho8zFtWfZNQZ
|
|
4Klc3LIeL7VyhzPbNRmgGlc3uR5PJQGeTqIOiodH19B6vI+6lZuP6zGgvWE4
|
|
fX0+DrZZ410XGOAQOnPsMbLYw6LVLHMGKHzla1ufX5Fh0+BIKwakVR34uj7/
|
|
O1RYeO/YMkCarpEegLx50VBCx5kB5f9iytfXD7v+auExVwYsDTWvrq8vUn6G
|
|
8p5bDPh4ZCP3TeQl20X9eR8GXFEpzlpfn7PVyX19/gwwLRA9YIc8Iaxh3xDI
|
|
gCH2l75WyIPf4+4+C2MA7dtojDFy0+nj2VgiA853v3qginy7wVfGL5UBG+Jq
|
|
WE8gS5ytffcpnQEDCsHn5NfnU1u3WjGPAbv2yciLI58ysP0pX8EA8U5tC7b1
|
|
/dCVe/lmDeqPW01oDe33l0bTlLf1DNDbxJq2iEy6dGdOph3F9y0r6xhy1eXI
|
|
TfsHGaA54bq/EtlluDvq6ihq/8BQvBh5t42QYCaOnvdQcjwX2fdqltjeGQbw
|
|
PqprjUFWuv5JRZjEhPbfOtP26/nvDs2Fex8TSPYfPrEg263KLOlKMIGT6KW0
|
|
hPKngJ/73XApJpTFB9+nIbvfWwvZeIQJgmVljl+QD4fwv2RVZ4L35V3JUcj5
|
|
sarfGVeZUCpxIYUH2WJ7kKmCExPemIdkEpG5nrUOebgw4Zn+A49plO+dkown
|
|
524z4XPlvMuX9fMj3ZltMoQJJWlxHYHIGW8Tjg+/Qv+/d1GNloXW87KpZE8B
|
|
ExKE8xS6kQ+e3rWzrYgJTStWazXIH3vSVt5/YIKSFOe/58ida68qI1uYECkh
|
|
Xq2FTNSpOK06zgRVASXbNHR+mf8Z1kuVXAa73fxmUui8E5XPUIuVWYbNT72d
|
|
eZHxu1flwg4vw3Vf5fNMdJ66c0/w3VZchunvKyENyI8UFn7oai6Dfu7Zdkvk
|
|
9w/ZLNYckEUuZweh85h/r5SjRc4yUNOvtr1D531E1COjnLxlyKNXPHyKzEka
|
|
V5t/uwyXeQI53JAJQzk7Q8uX4dpnv+syyBPJ/30pblmGlzcMStNT0Xm4Y+9B
|
|
rkn0fNJf7SB0/3Dn2bH44fAKuCpubNyH7itTAV7DG46twJSU9uBKIorXTE+b
|
|
3okV6Plve20X8uWOuCzqyRUQ2Hx98j6ydji/Ce+FFbg43tk28JwGezm5Pzp6
|
|
rkBwp0jtY3R/+kZkvyf4cQXE6FPpNXEoX+clWJyvWgFyNitvDDLHpQMngmpX
|
|
4HS7sO5VZKxQZ36+dQXa/1w6tBE53zrGrqMP9d+8J/l8LIrXZ1GtoLUVuF45
|
|
vv1bNNoPD5T5FtRW4eTm4IcFkTQoZr+Z2dG0CuJz9OFvoTSg+AT8rfiyCkNr
|
|
I4mJyNtnnsjnfV0FIWLWfjtkn97XNSG9q3CEfOsDHdXtp3Ip/Wq0VTCMsKjY
|
|
ifxN69K2YvZ/cFoi55BJEKqXwlWDEzT+wXV+L6W36P4sxb/V0bruH7R/O8hs
|
|
R/dx3oIPrzOa/oFjZhF3MDLzzNUp/Ms/KPyaPg7IjT4V7je6/4GTydRYvjfK
|
|
p6NOfj7UfyB3tP5viBe6zxQ1RcdyrEGj3iSfvCfKT/r3K5vPrYF4cAHNCNUH
|
|
U+GLfHLda2B+iY2t7iqa3+ldNdI/16B9O+maK/IffY0bEv1rMMPLHiSMPCoQ
|
|
3yRMWQPTA+Vj7nY0+Jl83Jd9cQ22M8TkRGxpYG1cMTfJScD4Mj6W2FvT4NxV
|
|
onmtJAEzPiHgWYHqH+34mKJqKQL29NkKrxWyZtN+zkoZAval3MKUjHzmgH7p
|
|
+8MELPx9BlXdFOXvqTTuAkUClsDijjeZoPuM56n6BE3Ufs9twUpUX+0NCpK9
|
|
4UjAiv1rPKxRfebWLe9r7UTANrnauS2j+q1KbLj1wnUCdqJi28ZoZItaJUcl
|
|
NwJG09bjrtVB90fibDqHNwH7sKHg8u5zNODxMduRHkLA0gT+C6w5i/Kd6yHW
|
|
3mwC1n4Tu1GC6ku9qn6D1lwC5j0d3KuKnLolLK3yNQETyjFobUX1qEo+BTLf
|
|
ELDquzFnhjAaeI8/975ZRsBeWD0NYgGU3203THM1ov48Sd5yJ1C9cOnXTzUq
|
|
AbthfLFRGtXDm5SNsy7TCNhdesLNpMPr33E6b/qOEzBZvST3TcjBI82byqcI
|
|
2J6P92/iB2kg61SucohOwHh6c0/Hy6D1dzchbTcHEfO7laXUvR/t91RjxxVJ
|
|
IlbdT9/3GdX3Kvc6j+6QJmKuZ2fUdyLb2+iSFWSJmOOWY/Fuu1C+ktBIvClH
|
|
xKpU7D7vEkbz+fZo258TRKzu3pZtzjvQ/qnhP9yrTcT0Mu7fH+RD8zXWySi+
|
|
TsQa6zgit3PQ4O6B8DsFLkTM97TMHit2GhS6nlnNdiNiGzCOrmw2Guz895GQ
|
|
6EHEZD72JR7ZgPavQCbbPV8iFnTpSdwpMqonz9zm1wknYnw/R7ceW8Vh8JXQ
|
|
IUoeEbNyPN9gM40D/2x34UABEStaExZ7MoWDpkKkfO9bIvbGud67bBKHolpW
|
|
hdZiInZgZYKN/S8OD/smVQo/EbEhCbGAZzQcpLZUa/t+IWL1AseyHg3jcNvN
|
|
1l7gLxFjVxg5Gt2JQ7DW5FXFKTSeR72ZD77hELfP86rFDBGbiJbJuvUVh5Lu
|
|
YLvMBSL2b6TyvF47DnOKr22O/iNipxZSuZaacbhOnrtstIWE2f8SMGFW43Al
|
|
2t8k9hAJ4/K1kviaj4ObM4dJuRwJe5Jk8jAiD4d76lEX+4+QsPp6W1md1zik
|
|
0l8aiyuSMGWNpya1OTj0mzVcKFEjYbeEWr88T8fhothm/W4DEnZOZqPUQgIO
|
|
OiXPNQU8SFhqKM6neh8H+znrNf7bJMzcre1OfwAO9w9KvuP3JmES43x7vf1x
|
|
KMstE+b3JWFnjz+TfH0XB9GU79O8D0nYq++7RpmeOCwGbYnjjiVhTbT6Q6pO
|
|
OCSb3B/ZVELCPF2kfa0NUPtYzfhNZSTssfNuymc9HDo7uc9tKidhjXd/a+49
|
|
jwO7TmrJxgoSBm/pxN/aaLxqn0I460kYMfskTV4dB/UDS7Ls3SQs7Q973j0F
|
|
HCZXHH3IiySs4t2Cqe9OHEwuau1nLJEw3OVGWLogDrVFB7onGSQsSys7uHEb
|
|
DgmOE7I/V0lYZWnGLw4+HE71OI+8YSVjGgeb8l034fC8yEXTgp+Myfzm2921
|
|
QoUzjh7b38uTsTKZrPyuX1QoqjOqyz9KxrafecD7ppcKu/Ycc0tXIGMLOadW
|
|
g39QYe7HUssTJTKmoHLFSK6TCsmnvfzsTpGxuJfUAYdmKsyL+FB4DckYv3yd
|
|
oVkZFV78CHh3/SYZ4/4i0q0eRQVK3cGB8FtkzK7ldFX8EypIvRvgKPAkY4zH
|
|
+xyoYVQoiVC2nLpDxiQfG4x7B1Gh9SyDwyWQjJllq1t6+1CB/sHF0jWGjL0l
|
|
GdzssaWCTqolp3spGRO0vVC8coQK0eGbj0S/J2Mt1OnawcNU6PX5ZPnuAxlT
|
|
jDlypFqWCjYmO4vnK8lYjOXqgfXv9V48PyxvNZKxaMFrIqVCVEgP1Cn26CVj
|
|
Rn/XogNJVGDaK1/2WiZj4kst6qotFND8IIndWiVjzfOqfLQGCjzn2i7iukbG
|
|
ig5ucXhcSwGlwtkBezILVmRhntLyiQK+y1mWFzeyYImXC1aF31CAHM5jeWwn
|
|
C/aVku+9PZoCm4qo5guKLNiTGxnXDE0oYMb6XXlGiQXTSbXPD75AgTzjGuG/
|
|
KixY4CE32fd6FNBZSewbVWPBlCfcRzZrUiDitL55lyYLlv5H+XuYIgX4ej6a
|
|
FV1iwXhOt8117KCA8Gqkqas3C7ZVI2jVsWcMzgyfex/nw4J1X3kzUd85Bu4N
|
|
HNsqfFkw/6qHe3a1j0FzZMA3zvss2G+lz3oVdWPgIe56Nv0RC9b7/vX9usIx
|
|
6NA9f+xHIgvmQts3OfFoDO6lbeZVrmTBbKcMrcIVx4Ci8aiZnYUVs1OXCI0P
|
|
HgVrrcsiYhtYsauNiVfb7o1Cn84RD1V2Vsw3OVlizWcUui4M7PHexIqZpW7V
|
|
0XMdhZorcl7jfKyYQO+3+VKTUUjy+/Vfmxgr9oSLLv14/ygYlh548FSDFQuP
|
|
EaNo1Y3AZ/FW2PWIFevm5DvTMjEMmuEDmgKPWbHI5CuhEpRh6FiYvbD5CSvG
|
|
zHfcHDAwDP21gk7/olgxjqMDPXu/DQPd+mp8/zNW7APtl83B0mGQSiHNJOey
|
|
YkTBf+02/sMQu+142u5mVqxKvsj82JZhcGTPZNnDsQF7tz9N323XEJSm7lP+
|
|
HLkBM9M7ZaWQ0QdtJ5Tq9LnZsIsDMxvSK3uA7vjc4HI4G8bKKnde8kYnNJ5P
|
|
ucAlwI4F/NhZbXmlGayPK2VlRbNjiYnG263lPoLD3y8Lv2PZMakOhmzB5w/g
|
|
8sLyFE8CO8bKcpkwZfAB/DjuD/kksWP0aM8kDfdySOxt2qmfyY7l7Xsdav2u
|
|
DLq9jCNWStmxEcvNns6Hi0Gz3M1L7xc7VhH9/H2CzmvQu87S+LCPHTvEYB8q
|
|
cHoFF0VjBT4OsGN6osGdZaG5cDX0fZH4KDtWt6jUkl6fDYGXCJPLE+zY2ub6
|
|
kWnlDKhgPrbO/MeOGezuL3e9kAh1+bvf/iJwYEmV/BrmEc+g1frt2lYyB3aT
|
|
b4qk1BIPv5q7Eu+wcWD4th03u7EYoD/b+eP8Vg7MPMfxmIxxGKzp5Ik95OHA
|
|
rowW8du3BsMGMrh/4OPAmAp2KzGqD4DvmjW3uCByroNbjrEP7Nw9b2m6kwPb
|
|
JcW78FX1Foh2PsiPEEbtY9scB42dQDJo22rdbg6MRpO+s+uiGRw6kaO1vIcD
|
|
a8Be5+cn3lH5H33mqdU=
|
|
"]]},
|
|
Annotation[#, "Charting`Private`Tag$14372#1"]& ],
|
|
TagBox[
|
|
{RGBColor[0.945109, 0.593901, 0.], Thickness[Large], Opacity[1.],
|
|
CapForm["Butt"], LineBox[CompressedData["
|
|
1:eJwV2Hk4lF0UAPCZsVcUWbImhSJSlhDOTVJRKolklz1ftkT2SrZKCCEk+1KE
|
|
qCSyby2KpFDWMWMZlGWG5Lv+4fk9950z75333nPPeXfYuhnakwgEghP+s/6f
|
|
qXbDxxFlD63txb8yz2wK0JKk1hwSe3AaJNt4L0RXmcLy83123+OsYEdIQPrZ
|
|
KmcY43WiV8a5QWfUba6dVdfhh25ofU5cMKArE8vtryPhq1WcdFrcfeiSZe98
|
|
9CoZDF0FfyTFPYZx5Z1h9PICiP1tXp4YVwKr/j700Cev4VCT3gZtr3ewdUmI
|
|
uce6Hdz9DGzK3VvB93fiSW3VLvjvlX00aWcnCLlbfB6v6oVuygmOPNtuGDvQ
|
|
6Jkv9ROi9i0SKk17oVLBZzvz6SHw8zkhS3bpBbd4XxH2C0PgXJt6nj+gF5qc
|
|
wJjVZgiOnz5SeC29F3SqnwTMeQ4Bm1vMuYMjvaAg5RF4M3EIQotlcl+5foc6
|
|
R9ec6P4hCJKz0n8T/APsH+sc1bcbBg/Z1oR3Of1wev/CtSO2IzBqPxqSUdkP
|
|
hxISs0qcR8A4g+Aa0tIPH2jm+/k9RkCdT00bUfthE3e8x5fgESCtFdBq9w7A
|
|
9V3K0WxpIxD35c6x2vIBcNnKEWfXMwJl108z3tb9BEa0h8O0zigsX7pcPHBl
|
|
EGTqXMXtuMfAmvuPb/W1QZikn/jCIjAGTTV+Rx4FDcLcz8mOTJExiBGM6r0Q
|
|
PQhCRtEpH6XHQPpTPqn72SCw2pypn9YcAyN1snH71CDcreffq+88BsVbbNYq
|
|
XYbgebvn5ajqMeCtobQl4N+FyvZc42HdGFy/7B5/1W8I4Oeg3+PmMdBpDt5z
|
|
IGoIeL5ZHcnsHIM+//RzzwqG4LeZuIzH6Biwj/flZVGGwM5CI0R5Ixls3xqf
|
|
iXEYhktrJ/Rsz5PhQOU2HkG3YbCwo8uii2QglfzoeuIzDOoRW0a2WZEhM8PS
|
|
pDxiGHSf3Ppe5USG4VsOlj2FwzCQu1e8zh/H07vmKjKDr1+MHe7NwP6WEJHv
|
|
MwJN7QayOuM4fqeJ3v6QEaDrFXaETOL4bYKbqiJG4LCSVtirGRy/Ku1+R/II
|
|
KKqgc4J0HD8tJ5H2ZgSCWq/dy2AfB1u7imwlwigQ2+7fb9k9Dpfmut+9ixiF
|
|
eDmrhAj7cbD2izF5FTMKY6eoR2acxsGc6SStJGkUdln3zZ51HQdjvgbhx/mj
|
|
MAHyBhu9xuG4Wum1wNZR+Fh25oxByDjI37i3V519DNqTDXQEUsaBvkU3qTx8
|
|
DAwvqpQ2tI/DfDJxX9H9MbgsuFmj+MM4zEm8bcp8OAbfHDZzJHSOw4SS0p/Y
|
|
vDEIFtHyNOkZh4ELEgbuLWPg/+B2TcnQONRn/GOSYyODk2KvzPOlcbir8NIt
|
|
N4wMnopfe9fEKdB+4BvZO5oMCQkD91x2UoBdecniaCIZ6jjzaJ8lKRCqdvDk
|
|
aA4ZzrwmVSfKUMBf++VuiSYytHGk1tEVKeBi9HIojWkcHvkVmIjrUuCY78tz
|
|
CXhe9p9uVG9ywp/3+9ZuFzEOFVlx3NwuFKgPWDqsFDMOQs/AhMeVAlo3Dip0
|
|
PR6Hx+HCbze6U0Al6uUm7lp8vffjfT98KLAr9WXT3dVxcIr3SBwPowDp3cuD
|
|
oX4U4Chyzu7KpEAhJ0/u6k0KkFkbuNKzKWBo5srrc4cCF4vWFOxzKZC1KD7n
|
|
nEqB7nitfGoBBXTkogpP11DgLP1eScdzCoSlmIsKk6gQ11MTvfiWAvKUyjvx
|
|
G6gw26/WeK+WAj3K3MucW6lgzftnYEcdBaQ/N/UQdlGBXCzfhhop0Mq2L4Z8
|
|
lApX87a/N22nwAZvIlNZJBVSdbynl79SoKzezEM2Dsc/9KPU5hu+ry2Vv7JT
|
|
qMDRdT+sqZcCRUUu1Q+LqFASPXI5tI8CJ4e7vAM/UCH762fPX4MUiD6dSznO
|
|
PQE1s6e+bpqkALeM/sdfSRNge6F/0mQVz5vtMXdrxgRYZ0qTjP5RoGrst9Hz
|
|
/Al4HKn39dQaBeyepPSFvJqAw+p1VepEKrzaNkHZ0TsBau/pNQxmKliyRTLZ
|
|
CUxCU2Z/NNcmKiiO9eue3D4JwzfMvcex2RsUopSkJ6H8wLZDNZxUKAvq3cJy
|
|
cBLgQbOr/WYqsCxKi+UaT0JEvld2Cg8Vno42q1ISJkFM5qZW5jYq3KgXCuhM
|
|
m4RbMu38FwWpOB9eqX2VMwmqwVyzm4WoQDDn142smASTuZFn3sJUONdlf07m
|
|
6ySkfV6L2SNGheU65iuuvFPwM8q/UWknFT49vlBqJDIF5vH6OR+wswOfzmvs
|
|
moKJL+L5dvi5GKgZ+XMqTUHAaZLIPUkqPHmeFVF8bgr6rCMWWqSpcPyxdtZs
|
|
3BSEaysqjctSIby1c+Dmoylw32oc8N9eKjTPWW7jy54C3Zi5V3PYR3X876lV
|
|
4OvvlQrOy1FBm1ruc/PbFJS4T9UO7sPz49Eu4x2cghvZXr+NFajw7lDnVC5l
|
|
Cm7nxcl1YEP0lE0HYwpGBmJanu2ngoai5ElekWkQYhHoNFOkgr95eVjurmkI
|
|
FaXdrceuun24TlVuGm4UyjtIK1FBrddCxUJrGpL/e+szia0SmCieaz0No0dD
|
|
zSxUqOCdu8tM1XkaBu0lUAX2i09lCe0e08DVUGS08SB+nhKfNszcnIZb1N0C
|
|
ZdgKLWwLB3Om4WzqjqMTqlRwm03Y1/5sGlpO+UwpqlGhWHCXi3nlNMitjff4
|
|
Y8u5ol8hLdNQ6pccxKpOBRnu621t1GnYke5qxnaICs7qbMzmv6fhsXaXxRHs
|
|
/EsJWrTlaXhUolAZiC1dWVrOs4kGd7x3eU5j7zKbSDOTp0HxmXmT1xpUuBTq
|
|
2zutQgMZpe36FOzMZ6xbQ4AGzdPNuXyaVNhB2BmRfYYGomKVGZexrfeU1quY
|
|
0qCiOfpIPHaGIay22tCgLI/1whtssRwzz2lPGgibjf9k1qKCxUfq02B/Giha
|
|
9ZyXxk5d8hnnDqXB61X3Y8exhfTizVUSaJCklJt1G9vUS+JhaxoNLKlveDKx
|
|
k1Kff76YSwMldy+Wt9gCM+91g1/SoKG3OIi2Ph5ba0OtpUHbVq8sZqDCNqWy
|
|
gHOtNAg/L2kriJ3Uk/3wbScNCl71Ve9dH7/+sEz6Ow1iOYoqtNbHhaM+xA7R
|
|
YLgp1+A0tmBNAGWFSoNV4aFIS+wUazcmh9/4+gkXZ1dsISZbsc5lGki9Ozfj
|
|
uz6eY6SmzjQDlT8KREOxhY8fM8reOAN7pP0W72GnTqi5cfHOwBrq9E/EFrm3
|
|
N8pXZAb6PSpL0tbH923PGd41AxKlyvFZ2KJfuN+dlJuB6KzzsvnY6VeZ+yqV
|
|
Z+B7iohPEbaYwNKCuNYM6Cfcv/5sffw1dcsd3Rm4rlmmVIy93bxfdsFgBpqp
|
|
YYXr4xn/PupamcyAcirXwPrnxZ/U2bRZzcAE8cTH9fgZR14EKDrNwJKnUkg2
|
|
9g5y7sM0d+y5D/Pp2JkRyWVs12egVZZbPglbQvbuB48bM4B86HIx6+Mfgih9
|
|
kTMw0B2wGIa9092DSTduBsJpCZEB2Nk8dmLPU/D1AupUd+xdFcZqQlkzQNaz
|
|
FLBbHzc5YRRaNAOrcot8xtiSy4fcaOUzYMI5T9bFloIdOfWNM9CiMcomiZ07
|
|
tPXd3g8zcOHKCzOe9fFQ1r7ErzPQZJkb+Q+vB+m2yS2XyTNQ657q34Wdf/mn
|
|
7FfaDMgWex2pxt7N9VkXlmbg4xDPdBZ2/B6zGg7mWRC4h6bdsLv9uju02Gfh
|
|
zPmHx4ywed+f+u61aRaKXujeOYidcAXND/DOAmlVoWcZr/fEckmZMslZcDC+
|
|
WnwVu4f58cHxPbMgOPM9/Aw2v/G2oyLys7DZ39dUFvshfYN1mMosnB+unBrA
|
|
+y1Jczbh4rFZOH1Mj/Ugdm+0c9Z9/VlcrcR1b8DeNjj8vPE0NiO1YADv3+Sb
|
|
XzvkL8zCGyNJtxDslJYqIpPzLBTSRpKrcH6YHXx+fcZ1FpJ72c9HYR9bzp3r
|
|
c5+FjFc5R0yx5/c+GHrhOwsqmgvv5nF+MYi7XOcQMQt793ldksAmWYjcaM+b
|
|
hZXJDyGmOF9duMbDqCyahXvnXgiLYpfcZ/fIKpmFD/fPEQZxvjOvn7cOeDkL
|
|
SoQ9Ty9hV0p/QPItsxDFRSu3VabC5d+BhDjyLBSbBBYjnF/rN171DZqYhUf6
|
|
d28zDuD5SbrMutBmoUsw5k0pdrOJ8eCRxVlQ//LkhDi2+Fv5dwssc3CFn8y9
|
|
iPN5d/ivYFPJOXCScHK7LY/zuejhNXG7ORjkCOTU2IPPF/NuT1unOfjbKZjX
|
|
t5sKRo8cyVmuc9Cf3VHqh31ZMPqDlPccOJAvib/E51EKX9+jvWFzUH/k8509
|
|
UlSgc3qrqubPwXetiOEFCZzP/+V7nJ6aAwPnjBAVESrIDm4ZDbz6G0Ty1t5m
|
|
4vP4WT6PU4XnH/ALZz1mOUuBgJ8WXbJh8/D+5n3r/k4KzB/TTLOPmoePWQkx
|
|
9tiupSKOj6Pn4UFY1CLtEwXMQvuWeR7OQ2NSrwMJW13GVGI5bx52sK1NyH6g
|
|
AMPbyKO1bR5Ghm9wRbVR4Bqn/mZ7zgXIDOpZu1ZPAQ8NVf30+AWoXrkzdKCC
|
|
AoQr8cH3kxbg2ZQNufsFrl8ez5aHpC4AiPSp+mAXkgpELmUvgAFJsbW6nALD
|
|
rYI06RcLsI+lJkW/jAJG51diSrsW4NJEuZVvCa4Hr9T0NPIsAj3i0+cthRRo
|
|
fCy0sZJ/Ec6MILW3uJ4z/HwN8oQWgTlcjeGMfUVpX36kxCKu31duNeZTIG/5
|
|
8XWDA4vwkHTsQ2AeBbaF3xDpPbsI5L8BHsQcCiw/1rGdjFkE6OteMcjA9eiS
|
|
Ztz+hEUYzeinE7BvGBys90leBMOnIU7lj3F9vLpHgjlzEa5sHskQxOa7uHlY
|
|
pHwRxha7gybTKKDA+8PG4OsiWJfcVcx5RAGvy12x8d8XgXpVLdgSu7L+fd2P
|
|
gUVY/XhWexu2pkftDkcyNtfovnspFND7mD0UvLQInqePPg9IpoB9hJtNqeAS
|
|
HNzQcMPzIQXyfznFLokuQS9XtJ0i9pSKbZ2mxBJ8/7tSP59IAc8xox3tMksw
|
|
I1/1xxc7RFt9aPjQEhQc9pINT6BAyl9mG15LHG9jkvSbBxTodE+x9slcgkyy
|
|
ddfNGArIxGxZuZq7BFtVvlYaY98qCUvwLFyC85zTG2WxVWie7f+VLYG8ZPLG
|
|
r/cpkHZZX8mufglYllrt5LFdHP6ynR1eggf+l1IX7+Hnddsz04C8BDGWZwo/
|
|
Y4vmUDROTizB3YMM2WfYnSPdHsd+L8HRocUoe+yDNs/6NEl0uHi1u6rvLgWY
|
|
zS1LZCTowPbOankA1/WW/t0ndkvRwX3+5Nl32C9T9EYlZehwuTBfNAvb5buK
|
|
4I4DdDgWukHABfuz8eZbAtp0MA1bjl6NwvO7dluUT5cOGYJDD0awQxNWXvLo
|
|
0SGGTOVqx1btHp/iNKTDr6cvHJOw08++M2a2pcOXjou56th0d5U5ogMd7Otv
|
|
WO7CNox5emfNmQ68U/b3uLBZPiW9W/aggyPb09OjkXi/nfSQmbtBh6J9LE4J
|
|
2M2Xxxtpt+mgcZj27Sb29jsWVlORdLg6w1/rjv2l7UT8eCwdPvLa/DmFrXZM
|
|
4t/AEzqwd19Y4MRWymqPaMmhA016j8taBO5X1jy3lhbQ4XX0ytk5bImXDbtD
|
|
S+mg0/TZrwdbZKtr+X8VdOA6NfGmDZvfjVfL5DUdBk3k3d9ib5TG9XYdnv89
|
|
ywO52Ky3OH9ubaKDUrY5eoRN+FXhtNpKhyi+wroY7PlE1qDOTjqksp8TC8Sm
|
|
/S5mr+qmw/6itwwvbIqByYOsXjrARMLxy9gDrPn51wbp0FlQgMywe23PKFqP
|
|
0uH8jTnqOewvNfS3Jyh08MiqZT2F/V7oyXHFKTp8NRd8qIvdfO1El8gsHXie
|
|
MD1C2O++zFmwztMhb8MtnkPYVfIplJklOgj1PVpVxn4Rpe31fYUOH5bPmu/H
|
|
LiFPrNav0UGFkS8vh12o/SDiKRMD3m3KvroHOzv90NZENgaM8OjKS2GnL4+k
|
|
BW9kgFBMrNlO7CTju7udNzNgoiTirzh2XJlSueFWBszpyHFvx77LNaCpIcCA
|
|
7taQZFHsMJfbrZLCDNAxD00Qwb7RLHdu83YGCLSosqw7QKJngC7BgN2+6RRh
|
|
7GtBQU7DUgxwu10B6+PuP6T+dMgw4HdR4Ib1eC4qnwIr5HH804vHxbDt4nzY
|
|
Hx9ggGaA2Mr691vStj+IUGFA0Mi8uAT2Bb1WUU91Bgz/9KnahX0u1z3fTAt/
|
|
/kpOizS2AUlQ8ag2AxrU/Y/LYh+3rHsrr4vvJ3ZRYx+2dpXz8W16DIhy5M1R
|
|
xNbg5+kiGjDgysXPIarYKp5VFpNnGXD+2Z5OTWyFj7aU7vMMaNETfHAEWzKs
|
|
fDXPggGshk+9zmCLD5tFxNowILbraKwJtpAW81Z/ewZwf7KVsMLmWjTabfAf
|
|
A0Tub37shs1uuFp20IMBFplxUb7YpOIczR3eDBh/H0y9gb1kv2g4H8CA5n3+
|
|
xETs33XpAwMhDPgxdb0qA3tK9JhTSygD0tsbyEXYg18fBqbcZUC9EH9yA3bb
|
|
UbV8lMqA5f5nl+jYvi1B8sEZDCAfsvvNhvfX7hONL95m4+d97j/2bdhhJ0/X
|
|
qT/Dv2+JRrsats45+x9KNQxw7BfIuoU9311o7VXPgF37S1weYmcZz5JLm/H3
|
|
JfG/LsImXfT/I/8Jz3fDxomv2O+sYzftGcTXz9ulKOB84T7cE+c4ygD2touJ
|
|
x7G324kI5lIYoNUWtM0GO8gxT3LnHH6ezEvFD7A1rrzVEiUtA22EV2IN+6U/
|
|
1Z171zKef/uGGZzvHFbll07vXgbn/zgsN+P8yR98NTB67zL4p3cpK2BfvbkW
|
|
uVF5Gcw5Yj29sA9E8mWx6C5D2VNNUQLOv8WJh78yHJeh4+wuoQPReH1tCzdT
|
|
dV2GR7zNuRexOVPeD11zX4ar5M6KW9iuaSa0P77LkKIbfvEbtkz2f2y0yGW4
|
|
LbWjKhSfBzmlyWrDRctQ51XwbAmfHy4rZjK9JcugpCixQTIWr5+jYsIfy5eB
|
|
sWnoqyF2dW/m39dvloGrLqmqBLtrrag2tmMZ5DJLXlyJowDRoObo4cllSFOW
|
|
PE6Mp4DFxPDZDJkV6DohWe2Dz0MJpRztRPkVsP+7WFKGTQl0VLx7YAUQ5TYn
|
|
Dfsq9xSvr/oKNN7gYnFIosAd1YVvp/VW4FHYtsGL+Lx9HcZmuea8Aj9u8Qtc
|
|
wOcz3869LpYFKyAkJ7Wcjs/7mLg7xgXPVqBhRKl+CnsDaVJ7vnQF1t7/WVXH
|
|
9QJhqEA4qmoFYq2VP/ViT6VLf6joWIGqM1GfBDPxeSi0U4GTtgLM3n4rz7Px
|
|
/fAILb458BcAXQ7aj+ubL0T2m4LVf4FwmTxlV4nz67NkyzPv/oKphkd9OzbH
|
|
RdlD4Y1/oVPsMk3hJQVQmcH8/Pu/wHS4/dg/7GLbBIfOgb+QkzP0O/U1nl+D
|
|
hH742l8odQx4S63G6/e2Ju+C9iqU29xJfNtAgQp2r9zOtlXgjxl03/eFAnv5
|
|
trjYNv0DvRufeVZoFJiJXuRV7FkDslF8sw0XFaZmxerlfqxBQ6lO3BfsCcNj
|
|
brt/roHT0WbpI5upMMqf1CZKXoPSTJOnO7dQ4Ue6WhD74hrIF6oShrmpYGtS
|
|
84e2gYDYvrDOG/JR4ZQj0aJRhoDk+/SG/wlT4WRSQnndXgLiFeD+44DrXb22
|
|
PRtq5Qko0K3o6Ufs47KGL18fIKDjBSt8aaJU0J7J5C5RJ6ATPHKZytupoOqj
|
|
05ysR0BXTmTnGuH6eWd4+D43FwLie3vHVBvX3549SkG2rgSkaHQn8hH2O8nh
|
|
9+evEJBpop72PLZlo4aLhieOx4kj4Ho+hfg7m8OPgH5X9t/7J0MFngBzoexI
|
|
Agou6qSkyFHBpoPD+eEdAhL/V7ttCvu50MuXUfcIyEf8YY0G7g8MXnOf94gl
|
|
oKXVXY792FGLzfe1kgnobPETDj7cT5A89rN8zyeg2OR/wS643zj77ue594V4
|
|
/mpC/mXYGZvvZtY+JSDWsZO96/2KVjEZcp8TEOeXwfIw3M/4TT7y83pFQAqt
|
|
0x1JSlT4bc86y9lKQBKO5RZpuB86XFGuRWwnILeR6F8/sGOYbe7NdxCQqM2L
|
|
YgHcT8lnvZHp+0RANlbh++5juwy62+d/IyDtxDcJ3qpUGL7Y90N7nIAiYyMa
|
|
xXD/tknTJM+aSkCbvAIKjbCVt3d5BU0SkF2ZSnYkdsRI+6aqGQKCtB8ds9j7
|
|
XKu09tMJiKM06XU57hcvGKhsPL1MQMcab2wcxr6pUPbN9S9+Hk1Ntptxv9kz
|
|
X+CeTyCiUh8uIUfsgMDkzO0cRNShuMt3A+5fc6343DQ3EpEl0b1OAfvT4dhD
|
|
ZpxE9MXTkGiMLcEa2Z3ITUTd1ZYWadgnKcxPXmwlIrG+Zu9abO/2kP++8BHR
|
|
n93agYPYrdG+rFxCRHQk7dfZ7bi//u0+/0VWhIgy5pSENbGFz7k/PiFGROGf
|
|
md6bYl8RcFK9LUFE6Yb2/ffX3/8wRpizdhGREqe4agF2fZ/V53dSRGQblu1V
|
|
h82XYeLyV4aINj3Xv7n+vkjrZpeKkBwRUZ3vnGUCKjjZnWZS3UdE1gsf6fzY
|
|
cbodn87vJyL/Szuu7cGu3n0s1UuRiMTt7raoY5M3NDjFKhORke62ST3szdNa
|
|
yiUHiciU3vHTFFv1UxXxgxr+PvZnGY7YtqUqHycOEREhq1b+KvbdB2Up7FpE
|
|
1JvIGh6MXeEt7yiFiMj97K28SOyfJoWKOtpEtHtIOToOm11dimCrQ0TKCyJq
|
|
KdgHRDLfB+sSUd+Acm4Gttk/0eS040RUcTegKwc7dDDZ/o0eEW1NmKwpwC6u
|
|
5zvw/SQRHdob4PAUuzc79t+iARG92iPVuv5+iBjO2cF7lojq2QaH1i3jHPnw
|
|
wDki8htJL12/3kifxe7MeSIyDjRWLsQOkruhcMWEiK6pMVxysfM3r/69Y0pE
|
|
rOK+Z55gf5nzbSswI6JHA/Uj6/e70jWf0GJBRA8bWiQerL//qXS3HbMioqhW
|
|
r41R2AZJU/JMtkSUHVH2aP338PVzWhG3IyJR3SufvdbfL5mPtmg54HHq/UIH
|
|
7Pda1vHmTkRUQ1rbdQF7Qbzf2s8F31/rE63j2MfHuhgVV4iIPYD32C7sQNlo
|
|
/xJ3IrpMNkzgxi7zOL6a70lEnFUqBavr6+tfNSH1GhHF87EIf8E+o+NzM8EX
|
|
35+hr3cVdmjUfub7fkSUdCkz+gk2jT+X7WYQEV0y2rF4GXunhXWkfwgR0b4v
|
|
otPYF7KENnrfJKKF4NAj+7Hr9t3ncgojojeeNU5zeL3HH/flM4gmIrSgQLLF
|
|
bos+8PBYDBEdDTP8ro79r3tq2+E4Ito48M+UB9vRxkZEKZGIPl34eOYt3o/q
|
|
fno7hdJxvAHaEAnb7R1zztYMIjL7ubWrE+/nbNZaKc5MIqILmlilYXM+UJQh
|
|
5BJRo/vM4QPYg0Ui+8nPiEi2TPGvHs4PfL97yn6V4PXqKfqAE1tPNVbpeykR
|
|
sZT5VX5Uo0J5I4vq+wq8P4V3PzqJHTZA0yp7S0Sz2jr5Kjg/vdlZ8K6olog8
|
|
HZqvTOP8Net8STunDt+PZndZJrbp4rejSU1EdOow51N27L2b604GfSCi0QPb
|
|
5OuVcf4+7//R5xMRWWyVeOqKnfhI+YzHZyK6zRqfxIe9Jl14zu4rEX3v21Rh
|
|
i/PrF/Tgot4AEZ27nN9MxfnY19PeiX+aiJ5HHk0t2Ifznz7NUX2GiE6IpeQq
|
|
YD/c5eNoOYeff4vziwqc/yt7IhxyF/D6Nb/W+RqfF3/Un9qp/CMifQdyQ4Es
|
|
zi9Mf6yNN5NQRKeZjZQ0Xj/9/tZ+3CR06lLg1btSeP9WMFunbyWhar5btrOS
|
|
VChy5LciC5BQjvV0Y+kuKlA61CyuiZMQ57ehi0L4/LsUH2KauJ+EbGJGQkPw
|
|
+en5H4dplSIJnYha4GrA5+1N3bgLP5VJSAPU9JiwM+hZJlLqJGTb39gWIIjz
|
|
gXnL+UptEjquUpN5jh+vL0kuw55zJORzI84xGp/3BpWP9PivkZCCY5uDJAHn
|
|
sz+2a3y+JJS690+DzBoFbinIvODzI6Gh5cEvcv8o8KrwlShfEAlt2cuzuvcv
|
|
rtcef53dGkZCv5Snj2ymU2AxfPND7kQSsvvTmmkzQ4EtTT363EkkVJOym+sw
|
|
rkdkSekE7hQSouccYBObpoB1wF6XLekkpBMil9w5QYF29xOam3NJKFqM8VeA
|
|
jPs501sjmypJKP+UbqNcP/7+RL2kTa9ISLQumD76A9eXXdynNlWREHfgx4Tk
|
|
77j/MMio3FhDQq4nfEkrPRTw1H4buaGZhCz8Qy6lf6aAruzSPvYeEmqYuwT2
|
|
zbg+++sSwLRIQmI556VHnlHA9IL+HsYSCbmZdRzQf4rrvXLZHhqDhGQNvl5/
|
|
juu7ZJepfT9WSSjjVn+pZx6ux3r/G3nOwoT8GhXufsX14qNydz1LPiZUq+K9
|
|
yvMA92cu17a9VmJCclXC/1l4U6C8ybipWIUJXeZOzHfyooDYjoOe2apMaElZ
|
|
/7u7BwX+fFvquK/BhDKD07l9/8PzP3o92EGHCf3cGJRhY4/7FfEA8lYjJuT8
|
|
5NLJx0YUePLtxosrXkyouNrmQYUCBchNCr+ivZkQL+EP5255XA+++MVR4sOE
|
|
tldPPkmUpUBljKbVjD8TMrjHtdFJCvfrJxgc7qFMSDltW0KfMAXob9ytPBKY
|
|
0DExWwkmVtxvZlhtuPqSCRVw6wgd/jYO8dFcyvGvmVD1wWLf/d3j8D3grdWL
|
|
N0zI5GNDsujncbAzFa6Yr2VC/6kbC1Lbx+E6zzcr71YmdHenQOPJmnHIDjWo
|
|
uPYdxwt96a+TPQ7LTprW11eYUN87lbMjruOg90YGea8yoU8sx+pDncfhEec2
|
|
cY81JmT266C6hMM4aJT9/uXExIxM47NUzlqNQ9BKntWFjcxoUy3sCT47DkzR
|
|
PFYHhZnRj77rKoLK47CpfNxiQZ0Z/TbN1lBlkMGc5avmnAYz8r6rWGm8QIZn
|
|
JvWi01rMqNzKku4+RwaDv6kDo9rMSF5H9FMSlQwxRw0tuvWYkU1OeVzFdzLw
|
|
9labl19kRhyqgn07XpNBdDXWzMOPGbUstnC9vkqG48OnXj8MYEZf62U0aG5k
|
|
uNrCIVATxIzO08YVxS6ToT32xpcNt5hRSbmI3xUbMlyT8jiRfYcZreWVS3ee
|
|
IkPn6TMHv6Uyo6dFCdqJkmS4mcm1VbOWGc0n5A1v/zwG5GN32tmZWVARew9n
|
|
s8AY2Opbi0uysqBhj7W/b7jHYMBA+dphdhYkZVcS8HTjGHSf/7XDbxMLivj2
|
|
dnfg2ijUX1K8PsnLguhJ3DwD5FFIC+6T/ijJgi5UD+xOfDEKRi9lbz84xoLe
|
|
7VkRJuuPQoPUexC7w4I4iX1zH51HQC/6lx7/PRa0dTowbMh2BDoXfp/nus+C
|
|
/ks6pDxjNgI/GwVd/8WxoIR8qcGVUyNAt3VM+pnCgmw89Bx+7B+BvY9Jc+mF
|
|
LEi3sonnKX0YEgXUMre3YxN33n9ycxhc2HOZd3CwouSr+QID4UPwMmOXZkMs
|
|
K1K8auc+o/8TPh7SaDLkZkMPXG65vNT6DnSXR+eso9mQUjT7huL2Lmg98/g8
|
|
Jz87quCnVvH0tIOtmkZeXjw72hJRm/glrxqcpz8s9Ceyo1BpziegUg3uT6x0
|
|
eJLZUVNkA2dG4xsI5rg1FJDGjuZv5/UcGqqC1O9twoa57MhfXiZrVPA19Fw3
|
|
ifn7kh3Jy6Ycko6sAL0qz+tn+9hR/5yASl7dUzh7hbk1bADHezj2SbS/CC5I
|
|
JPJX/2JHGjnTQ+GLheAY9bpcapQd9S2f2aAqWwChFwm0lSl2dKty8fnW+Byo
|
|
Wb5nm/uPHQmZch6TbE2FpuLtpX0EDsQvPrd/eCUF3tuWrm1h4kD+B24vxO1L
|
|
hr727lR/Ng7EeOJxpCsxAegpwt/ObOFAdda8Jzva7sKawTPJMB4OZLjpEtNz
|
|
hUhgZYKrb3g5UN8ZNZvIh7eB97Itt5QgB5qebtl2uD0AhLfPW5kJc6AnldH7
|
|
Gh56g0TX7eIYUQ6U27tfwKfdFWTCBVabtnMgt0qXpxXt5rD/UIH+yg4OdNcz
|
|
58/pTQFa/wM6b9O7
|
|
"]]},
|
|
Annotation[#, "Charting`Private`Tag$14372#1"]& ]}, {}}, InsetBox[
|
|
TemplateBox[{
|
|
StyleBox["\"\[Mu] = -8\"", FontSize -> 18, StripOnInput -> False],
|
|
StyleBox["\"\[Mu] = -7\"", FontSize -> 18, StripOnInput -> False],
|
|
StyleBox["\"\[Mu] = -6\"", FontSize -> 18, StripOnInput -> False]},
|
|
"LineLegend",
|
|
DisplayFunction->(FormBox[
|
|
StyleBox[
|
|
StyleBox[
|
|
PaneBox[
|
|
TagBox[
|
|
GridBox[{{
|
|
TagBox[
|
|
GridBox[{{
|
|
GraphicsBox[{{
|
|
Directive[
|
|
EdgeForm[
|
|
Directive[
|
|
Opacity[0.3],
|
|
GrayLevel[0]]],
|
|
PointSize[0.5],
|
|
Opacity[1.],
|
|
RGBColor[0.9, 0.36, 0.054],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6],
|
|
Thickness[Large]], {
|
|
LineBox[{{0, 10}, {20, 10}}]}}, {
|
|
Directive[
|
|
EdgeForm[
|
|
Directive[
|
|
Opacity[0.3],
|
|
GrayLevel[0]]],
|
|
PointSize[0.5],
|
|
Opacity[1.],
|
|
RGBColor[0.9, 0.36, 0.054],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6],
|
|
Thickness[Large]], {}}}, AspectRatio -> Full,
|
|
ImageSize -> {20, 10}, PlotRangePadding -> None,
|
|
ImagePadding -> Automatic,
|
|
BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
|
|
GraphicsBox[{{
|
|
Directive[
|
|
EdgeForm[
|
|
Directive[
|
|
Opacity[0.3],
|
|
GrayLevel[0]]],
|
|
PointSize[0.5],
|
|
Opacity[1.],
|
|
RGBColor[0.365248, 0.427802, 0.758297],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6],
|
|
Thickness[Large]], {
|
|
LineBox[{{0, 10}, {20, 10}}]}}, {
|
|
Directive[
|
|
EdgeForm[
|
|
Directive[
|
|
Opacity[0.3],
|
|
GrayLevel[0]]],
|
|
PointSize[0.5],
|
|
Opacity[1.],
|
|
RGBColor[0.365248, 0.427802, 0.758297],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6],
|
|
Thickness[Large]], {}}}, AspectRatio -> Full,
|
|
ImageSize -> {20, 10}, PlotRangePadding -> None,
|
|
ImagePadding -> Automatic,
|
|
BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
|
|
GraphicsBox[{{
|
|
Directive[
|
|
EdgeForm[
|
|
Directive[
|
|
Opacity[0.3],
|
|
GrayLevel[0]]],
|
|
PointSize[0.5],
|
|
Opacity[1.],
|
|
RGBColor[0.945109, 0.593901, 0.],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6],
|
|
Thickness[Large]], {
|
|
LineBox[{{0, 10}, {20, 10}}]}}, {
|
|
Directive[
|
|
EdgeForm[
|
|
Directive[
|
|
Opacity[0.3],
|
|
GrayLevel[0]]],
|
|
PointSize[0.5],
|
|
Opacity[1.],
|
|
RGBColor[0.945109, 0.593901, 0.],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6],
|
|
Thickness[Large]], {}}}, AspectRatio -> Full,
|
|
ImageSize -> {20, 10}, PlotRangePadding -> None,
|
|
ImagePadding -> Automatic,
|
|
BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}},
|
|
GridBoxAlignment -> {
|
|
"Columns" -> {Center, Left}, "Rows" -> {{Baseline}}},
|
|
AutoDelete -> False,
|
|
GridBoxDividers -> {
|
|
"Columns" -> {{False}}, "Rows" -> {{False}}},
|
|
GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
|
|
GridBoxSpacings -> {
|
|
"Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}},
|
|
GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}},
|
|
AutoDelete -> False,
|
|
GridBoxItemSize -> {
|
|
"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
|
|
GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}],
|
|
"Grid"], Alignment -> Left, AppearanceElements -> None,
|
|
ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction ->
|
|
"ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
|
|
FontFamily -> "Times"}, Background -> Automatic, StripOnInput ->
|
|
False], TraditionalForm]& ),
|
|
Editable->True,
|
|
InterpretationFunction:>(RowBox[{"LineLegend", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"Directive", "[",
|
|
RowBox[{
|
|
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
|
|
|
|
TemplateBox[<|"color" -> RGBColor[0.9, 0.36, 0.054]|>,
|
|
"RGBColorSwatchTemplate"], ",",
|
|
RowBox[{"CapForm", "[", "\"Butt\"", "]"}], ",",
|
|
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",",
|
|
RowBox[{"Thickness", "[", "Large", "]"}]}], "]"}], ",",
|
|
RowBox[{"Directive", "[",
|
|
RowBox[{
|
|
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
|
|
|
|
TemplateBox[<|
|
|
"color" -> RGBColor[0.365248, 0.427802, 0.758297]|>,
|
|
"RGBColorSwatchTemplate"], ",",
|
|
RowBox[{"CapForm", "[", "\"Butt\"", "]"}], ",",
|
|
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",",
|
|
RowBox[{"Thickness", "[", "Large", "]"}]}], "]"}], ",",
|
|
RowBox[{"Directive", "[",
|
|
RowBox[{
|
|
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
|
|
|
|
TemplateBox[<|
|
|
"color" -> RGBColor[0.945109, 0.593901, 0.]|>,
|
|
"RGBColorSwatchTemplate"], ",",
|
|
RowBox[{"CapForm", "[", "\"Butt\"", "]"}], ",",
|
|
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",",
|
|
RowBox[{"Thickness", "[", "Large", "]"}]}], "]"}]}], "}"}],
|
|
",",
|
|
RowBox[{"{",
|
|
RowBox[{#, ",", #2, ",", #3}], "}"}], ",",
|
|
RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",",
|
|
RowBox[{"LabelStyle", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{"FontFamily", "\[Rule]", "\"Times\""}], "}"}]}], ",",
|
|
RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& )],
|
|
Scaled[{0.5, 0.01}], ImageScaled[{0.5, 0}],
|
|
BaseStyle->{FontSize -> Larger},
|
|
FormatType->StandardForm]},
|
|
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
|
|
Axes->{False, False},
|
|
AxesLabel->{None, None},
|
|
AxesOrigin->{0, 0},
|
|
AxesStyle->Thickness[Large],
|
|
BaseStyle->18,
|
|
DisplayFunction->Identity,
|
|
Frame->{{True, True}, {True, True}},
|
|
FrameLabel->{{
|
|
FormBox[
|
|
StyleBox[
|
|
"\"\\!\\(\\*SuperscriptBox[OverscriptBox[\\(\[Rho]\\), \\(~\\)], \\(HF\
|
|
\\)]\\)(\[Theta])\"", FontSize -> 16, StripOnInput -> False],
|
|
TraditionalForm], None}, {
|
|
FormBox[
|
|
StyleBox["\"\[Theta]\"", FontSize -> 18, StripOnInput -> False],
|
|
TraditionalForm], None}},
|
|
FrameStyle->Directive[
|
|
GrayLevel[0],
|
|
Thickness[Large]],
|
|
FrameTicks->{{Automatic, {}}, {{{0,
|
|
FormBox["0", TraditionalForm]}, {
|
|
NCache[Rational[1, 2] Pi, 1.5707963267948966`],
|
|
FormBox[
|
|
FractionBox["\[Pi]", "2"], TraditionalForm]}, {
|
|
NCache[Pi, 3.141592653589793],
|
|
FormBox["\[Pi]", TraditionalForm]}}, {}}},
|
|
GridLines->{{}, Automatic},
|
|
GridLinesStyle->Directive[
|
|
GrayLevel[0.5, 0.4]],
|
|
ImagePadding->All,
|
|
ImageSize->400,
|
|
LabelStyle->{FontFamily -> "Times"},
|
|
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->{All, All},
|
|
PlotRangeClipping->True,
|
|
PlotRangePadding->{{
|
|
Scaled[0.02],
|
|
Scaled[0.02]}, {
|
|
Scaled[0.05],
|
|
Scaled[0.05]}},
|
|
Ticks->{Automatic, Automatic}],
|
|
InterpretTemplate[Legended[
|
|
Graphics[{{{{}, {},
|
|
Annotation[{
|
|
Directive[
|
|
Opacity[1.],
|
|
RGBColor[0.9, 0.36, 0.054],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6],
|
|
Thickness[Large]],
|
|
Line[CompressedData["
|
|
1:eJwV13k8VdsXAHDudblIMo898qK6lQYh4zrkSciUKRVSxhAqKooiQ3qFKBkr
|
|
GR9JMqSJIvI8L/OU4rruvQ5PCnckv/3763y+n8/+fM5e+6y91lmbfM46+RIE
|
|
BATcBAUE/v8kvhPrntINN60cqeDnOUWbas68Nfrtrj3kddkW6W44Crxnu06P
|
|
ZHhBXfyNTq5kIEzLBnDqM87C1w1L5Z8kL8GoZcL74oxY0En37QyQTIEBr4wt
|
|
+Rl3wJlB2y23/gE4BSuNZmcUwofR8Nlv5HJI/3m89l5GNVgdq9hBWWoEozZr
|
|
MfNzzWApl+q+/fEnCLtsd7I2rAM+3zXJWf+wF0IafW8Tfv8MAn6bI0snh6Cf
|
|
eUi01KcfTpICG+JXv8DNXSyB+qPDoNrzRacgYwIuRx3aTg8aBknulc1LORMQ
|
|
+C7PRT5mGEaVjT0siibAyv5ARWTBMAQ5fsnqq50AkbNpR/SnhiHrdJ5zVf8E
|
|
JDyllDQGj4CWm5+RndwkXN3pZfMqdhQwDg0OZUxC+PaOrObiL+DYWxx6JJoK
|
|
NF9a3MP6L/B9Wb5A7ToVXB8KBMe1f4HrKTtj6clUMJQzMMdmvoCgj+Xx0/eo
|
|
QFgrn3+3Yxz2DAhWqddQIaM39eC72nHwVOdI5E9T4fkle+6blq+gopo98sx6
|
|
CninzjwdD52AyvcBys9JNPCWWrz4OnICtHYmaY6K0aDt7eUDuVcnoMbfR/CX
|
|
JA3SlG4Ou9+egBVNEx0DZRps+beM0F81ATkWCQ1XtGngbEh37ZybgNfhpaJm
|
|
rjR4uuHkWn3QJDS3VF5595gGPm9cHdL8qJCsVbJVYfc07K1XlFY6S4W2T5XW
|
|
BfumgVA92vcoigoRjfpbNxlMw+OHnm61KE4xXFtD2XwaqPF+noMVVNCbsg4Y
|
|
OTINPtaRwarfqeBFOsu+E4k8lJVcFjUF+78sGCw2TsOpH/3Nzck0+G+L0GXL
|
|
vXTwvpzm1phGg+ehZ5Uf6NLhONF2vjqbBiGLk3XM/XRwlfugUlhGg56QO8yr
|
|
QAcrg5rIKx00ENdfSEqypYP2tT93GJKngVnQTVrnRwfOBsvs2qRpyI7wql66
|
|
R4dbuxvOliTSoXLsgeHIAh069w7RL9ymQ976coOIRTqQddkn/kDrtFJ3LZFZ
|
|
dEgw0LelFdNhQ5xt8S4+HaLNG7ZqtNFBBzc18iExIMi5YTKfyIDw0yw7TyUG
|
|
HLzYcCQrjgEn1C9XvgcGEJob9BMuM8Hlz+RrbxIZUCEhXbJ6nQl7nk5fIKUw
|
|
wOlYsGxUKhMMDAvP2KQyoIil/iMwjwnrJSX8eu4wwGLnzQr7t0xYk6+ktmUz
|
|
IDHn+EYVwgwkeO88cqSCAWIXBInPU2YgW7vXT7qLAVIUm+5v2Thss7VkVIox
|
|
gS5SKNXxEAe+durVwHVMaJr+6fysDIcat8PUzeuZcPpRzlhcIw4ERxf5bCkm
|
|
NCrizE3DOITu8zoZpsgET5EU4mmFWWDH5wnhmkyopH3cz8yaBfeakC0SGBOs
|
|
Cs2LFjLmQF2ulBoYzgSF712WsQ3zUG/ZSxnvYUJOe5MgMXABHOnbEyO0ZsB4
|
|
o9ma+ukfUOvy4mt/6Axsn9hAu3L+J7y8fUbVsGEGqsqkA+oiFtE5V+t3LKE4
|
|
B96ZEaMWYaeqFLN1eQaOE0JUHKMXIYI3qtjCmgGx4+3dc/GLQO+R5TVwZsBP
|
|
MkZ3c9YifD4l/qxwZQbUI6cJdxsWAZRJaa5COGQeaMwPW1mEYVtPEy8ZHGK+
|
|
nujbnrgE3cvVjq27cFg6aJLve3MJfi2ofnmwG4fgGlX/wttLUPyB0hO6B4dj
|
|
CWM86ftLYNMTxZXXwcGQclSDV7oEdjJret56OHAvOId3fFqC/BlBkUFjHCIl
|
|
bCR9JZZhxKBI2PYQDvORlJECqWUIXn0ns94aB78J0aJhuWXwyxG6+i+ya22H
|
|
nu1vy6guHgtwsMVB96ilp86uZRgwLUm2tkf7e2JWJei4DGcO2eaqueAQbrzf
|
|
piBzGaheIrusvXEQCM2MvZO9DDMFxddmkW8XLtTG5S1D/GFLo1sncagglKue
|
|
erIMNvGHqH/74EDtUJrf8mIZ3FejWQd8cXB24afV9KH14d4/5INw0At9O9gq
|
|
zQLvwV9iludwaC1UFq+XZ4GLvdGTPmSnnkgoVWbB67aGHO/z/8+bXWUpGixg
|
|
eloVXLyAQymv8JLdXhYcZ71mP4zCQTHpmuqwIwvmFGJe9EbjwCu08JlNY4Hv
|
|
nHtAYzwOpmyTjD1ZLFDe0GBmlIDDNTv991EPWOBKuuL4Bpm8uk1D6DEL6G4s
|
|
6Xc3cJDzkKSq1rJgw+Iz2ZdJOOyWHT1pN8CCh9UO/ySm4nDuTF965ggLTP4J
|
|
Yqwg17/vahkdZ4F+PmdvxC0cTMLfbfKns2CPv/kJjz9xsO5+MhnLZsGLZ6Es
|
|
9Ts4+CafPVmjxIb799/wEzNwKPsWkM7eyAbrgi6xBeQ5PZ8WEw02MIL7LN3v
|
|
4hAx7bypk8KGyIwmC61MHOLMDSepRmz4GF7h0JiFQ86K0ElZTzaE6d8Le4Hu
|
|
6eewHO+ox2woOo9vES/AgZK2gX++hA2zbpk6zsjx1YlZERVsmMjtistD1puP
|
|
6Ax5zoaXpAPfKIU45J+x2Xf6PRvSh0dKTdE9D/JbEXGksqH/xqM/zB+j73Uj
|
|
4rEdnQ0Pyp+5xSJvLGYa2+JsMMmdKXuF/HmqP/zgTzbkXrcj7y3CQf9k1ZgJ
|
|
gQMLF3Qa5J7gIHTcs5qiwQFFUeuXjcU4eEb3H9qqxQGd2odPZ5AbcqxpmhQO
|
|
nDuwbVKpBL1/RE9p014OHNU9uRqF3OMqGa9gzoGsuzGS20tRfJE3NspZcuBt
|
|
ztlZF+SELH6DtDUHlhXfE+OQ9/cz5iScOJB+Z/NMD3KBY7OrkA8HDqc4JgSj
|
|
usUJ0/sh6MeB98ersXRkp7TK1LVADmga1++vQyb9m93MC+eAiWXwGA852Dac
|
|
8uMaB7qO2s3ElOPw8Qyjdf4GB+atPsblIqulnvCaS+HANunDR14i9346lMlI
|
|
5wA3wbz8J7LBQY1f4484cFKCpHC8Aod9RZ3J7cUcMIg1XXceWXstQqamnAOR
|
|
Q/UHUpE1Gj5sTajhwKfJ3ZcakFVlgmtD6jhA/q4U1YUsf1bW1O0lBxQebGiY
|
|
QBbf4nuE0sIBFpG3IvwXDsLxEl9l2jhgETJEUEIW+FYXsNrBgYut960pyEv3
|
|
hK9+/syBu0q5hdbI8z+fkpv6OfD3+q7Ko8hMO7e7RcMcuDnxiu+PPC5cVhY5
|
|
wQGZe42e15GHfRx0vGkc0G6pj7iN3PuW8+YQkwMJbq4dD5C7lB9Z6cxxQEg4
|
|
3esJ8sfIQ32qCxxonfLe/xS5uffHCeElDpAimp0akJu0c5jf2Rwwy6t4+g75
|
|
xU3zcyN8DmxuVLZtR66m46vv1zjw+Ma67d3IFeZ3kyuJXJjVjrHpR35SYCRz
|
|
T4QLcVZ+VSPIBbyp/FhxLmzsaXf4ipztemtroCQXqHsKdKnIGc/31TrJcGGP
|
|
KePYNPKt9eMmxgpcaNF59IGBnBh0o0NThQtPmjqDZ5Cvfdx5RFKNCxbTPm44
|
|
cozG4DhHgwvHdwfG/9+RV68GULW4QIofX/j/+rBRrcW/KVyo1m4uZCIH6f17
|
|
pU6bC5u+S6XRkU9nRJEL93IhFu9rmUL2nFe7m6zHBaMaEd0JZHfrjo0RhlzY
|
|
bFo9M4Z8pCSs7JgpF1xZXd8Gke0ISjp/mHPBtPyUQg+ylWfLG21LLtxLi0zr
|
|
RDZvCrRStObCaQdRmw/IxvLSfYJ26LxYagdfIetFNJ2YdeTCm5W3Cc+Rd3f7
|
|
MPtduJBrMUssR9ZMrF0tPcGFh/sF2+8iq1OPJaef5ILdG5ZYMrKyqZBMtC+K
|
|
Vzc9LRp5Pct5q10IF5RMe7y9kclOq8/1w7kwzrnxlyMy4WmxyaYLXDjPXdU3
|
|
R2b7spyWYriwVukhvwn5Z0vB+HgcF4xHHAMkkec2HgxoT+BCp8melRWU3xMD
|
|
96/k3OJCm3bvzADypz8MyrA8dD7Wg+NXkS+2X9WOfYjia76j54u89VDrizdP
|
|
uCD1h8Aza+REW/sWwyouNOXYkmSQLY74ju57y4VE/3yjB+h+LvVXeJ97zwUb
|
|
Pfm8i8hFrgv0mo9cYG6b3OiGTPCIXtT+lwvEobYbUsjN3unrtk1wYeK080w0
|
|
qg9h1MEMfxoXumNors7IaqdVlUqYXBj4LZG+Hfmqf6nm7z+4MBoSEDyM6pFx
|
|
6BvTjQQeiFfXyG1BboieCZPazINPR8I5Oage+q1qs+238iBZ+XWmL7J87Pkr
|
|
t3fwIFaB6LIL+fz1tRRxXR6EjsmYN6P6ujdFrohkyQOFZPPeIVR/n94zG+D6
|
|
88BsvmZu/BHKL8WkY/uDeWAOt0ZzkCVyuiYjw3igIzU274ocnO82v3iRB5/d
|
|
k1K7UP2nPAkRmU/hgeL1DTlVqD8U1zwwoP7Fg3/Xu+kezEf5zD9GGa7mgV66
|
|
uuhKHsqfP35T6a7lgeM/0hrPkF8PP155+YoHdf2qm+WR+9b+epf+Nw/YP26F
|
|
jOTgIGj39g+zWR6cfepiYoL61wmc6viQwgej4Bz1aNQPNfYVm9/T5sOo/uii
|
|
IjLzir/Orb18mM32kK5PR/FLzcleNOSDii13z3waDqn7l4fsrflQo9Yh6Ir6
|
|
7ctEEc+1QD6MBZbICaH+LPf7jiDPcj40B1Y9G0P9Py0j1bW8ig9dz1/CUWQx
|
|
wqz5Ug0fijd7EAfR/4PAZLnKzSY+XJcv2/bPdZSPBVv+qfubDxGjrfyaONQP
|
|
lX/fLTHPhxeDPYKuMWg/0sqsV3tXYFkqQ1QM/c98v3aJKqy/AktcymBoBDqv
|
|
H8PdjkYrgA+WUnvDcfD+fL+UcWAFvp3seZ0dhoPtbbmjMi4rICh/N04lFIff
|
|
xaReB0WtwID7mbzVAFRfBcnXlV6vQGD7tlk9T1Svqx54OjSvgFntuqakEziI
|
|
emw3Smpdgckh8S9Dx3HAntstLXWtwMLNn8qRx1A++GT5fR5fAdmjF+9UuKPz
|
|
+qBhk7S2Avsf/FO56ITuww0T2WXzVTAqbvtT9CAOdeRzJZ8/rYKqwwvhYztx
|
|
2CG3Icin7RdcGpnVuciege+3WbI6g2vwq+fj1ui6Gfg9KWnX2SABTO1QMaU/
|
|
fAaoHmOj5gwB7Itx62Y1ygxYTfdx60IFMZ+QyECvASZcjPANkP9PEPPoeicX
|
|
dIUJyTbz/obfBbH/pOzc+qOZcH9zlL/nD0HsdLVBpQmae+oHk/1KlgWxvdld
|
|
KRJRTFg0rDyt90sQe2vVTn8UxoRQ4qK3qyQBO3wrtz73FBNOZcYdvbeHgE1Y
|
|
Jt1vt2KCXX2utXwkAVuUPSN8X5IJAYs+a3IXCdip4v0NQxJMiN9NeSF3mYCV
|
|
pVF2KaD5prGicaPcVQLm2LIzJIPMBI3CgQWZRAJGZGrOXxJkAitJ8r7UPQL2
|
|
F93wpPgiAwqOxk+tqydgDhIDdykDDJhfCYohsgiYec7WQGYmA46622zjsgmY
|
|
h/wx1kAGA1prtw/OcwmY156/h1vSGPAgaG7X6CoBIzEHMzNvoXltOGTqGYmI
|
|
7VQJrdJMYEBubZi1pxwRc5+4fnkpggFWQZGKL/cRMf0P98V17RnwaOjai9Bz
|
|
RKzdQm/je0EG0Nt2f7t9gYgtOvPf8H/RYceLb6LVUURsQrcMpSkd6tNMvL5H
|
|
EzFLI7uWbDSfdh3iioYlELG1D7kFFrNo3n0V5hWeRcTavFRoiv10sHvoJXa+
|
|
gYhV2ypfyS+iAy/AxPsSn4j5D+heOGVAB+tXFOzCKlqftfWFgh4dciUU1cPX
|
|
iFhmWtNSB5rHjZ///BZAFMLCvShhGjvocJVf6uUuLoQ58TDhmt/oQLwt7aWv
|
|
IoS11i95GRLpsK6WcWLZUAh7JL/oMftpGjauph8LvyyEbfNMOrPv8DRYUQ+/
|
|
vB8jhFmwpBZfWU3D+XZRhbdXhbCtwck6qElDZ/q1XrF4IYxhkdy732gaIrXC
|
|
Dz1JFcJG1T12c7ZOw2d7B/2hPCHM/aZy1RPiNFx/vF7G5J0QZhJxU7Wwjgb0
|
|
g6mdZCES1nfGvfy8OA18bLzVNYVJmIaQA/k/Eg3G7XQjzcgkLG3gTKa3AA36
|
|
Xb5turyOhKWonaIYLE/B+1M6l2ZlSVjoYwuxZ1+nID92bEu3Jgm75ryW+vzZ
|
|
FDg3bL9x9yAJaxLYM8JzmIIPWl3wWyoJ+5nwpFzrOhWsb3+zlv+ThJ36zS6j
|
|
O5oKn5d/uqy/Q8JkCu1Hwy9Q4WurUvCvDBIWtlAYXxFABY6Pf/bXHBJmpqCu
|
|
QrOjwo5Cwo+CChJ26cINvyhlKtxTMHis1knCqE3rzys8nYQgconQJlFhzLbz
|
|
55pU+wQ0PNxs8iFdGJu23+EC6uPQbWTc5iQlgp0a6Su55DkMnKDcI963RbB8
|
|
GbMlix190OFQ6CIhT8Yi5YgjnjKd4GNgXFqaScYCfO2LemmvIPC/f5a/3CNj
|
|
058y9wRHvoKwR14W0g/I2HfeUiFb5BXEisZPxuSTMcZwHp9GaYK8kU8qTiVk
|
|
TKvQ/pNaWCMMXnJLW2kgYyUpVwYtOS/AuinikuMYGWO7/enRLVgJjqFCHYnj
|
|
ZCxoKP37EY2/wF3jnvzrb2RM/+7hc3+bV4D/zZe1WjQy1vn5sGxGfBkkeAjM
|
|
8+fImNnjIs+bQsXwlvenT8kvtD9n+1ZF0Txoe6pWMyYgipmSXfS6rXKgy6dm
|
|
bQNRFAsTFRWMTM6Gsc7+vGgRUUxdZfOBhyJZwMlRGXLYIIppHLg7+UPsFqzZ
|
|
VWkmSotiTXWpxnUpySBMhPOvZEWxi5fnBs+Qb4DsGR8pLSVR7Mnres3z4jGg
|
|
orbkdUxFFPPgyz+vIF8Ajb4bT9M2imK7BFMKK8WDgZKksNqmJop1m524jYsf
|
|
hz1G5Tb8TaLYFnb2cIRTtOn/ANysuKY=
|
|
"]]},
|
|
"Charting`Private`Tag$14372#1"],
|
|
Annotation[{
|
|
Directive[
|
|
Opacity[1.],
|
|
RGBColor[0.365248, 0.427802, 0.758297],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6],
|
|
Thickness[Large]],
|
|
Line[CompressedData["
|
|
1:eJwV2Hk4VF0YAPBZyFIqaylKik+yVFQS3ktFIbJEskUIUUhEspSyJCFr2ZK9
|
|
UGRJZctOKBKVnZk7kX2ZGeQ7/prn9zxzzr3nPee857x3j/UNfVsSgUCYIxII
|
|
67/kSs62kSOuKuHXOt1JSXdUxGgVJ3Y91YVfw7bn3Q1NgPlG1qY3yhI66J/l
|
|
FQwdYIzPnl4SdQNs1YO5OQy94Kd6YE1GlB9k6nsfyDMIge+WUf8lRT2BuJmh
|
|
RWf9BNB3EvwZH5UC0o936Ieey4HIWbOi2KgC6Cjfw9ym+B5O1Glyqt2sAuEd
|
|
84ys6SZw8daxKnJphGVvK1x38Bs4l9mGk/Z2gGnEBaiEHujCz3JkWXdBPzU5
|
|
yyegD0JlFwklJj1wTYE5MU8dBG/Pswcojj0gsBJ0NnV6EBwqEy8I+PRAccuv
|
|
v6cZg3BG92SuR3IPpBNdN/lzDgHbjQiDYyM9sDWrIb5AaggC8yUzy5x6of96
|
|
/4flG0PgK22p9cHvJ2RNXSvRmB0C1wONMVUZv8HKtFLk49gwjNqO+qeW/IYF
|
|
6TPaPRPDYJRKcPJv+A0jrT83TM0NgyL/cTWM9hvS07OlNpFGgLSWM1kp1Qda
|
|
ZZmGrLtGIOrbI43Koj4oUN0/O2c4AoVeuoxP1f2wWaRSuLliBJhXruX3XR+E
|
|
Ey0k1ox7o3CZe+72R49ByLq0h29j8CjUVXiffO47CLHwqMjp8ShECIb2XAwf
|
|
hAJJ+RzR+FH4rz2b1JU3COJDbM9M8kbBUJFi1DwxCIvaf//Md49C/lartRLH
|
|
IXga9vbRhPgY8FXgTTFuQxAWzFnYcGAMvK65RLt7D4FjaFZi8sExOFXvt/9w
|
|
6BC4vPhYB4pj8OtOskFezhCkbDiQoHtuDNipv7Je4kPw1e/Qz0y3MbD+ZHQ+
|
|
wm4YZBtK2rDyMThcsp1H8MYw6Jyfeb5QMQakgp+dLzyHofl3SnHG5zFIS7Uw
|
|
LgoeBsuoOz1LrWMwfN/Oojt3GIKqY/baDKD+ND2chKaGYY5Vh9uSTAHrHzHB
|
|
2Z4jUC29v3JagwKHO4w1D/mPgJAhYT+fNgVITYKbyoNHQNSfQ17uPAXSypOe
|
|
tCSMwEHvDwo2FykwnJQRO/lhBASXD2lG2aP+bIrT5QmjwApR/0SCKXBlpquq
|
|
CsX5cbbFbaFaClz2jjAuixgF2Wd2e30aKGBG1p4sQHEmCGA6Pc0UMOL/vDMl
|
|
exROcP6UeviVAmeOv/W42zgK2zb81S3rp4BMwGMpRfYxaFgOUb1NpwB9q3p8
|
|
UdAY2geSYZ77qTCfQJR99WQMXORa265JUWFG9FNdWtwYYGM1fWayVPgjLz8X
|
|
mTUGg8IXHY8coULfRVEdl4Yx4OGsC6jCqFCT+o8szUaB25onGzBjKoQdLL2R
|
|
+ZAC1cOFScwAKjQf/kG5FU4Bkdt3pP0DqcB+ZMn8dCwFirkH50hBVAg8fkx7
|
|
NIMCjnNx0oQwKtxRK5UQraPANa6b0b0xVHA0LB1KIlMheOC1FGcOFTRulxrE
|
|
+FNBwK3M0u0Lau/9o9kmmAopTMv/Xraj9/FZUpWPoMJ7z0Xnr1+poBJw7GBn
|
|
ChWeUIb8xbupcDS0dBN3JRWWXx1eKeynwr7E0rqwVSpM8m45YTxFBVJV6bFA
|
|
bxwW3+Xo/N6MQy4XT+bqPRxuFWSa/9mKg76pE5/nIxy23tr7ZYEHh5eLIjMO
|
|
iTjo/U3vYdmGwynp0FzdChxCLzVNknfj8PCZmfBOEg0+sor6BMvgwHmLSC4M
|
|
ocF/xi/IFVo4FNaYuh6IooEazw/bu+dwuLS1ZCD9GQ14nLN8FXVxePXK8WPc
|
|
Kxoc2R3cn6ePg/Zw5627X2hQCptTvUxwCNfNxM9w/wEvncZrWXY4cEtqtQ3E
|
|
/wGRHbZUZz8cKGwp3I2pfyC77Fh1uz8O5WOzhm+y/8DtwrARWTQumxfPfvmX
|
|
/YGN2Skc44E4lG3/g+/p+QNHtAx4zoXiYMEWQrbZNg6ZSwpN1dE4vB6tV8Bj
|
|
xiFnv7/YnWwcAmp2+HQkjQPnyYymnBwc5aPrlWUZ4/BcgjnbnYsDwUxAPaR4
|
|
HGzD3H5L5eFg0GlrIPl9HN485lJueIsDs5rluhPfBMiWsdSWluNwJkXt5XTU
|
|
BDya8tgR3YJDUGNH373nE0DteOP5uhWH+hmL7fzpE/Dq0laTz19wOH3qzuPj
|
|
xRPQx/X8zUQ7Dmq0Is97Pybg/fTEhHQXDkpyYtp8Qn9B7k6EjdNvHA42sC0c
|
|
y/gLBT+eHKeO43BjOka2Oe8vNHCEk7omcMgX3OdoVvIX9ol/Ca/8i4O0Ezbg
|
|
3/AXxlKd6VFTOEhyezU10f7Cfi/bkwfmcNhn+ifJVGYSwu1FtfYycdg21aru
|
|
VzoJyS/T9JTZaBAfWWlFq5yEN4lj6iR2GmyXL/QxaJyEJ+/4sPp1e8UV/teL
|
|
2iepndLipMEOsvWuDuYkPIWGT2e5aLBr29KCiMoUxHB1Vgjy0kAc9mTU1E4B
|
|
u8aDsS27aJA5xFsl9WUK3ud82FuGLB644Vfs9yngT2mJstyN1lnT+NZrlClQ
|
|
X0lmfy1Cg+j9phUcLNNQ2FflcWIvDWKLxCQLxabh1WiO+xEJGjxrKCeSHaZB
|
|
uLLwUvIhGkwPvvGacpqGo09xI7HDNNBgZs78cpkGn4dDla+Q56WeDr27PQ2M
|
|
ime/SuRooBN1rdoueBqufDTSrz9CA5K5UEBz1jTQpc8xm4/T4NrsXUIUZRos
|
|
NE4PuKjSoGaj+23fP6i/y21cVOTtYo7TjpPTQGIrrzFTo0G9sdHgycVp+Pw+
|
|
qUb9JA1EPslULbDOQHB7nAz/aRp0BQ34mYjNQDZvlkHiGRooCauuidjMQDuH
|
|
qvdFXRqcMetys7afgdXmTTFNyIbPr1JeOs3A+Meo44rn0fsIhn8RvzUDXAXN
|
|
ojv00Pj5fz2XejgDdsSQ0C59GtC5bikoZM/AbGmYrrwRDd79y3bVnZiBxVcJ
|
|
DulmNDgwuHX0rvssvMKvWNjbo/FTRWo8bs9C9ZPNXB+QXSYPpt7wmYXJhgu3
|
|
uBxQ+5XzZlaBs/CYQ9T9LbKSYGTXqehZKB4xk190pIG2Pnfdxnez4Le2lfOm
|
|
Mw2carkzE+Zm4bOx7DElNxrkZfPYF7vNQZ5DavzOOzQI/F6pSvacg0/JlvE2
|
|
yGYk5516d+bAXEvMJA+Z06yhbeL+HGwXfbVLxYcGdlt8juyLmQNKXH2l2V0U
|
|
T48x0tPSOcim48Hhfmh9nCxLclmZA+nu/gd192ng02/eeeDhPBBbKm+GPELz
|
|
raGcZBs6D+ejxZg1yE5vha6mhM+DfEyu9gqyaeAvJk/cPDj4GRldD6OBoqSJ
|
|
KDNrHnTx5VXdxzRg3DJ0bWyaB+FFvVccT2jgwaW1xZZrAdR7PTqMUB6c9JDs
|
|
TeZegI0E9fkQZLtBjpc9/AuwNSF+7COyUVHjUe1dC7Dfpu+g6FOUF03ULeRk
|
|
F0BQ28HxD/J8umoeUW8BLu8tcXKNoYGrkoJWcvQC5F9xfG8STwPC9Wi/J/EL
|
|
UF2AR95HDk+ZLvJPXIAFvXiVPORcUo7QlfQF2Dd0j4+QQIPhRsHJ/94tgNEg
|
|
FL5ENrywHPG2cwHOfysrHEZ5+uj1iu5ankV4PzDxCpJoUJuyY2OJwCLsL+ki
|
|
2yDrf/WArB2LsNnTQTYY+bq8bHaI6CJ8ItwjdiBnMVO8dA4vgkBAbYR5Mlr/
|
|
QQFCPXqLUK5Ov+CSQgNmyinr8YhF6LswoOn+ggYqS8pRh2IWYXjUMTUGOUDn
|
|
WI1nwiJ81vteVYLMvrpflCVtEZJZdlvTkfkvbRkWKlqEbnlnMa80Ghzk+2ml
|
|
830RFGp5Ml1e0uDmtc7I6N5FMDXoSA9HLqlprf7ZtwgafU3Or5GVXSv3XKUs
|
|
wklrDQsqsmZb+pDf0iJIwNmyS+k0sA2+YfVWcAm2zehoHMugQfaAfeSS8BK8
|
|
v/h3VA954qh1tbLoEiSn7tF2QnYbM9zTLLkEys9EPVOR/dUUh4ZPLIHwkJ3K
|
|
hky0/1ZYrPgslgBX4QtpQO5weXbZM20JgqVqm0SyaSAZsXXZPXMJOj+oH5dD
|
|
vl/wMMYtdwl+HtG8fRr56KRbs3PhEgxTSmwckJOuacnb1CyBDslyMR/Z0W6F
|
|
TW94CWLvfl88mIPm64Fbmg5lCbL8hUwxZOEMXEn7zxJI5XmE6yJ3jHS5aswu
|
|
wetdWtbOyMes8n4pk+iQrVD/KROZxcyiQFKUDqUqLSpbc2lgcafrrIQ4HX5X
|
|
OkcKIZc+0xwVk6SDekhdoQSyY+9RwT2H6RA74WeFIX812nJ/mxod1n5FXHdG
|
|
lvR4IMyvToefLDpHbyMHxiyX8mjSQcEwvvUeskIXdYJLnw489dU2ccjJelVG
|
|
LNZ0KJmiqVUg012OzhDt6MD+KdK3AVk/4vWjNQc69Hu9DO5AZm2Pr2K60qEu
|
|
Z55tGNlJ21VyJoAOIQ1DhSR0z6i/Rq2dfEAHMTsnK07k3Y/MLSdC6OA3qtbP
|
|
jfyt6Ww0NZIOLzbWq4kgH9cQ/df3gg5HH7WUKCLLv2wObsigw+6L7O8xZJk1
|
|
N963OXR4/J/9I3Vk0dLPEoFv6bCx4GGqHrIQr1ORczF6n1BsxAhZ4AafivF7
|
|
OoS+4V00Rd74H7ovVNNhlrz6yBZ5w32uft46OigzN29xRCYMFNuvNtKB3nLI
|
|
+jryfOwG344OOjR7pt32QJ6czWcv76KDXPXECW9kXMf46cseOrypxdrvIvdt
|
|
yM72GKSDfuWabSByj/V5ucujdGj7ctUhaH28FfRPZ3E6CNV1KoUit+54cUZu
|
|
gg7ltmqDYevx8jjbKTRNB8MHhQZPkKu+zZhvmEfj2bw3LhK5XOYZPrVEB2nS
|
|
09ynyO9C1W72LtOB4k4Mj0EuoPxZrVmjQ2qks+r6PS9X7WnwazIDzsZ318Yj
|
|
pyef4I1lY8DB/hPbnyEnM0eS/DYyYOpL4onnyPFGYRIOWxgQRqXLJCJHFcoX
|
|
6fMy4GKV7uy6wzb3KSttY8BW8osHScgPHR80iu1kQOeNCXzdAfXSBlt2M2Dv
|
|
70NCycg+ot19dFEG4Iddd6/bw9fXflicAS7uubPr/3f5KT7XIsmAmyV9Met2
|
|
PNp+t1iGARz7NnKs2ybKkz3lMAMKVw9rrz/fYnL30+CjDDBMuGC5/r4XNRuF
|
|
3RQZcNj6ptr6eAwyXbJNVRiw0BO2sD5eHZKg3Gk1BiQ8Tbu9Ho8zFtWfZNQZ
|
|
4Klc3LIeL7VyhzPbNRmgGlc3uR5PJQGeTqIOiodH19B6vI+6lZuP6zGgvWE4
|
|
fX0+DrZZ410XGOAQOnPsMbLYw6LVLHMGKHzla1ufX5Fh0+BIKwakVR34uj7/
|
|
O1RYeO/YMkCarpEegLx50VBCx5kB5f9iytfXD7v+auExVwYsDTWvrq8vUn6G
|
|
8p5bDPh4ZCP3TeQl20X9eR8GXFEpzlpfn7PVyX19/gwwLRA9YIc8Iaxh3xDI
|
|
gCH2l75WyIPf4+4+C2MA7dtojDFy0+nj2VgiA853v3qginy7wVfGL5UBG+Jq
|
|
WE8gS5ytffcpnQEDCsHn5NfnU1u3WjGPAbv2yciLI58ysP0pX8EA8U5tC7b1
|
|
/dCVe/lmDeqPW01oDe33l0bTlLf1DNDbxJq2iEy6dGdOph3F9y0r6xhy1eXI
|
|
TfsHGaA54bq/EtlluDvq6ihq/8BQvBh5t42QYCaOnvdQcjwX2fdqltjeGQbw
|
|
PqprjUFWuv5JRZjEhPbfOtP26/nvDs2Fex8TSPYfPrEg263KLOlKMIGT6KW0
|
|
hPKngJ/73XApJpTFB9+nIbvfWwvZeIQJgmVljl+QD4fwv2RVZ4L35V3JUcj5
|
|
sarfGVeZUCpxIYUH2WJ7kKmCExPemIdkEpG5nrUOebgw4Zn+A49plO+dkown
|
|
524z4XPlvMuX9fMj3ZltMoQJJWlxHYHIGW8Tjg+/Qv+/d1GNloXW87KpZE8B
|
|
ExKE8xS6kQ+e3rWzrYgJTStWazXIH3vSVt5/YIKSFOe/58ida68qI1uYECkh
|
|
Xq2FTNSpOK06zgRVASXbNHR+mf8Z1kuVXAa73fxmUui8E5XPUIuVWYbNT72d
|
|
eZHxu1flwg4vw3Vf5fNMdJ66c0/w3VZchunvKyENyI8UFn7oai6Dfu7Zdkvk
|
|
9w/ZLNYckEUuZweh85h/r5SjRc4yUNOvtr1D531E1COjnLxlyKNXPHyKzEka
|
|
V5t/uwyXeQI53JAJQzk7Q8uX4dpnv+syyBPJ/30pblmGlzcMStNT0Xm4Y+9B
|
|
rkn0fNJf7SB0/3Dn2bH44fAKuCpubNyH7itTAV7DG46twJSU9uBKIorXTE+b
|
|
3okV6Plve20X8uWOuCzqyRUQ2Hx98j6ydji/Ce+FFbg43tk28JwGezm5Pzp6
|
|
rkBwp0jtY3R/+kZkvyf4cQXE6FPpNXEoX+clWJyvWgFyNitvDDLHpQMngmpX
|
|
4HS7sO5VZKxQZ36+dQXa/1w6tBE53zrGrqMP9d+8J/l8LIrXZ1GtoLUVuF45
|
|
vv1bNNoPD5T5FtRW4eTm4IcFkTQoZr+Z2dG0CuJz9OFvoTSg+AT8rfiyCkNr
|
|
I4mJyNtnnsjnfV0FIWLWfjtkn97XNSG9q3CEfOsDHdXtp3Ip/Wq0VTCMsKjY
|
|
ifxN69K2YvZ/cFoi55BJEKqXwlWDEzT+wXV+L6W36P4sxb/V0bruH7R/O8hs
|
|
R/dx3oIPrzOa/oFjZhF3MDLzzNUp/Ms/KPyaPg7IjT4V7je6/4GTydRYvjfK
|
|
p6NOfj7UfyB3tP5viBe6zxQ1RcdyrEGj3iSfvCfKT/r3K5vPrYF4cAHNCNUH
|
|
U+GLfHLda2B+iY2t7iqa3+ldNdI/16B9O+maK/IffY0bEv1rMMPLHiSMPCoQ
|
|
3yRMWQPTA+Vj7nY0+Jl83Jd9cQ22M8TkRGxpYG1cMTfJScD4Mj6W2FvT4NxV
|
|
onmtJAEzPiHgWYHqH+34mKJqKQL29NkKrxWyZtN+zkoZAval3MKUjHzmgH7p
|
|
+8MELPx9BlXdFOXvqTTuAkUClsDijjeZoPuM56n6BE3Ufs9twUpUX+0NCpK9
|
|
4UjAiv1rPKxRfebWLe9r7UTANrnauS2j+q1KbLj1wnUCdqJi28ZoZItaJUcl
|
|
NwJG09bjrtVB90fibDqHNwH7sKHg8u5zNODxMduRHkLA0gT+C6w5i/Kd6yHW
|
|
3mwC1n4Tu1GC6ku9qn6D1lwC5j0d3KuKnLolLK3yNQETyjFobUX1qEo+BTLf
|
|
ELDquzFnhjAaeI8/975ZRsBeWD0NYgGU3203THM1ov48Sd5yJ1C9cOnXTzUq
|
|
AbthfLFRGtXDm5SNsy7TCNhdesLNpMPr33E6b/qOEzBZvST3TcjBI82byqcI
|
|
2J6P92/iB2kg61SucohOwHh6c0/Hy6D1dzchbTcHEfO7laXUvR/t91RjxxVJ
|
|
IlbdT9/3GdX3Kvc6j+6QJmKuZ2fUdyLb2+iSFWSJmOOWY/Fuu1C+ktBIvClH
|
|
xKpU7D7vEkbz+fZo258TRKzu3pZtzjvQ/qnhP9yrTcT0Mu7fH+RD8zXWySi+
|
|
TsQa6zgit3PQ4O6B8DsFLkTM97TMHit2GhS6nlnNdiNiGzCOrmw2Guz895GQ
|
|
6EHEZD72JR7ZgPavQCbbPV8iFnTpSdwpMqonz9zm1wknYnw/R7ceW8Vh8JXQ
|
|
IUoeEbNyPN9gM40D/2x34UABEStaExZ7MoWDpkKkfO9bIvbGud67bBKHolpW
|
|
hdZiInZgZYKN/S8OD/smVQo/EbEhCbGAZzQcpLZUa/t+IWL1AseyHg3jcNvN
|
|
1l7gLxFjVxg5Gt2JQ7DW5FXFKTSeR72ZD77hELfP86rFDBGbiJbJuvUVh5Lu
|
|
YLvMBSL2b6TyvF47DnOKr22O/iNipxZSuZaacbhOnrtstIWE2f8SMGFW43Al
|
|
2t8k9hAJ4/K1kviaj4ObM4dJuRwJe5Jk8jAiD4d76lEX+4+QsPp6W1md1zik
|
|
0l8aiyuSMGWNpya1OTj0mzVcKFEjYbeEWr88T8fhothm/W4DEnZOZqPUQgIO
|
|
OiXPNQU8SFhqKM6neh8H+znrNf7bJMzcre1OfwAO9w9KvuP3JmES43x7vf1x
|
|
KMstE+b3JWFnjz+TfH0XB9GU79O8D0nYq++7RpmeOCwGbYnjjiVhTbT6Q6pO
|
|
OCSb3B/ZVELCPF2kfa0NUPtYzfhNZSTssfNuymc9HDo7uc9tKidhjXd/a+49
|
|
jwO7TmrJxgoSBm/pxN/aaLxqn0I460kYMfskTV4dB/UDS7Ls3SQs7Q973j0F
|
|
HCZXHH3IiySs4t2Cqe9OHEwuau1nLJEw3OVGWLogDrVFB7onGSQsSys7uHEb
|
|
DgmOE7I/V0lYZWnGLw4+HE71OI+8YSVjGgeb8l034fC8yEXTgp+Myfzm2921
|
|
QoUzjh7b38uTsTKZrPyuX1QoqjOqyz9KxrafecD7ppcKu/Ycc0tXIGMLOadW
|
|
g39QYe7HUssTJTKmoHLFSK6TCsmnvfzsTpGxuJfUAYdmKsyL+FB4DckYv3yd
|
|
oVkZFV78CHh3/SYZ4/4i0q0eRQVK3cGB8FtkzK7ldFX8EypIvRvgKPAkY4zH
|
|
+xyoYVQoiVC2nLpDxiQfG4x7B1Gh9SyDwyWQjJllq1t6+1CB/sHF0jWGjL0l
|
|
GdzssaWCTqolp3spGRO0vVC8coQK0eGbj0S/J2Mt1OnawcNU6PX5ZPnuAxlT
|
|
jDlypFqWCjYmO4vnK8lYjOXqgfXv9V48PyxvNZKxaMFrIqVCVEgP1Cn26CVj
|
|
Rn/XogNJVGDaK1/2WiZj4kst6qotFND8IIndWiVjzfOqfLQGCjzn2i7iukbG
|
|
ig5ucXhcSwGlwtkBezILVmRhntLyiQK+y1mWFzeyYImXC1aF31CAHM5jeWwn
|
|
C/aVku+9PZoCm4qo5guKLNiTGxnXDE0oYMb6XXlGiQXTSbXPD75AgTzjGuG/
|
|
KixY4CE32fd6FNBZSewbVWPBlCfcRzZrUiDitL55lyYLlv5H+XuYIgX4ej6a
|
|
FV1iwXhOt8117KCA8Gqkqas3C7ZVI2jVsWcMzgyfex/nw4J1X3kzUd85Bu4N
|
|
HNsqfFkw/6qHe3a1j0FzZMA3zvss2G+lz3oVdWPgIe56Nv0RC9b7/vX9usIx
|
|
6NA9f+xHIgvmQts3OfFoDO6lbeZVrmTBbKcMrcIVx4Ci8aiZnYUVs1OXCI0P
|
|
HgVrrcsiYhtYsauNiVfb7o1Cn84RD1V2Vsw3OVlizWcUui4M7PHexIqZpW7V
|
|
0XMdhZorcl7jfKyYQO+3+VKTUUjy+/Vfmxgr9oSLLv14/ygYlh548FSDFQuP
|
|
EaNo1Y3AZ/FW2PWIFevm5DvTMjEMmuEDmgKPWbHI5CuhEpRh6FiYvbD5CSvG
|
|
zHfcHDAwDP21gk7/olgxjqMDPXu/DQPd+mp8/zNW7APtl83B0mGQSiHNJOey
|
|
YkTBf+02/sMQu+142u5mVqxKvsj82JZhcGTPZNnDsQF7tz9N323XEJSm7lP+
|
|
HLkBM9M7ZaWQ0QdtJ5Tq9LnZsIsDMxvSK3uA7vjc4HI4G8bKKnde8kYnNJ5P
|
|
ucAlwI4F/NhZbXmlGayPK2VlRbNjiYnG263lPoLD3y8Lv2PZMakOhmzB5w/g
|
|
8sLyFE8CO8bKcpkwZfAB/DjuD/kksWP0aM8kDfdySOxt2qmfyY7l7Xsdav2u
|
|
DLq9jCNWStmxEcvNns6Hi0Gz3M1L7xc7VhH9/H2CzmvQu87S+LCPHTvEYB8q
|
|
cHoFF0VjBT4OsGN6osGdZaG5cDX0fZH4KDtWt6jUkl6fDYGXCJPLE+zY2ub6
|
|
kWnlDKhgPrbO/MeOGezuL3e9kAh1+bvf/iJwYEmV/BrmEc+g1frt2lYyB3aT
|
|
b4qk1BIPv5q7Eu+wcWD4th03u7EYoD/b+eP8Vg7MPMfxmIxxGKzp5Ik95OHA
|
|
rowW8du3BsMGMrh/4OPAmAp2KzGqD4DvmjW3uCByroNbjrEP7Nw9b2m6kwPb
|
|
JcW78FX1Foh2PsiPEEbtY9scB42dQDJo22rdbg6MRpO+s+uiGRw6kaO1vIcD
|
|
a8Be5+cn3lH5H33mqdU=
|
|
"]]}, "Charting`Private`Tag$14372#1"],
|
|
Annotation[{
|
|
Directive[
|
|
Opacity[1.],
|
|
RGBColor[0.945109, 0.593901, 0.],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6],
|
|
Thickness[Large]],
|
|
Line[CompressedData["
|
|
1:eJwV2Hk4lF0UAPCZsVcUWbImhSJSlhDOTVJRKolklz1ftkT2SrZKCCEk+1KE
|
|
qCSyby2KpFDWMWMZlGWG5Lv+4fk9950z75333nPPeXfYuhnakwgEghP+s/6f
|
|
qXbDxxFlD63txb8yz2wK0JKk1hwSe3AaJNt4L0RXmcLy83123+OsYEdIQPrZ
|
|
KmcY43WiV8a5QWfUba6dVdfhh25ofU5cMKArE8vtryPhq1WcdFrcfeiSZe98
|
|
9CoZDF0FfyTFPYZx5Z1h9PICiP1tXp4YVwKr/j700Cev4VCT3gZtr3ewdUmI
|
|
uce6Hdz9DGzK3VvB93fiSW3VLvjvlX00aWcnCLlbfB6v6oVuygmOPNtuGDvQ
|
|
6Jkv9ROi9i0SKk17oVLBZzvz6SHw8zkhS3bpBbd4XxH2C0PgXJt6nj+gF5qc
|
|
wJjVZgiOnz5SeC29F3SqnwTMeQ4Bm1vMuYMjvaAg5RF4M3EIQotlcl+5foc6
|
|
R9ec6P4hCJKz0n8T/APsH+sc1bcbBg/Z1oR3Of1wev/CtSO2IzBqPxqSUdkP
|
|
hxISs0qcR8A4g+Aa0tIPH2jm+/k9RkCdT00bUfthE3e8x5fgESCtFdBq9w7A
|
|
9V3K0WxpIxD35c6x2vIBcNnKEWfXMwJl108z3tb9BEa0h8O0zigsX7pcPHBl
|
|
EGTqXMXtuMfAmvuPb/W1QZikn/jCIjAGTTV+Rx4FDcLcz8mOTJExiBGM6r0Q
|
|
PQhCRtEpH6XHQPpTPqn72SCw2pypn9YcAyN1snH71CDcreffq+88BsVbbNYq
|
|
XYbgebvn5ajqMeCtobQl4N+FyvZc42HdGFy/7B5/1W8I4Oeg3+PmMdBpDt5z
|
|
IGoIeL5ZHcnsHIM+//RzzwqG4LeZuIzH6Biwj/flZVGGwM5CI0R5Ixls3xqf
|
|
iXEYhktrJ/Rsz5PhQOU2HkG3YbCwo8uii2QglfzoeuIzDOoRW0a2WZEhM8PS
|
|
pDxiGHSf3Ppe5USG4VsOlj2FwzCQu1e8zh/H07vmKjKDr1+MHe7NwP6WEJHv
|
|
MwJN7QayOuM4fqeJ3v6QEaDrFXaETOL4bYKbqiJG4LCSVtirGRy/Ku1+R/II
|
|
KKqgc4J0HD8tJ5H2ZgSCWq/dy2AfB1u7imwlwigQ2+7fb9k9Dpfmut+9ixiF
|
|
eDmrhAj7cbD2izF5FTMKY6eoR2acxsGc6SStJGkUdln3zZ51HQdjvgbhx/mj
|
|
MAHyBhu9xuG4Wum1wNZR+Fh25oxByDjI37i3V519DNqTDXQEUsaBvkU3qTx8
|
|
DAwvqpQ2tI/DfDJxX9H9MbgsuFmj+MM4zEm8bcp8OAbfHDZzJHSOw4SS0p/Y
|
|
vDEIFtHyNOkZh4ELEgbuLWPg/+B2TcnQONRn/GOSYyODk2KvzPOlcbir8NIt
|
|
N4wMnopfe9fEKdB+4BvZO5oMCQkD91x2UoBdecniaCIZ6jjzaJ8lKRCqdvDk
|
|
aA4ZzrwmVSfKUMBf++VuiSYytHGk1tEVKeBi9HIojWkcHvkVmIjrUuCY78tz
|
|
CXhe9p9uVG9ywp/3+9ZuFzEOFVlx3NwuFKgPWDqsFDMOQs/AhMeVAlo3Dip0
|
|
PR6Hx+HCbze6U0Al6uUm7lp8vffjfT98KLAr9WXT3dVxcIr3SBwPowDp3cuD
|
|
oX4U4Chyzu7KpEAhJ0/u6k0KkFkbuNKzKWBo5srrc4cCF4vWFOxzKZC1KD7n
|
|
nEqB7nitfGoBBXTkogpP11DgLP1eScdzCoSlmIsKk6gQ11MTvfiWAvKUyjvx
|
|
G6gw26/WeK+WAj3K3MucW6lgzftnYEcdBaQ/N/UQdlGBXCzfhhop0Mq2L4Z8
|
|
lApX87a/N22nwAZvIlNZJBVSdbynl79SoKzezEM2Dsc/9KPU5hu+ry2Vv7JT
|
|
qMDRdT+sqZcCRUUu1Q+LqFASPXI5tI8CJ4e7vAM/UCH762fPX4MUiD6dSznO
|
|
PQE1s6e+bpqkALeM/sdfSRNge6F/0mQVz5vtMXdrxgRYZ0qTjP5RoGrst9Hz
|
|
/Al4HKn39dQaBeyepPSFvJqAw+p1VepEKrzaNkHZ0TsBau/pNQxmKliyRTLZ
|
|
CUxCU2Z/NNcmKiiO9eue3D4JwzfMvcex2RsUopSkJ6H8wLZDNZxUKAvq3cJy
|
|
cBLgQbOr/WYqsCxKi+UaT0JEvld2Cg8Vno42q1ISJkFM5qZW5jYq3KgXCuhM
|
|
m4RbMu38FwWpOB9eqX2VMwmqwVyzm4WoQDDn142smASTuZFn3sJUONdlf07m
|
|
6ySkfV6L2SNGheU65iuuvFPwM8q/UWknFT49vlBqJDIF5vH6OR+wswOfzmvs
|
|
moKJL+L5dvi5GKgZ+XMqTUHAaZLIPUkqPHmeFVF8bgr6rCMWWqSpcPyxdtZs
|
|
3BSEaysqjctSIby1c+Dmoylw32oc8N9eKjTPWW7jy54C3Zi5V3PYR3X876lV
|
|
4OvvlQrOy1FBm1ruc/PbFJS4T9UO7sPz49Eu4x2cghvZXr+NFajw7lDnVC5l
|
|
Cm7nxcl1YEP0lE0HYwpGBmJanu2ngoai5ElekWkQYhHoNFOkgr95eVjurmkI
|
|
FaXdrceuun24TlVuGm4UyjtIK1FBrddCxUJrGpL/e+szia0SmCieaz0No0dD
|
|
zSxUqOCdu8tM1XkaBu0lUAX2i09lCe0e08DVUGS08SB+nhKfNszcnIZb1N0C
|
|
ZdgKLWwLB3Om4WzqjqMTqlRwm03Y1/5sGlpO+UwpqlGhWHCXi3nlNMitjff4
|
|
Y8u5ol8hLdNQ6pccxKpOBRnu621t1GnYke5qxnaICs7qbMzmv6fhsXaXxRHs
|
|
/EsJWrTlaXhUolAZiC1dWVrOs4kGd7x3eU5j7zKbSDOTp0HxmXmT1xpUuBTq
|
|
2zutQgMZpe36FOzMZ6xbQ4AGzdPNuXyaVNhB2BmRfYYGomKVGZexrfeU1quY
|
|
0qCiOfpIPHaGIay22tCgLI/1whtssRwzz2lPGgibjf9k1qKCxUfq02B/Giha
|
|
9ZyXxk5d8hnnDqXB61X3Y8exhfTizVUSaJCklJt1G9vUS+JhaxoNLKlveDKx
|
|
k1Kff76YSwMldy+Wt9gCM+91g1/SoKG3OIi2Ph5ba0OtpUHbVq8sZqDCNqWy
|
|
gHOtNAg/L2kriJ3Uk/3wbScNCl71Ve9dH7/+sEz6Ow1iOYoqtNbHhaM+xA7R
|
|
YLgp1+A0tmBNAGWFSoNV4aFIS+wUazcmh9/4+gkXZ1dsISZbsc5lGki9Ozfj
|
|
uz6eY6SmzjQDlT8KREOxhY8fM8reOAN7pP0W72GnTqi5cfHOwBrq9E/EFrm3
|
|
N8pXZAb6PSpL0tbH923PGd41AxKlyvFZ2KJfuN+dlJuB6KzzsvnY6VeZ+yqV
|
|
Z+B7iohPEbaYwNKCuNYM6Cfcv/5sffw1dcsd3Rm4rlmmVIy93bxfdsFgBpqp
|
|
YYXr4xn/PupamcyAcirXwPrnxZ/U2bRZzcAE8cTH9fgZR14EKDrNwJKnUkg2
|
|
9g5y7sM0d+y5D/Pp2JkRyWVs12egVZZbPglbQvbuB48bM4B86HIx6+Mfgih9
|
|
kTMw0B2wGIa9092DSTduBsJpCZEB2Nk8dmLPU/D1AupUd+xdFcZqQlkzQNaz
|
|
FLBbHzc5YRRaNAOrcot8xtiSy4fcaOUzYMI5T9bFloIdOfWNM9CiMcomiZ07
|
|
tPXd3g8zcOHKCzOe9fFQ1r7ErzPQZJkb+Q+vB+m2yS2XyTNQ657q34Wdf/mn
|
|
7FfaDMgWex2pxt7N9VkXlmbg4xDPdBZ2/B6zGg7mWRC4h6bdsLv9uju02Gfh
|
|
zPmHx4ywed+f+u61aRaKXujeOYidcAXND/DOAmlVoWcZr/fEckmZMslZcDC+
|
|
WnwVu4f58cHxPbMgOPM9/Aw2v/G2oyLys7DZ39dUFvshfYN1mMosnB+unBrA
|
|
+y1Jczbh4rFZOH1Mj/Ugdm+0c9Z9/VlcrcR1b8DeNjj8vPE0NiO1YADv3+Sb
|
|
XzvkL8zCGyNJtxDslJYqIpPzLBTSRpKrcH6YHXx+fcZ1FpJ72c9HYR9bzp3r
|
|
c5+FjFc5R0yx5/c+GHrhOwsqmgvv5nF+MYi7XOcQMQt793ldksAmWYjcaM+b
|
|
hZXJDyGmOF9duMbDqCyahXvnXgiLYpfcZ/fIKpmFD/fPEQZxvjOvn7cOeDkL
|
|
SoQ9Ty9hV0p/QPItsxDFRSu3VabC5d+BhDjyLBSbBBYjnF/rN171DZqYhUf6
|
|
d28zDuD5SbrMutBmoUsw5k0pdrOJ8eCRxVlQ//LkhDi2+Fv5dwssc3CFn8y9
|
|
iPN5d/ivYFPJOXCScHK7LY/zuejhNXG7ORjkCOTU2IPPF/NuT1unOfjbKZjX
|
|
t5sKRo8cyVmuc9Cf3VHqh31ZMPqDlPccOJAvib/E51EKX9+jvWFzUH/k8509
|
|
UlSgc3qrqubPwXetiOEFCZzP/+V7nJ6aAwPnjBAVESrIDm4ZDbz6G0Ty1t5m
|
|
4vP4WT6PU4XnH/ALZz1mOUuBgJ8WXbJh8/D+5n3r/k4KzB/TTLOPmoePWQkx
|
|
9tiupSKOj6Pn4UFY1CLtEwXMQvuWeR7OQ2NSrwMJW13GVGI5bx52sK1NyH6g
|
|
AMPbyKO1bR5Ghm9wRbVR4Bqn/mZ7zgXIDOpZu1ZPAQ8NVf30+AWoXrkzdKCC
|
|
AoQr8cH3kxbg2ZQNufsFrl8ez5aHpC4AiPSp+mAXkgpELmUvgAFJsbW6nALD
|
|
rYI06RcLsI+lJkW/jAJG51diSrsW4NJEuZVvCa4Hr9T0NPIsAj3i0+cthRRo
|
|
fCy0sZJ/Ec6MILW3uJ4z/HwN8oQWgTlcjeGMfUVpX36kxCKu31duNeZTIG/5
|
|
8XWDA4vwkHTsQ2AeBbaF3xDpPbsI5L8BHsQcCiw/1rGdjFkE6OteMcjA9eiS
|
|
Ztz+hEUYzeinE7BvGBys90leBMOnIU7lj3F9vLpHgjlzEa5sHskQxOa7uHlY
|
|
pHwRxha7gybTKKDA+8PG4OsiWJfcVcx5RAGvy12x8d8XgXpVLdgSu7L+fd2P
|
|
gUVY/XhWexu2pkftDkcyNtfovnspFND7mD0UvLQInqePPg9IpoB9hJtNqeAS
|
|
HNzQcMPzIQXyfznFLokuQS9XtJ0i9pSKbZ2mxBJ8/7tSP59IAc8xox3tMksw
|
|
I1/1xxc7RFt9aPjQEhQc9pINT6BAyl9mG15LHG9jkvSbBxTodE+x9slcgkyy
|
|
ddfNGArIxGxZuZq7BFtVvlYaY98qCUvwLFyC85zTG2WxVWie7f+VLYG8ZPLG
|
|
r/cpkHZZX8mufglYllrt5LFdHP6ynR1eggf+l1IX7+Hnddsz04C8BDGWZwo/
|
|
Y4vmUDROTizB3YMM2WfYnSPdHsd+L8HRocUoe+yDNs/6NEl0uHi1u6rvLgWY
|
|
zS1LZCTowPbOankA1/WW/t0ndkvRwX3+5Nl32C9T9EYlZehwuTBfNAvb5buK
|
|
4I4DdDgWukHABfuz8eZbAtp0MA1bjl6NwvO7dluUT5cOGYJDD0awQxNWXvLo
|
|
0SGGTOVqx1btHp/iNKTDr6cvHJOw08++M2a2pcOXjou56th0d5U5ogMd7Otv
|
|
WO7CNox5emfNmQ68U/b3uLBZPiW9W/aggyPb09OjkXi/nfSQmbtBh6J9LE4J
|
|
2M2Xxxtpt+mgcZj27Sb29jsWVlORdLg6w1/rjv2l7UT8eCwdPvLa/DmFrXZM
|
|
4t/AEzqwd19Y4MRWymqPaMmhA016j8taBO5X1jy3lhbQ4XX0ytk5bImXDbtD
|
|
S+mg0/TZrwdbZKtr+X8VdOA6NfGmDZvfjVfL5DUdBk3k3d9ib5TG9XYdnv89
|
|
ywO52Ky3OH9ubaKDUrY5eoRN+FXhtNpKhyi+wroY7PlE1qDOTjqksp8TC8Sm
|
|
/S5mr+qmw/6itwwvbIqByYOsXjrARMLxy9gDrPn51wbp0FlQgMywe23PKFqP
|
|
0uH8jTnqOewvNfS3Jyh08MiqZT2F/V7oyXHFKTp8NRd8qIvdfO1El8gsHXie
|
|
MD1C2O++zFmwztMhb8MtnkPYVfIplJklOgj1PVpVxn4Rpe31fYUOH5bPmu/H
|
|
LiFPrNav0UGFkS8vh12o/SDiKRMD3m3KvroHOzv90NZENgaM8OjKS2GnL4+k
|
|
BW9kgFBMrNlO7CTju7udNzNgoiTirzh2XJlSueFWBszpyHFvx77LNaCpIcCA
|
|
7taQZFHsMJfbrZLCDNAxD00Qwb7RLHdu83YGCLSosqw7QKJngC7BgN2+6RRh
|
|
7GtBQU7DUgxwu10B6+PuP6T+dMgw4HdR4Ib1eC4qnwIr5HH804vHxbDt4nzY
|
|
Hx9ggGaA2Mr691vStj+IUGFA0Mi8uAT2Bb1WUU91Bgz/9KnahX0u1z3fTAt/
|
|
/kpOizS2AUlQ8ag2AxrU/Y/LYh+3rHsrr4vvJ3ZRYx+2dpXz8W16DIhy5M1R
|
|
xNbg5+kiGjDgysXPIarYKp5VFpNnGXD+2Z5OTWyFj7aU7vMMaNETfHAEWzKs
|
|
fDXPggGshk+9zmCLD5tFxNowILbraKwJtpAW81Z/ewZwf7KVsMLmWjTabfAf
|
|
A0Tub37shs1uuFp20IMBFplxUb7YpOIczR3eDBh/H0y9gb1kv2g4H8CA5n3+
|
|
xETs33XpAwMhDPgxdb0qA3tK9JhTSygD0tsbyEXYg18fBqbcZUC9EH9yA3bb
|
|
UbV8lMqA5f5nl+jYvi1B8sEZDCAfsvvNhvfX7hONL95m4+d97j/2bdhhJ0/X
|
|
qT/Dv2+JRrsats45+x9KNQxw7BfIuoU9311o7VXPgF37S1weYmcZz5JLm/H3
|
|
JfG/LsImXfT/I/8Jz3fDxomv2O+sYzftGcTXz9ulKOB84T7cE+c4ygD2touJ
|
|
x7G324kI5lIYoNUWtM0GO8gxT3LnHH6ezEvFD7A1rrzVEiUtA22EV2IN+6U/
|
|
1Z171zKef/uGGZzvHFbll07vXgbn/zgsN+P8yR98NTB67zL4p3cpK2BfvbkW
|
|
uVF5Gcw5Yj29sA9E8mWx6C5D2VNNUQLOv8WJh78yHJeh4+wuoQPReH1tCzdT
|
|
dV2GR7zNuRexOVPeD11zX4ar5M6KW9iuaSa0P77LkKIbfvEbtkz2f2y0yGW4
|
|
LbWjKhSfBzmlyWrDRctQ51XwbAmfHy4rZjK9JcugpCixQTIWr5+jYsIfy5eB
|
|
sWnoqyF2dW/m39dvloGrLqmqBLtrrag2tmMZ5DJLXlyJowDRoObo4cllSFOW
|
|
PE6Mp4DFxPDZDJkV6DohWe2Dz0MJpRztRPkVsP+7WFKGTQl0VLx7YAUQ5TYn
|
|
Dfsq9xSvr/oKNN7gYnFIosAd1YVvp/VW4FHYtsGL+Lx9HcZmuea8Aj9u8Qtc
|
|
wOcz3869LpYFKyAkJ7Wcjs/7mLg7xgXPVqBhRKl+CnsDaVJ7vnQF1t7/WVXH
|
|
9QJhqEA4qmoFYq2VP/ViT6VLf6joWIGqM1GfBDPxeSi0U4GTtgLM3n4rz7Px
|
|
/fAILb458BcAXQ7aj+ubL0T2m4LVf4FwmTxlV4nz67NkyzPv/oKphkd9OzbH
|
|
RdlD4Y1/oVPsMk3hJQVQmcH8/Pu/wHS4/dg/7GLbBIfOgb+QkzP0O/U1nl+D
|
|
hH742l8odQx4S63G6/e2Ju+C9iqU29xJfNtAgQp2r9zOtlXgjxl03/eFAnv5
|
|
trjYNv0DvRufeVZoFJiJXuRV7FkDslF8sw0XFaZmxerlfqxBQ6lO3BfsCcNj
|
|
brt/roHT0WbpI5upMMqf1CZKXoPSTJOnO7dQ4Ue6WhD74hrIF6oShrmpYGtS
|
|
84e2gYDYvrDOG/JR4ZQj0aJRhoDk+/SG/wlT4WRSQnndXgLiFeD+44DrXb22
|
|
PRtq5Qko0K3o6Ufs47KGL18fIKDjBSt8aaJU0J7J5C5RJ6ATPHKZytupoOqj
|
|
05ysR0BXTmTnGuH6eWd4+D43FwLie3vHVBvX3549SkG2rgSkaHQn8hH2O8nh
|
|
9+evEJBpop72PLZlo4aLhieOx4kj4Ho+hfg7m8OPgH5X9t/7J0MFngBzoexI
|
|
Agou6qSkyFHBpoPD+eEdAhL/V7ttCvu50MuXUfcIyEf8YY0G7g8MXnOf94gl
|
|
oKXVXY792FGLzfe1kgnobPETDj7cT5A89rN8zyeg2OR/wS643zj77ue594V4
|
|
/mpC/mXYGZvvZtY+JSDWsZO96/2KVjEZcp8TEOeXwfIw3M/4TT7y83pFQAqt
|
|
0x1JSlT4bc86y9lKQBKO5RZpuB86XFGuRWwnILeR6F8/sGOYbe7NdxCQqM2L
|
|
YgHcT8lnvZHp+0RANlbh++5juwy62+d/IyDtxDcJ3qpUGL7Y90N7nIAiYyMa
|
|
xXD/tknTJM+aSkCbvAIKjbCVt3d5BU0SkF2ZSnYkdsRI+6aqGQKCtB8ds9j7
|
|
XKu09tMJiKM06XU57hcvGKhsPL1MQMcab2wcxr6pUPbN9S9+Hk1Ntptxv9kz
|
|
X+CeTyCiUh8uIUfsgMDkzO0cRNShuMt3A+5fc6343DQ3EpEl0b1OAfvT4dhD
|
|
ZpxE9MXTkGiMLcEa2Z3ITUTd1ZYWadgnKcxPXmwlIrG+Zu9abO/2kP++8BHR
|
|
n93agYPYrdG+rFxCRHQk7dfZ7bi//u0+/0VWhIgy5pSENbGFz7k/PiFGROGf
|
|
md6bYl8RcFK9LUFE6Yb2/ffX3/8wRpizdhGREqe4agF2fZ/V53dSRGQblu1V
|
|
h82XYeLyV4aINj3Xv7n+vkjrZpeKkBwRUZ3vnGUCKjjZnWZS3UdE1gsf6fzY
|
|
cbodn87vJyL/Szuu7cGu3n0s1UuRiMTt7raoY5M3NDjFKhORke62ST3szdNa
|
|
yiUHiciU3vHTFFv1UxXxgxr+PvZnGY7YtqUqHycOEREhq1b+KvbdB2Up7FpE
|
|
1JvIGh6MXeEt7yiFiMj97K28SOyfJoWKOtpEtHtIOToOm11dimCrQ0TKCyJq
|
|
KdgHRDLfB+sSUd+Acm4Gttk/0eS040RUcTegKwc7dDDZ/o0eEW1NmKwpwC6u
|
|
5zvw/SQRHdob4PAUuzc79t+iARG92iPVuv5+iBjO2cF7lojq2QaH1i3jHPnw
|
|
wDki8htJL12/3kifxe7MeSIyDjRWLsQOkruhcMWEiK6pMVxysfM3r/69Y0pE
|
|
rOK+Z55gf5nzbSswI6JHA/Uj6/e70jWf0GJBRA8bWiQerL//qXS3HbMioqhW
|
|
r41R2AZJU/JMtkSUHVH2aP338PVzWhG3IyJR3SufvdbfL5mPtmg54HHq/UIH
|
|
7Pda1vHmTkRUQ1rbdQF7Qbzf2s8F31/rE63j2MfHuhgVV4iIPYD32C7sQNlo
|
|
/xJ3IrpMNkzgxi7zOL6a70lEnFUqBavr6+tfNSH1GhHF87EIf8E+o+NzM8EX
|
|
35+hr3cVdmjUfub7fkSUdCkz+gk2jT+X7WYQEV0y2rF4GXunhXWkfwgR0b4v
|
|
otPYF7KENnrfJKKF4NAj+7Hr9t3ncgojojeeNU5zeL3HH/flM4gmIrSgQLLF
|
|
bos+8PBYDBEdDTP8ro79r3tq2+E4Ito48M+UB9vRxkZEKZGIPl34eOYt3o/q
|
|
fno7hdJxvAHaEAnb7R1zztYMIjL7ubWrE+/nbNZaKc5MIqILmlilYXM+UJQh
|
|
5BJRo/vM4QPYg0Ui+8nPiEi2TPGvHs4PfL97yn6V4PXqKfqAE1tPNVbpeykR
|
|
sZT5VX5Uo0J5I4vq+wq8P4V3PzqJHTZA0yp7S0Sz2jr5Kjg/vdlZ8K6olog8
|
|
HZqvTOP8Net8STunDt+PZndZJrbp4rejSU1EdOow51N27L2b604GfSCi0QPb
|
|
5OuVcf4+7//R5xMRWWyVeOqKnfhI+YzHZyK6zRqfxIe9Jl14zu4rEX3v21Rh
|
|
i/PrF/Tgot4AEZ27nN9MxfnY19PeiX+aiJ5HHk0t2Ifznz7NUX2GiE6IpeQq
|
|
YD/c5eNoOYeff4vziwqc/yt7IhxyF/D6Nb/W+RqfF3/Un9qp/CMifQdyQ4Es
|
|
zi9Mf6yNN5NQRKeZjZQ0Xj/9/tZ+3CR06lLg1btSeP9WMFunbyWhar5btrOS
|
|
VChy5LciC5BQjvV0Y+kuKlA61CyuiZMQ57ehi0L4/LsUH2KauJ+EbGJGQkPw
|
|
+en5H4dplSIJnYha4GrA5+1N3bgLP5VJSAPU9JiwM+hZJlLqJGTb39gWIIjz
|
|
gXnL+UptEjquUpN5jh+vL0kuw55zJORzI84xGp/3BpWP9PivkZCCY5uDJAHn
|
|
sz+2a3y+JJS690+DzBoFbinIvODzI6Gh5cEvcv8o8KrwlShfEAlt2cuzuvcv
|
|
rtcef53dGkZCv5Snj2ymU2AxfPND7kQSsvvTmmkzQ4EtTT363EkkVJOym+sw
|
|
rkdkSekE7hQSouccYBObpoB1wF6XLekkpBMil9w5QYF29xOam3NJKFqM8VeA
|
|
jPs501sjmypJKP+UbqNcP/7+RL2kTa9ISLQumD76A9eXXdynNlWREHfgx4Tk
|
|
77j/MMio3FhDQq4nfEkrPRTw1H4buaGZhCz8Qy6lf6aAruzSPvYeEmqYuwT2
|
|
zbg+++sSwLRIQmI556VHnlHA9IL+HsYSCbmZdRzQf4rrvXLZHhqDhGQNvl5/
|
|
juu7ZJepfT9WSSjjVn+pZx6ux3r/G3nOwoT8GhXufsX14qNydz1LPiZUq+K9
|
|
yvMA92cu17a9VmJCclXC/1l4U6C8ybipWIUJXeZOzHfyooDYjoOe2apMaElZ
|
|
/7u7BwX+fFvquK/BhDKD07l9/8PzP3o92EGHCf3cGJRhY4/7FfEA8lYjJuT8
|
|
5NLJx0YUePLtxosrXkyouNrmQYUCBchNCr+ivZkQL+EP5255XA+++MVR4sOE
|
|
tldPPkmUpUBljKbVjD8TMrjHtdFJCvfrJxgc7qFMSDltW0KfMAXob9ytPBKY
|
|
0DExWwkmVtxvZlhtuPqSCRVw6wgd/jYO8dFcyvGvmVD1wWLf/d3j8D3grdWL
|
|
N0zI5GNDsujncbAzFa6Yr2VC/6kbC1Lbx+E6zzcr71YmdHenQOPJmnHIDjWo
|
|
uPYdxwt96a+TPQ7LTprW11eYUN87lbMjruOg90YGea8yoU8sx+pDncfhEec2
|
|
cY81JmT266C6hMM4aJT9/uXExIxM47NUzlqNQ9BKntWFjcxoUy3sCT47DkzR
|
|
PFYHhZnRj77rKoLK47CpfNxiQZ0Z/TbN1lBlkMGc5avmnAYz8r6rWGm8QIZn
|
|
JvWi01rMqNzKku4+RwaDv6kDo9rMSF5H9FMSlQwxRw0tuvWYkU1OeVzFdzLw
|
|
9labl19kRhyqgn07XpNBdDXWzMOPGbUstnC9vkqG48OnXj8MYEZf62U0aG5k
|
|
uNrCIVATxIzO08YVxS6ToT32xpcNt5hRSbmI3xUbMlyT8jiRfYcZreWVS3ee
|
|
IkPn6TMHv6Uyo6dFCdqJkmS4mcm1VbOWGc0n5A1v/zwG5GN32tmZWVARew9n
|
|
s8AY2Opbi0uysqBhj7W/b7jHYMBA+dphdhYkZVcS8HTjGHSf/7XDbxMLivj2
|
|
dnfg2ijUX1K8PsnLguhJ3DwD5FFIC+6T/ijJgi5UD+xOfDEKRi9lbz84xoLe
|
|
7VkRJuuPQoPUexC7w4I4iX1zH51HQC/6lx7/PRa0dTowbMh2BDoXfp/nus+C
|
|
/ks6pDxjNgI/GwVd/8WxoIR8qcGVUyNAt3VM+pnCgmw89Bx+7B+BvY9Jc+mF
|
|
LEi3sonnKX0YEgXUMre3YxN33n9ycxhc2HOZd3CwouSr+QID4UPwMmOXZkMs
|
|
K1K8auc+o/8TPh7SaDLkZkMPXG65vNT6DnSXR+eso9mQUjT7huL2Lmg98/g8
|
|
Jz87quCnVvH0tIOtmkZeXjw72hJRm/glrxqcpz8s9Ceyo1BpziegUg3uT6x0
|
|
eJLZUVNkA2dG4xsI5rg1FJDGjuZv5/UcGqqC1O9twoa57MhfXiZrVPA19Fw3
|
|
ifn7kh3Jy6Ycko6sAL0qz+tn+9hR/5yASl7dUzh7hbk1bADHezj2SbS/CC5I
|
|
JPJX/2JHGjnTQ+GLheAY9bpcapQd9S2f2aAqWwChFwm0lSl2dKty8fnW+Byo
|
|
Wb5nm/uPHQmZch6TbE2FpuLtpX0EDsQvPrd/eCUF3tuWrm1h4kD+B24vxO1L
|
|
hr727lR/Ng7EeOJxpCsxAegpwt/ObOFAdda8Jzva7sKawTPJMB4OZLjpEtNz
|
|
hUhgZYKrb3g5UN8ZNZvIh7eB97Itt5QgB5qebtl2uD0AhLfPW5kJc6AnldH7
|
|
Gh56g0TX7eIYUQ6U27tfwKfdFWTCBVabtnMgt0qXpxXt5rD/UIH+yg4OdNcz
|
|
58/pTQFa/wM6b9O7
|
|
"]]}, "Charting`Private`Tag$14372#1"]}}, {}}, {
|
|
DisplayFunction -> Identity, Ticks -> {Automatic, Automatic},
|
|
AxesOrigin -> {0, 0},
|
|
FrameTicks -> {{Automatic, {}}, {{0, Rational[1, 2] Pi, Pi}, {}}},
|
|
GridLines -> {{}, Automatic}, DisplayFunction -> Identity,
|
|
PlotRangePadding -> {{
|
|
Scaled[0.02],
|
|
Scaled[0.02]}, {
|
|
Scaled[0.05],
|
|
Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All,
|
|
DisplayFunction -> Identity, AspectRatio -> GoldenRatio^(-1),
|
|
Axes -> {False, False}, AxesLabel -> {None, None}, AxesOrigin -> {0, 0},
|
|
AxesStyle -> Thickness[Large], BaseStyle -> 18, DisplayFunction :>
|
|
Identity, Frame -> {{True, True}, {True, True}}, FrameLabel -> {{
|
|
Style[
|
|
"\!\(\*SuperscriptBox[OverscriptBox[\(\[Rho]\), \(~\)], \(HF\)]\)(\
|
|
\[Theta])", FontSize -> 16], None}, {
|
|
Style["\[Theta]", FontSize -> 18], None}}, FrameStyle -> Directive[
|
|
GrayLevel[0],
|
|
Thickness[Large]],
|
|
FrameTicks -> {{Automatic, None}, {{0, Rational[1, 2] Pi, Pi}, None}},
|
|
GridLines -> {Automatic, Automatic}, GridLinesStyle -> Directive[
|
|
GrayLevel[0.5, 0.4]], ImageSize -> 400,
|
|
LabelStyle -> {FontFamily -> "Times"},
|
|
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 -> {All, All}, PlotRangeClipping ->
|
|
True, PlotRangePadding -> {{Automatic, Automatic}, {
|
|
Automatic, Automatic}}, Ticks -> {Automatic, Automatic}}],
|
|
Placed[
|
|
Unevaluated[
|
|
LineLegend[{
|
|
Directive[
|
|
Opacity[1.],
|
|
RGBColor[0.9, 0.36, 0.054],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6],
|
|
Thickness[Large]],
|
|
Directive[
|
|
Opacity[1.],
|
|
RGBColor[0.365248, 0.427802, 0.758297],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6],
|
|
Thickness[Large]],
|
|
Directive[
|
|
Opacity[1.],
|
|
RGBColor[0.945109, 0.593901, 0.],
|
|
CapForm["Butt"],
|
|
AbsoluteThickness[1.6],
|
|
Thickness[Large]]}, {
|
|
Style["\[Mu] = -8", FontSize -> 18],
|
|
Style["\[Mu] = -7", FontSize -> 18],
|
|
Style["\[Mu] = -6", FontSize -> 18]}, LegendMarkers -> None,
|
|
LabelStyle -> {FontFamily -> "Times"}, LegendLayout -> "Column"]], {
|
|
Center, Bottom}, Identity]]& ],
|
|
AutoDelete->True,
|
|
Editable->True,
|
|
SelectWithContents->False,
|
|
Selectable->True]], "Output",
|
|
CellLabel->"Out[23]=",ExpressionUUID->"fab28477-49a9-4922-9e62-38257f87c619"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData["\[IndentingNewLine]"], "Input",
|
|
CellChangeTimes->{
|
|
3.8307422330267467`*^9},ExpressionUUID->"d453d858-8a7b-4124-abfb-\
|
|
9e6f74a501dc"],
|
|
|
|
Cell[BoxData["\[IndentingNewLine]"], "Input",
|
|
CellChangeTimes->{
|
|
3.830741197492989*^9},ExpressionUUID->"eead3199-3345-46f2-a4c0-\
|
|
2fec2d348b90"]
|
|
}, Closed]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell["Singlet P state", "Subsection",
|
|
CellChangeTimes->{{3.742903401180684*^9,
|
|
3.742903411063073*^9}},ExpressionUUID->"d406c2ba-4ab0-44d0-9b6f-\
|
|
c0c1db6c1acf"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"\[CapitalPhi]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}],
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "\t",
|
|
SuperscriptBox[
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "2"]}], "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}], "\[Infinity]"],
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"],
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Gamma]", "]"}], "]"}], "\t",
|
|
SubscriptBox["c", "\[ScriptL]"]}]}], "=",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]"}], "+", "1"}], "2"],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0", "\[Pi]"],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Gamma]", "]"}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "2"],
|
|
RowBox[{"Sin", "[", "\[Gamma]", "]"}],
|
|
RowBox[{"\[DifferentialD]", "\[Gamma]"}]}]}]}]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.742897993868801*^9, 3.7428981067548847`*^9}, {
|
|
3.742898182660631*^9,
|
|
3.742898271183833*^9}},ExpressionUUID->"5964132e-935a-46a6-b153-\
|
|
12b5727d94a0"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"\[Rho]", "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "2"],
|
|
SuperscriptBox[
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "2"],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}]}], "=",
|
|
RowBox[{"2",
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}], "\[Infinity]"],
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"],
|
|
FractionBox[
|
|
RowBox[{"4", "\[Pi]"}],
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]"}], "+", "1"}]],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"m", "=",
|
|
RowBox[{"-", "\[ScriptL]"}]}], "\[ScriptL]"],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}], "*"], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "2"],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}]}]}]}]}]}]}]}]], "Input",\
|
|
|
|
CellChangeTimes->{{3.742898286664424*^9,
|
|
3.7428983914044456`*^9}},ExpressionUUID->"9e3ef216-9ad2-4adb-b9e7-\
|
|
96392657d2b3"],
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "2"],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}], "=",
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"4", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"4", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}]}]}], ")"}],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}]}], "\[IndentingNewLine]",
|
|
RowBox[{"\t\t\t\t\t ",
|
|
RowBox[{"=",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"\[ScriptL]", ",", "0"}]],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"m", ",", "0"}]]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"4", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"\[ScriptL]", ",", "0"}]],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"m", ",", "0"}]]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"\[ScriptL]", ",", "1"}]],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"m", ",", "0"}]]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"\[ScriptL]", ",", "2"}]],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"m", ",", "0"}]]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"4", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"\[ScriptL]", ",", "0"}]],
|
|
SubscriptBox["\[Delta]",
|
|
RowBox[{"m", ",", "0"}]]}]}]}]}]}], "Input",
|
|
CellChangeTimes->{3.742903519772635*^9, 3.819523154980489*^9},
|
|
EmphasizeSyntaxErrors->
|
|
True,ExpressionUUID->"fd5e482a-7176-4bda-b608-c9d284776293"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{"Simplify", "[",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "+",
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], ")"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}]}],
|
|
"]"}], "\[IndentingNewLine]",
|
|
RowBox[{"Simplify", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "\[Equal]",
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
SqrtBox["5"], "2"]}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}]}],
|
|
"]"}]}], "Input",
|
|
CellChangeTimes->{{3.742880368692409*^9, 3.7428804029481373`*^9}, {
|
|
3.742880525109131*^9, 3.7428805458700542`*^9}, {3.742898467130229*^9,
|
|
3.7428985242579517`*^9}, {3.7428992114127827`*^9, 3.742899287783554*^9}, {
|
|
3.7429000811947393`*^9, 3.742900096336309*^9}, {3.7429001529365797`*^9,
|
|
3.742900153845666*^9}, {3.7429004278822927`*^9, 3.742900428277691*^9}, {
|
|
3.742903418965905*^9, 3.7429034224918003`*^9}, {3.742903559452738*^9,
|
|
3.7429035641164207`*^9}, {3.8195280712399893`*^9, 3.819528073279229*^9}},
|
|
CellLabel->
|
|
"In[108]:=",ExpressionUUID->"d44672a8-904c-49d5-a749-404599638355"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.742880543408547*^9, 3.742880546332151*^9}, {
|
|
3.7428984748725023`*^9, 3.742898524985319*^9}, 3.742899228848856*^9, {
|
|
3.7428992728911753`*^9, 3.742899296001245*^9}, {3.742900084424329*^9,
|
|
3.74290010643225*^9}, 3.7429001543651667`*^9, 3.7429004286643667`*^9,
|
|
3.742903423093584*^9, {3.742903537210059*^9, 3.742903564703141*^9},
|
|
3.819444693584455*^9, 3.8194462226703672`*^9, 3.819522892066416*^9,
|
|
3.819523152348187*^9, 3.819528073972172*^9, 3.819529116161902*^9},
|
|
CellLabel->
|
|
"Out[108]=",ExpressionUUID->"f95cdf80-034d-490c-9052-1ab0cd6440d3"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.742880543408547*^9, 3.742880546332151*^9}, {
|
|
3.7428984748725023`*^9, 3.742898524985319*^9}, 3.742899228848856*^9, {
|
|
3.7428992728911753`*^9, 3.742899296001245*^9}, {3.742900084424329*^9,
|
|
3.74290010643225*^9}, 3.7429001543651667`*^9, 3.7429004286643667`*^9,
|
|
3.742903423093584*^9, {3.742903537210059*^9, 3.742903564703141*^9},
|
|
3.819444693584455*^9, 3.8194462226703672`*^9, 3.819522892066416*^9,
|
|
3.819523152348187*^9, 3.819528073972172*^9, 3.819529116234906*^9},
|
|
CellLabel->
|
|
"Out[109]=",ExpressionUUID->"1b714e96-da79-4d94-a1ba-aad82b46c1b7"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "9"],
|
|
SubscriptBox["c", "1"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"15", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "2"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], "==",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], ")"}]}]}], "//",
|
|
"Simplify"}]], "Input",ExpressionUUID->"47e6ea8d-fe96-432b-bc8f-\
|
|
37af178f58c4"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "9"],
|
|
SubscriptBox["c", "1"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"15", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "2"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], "==",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], ")"}]}]}], "//",
|
|
"Simplify"}]], "Input",
|
|
CellChangeTimes->{{3.819529156879609*^9, 3.819529202570097*^9}},
|
|
CellLabel->
|
|
"In[116]:=",ExpressionUUID->"41ad596d-10ce-4e99-baba-2ce47459342c"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.81952919827662*^9, 3.819529203008608*^9}},
|
|
CellLabel->
|
|
"Out[116]=",ExpressionUUID->"564d55f1-fbb5-4701-bf39-19b29e089fa9"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}], "==",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
SqrtBox["5"], "2"]}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}], ")"}]}],
|
|
"+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "9"],
|
|
SubscriptBox["c", "1"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"15", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
SqrtBox["5"], "2"]}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}], ")"}]}],
|
|
"+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}]}], "//",
|
|
"FullSimplify"}]], "Input",
|
|
CellChangeTimes->{{3.81952842298248*^9, 3.819528452134273*^9}},
|
|
CellLabel->"In[62]:=",ExpressionUUID->"0539ebc8-55d1-4e61-8059-2b873a109fd0"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"15", " ",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "+",
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], ")"}], "2"]}], "\[Equal]",
|
|
RowBox[{"4", " ", "\[Pi]", " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"25", " ",
|
|
SubscriptBox["c", "0"]}], "+",
|
|
RowBox[{"10", " ",
|
|
SubscriptBox["c", "1"]}], "+",
|
|
SubscriptBox["c", "2"], "+",
|
|
RowBox[{
|
|
RowBox[{"Cos", "[",
|
|
RowBox[{"2", " ",
|
|
SubscriptBox["\[Theta]", "1"]}], "]"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"15", " ",
|
|
SubscriptBox["c", "0"]}], "+",
|
|
RowBox[{"10", " ",
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{"3", " ",
|
|
SubscriptBox["c", "2"]}]}], ")"}]}]}], ")"}]}]}]], "Output",
|
|
CellChangeTimes->{{3.819528427637335*^9, 3.819528452956792*^9}},
|
|
CellLabel->"Out[62]=",ExpressionUUID->"eb2da5a6-57c0-4846-bf3e-a339f3051de0"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
SqrtBox["5"], "2"]}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}], ")"}]}],
|
|
"+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "9"],
|
|
SubscriptBox["c", "1"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"15", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
SqrtBox["5"], "2"]}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}], ")"}]}],
|
|
"+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], "==",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
SqrtBox["5"], "2"]}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}], ")"}]}],
|
|
"+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "9"],
|
|
SubscriptBox["c", "1"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"15", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
SqrtBox["5"], "2"]}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}], ")"}]}],
|
|
"+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}]}], "//",
|
|
"FullSimplify"}]], "Input",
|
|
CellChangeTimes->{{3.819523269050538*^9, 3.819523327877223*^9}, {
|
|
3.819523473638289*^9, 3.819523504696064*^9}, {3.819523550056871*^9,
|
|
3.819523649461877*^9}, {3.819523699741858*^9, 3.819523740945754*^9}, {
|
|
3.819523847347278*^9, 3.819523884985684*^9}, {3.819523947770347*^9,
|
|
3.819523980605163*^9}, {3.8195280859844933`*^9, 3.819528126180491*^9},
|
|
3.819528247868373*^9},
|
|
CellLabel->"In[60]:=",ExpressionUUID->"ba29c20b-dea9-41b8-b3d4-fc57943bb3a3"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{
|
|
3.819523329494213*^9, 3.819523506333411*^9, 3.819523552413641*^9, {
|
|
3.819523599257063*^9, 3.819523649903213*^9}, 3.819523701307633*^9,
|
|
3.819523745307156*^9, {3.8195238636967583`*^9, 3.819523885690692*^9}, {
|
|
3.819523974036787*^9, 3.819523981326833*^9}, {3.8195280894877987`*^9,
|
|
3.819528127532626*^9}, 3.819528248659236*^9},
|
|
CellLabel->"Out[60]=",ExpressionUUID->"a45ecd9f-4177-4783-8c1c-5a81ef2ad1df"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
SqrtBox["5"], "2"]}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}], ")"}]}],
|
|
"+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "9"],
|
|
SubscriptBox["c", "1"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"15", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
SqrtBox["5"], "2"]}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}], ")"}]}],
|
|
"+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], "==",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "9"],
|
|
SubscriptBox["c", "1"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"15", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "2"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}]}], "//",
|
|
"FullSimplify"}]], "Input",
|
|
CellChangeTimes->{{3.819446229984541*^9, 3.8194462800814953`*^9}},
|
|
CellLabel->"In[16]:=",ExpressionUUID->"5f1d575c-4c3c-4bde-8f8f-240d45244a88"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.819446240084282*^9, 3.8194462809734297`*^9},
|
|
3.8195228922632103`*^9},
|
|
CellLabel->"Out[16]=",ExpressionUUID->"1f981ff0-2415-481e-9272-8f05a9125627"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"8", " ", "\[Pi]",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "+",
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], ")"}], "2"]}], "==",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "9"],
|
|
SubscriptBox["c", "1"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"15", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "2"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}]}], "//",
|
|
"FullSimplify"}]], "Input",
|
|
CellChangeTimes->{3.8195229398158827`*^9, 3.81952300278867*^9},
|
|
CellLabel->"In[19]:=",ExpressionUUID->"d0f32758-1361-44ee-bb02-8950288c60b3"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"25", " ",
|
|
SubscriptBox["c", "0"]}], "+",
|
|
RowBox[{"20", " ",
|
|
SuperscriptBox[
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "2"], " ",
|
|
SubscriptBox["c", "1"]}], "+",
|
|
SubscriptBox["c", "2"], "+",
|
|
RowBox[{"3", " ",
|
|
RowBox[{"Cos", "[",
|
|
RowBox[{"2", " ",
|
|
SubscriptBox["\[Theta]", "1"]}], "]"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"5", " ",
|
|
SubscriptBox["c", "0"]}], "+",
|
|
SubscriptBox["c", "2"]}], ")"}]}]}], "\[Equal]",
|
|
RowBox[{"30", " ",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "+",
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], ")"}], "2"]}]}]], "Output",
|
|
CellChangeTimes->{3.819522942340241*^9, 3.81952300387868*^9},
|
|
CellLabel->"Out[19]=",ExpressionUUID->"55173617-34ac-4fdc-9406-99bf575c07a4"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "9"],
|
|
SubscriptBox["c", "1"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"15", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "2"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], "==",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], ")"}]}]}], "//",
|
|
"FullSimplify"}]], "Input",
|
|
CellChangeTimes->{{3.819524042605442*^9, 3.819524078491332*^9}},
|
|
CellLabel->"In[53]:=",ExpressionUUID->"c1307343-2cfb-4e0b-83cc-02e91fb1c0ed"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.819524053790895*^9, 3.819524078957933*^9}},
|
|
CellLabel->"Out[53]=",ExpressionUUID->"3b48e172-c35e-4179-ad01-d64d2ba564df"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "9"],
|
|
SubscriptBox["c", "1"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"15", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "2"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], "==",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], ")"}]}]}], "//",
|
|
"FullSimplify"}]], "Input",
|
|
CellChangeTimes->{{3.742903615997718*^9, 3.742903634439269*^9}, {
|
|
3.819446306819173*^9, 3.819446321359915*^9}},
|
|
CellLabel->
|
|
"In[117]:=",ExpressionUUID->"318015e8-2886-4487-be95-e7f69ff7a94c"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{3.819446322096216*^9},
|
|
CellLabel->
|
|
"Out[117]=",ExpressionUUID->"3c0943dd-d696-48fb-95bf-e076fa93c9b0"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{"\[Rho]", "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "9"],
|
|
SubscriptBox["c", "1"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}],
|
|
RowBox[{"15", " ",
|
|
SqrtBox["5"]}]],
|
|
SubscriptBox["c", "2"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
"2"]}]}]}], "\[IndentingNewLine]",
|
|
RowBox[{"\t ",
|
|
RowBox[{"=",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}]}],
|
|
")"}]}]}]}]}], "Input",
|
|
CellChangeTimes->{3.742903435971887*^9,
|
|
3.74290368331061*^9},ExpressionUUID->"b4079bea-4a03-45f8-9706-9190d1a1a2fd"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"Solve", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0", "\[Pi]"],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0",
|
|
RowBox[{"2", "\[Pi]"}]], " ",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], ")"}],
|
|
RowBox[{"Sin", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[Phi]", "1"]}],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[Theta]", "1"]}]}]}]}], "\[Equal]", "2"}], ",",
|
|
SubscriptBox["c", "0"]}], "]"}], "//", "Expand"}]], "Input",
|
|
CellChangeTimes->{{3.819446339018919*^9, 3.819446363714183*^9}, {
|
|
3.819446590201914*^9, 3.819446591088716*^9}, {3.819447309899662*^9,
|
|
3.819447319139097*^9}},
|
|
CellLabel->
|
|
"In[166]:=",ExpressionUUID->"523e901d-07d6-4226-ab0a-a0f8b4022ef8"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "\[Rule]",
|
|
RowBox[{"1", "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"]}]}], "}"}], "}"}]], "Output",
|
|
CellChangeTimes->{3.819446364233666*^9, 3.8194465914559927`*^9,
|
|
3.819447319610235*^9, 3.8194476543197317`*^9, 3.819448144409718*^9},
|
|
CellLabel->
|
|
"Out[166]=",ExpressionUUID->"cdd496d7-6f57-4d4b-9410-784a9d2ec602"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], ",",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}]}], "}"}], "/.",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "\[Rule]",
|
|
RowBox[{"1", "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.819447325708128*^9, 3.819447336599598*^9}},
|
|
CellLabel->
|
|
"In[156]:=",ExpressionUUID->"a2621bef-7c52-4cc5-b04b-4a41d784cd3d"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"1", "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"], "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], ",",
|
|
RowBox[{"1", "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}]}], "}"}]], "Output",
|
|
CellChangeTimes->{3.8194473369186583`*^9, 3.819447655705583*^9},
|
|
CellLabel->
|
|
"Out[156]=",ExpressionUUID->"47b658d6-e43b-40a5-bd62-147a938a1d86"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], "/.",
|
|
RowBox[{
|
|
SubscriptBox["c", "2"], "\[Rule]",
|
|
RowBox[{
|
|
RowBox[{"-", "10"}], "+",
|
|
RowBox[{"5", " ",
|
|
SubscriptBox["c", "0"]}]}]}]}], "//", "Simplify"}]], "Input",
|
|
CellChangeTimes->{{3.8194468444392157`*^9, 3.819446857015703*^9}},
|
|
CellLabel->
|
|
"In[138]:=",ExpressionUUID->"ab059271-ba95-494b-97be-904cc891c23e"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
FractionBox["2", "3"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "3"}], "+",
|
|
RowBox[{"3", " ",
|
|
SubscriptBox["c", "0"]}], "+",
|
|
SubscriptBox["c", "1"]}], ")"}]}]], "Output",
|
|
CellChangeTimes->{{3.819446845534431*^9, 3.819446857285016*^9}},
|
|
CellLabel->
|
|
"Out[138]=",ExpressionUUID->"8f57ea33-6026-4373-bdf2-c97365a6aff0"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"Plot", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "0"], "[",
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}], "]"}],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}]}], "]"}]], "Input",
|
|
CellChangeTimes->{{3.819447580369944*^9, 3.819447646849441*^9}},
|
|
CellLabel->
|
|
"In[154]:=",ExpressionUUID->"1423d03d-0009-4a98-923c-6616c220bc62"],
|
|
|
|
Cell[BoxData[
|
|
GraphicsBox[{{{}, {},
|
|
TagBox[
|
|
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
|
|
1.], LineBox[CompressedData["
|
|
1:eJwt2Hk4VF/8B3BLZSiVrQgt2iSRFhJ6D99KUbZKiwilJGUrVKJFKkpIkiyV
|
|
EKEklCREIWlBoVRkj7nWmXtnRn7n93t+f32e1/PMPOeecz/nfc7MPGcPGxcx
|
|
ERERcVERkf+rr6Vq/6z2Wify/3VhT7HB7BuWOK9c0aNKKv+J9oGmqH2Y+9NK
|
|
pZHUDnlXOj/KA1cLxxpzSG3eGFyWEhWEm/bj6yNJbdgXtTgh6jpaEwZ1zEm1
|
|
cVdqjo1KwsSdsySsI5MQObQ3NybqMaJgFut37TEMKsykTHxKwM27VZZ5qASe
|
|
pyyccj0rwbvedKvErBJHn7uEi83/hKGyT4OlnI+o794smeZcj8HQBSPNUvUI
|
|
1eaK5O9uxO+FukYu5d/gtbTyZknKD7yOeexlnvsd/P1HsluO/YZli822Cs9f
|
|
cH5laxVxsA33n508YHCoFfsH60tKLrcjYLq5567Ff3B1eYFHakgnmoZvnZma
|
|
3w6xkgK94FPd6Gg+oSeypBMyGua1v2J7wdGcwrua3IVNSSbJA1F9GJs21/JP
|
|
XzdmUjUbgwo4GOCwj+zS7UXcu0JR8cMDEHseuOfS3r8wVDUen3tgEN9+3Fv5
|
|
YFsflv6e3n7m+BBG0vUT69n9sOiaW+brP4T07dfkp6zvhydn+V2PgCG02s19
|
|
ZWzaj2dCq71OwUNYM2Xtg7St/TBUiqxfHz0EeuKLcvs9/dhiI1Mx+dkQFpxd
|
|
Ot/Hpx/u5TKpt4eHcLtvYIz9oB9ZD2Vd87yHYVhWXOUgwkFww2tjcb9hMK1y
|
|
ZnvFOdgrdlTZ+vQwLp1wTdw5iQOpve9q+y4MI0dzZZnpFA4OTgtYveDmMG7O
|
|
shiQVuRgrm+H2I2CYXToKRboaHMQ/d/zBE/hMB4o6J9usOMg4Kd93dKQERiI
|
|
FZWfz+ZgxNQowSV0BPKJLKvuJxy456gcSgofQUjS5gLzXA7sgr/zZW+N4Kzz
|
|
P8UpzzlYq7FbjZ82AkonaoFPKQfMie1elVUjONnarNdcx4GvtPk0F+lRCJOu
|
|
rZjM44Djq9GUKDMKU4vMvqUMed7fksmNCqM4zDw7YybgwDa3UnfL7FFkSvXP
|
|
PzfOwerdGx1Wao9idm9LQL0EhZEHxlmi1qMo7PJgyylS8DJcY54YPQr19Gy5
|
|
AV0KIseig67HjmLRw5LIR2sohCcN5J6NH8X25/EaLmspZIilq+x/MIqtHNPM
|
|
L0YU2iqVOIufjcLa+kJfzHoK23cIInLqRpFRmLu53JqC7rHir+WyXOT56L3N
|
|
caNQnjRrcv4MLj5c+HpkuTsFm8++SJvFxf6x2UuyjlI4tkr74RU1Lny+Wvbe
|
|
9aSQxk86abGCi7R1OcFevhQUL51TabTmIlq/YWLBOQr8pPXOfyO4ODD2/v6X
|
|
GArreEZROje5WLV0VFo7lsI5C70yv9tcSGpSelduU2CNLVGbcJ8LW5Hhd7rx
|
|
FBT2TGtTyeWi8XBEg+89Csvlm50sGriI0bOPCn1EwedIXWR0Exf9brt/lWVS
|
|
yC+rKW1u4YIVkt1DZ1Ew8no971AnF39VJus6PKFgVvugNYjHhYa/5iPpPAou
|
|
lz2ccpR4+F53dWT8FYWHv1wjeao8JHTLSsu/ptCn61xqpMbDm/XJrQtLKHh3
|
|
bJ9XrcFD0ZfoYpMyCmdN1ra2GfAgbXV/g9NbCnHCCU7yDjz8kFzsr1NL4ZNn
|
|
nKPffR72a+0eVf1BQSNiuuB4KrHm6vHvxBceh9z0zuBhWWKKdGwLeR8c7+qj
|
|
T3nYpaOwRuoXhYQj5qsOlPGQaU6Vfm2l4HZQKGHdxoNmPJ00vYu8r4ve9y06
|
|
eehT6OjPJlZN6Tbc0stDQ/ILmHeT8f/Ue5kO8TBVd4RzpoeCnlPWdyMxGl25
|
|
qafe/6UwYa/DYw01GmF1CyAxQMHhdP1m9UU0eLWb3l0kLogza1+oQcNwVqWN
|
|
2CAZv0lXad4KGo5lL3xGiT/bTrsw04SGx8rYH2+Gyfx8L6oqbKQRm1EeuGKE
|
|
QvBNQYGsGY0LfTILkojX1Hf1SdvQ8Osa9vMepZBoXWI7wZlG2sa560V5FGhP
|
|
3UHRgzSU38T/20dsE5EZNn6YhpaHRFER8cSPsSV8LxqmzhHwpCm4b/HSGDxH
|
|
4z/uV9fXDIW3R7rKORdpyG/XWDuVT2FOmP2+vis05ukYT7Uj/lK1Oborkkac
|
|
W2oxh1jfVO1fyz0yfv0n/BNQWJVcffldCo0zNR6UgZCC1ri3XE46jcX5gXl+
|
|
xGoFb9SDc2g8Wv4zuIdYRc4992gejYjhxeFzxijM8JBft/MFDbsp9VnbiCcv
|
|
dtmmUUqjqGPj8nziSRekf8pV0Agtk7jRTizyK891rJLGs2Vzpsj8I/s/ZlLg
|
|
p080opaYGh8g5gxlswrraRSU2IyFEndb7LyR3EhDYTjj42PilkkPH/r+puHu
|
|
v6ZgmLjR2WqlYzuNaUWHa2THyXyL6Vebu2msC/jF0yaumXVv08o+Guf5t/TN
|
|
id/6bq5TGSDzuRkZeYC45Mug/aQRGp+rqsdPExdqxXVTPBrblpsERxI/CzXx
|
|
aRLQ+B7EnZ1C/Lizd6xsnMauq50f84kzTG5czhRnIGYqc+st8YNEA7kYCQZ7
|
|
i08crydO5P9JCJrMYNlsOdffxLG2V9UPT2MQ+rjbq5c46umqXBs5BtWNo5FD
|
|
xFenthgZzmRwQ3VtJU0c4naxcqEyg4+z8+THiM+9XbZt2hwGuXEH/caJA9S+
|
|
ttBqDArdLQb+176Bga5tixhkXnMP+kfs2bxo+L0Ggxi50gUCYjfdj2fytBjU
|
|
6mz5PUp8IMqPlbSCwfCaqU85xA6cOTcu6zKgYiTiOoh3mVWqeq9lMPh1TWwz
|
|
8bZUz4d26xh437uf+YHYQkxp5QYTBiuLNnwrJt7kUPpKayMDSM1XzCY2KTy8
|
|
SdGMQU+YgccdYsMZsnWiFgyqHCJ+hBDrehfa/7VmUPFKzdGTeHmtc3f9DgaT
|
|
REeYncQLQ3LH0uwZeCze7TmPeG6b3eVIJwY7tg5sESeetW6C3GkXBv9+1OAP
|
|
6Yep3O3qFkcZaIg6uCYQs2zGnup5MUgvm5HoRyyWnWI07wSDdlPVXktingvX
|
|
ZiSArLe+agWf9OdQaWJLy1kGRq+Ut38g7lM1dX0XzGDqSm8mgfh3w60zcVcZ
|
|
3HFZcUmfuGqD/kN2PAPa0fbxbrI//N8FagXdZXDd0zN3JrH65vJnrx6Q9eQ6
|
|
+dWR/RayxbJ0bRYD7Yqf69YTr9/m0ryqmMHLzx9rpMj+HKnPcPQpY9DZsepT
|
|
PtnfybYDnTlvGchvjr/hSCy25/Sw1kcGBW6he7JIHpQ4Rk5Z8puBsfBWz1KS
|
|
F55tX6MOtTPgbi3rr+CSPDigopTazaCme/5Te+LAQ2kL5w8yeOufcTqE5JHh
|
|
sVfrVMX4UNgZL/uK5FnB6R5PmQV8XEyw2VlMUTg4psWzVOdjkVGh8yriGUHH
|
|
z4Rr8tF7ulXrIYfC8fPjVyavJp8/ESN5pZ/CiisKyRM38jF25XmVNsnb7Bjj
|
|
BuYQH6yL2wJlOkl/KV6yW+POh+B4Vtz+DgrScTWtvp58LKn3889tJ/mWsJMz
|
|
7M9H9Z3r/lv+kHx9cFSCc4WP9k3Lr+7/TSEl57Z+2yM+np5sm7KomfSzwE6j
|
|
8TEfVccb7JybSP9smK1cm0u+/1G9IL6RQlHjfeGLl3xI6M67MfkbhbrxR68j
|
|
3/Px1zW39XMdBVGL4g3Gf/moFMa0i3ygYN/bZn1XQ4AlIkdbu8n5qLYqxSRG
|
|
S4CDn1d+7SwieXTm0MqrKwQY+6zU1PaSzF+mT95/rQBP9C9INrygELZm9Jul
|
|
mQBn10bOuE/O2xchEg7jhwUQvNUY+EnOa4X5mm4O6QKYhimptJPzPyIqzDY9
|
|
SwBtY3WpK+R+ICX212QkRwAv3/GcpbdIXramK4cWCuA4213bLZr0Y+LiD3nv
|
|
BXhexWp/H07Ow1nzl0tzBGDN1TRXu0CeR3YW9+UKIVTVbnxSJvcb6tzJtkl6
|
|
QkjR0Uv9Xcl6DTbWWhsIYSje8N+XgxQcP91K6/pPiPa9VzKD9lPYEq6wW26H
|
|
EEdz5ji/3kthvpRMkZufEPFTPE9+sSD5Kso6r1QkhF51uOEmHZLXWbcdrEqE
|
|
YF6mBrhoU5Dcs9TgUrkQOhVtUWeXUWA/tRgZqRHCqmGryZMlpB+cbx781CLE
|
|
btu0J6PzyHq9UTO/NC7EasV7PYqyZD9cNJIfNRnDrBU73pYOcJDH8kn9VDWG
|
|
a/vYJ1LSOOgMONdf/GEMXySj1fencKA4eH1V1ucx+HYcEJuTTO6/TZllV5rG
|
|
0LZXSiMykYP1GZ0/TXrGIFKCrftucvDFfM/MPNY/1MRcE0s+T343hBtfvm36
|
|
D89bbNWryP1ZU2G6m3PFP6ygygtjWRxQ4Vz5lV/HsbZiWYW9QT/mX7qk7eEm
|
|
wq7Vtjr42b4PbXu+N5t0ibAnjucr7z/8F5s66pi8Y6Lsw5Sv8TOTXvh7u7jO
|
|
6Bdl1+SdOa6v0AOL/DtmM3zF2CMiosn1T7vAEboFiHPF2BdMjxjus+zEvW/n
|
|
nh3zEWfv2GjZs66lHXxXI8eTAnG2zr65bZqr/0B1LNLO69QEdvAduvvdzVZ0
|
|
moZVsyZMZHdYduZbnv2FN4tqMDtsInuC7qkPpWXf4cZKnTBPchK7xf1PQOSS
|
|
RhTcXWD0JnISW1G5o9pJvR61BoYVNjIS7JQi+9jjtp9Au93Z5hguwd5TP6eH
|
|
N60KlVZJO6RnsNgROT4qD5+WwFnfMC0tmsX+zOvi/0zNweH+D6M/Ylhs1TDf
|
|
sH2OOfC8t2+97G0WO0NmZtVPpRwESV5oDUhgse8XSzk1XX2C+KYqZZtUFvs3
|
|
bbsqqCMbX0/ujBAWsNgHq7Wq0wMyYFbofdL6O4ttOGuZSGT6PVgfm1AZ0sJi
|
|
71w3om+jcg+71GJmFP1isWOfChfKXr+LQ6Evche1s9iNKkVBKj2JCN4jwhH0
|
|
sdiurwKtBgPjUMy/5pz6j8Wu2Gh1FBmRqMiek/NdRJIdH2bNvn89AjXOOePT
|
|
xSXZzNnYuxK94fheXR9/WkKS3ca+yw8JCgUdp/zNaroku6Bb6sOxjHMYt8ha
|
|
GCIryU7skR/c3BuISeI4/lJekq3/Q7Y/N+gU5I84yyxSkmQ3bIvXPJ/hBeU5
|
|
I/vslMl47q1raoPcoFZ3MTtCVZItavJILibDCRqXZo5VzJFkTxUWL32RYQ0d
|
|
g3RzwTxJtrbOtf/7f+B/AAObe4U=
|
|
"]]},
|
|
Annotation[#, "Charting`Private`Tag$6490849#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, Automatic}, {Automatic, Automatic}},
|
|
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->
|
|
NCache[{{0, Pi}, {0., 0.9999999707682925}}, {{0, 3.141592653589793}, {0.,
|
|
0.9999999707682925}}],
|
|
PlotRangeClipping->True,
|
|
PlotRangePadding->{{
|
|
Scaled[0.02],
|
|
Scaled[0.02]}, {
|
|
Scaled[0.05],
|
|
Scaled[0.05]}},
|
|
Ticks->{Automatic, Automatic}]], "Output",
|
|
CellChangeTimes->{{3.819447591278878*^9, 3.819447647286221*^9}},
|
|
CellLabel->
|
|
"Out[154]=",ExpressionUUID->"a9257c0c-b5e1-4c1f-b935-f11312fc5f0c"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"Solve", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox["2", "3"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"3", " ",
|
|
SubscriptBox["c", "0"]}], "+",
|
|
SubscriptBox["c", "1"]}], ")"}]}], "\[Equal]", "2"}], ",",
|
|
SubscriptBox["c", "0"]}], "]"}], "//", "Expand"}]], "Input",
|
|
CellChangeTimes->{{3.8194463704912663`*^9, 3.819446378817926*^9}, {
|
|
3.819446594262562*^9, 3.81944659977628*^9}},
|
|
CellLabel->
|
|
"In[132]:=",ExpressionUUID->"7d937c46-315c-4127-85c4-712b14bc01aa"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "\[Rule]",
|
|
RowBox[{"1", "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"]}]}], "}"}], "}"}]], "Output",
|
|
CellChangeTimes->{
|
|
3.819446373556425*^9, 3.819446457246375*^9, {3.819446596071899*^9,
|
|
3.819446600165804*^9}},
|
|
CellLabel->
|
|
"Out[132]=",ExpressionUUID->"cd9d35dd-d570-4a5a-8d26-67dfbe5a07bb"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
SubscriptBox["c", "1"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], "/.",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "\[Rule]",
|
|
RowBox[{"1", "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.819446938558178*^9, 3.8194469387544727`*^9}},
|
|
CellLabel->
|
|
"In[139]:=",ExpressionUUID->"a2ac8ff2-1cae-41e1-a20b-4fbb997dec08"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"1", "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], "/.",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "\[Rule]",
|
|
RowBox[{"1", "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.819446972587152*^9, 3.819446972587624*^9}},
|
|
CellLabel->
|
|
"In[140]:=",ExpressionUUID->"2f20c949-180a-497c-b460-fc41151522d8"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"1", "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}]], "Output",
|
|
CellChangeTimes->{3.8194469736722193`*^9},
|
|
CellLabel->
|
|
"Out[140]=",ExpressionUUID->"0b25d327-e92b-4494-a4e0-91dc831b2739"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}]], "Input",ExpressionUUID->"939751eb-557e-4570-\
|
|
ac5e-0177a1ac50cf"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{"\[Rho]", "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "1"]}]}]}], "=",
|
|
RowBox[{
|
|
RowBox[{"2", "\t", "\[Implies]", "\t",
|
|
SubscriptBox["c", "0"]}], "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"1", "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"]}], "\t", "\[Implies]", "\t",
|
|
RowBox[{"\[Rho]", "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}]}], "=",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ",
|
|
SuperscriptBox["\[Pi]", "2"]}], "3"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"1", "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"1", "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "1"], "3"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}]}],
|
|
")"}]}]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.74290046592192*^9, 3.742900508615451*^9}, {
|
|
3.7429008186008587`*^9, 3.742900822411848*^9}, {3.742901066474793*^9,
|
|
3.7429010697015457`*^9}, {3.7429037586511917`*^9, 3.742903804969626*^9},
|
|
3.819446463588112*^9, 3.819446602336863*^9, {3.819446946046637*^9,
|
|
3.8194469837946663`*^9}},ExpressionUUID->"7f39c9ab-32fa-41ee-a84c-\
|
|
0db48d3fd4ca"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"2", "-",
|
|
SubscriptBox["c", "0"], "+",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
SubscriptBox["c", "2"]}]}], "=",
|
|
RowBox[{"0", "\t", "\[Implies]", "\t",
|
|
RowBox[{
|
|
SubscriptBox["c", "2"], "\[Equal]",
|
|
RowBox[{
|
|
RowBox[{"5",
|
|
SubscriptBox["c", "0"]}], "-", "10"}]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.74290109712473*^9,
|
|
3.742901159497686*^9}},ExpressionUUID->"59da42ed-948c-40cc-9a75-\
|
|
afe1a8b88822"],
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "n_"], "[", "u_", "]"}], "=",
|
|
SuperscriptBox["u",
|
|
RowBox[{"n", "-", "1"}]]}], ";"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"M", "=", "10"}], ",",
|
|
RowBox[{"d", "=", "2"}]}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"H", "[", "R_", "]"}], "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0",
|
|
RowBox[{"2", "R"}]],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "i"], "[", "u", "]"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox[
|
|
SuperscriptBox["u", "2"],
|
|
RowBox[{"4",
|
|
SuperscriptBox["R", "2"]}]], "-", "1"}], ")"}],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Psi]", "j", "\[DoublePrime]"], "[", "u",
|
|
"]"}]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "d"}], "+", "1"}], ")"}], "u"}],
|
|
RowBox[{"4",
|
|
SuperscriptBox["R", "2"]}]], "-",
|
|
FractionBox[
|
|
RowBox[{"d", "-", "1"}], "u"]}], ")"}], " ",
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Psi]", "j", "\[Prime]"], "[", "u", "]"}]}],
|
|
"+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox["1", "u"], "+",
|
|
FractionBox["d",
|
|
RowBox[{"2",
|
|
SuperscriptBox["R", "2"]}]]}], ")"}],
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "j"], "[", "u", "]"}]}]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
FractionBox["u", "R"], ")"}],
|
|
RowBox[{"d", "-", "1"}]],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"1", "-",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
FractionBox["u",
|
|
RowBox[{"2", "R"}]], ")"}], "2"]}], ")"}],
|
|
FractionBox[
|
|
RowBox[{"d", "-", "2"}], "2"]],
|
|
RowBox[{"\[DifferentialD]", "u"}]}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"i", ",", "M"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"j", ",", "M"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"S", "[", "R_", "]"}], "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0",
|
|
RowBox[{"2", "R"}]],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "i"], "[", "u", "]"}],
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "j"], "[", "u", "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
FractionBox["u", "R"], ")"}],
|
|
RowBox[{"d", "-", "1"}]],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"1", "-",
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
FractionBox["u",
|
|
RowBox[{"2", "R"}]], ")"}], "2"]}], ")"}],
|
|
FractionBox[
|
|
RowBox[{"d", "-", "2"}], "2"]],
|
|
RowBox[{"\[DifferentialD]", "u"}]}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"i", ",", "M"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"j", ",", "M"}], "}"}]}], "]"}]}], ";"}]}],
|
|
"\[IndentingNewLine]", "]"}], ";"}]}], "Input",
|
|
CellChangeTimes->{{3.742918604620111*^9, 3.7429186131351423`*^9},
|
|
3.742918719955948*^9, {3.74291885295679*^9, 3.742918854648775*^9},
|
|
3.742922362967875*^9, 3.742980439148241*^9, 3.742980540306929*^9, {
|
|
3.742994989188118*^9, 3.742995016518692*^9}, {3.742995150772037*^9,
|
|
3.7429951513978567`*^9}, 3.7429952985264072`*^9, {3.74299538074587*^9,
|
|
3.7429953808123302`*^9}, {3.742996132486848*^9, 3.7429961349036427`*^9},
|
|
3.7429963078815823`*^9, {3.742996660743409*^9, 3.742996660843338*^9}, {
|
|
3.742996945034573*^9, 3.742996945161457*^9}, 3.7430081967857656`*^9,
|
|
3.743009059579871*^9, 3.743009234820531*^9, 3.743009382026333*^9, {
|
|
3.7430094920285807`*^9, 3.74300951455619*^9}, 3.74300961041049*^9,
|
|
3.743009666438663*^9, {3.7430098539824047`*^9, 3.743009854170718*^9},
|
|
3.743009922023739*^9, 3.743134546286873*^9, 3.743134666275275*^9, {
|
|
3.74322049794233*^9, 3.7432204980603647`*^9}, {3.743247376064542*^9,
|
|
3.743247418681962*^9}, {3.819389816415174*^9, 3.819389816573246*^9}, {
|
|
3.819442666471469*^9, 3.819442666582307*^9}, 3.8194494164767103`*^9, {
|
|
3.81952870547421*^9, 3.819528716305327*^9}},
|
|
CellLabel->"In[82]:=",ExpressionUUID->"47cbd7eb-4244-4a5a-b725-eb6c2ae63c11"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "10"}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{"tab", "=",
|
|
RowBox[{"Table", "[", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"\[Epsilon]", ",", "c"}], "}"}], "=",
|
|
RowBox[{"SortEigensystem", "[",
|
|
RowBox[{"Eigensystem", "[",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"N", "[",
|
|
RowBox[{
|
|
RowBox[{"H", "[", "R", "]"}], ",", "200"}], "]"}], ",",
|
|
RowBox[{"N", "[",
|
|
RowBox[{
|
|
RowBox[{"S", "[", "R", "]"}], ",", "200"}], "]"}]}], "}"}],
|
|
"]"}], "]"}]}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"f", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "n"], "[",
|
|
RowBox[{"2", " ", "R", " ",
|
|
RowBox[{"Sin", "[",
|
|
RowBox[{"\[Theta]", "/", "2"}], "]"}]}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"n", ",", "M"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"\[Rho]", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"\[ScriptL]", "+",
|
|
FractionBox["1", "2"]}], ")"}],
|
|
RowBox[{"NIntegrate", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
"c", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}],
|
|
".", "f"}], ")"}], "2"],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}], ",",
|
|
RowBox[{"WorkingPrecision", "\[Rule]", "50"}]}], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",", "2"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"\"\<R: \>\"", ",",
|
|
RowBox[{"N", "[", "R", "]"}]}], "]"}], ";", "\[IndentingNewLine]",
|
|
|
|
RowBox[{"Print", "[",
|
|
RowBox[{"\"\<\[Rho]: \>\"", ",", "\[Rho]"}], "]"}], ";"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"N", "[", "R", "]"}], ",",
|
|
RowBox[{"Chop", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
|
|
"+",
|
|
RowBox[{
|
|
FractionBox["2", "3"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "2",
|
|
"\[RightDoubleBracket]"}]}], "-",
|
|
RowBox[{
|
|
FractionBox["1", "5"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "3",
|
|
"\[RightDoubleBracket]"}]}]}], "]"}]}], "}"}]}],
|
|
"\[IndentingNewLine]", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",",
|
|
RowBox[{
|
|
RowBox[{"-", "20"}], "+",
|
|
RowBox[{"1", "/", "10"}]}], ",",
|
|
RowBox[{
|
|
RowBox[{"-", "5"}], "+",
|
|
RowBox[{"10", "/", "10"}]}], ",", "1"}], "}"}]}], "]"}]}]}],
|
|
"\[IndentingNewLine]", "]"}], "\[IndentingNewLine]",
|
|
RowBox[{"ListPlot", "[",
|
|
RowBox[{"tab", ",",
|
|
RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}]}], "Input",
|
|
CellChangeTimes->{
|
|
3.7169719668102694`*^9, 3.725887849338797*^9, {3.725887899762218*^9,
|
|
3.725887922914515*^9}, {3.725887992098515*^9, 3.725888054354484*^9}, {
|
|
3.725888190363358*^9, 3.725888220466589*^9}, {3.725888405954722*^9,
|
|
3.7258884143609447`*^9}, {3.725888474666101*^9, 3.725888479977105*^9}, {
|
|
3.725888867994993*^9, 3.725888870697344*^9}, {3.7258889297858877`*^9,
|
|
3.725888934808717*^9}, {3.725888967938243*^9, 3.725889013634396*^9}, {
|
|
3.725889098059265*^9, 3.725889127921206*^9}, {3.725948058954719*^9,
|
|
3.7259480590574303`*^9}, 3.72594816605788*^9, {3.7259484228037577`*^9,
|
|
3.7259484452333307`*^9}, {3.7428020644337606`*^9,
|
|
3.7428020663834143`*^9}, {3.74280212730392*^9, 3.74280222326132*^9},
|
|
3.742813402384555*^9, {3.7428134755684967`*^9, 3.742813490200959*^9},
|
|
3.742814183560895*^9, {3.742819919975389*^9, 3.742819921001403*^9}, {
|
|
3.7428199815500298`*^9, 3.742819983199623*^9}, {3.742877775652999*^9,
|
|
3.7428779074014883`*^9}, {3.7428779855771227`*^9, 3.742878008161315*^9}, {
|
|
3.7428782383972187`*^9, 3.742878269832116*^9}, {3.742878722461308*^9,
|
|
3.7428787571128817`*^9}, {3.742878822183488*^9, 3.742878822578849*^9}, {
|
|
3.7428788828839493`*^9, 3.7428788901191797`*^9}, {3.74287901611771*^9,
|
|
3.742879142617798*^9}, {3.742879199059029*^9, 3.7428791995390997`*^9},
|
|
3.742901214891993*^9, {3.74290164400101*^9, 3.742901906207686*^9}, {
|
|
3.742901977623595*^9, 3.742902002095676*^9}, {3.742902032247851*^9,
|
|
3.742902129781516*^9}, {3.742902162525971*^9, 3.74290222166597*^9}, {
|
|
3.742902276796481*^9, 3.742902287956953*^9}, {3.74290235927039*^9,
|
|
3.7429024146277122`*^9}, {3.7429024507177353`*^9,
|
|
3.7429025388586197`*^9}, {3.742903006310214*^9, 3.7429030105077744`*^9}, {
|
|
3.742903134891645*^9, 3.742903234602419*^9}, {3.742903317285879*^9,
|
|
3.7429033173754187`*^9}, {3.742903361602311*^9, 3.74290336281636*^9}, {
|
|
3.742905076823636*^9, 3.7429050778905582`*^9}, {3.742918166486006*^9,
|
|
3.742918220012596*^9}, {3.742918311916502*^9, 3.742918313196629*^9}, {
|
|
3.7429183606868353`*^9, 3.742918373040654*^9}, 3.742918421383092*^9, {
|
|
3.742918494233326*^9, 3.742918623848249*^9}, {3.74291880637696*^9,
|
|
3.7429188584054213`*^9}, {3.742918994743949*^9, 3.742919000933652*^9}, {
|
|
3.742919057477284*^9, 3.7429190853953876`*^9}, {3.742919151618346*^9,
|
|
3.742919208160902*^9}, {3.742920743629745*^9, 3.742920743849949*^9},
|
|
3.742922144965681*^9, {3.742922177083435*^9, 3.742922183503256*^9},
|
|
3.742922225061594*^9, 3.742922262893311*^9, {3.742922314745081*^9,
|
|
3.7429223742620287`*^9}, {3.74292246647335*^9, 3.742922597303072*^9}, {
|
|
3.742922649922433*^9, 3.7429226518828707`*^9}, {3.742923296115052*^9,
|
|
3.742923318322493*^9}, {3.742980141599243*^9, 3.74298028080587*^9}, {
|
|
3.742980310806139*^9, 3.7429803255358543`*^9}, {3.742980357754479*^9,
|
|
3.742980398957408*^9}, {3.7429804420837727`*^9, 3.7429804467641287`*^9}, {
|
|
3.742980541432966*^9, 3.742980548122097*^9}, {3.742980578285955*^9,
|
|
3.742980578400919*^9}, {3.7429806326930037`*^9, 3.742980650442853*^9}, {
|
|
3.742980694195736*^9, 3.742980749099784*^9}, {3.742981142831009*^9,
|
|
3.742981146671338*^9}, {3.742995040906142*^9, 3.7429950736953487`*^9}, {
|
|
3.742995103988391*^9, 3.742995134262944*^9}, {3.742995247787807*^9,
|
|
3.742995324266892*^9}, {3.742995360656518*^9, 3.742995384384591*^9}, {
|
|
3.7429954237133417`*^9, 3.742995433990855*^9}, {3.74299547198099*^9,
|
|
3.742995484920415*^9}, {3.742995760731353*^9, 3.7429957673259373`*^9}, {
|
|
3.742995847653798*^9, 3.7429958543557777`*^9}, {3.7429960931764708`*^9,
|
|
3.742996100192951*^9}, {3.742996300021468*^9, 3.742996312749928*^9}, {
|
|
3.742996623983343*^9, 3.742996683485918*^9}, {3.742996763260223*^9,
|
|
3.7429967667513227`*^9}, {3.742996823435986*^9, 3.742996947881322*^9}, {
|
|
3.7429969858904467`*^9, 3.7429969890918093`*^9}, {3.742997154797719*^9,
|
|
3.742997179630937*^9}, {3.742997221183319*^9, 3.7429972234251423`*^9}, {
|
|
3.742997256190982*^9, 3.742997295285985*^9}, {3.742997325738884*^9,
|
|
3.7429973513749123`*^9}, {3.74299738735357*^9, 3.7429974112679663`*^9}, {
|
|
3.742997461552939*^9, 3.7429974669219646`*^9}, {3.743008210683326*^9,
|
|
3.743008225538146*^9}, 3.743009057265111*^9, {3.743009239073036*^9,
|
|
3.7430092656499767`*^9}, {3.743009361125576*^9, 3.743009373039097*^9}, {
|
|
3.7430094955856752`*^9, 3.7430095437002373`*^9}, {3.7430096137618933`*^9,
|
|
3.743009669733102*^9}, {3.743009863885*^9, 3.7430099872406483`*^9}, {
|
|
3.743010046219955*^9, 3.743010048241816*^9}, {3.7430103170795507`*^9,
|
|
3.743010344854659*^9}, {3.743011088494897*^9, 3.7430111264389553`*^9}, {
|
|
3.7430111611489353`*^9, 3.743011161959427*^9}, {3.743011716328226*^9,
|
|
3.7430117899482517`*^9}, 3.743221076129325*^9, {3.8193907581118402`*^9,
|
|
3.8193907617791357`*^9}, {3.8193907925481987`*^9, 3.819390804206044*^9}, {
|
|
3.819390849865067*^9, 3.819390936727295*^9}, {3.819391001811208*^9,
|
|
3.8193910257883453`*^9}, {3.819391085700403*^9, 3.819391087526915*^9}, {
|
|
3.8193914241938553`*^9, 3.819391470682129*^9}, {3.819391627347579*^9,
|
|
3.8193917104671087`*^9}, {3.819391752709236*^9, 3.8193917589749203`*^9},
|
|
3.8194447427358437`*^9, {3.81944477511159*^9, 3.819444799254642*^9}, {
|
|
3.819445423554438*^9, 3.8194454485467577`*^9}, {3.8194455041540318`*^9,
|
|
3.8194455101392508`*^9}, 3.819445596217606*^9, {3.8194456567851753`*^9,
|
|
3.819445656839918*^9}, {3.819445746264432*^9, 3.819445757912693*^9}, {
|
|
3.819445813352127*^9, 3.819445825887064*^9}, 3.8194458612711887`*^9,
|
|
3.8194458919673147`*^9, {3.819445967319127*^9, 3.819445968614059*^9}, {
|
|
3.819449084439749*^9, 3.819449109599296*^9}, {3.8194607735707207`*^9,
|
|
3.81946092478191*^9}, {3.8195288573268127`*^9, 3.819528972919237*^9}},
|
|
CellLabel->
|
|
"In[106]:=",ExpressionUUID->"54cba639-78de-41b7-b09f-3fb5cc912380"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "19.9`"}], ",",
|
|
"0.0193165223712549558801207961467713363061784278202738157030514070075899\
|
|
7056432`49.75270130032005"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "18.9`"}], ",",
|
|
"0.0213093039987504169089508190847709275084333078336448517542534567918590\
|
|
0867429`49.75826130792854"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "17.9`"}], ",",
|
|
"0.0237208069059177255259757424204885161533706351206221876899879470335901\
|
|
1626155`49.76471534090756"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "16.9`"}], ",",
|
|
"0.0266595597505443968925008327809039910269487898920431662242882150979899\
|
|
390815`49.772256425802446"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "15.9`"}], ",",
|
|
"0.0302724563442335630034576417891223014362763988117905567051279645054823\
|
|
5760075`49.78113230960456"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "14.9`"}], ",",
|
|
"0.0347621321515244352671696877908848895523571488612491064938951838285668\
|
|
2431894`49.791662490578894"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "13.9`"}], ",",
|
|
"0.0404135461833283730998441106714793740619741858633252928153070169741450\
|
|
8468716`49.80426010632854"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "12.9`"}], ",",
|
|
"0.0476349191520763600144971123716230901489678570754188268475542007203830\
|
|
0295209`49.81945796451975"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "11.9`"}], ",",
|
|
"0.0570201666204428000960724844971322870662825275592928477947138478030155\
|
|
7187635`49.83793299554744"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "10.9`"}], ",",
|
|
"0.0694393943366061446072338935462256580105606649763729234083155906214026\
|
|
1967124`49.86050966471025"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "9.9`"}], ",",
|
|
"0.0861497309645649111324270283719182404172138103305646308871134500224728\
|
|
5871357`49.88809192573045"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "8.9`"}], ",",
|
|
"0.1088549841304922757531415338524922819858863046235745101837957894411110\
|
|
0188416`49.921422854934626"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "7.9`"}], ",",
|
|
"0.1394437057767699930738633739938731955808149153069395056512717230882002\
|
|
623614`49.96054383509902"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "6.9`"}], ",",
|
|
"0.1787029747216908511253518000621616782231610702671098403202819988717117\
|
|
7935592`50."}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "5.9`"}], ",",
|
|
"0.2228989928237469462516190730688585583195060448990782256843471047329576\
|
|
678213`50."}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "4.9`"}], ",",
|
|
"0.2581878699584209666485276561405826530410099655689331349408684956846323\
|
|
9843563`50."}], "}"}]}], "}"}]], "Output",
|
|
CellChangeTimes->{
|
|
3.819391014749713*^9, {3.819391071671455*^9, 3.819391093328039*^9}, {
|
|
3.81939143621446*^9, 3.819391475405188*^9}, 3.819391636446169*^9, {
|
|
3.8193916949654408`*^9, 3.819391720160043*^9}, 3.8193917634000683`*^9, {
|
|
3.8194447707974577`*^9, 3.819444802118456*^9}, 3.819445429630782*^9, {
|
|
3.81944548901746*^9, 3.819445510028133*^9}, 3.8194455422005568`*^9,
|
|
3.819445630309391*^9, 3.819445726083826*^9, {3.81944581458074*^9,
|
|
3.8194458335917597`*^9}, 3.819445882243606*^9, 3.8194459359917192`*^9,
|
|
3.819446005097937*^9, {3.819449087924513*^9, 3.81944911372517*^9}, {
|
|
3.8194607891681128`*^9, 3.819460928218804*^9}, 3.819528723378552*^9, {
|
|
3.819528860989966*^9, 3.819528976120275*^9}},
|
|
CellLabel->
|
|
"Out[106]=",ExpressionUUID->"278ca01a-9bd3-4962-aa4f-fe7918d70fe0"],
|
|
|
|
Cell[BoxData[
|
|
GraphicsBox[{{}, {{{}, {},
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[
|
|
0.012833333333333334`], AbsoluteThickness[1.6],
|
|
LineBox[{{-19.9, 0.019316522371254956`}, {-18.9,
|
|
0.021309303998750417`}, {-17.9, 0.023720806905917727`}, {-16.9,
|
|
0.026659559750544397`}, {-15.9, 0.03027245634423356}, {-14.9,
|
|
0.03476213215152443}, {-13.9, 0.040413546183328375`}, {-12.9,
|
|
0.04763491915207636}, {-11.9, 0.0570201666204428}, {-10.9,
|
|
0.06943939433660615}, {-9.9, 0.08614973096456491}, {-8.9,
|
|
0.10885498413049227`}, {-7.9, 0.13944370577676998`}, {-6.9,
|
|
0.17870297472169086`}, {-5.9, 0.22289899282374695`}, {-4.9,
|
|
0.25818786995842097`}}]}},
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.012833333333333334`],
|
|
AbsoluteThickness[1.6]}, {
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[
|
|
0.012833333333333334`], AbsoluteThickness[1.6]}, {}}, {
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[
|
|
0.012833333333333334`], AbsoluteThickness[1.6]}, {}}}, {{}, {}}},
|
|
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
|
|
Axes->{True, True},
|
|
AxesLabel->{None, None},
|
|
AxesOrigin->{-4.587500000000001, 0},
|
|
DisplayFunction->Identity,
|
|
Frame->{{False, False}, {False, False}},
|
|
FrameLabel->{{None, None}, {None, None}},
|
|
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
|
|
GridLines->{None, None},
|
|
GridLinesStyle->Directive[
|
|
GrayLevel[0.5, 0.4]],
|
|
Method->{
|
|
"OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> True,
|
|
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
|
|
Identity[
|
|
Part[#, 1]],
|
|
Identity[
|
|
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
|
|
Identity[
|
|
Part[#, 1]],
|
|
Identity[
|
|
Part[#, 2]]}& )}},
|
|
PlotRange->{{-19.9, -4.9}, {0, 0.25818786995842097`}},
|
|
PlotRangeClipping->True,
|
|
PlotRangePadding->{{
|
|
Scaled[0.02],
|
|
Scaled[0.02]}, {
|
|
Scaled[0.02],
|
|
Scaled[0.05]}},
|
|
Ticks->{Automatic, Automatic}]], "Output",
|
|
CellChangeTimes->{
|
|
3.819391014749713*^9, {3.819391071671455*^9, 3.819391093328039*^9}, {
|
|
3.81939143621446*^9, 3.819391475405188*^9}, 3.819391636446169*^9, {
|
|
3.8193916949654408`*^9, 3.819391720160043*^9}, 3.8193917634000683`*^9, {
|
|
3.8194447707974577`*^9, 3.819444802118456*^9}, 3.819445429630782*^9, {
|
|
3.81944548901746*^9, 3.819445510028133*^9}, 3.8194455422005568`*^9,
|
|
3.819445630309391*^9, 3.819445726083826*^9, {3.81944581458074*^9,
|
|
3.8194458335917597`*^9}, 3.819445882243606*^9, 3.8194459359917192`*^9,
|
|
3.819446005097937*^9, {3.819449087924513*^9, 3.81944911372517*^9}, {
|
|
3.8194607891681128`*^9, 3.819460928218804*^9}, 3.819528723378552*^9, {
|
|
3.819528860989966*^9, 3.819528976162653*^9}},
|
|
CellLabel->
|
|
"Out[107]=",ExpressionUUID->"44916109-9e4c-44de-8ffc-11faec7bc38d"]
|
|
}, Open ]]
|
|
}, Closed]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[TextData[{
|
|
"Triplet ",
|
|
Cell[BoxData[
|
|
FormBox[
|
|
SuperscriptBox["p", "2"], TraditionalForm]],ExpressionUUID->
|
|
"57d5e92b-0647-42c8-93a1-b798006a46c1"]
|
|
}], "Subsection",
|
|
CellChangeTimes->{{3.742921809427841*^9,
|
|
3.742921815126781*^9}},ExpressionUUID->"c3267724-2a1e-46ae-a70a-\
|
|
24dbe2bc9597"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"Sin", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}],
|
|
RowBox[{"Sin", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}],
|
|
RowBox[{"Cos", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Phi]", "1"], "-",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], ")"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
FractionBox[
|
|
RowBox[{"4", " ", "\[Pi]"}], "3"], ")"}], "2"],
|
|
SuperscriptBox[
|
|
RowBox[{"(", " ",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "1"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",",
|
|
RowBox[{"-", "1"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",",
|
|
RowBox[{"-", "1"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "1"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}], ")"}], "2"]}]}], "//",
|
|
"FullSimplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "1"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",",
|
|
RowBox[{"-", "1"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "\[Equal]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox["1",
|
|
RowBox[{"2", " ",
|
|
SqrtBox["\[Pi]"]}]]}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["1",
|
|
RowBox[{"2", " ",
|
|
SqrtBox[
|
|
RowBox[{"5", " ", "\[Pi]"}]]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}]}]}], "//",
|
|
"Simplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "\[Equal]",
|
|
RowBox[{
|
|
FractionBox["1", "96"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"160", " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "-",
|
|
RowBox[{"80", " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{"16", " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], ")"}]}]}], "//",
|
|
"Simplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",",
|
|
RowBox[{"-", "1"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
SqrtBox[
|
|
FractionBox["3",
|
|
RowBox[{"10", " ", "\[Pi]"}]]], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}]}], ",",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "1"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
SqrtBox[
|
|
FractionBox["3",
|
|
RowBox[{"10", " ", "\[Pi]"}]]], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}]}]}], "}"}], "//",
|
|
"Simplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"Sin", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}],
|
|
RowBox[{"Sin", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}],
|
|
RowBox[{"Cos", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Phi]", "1"], "-",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], ")"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", "\[Pi]"}], "9"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "-",
|
|
RowBox[{
|
|
FractionBox["1",
|
|
RowBox[{" ",
|
|
SqrtBox["5"]}]], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}], ")"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["9", "45"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["9", "15"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}], ")"}]}]}], ")"}]}]}], "//",
|
|
"FullSimplify"}], "\[IndentingNewLine]"}], "Input",
|
|
CellChangeTimes->{{3.742921541073929*^9, 3.7429217915991783`*^9}, {
|
|
3.743221206846005*^9, 3.7432213027031612`*^9}, {3.743223071879881*^9,
|
|
3.7432230721557083`*^9}, {3.743223122804291*^9, 3.743223160854814*^9}, {
|
|
3.743229983868244*^9, 3.743229987103587*^9}, 3.743230196503038*^9, {
|
|
3.743230229246484*^9, 3.743230392876593*^9}, {3.74323042341105*^9,
|
|
3.743230423574142*^9}, {3.74323046932085*^9, 3.74323050342354*^9}, {
|
|
3.743230609148362*^9, 3.743230658741049*^9}, {3.743232501718238*^9,
|
|
3.743232502023597*^9}, {3.7432396332522507`*^9, 3.743239693010103*^9}, {
|
|
3.743239813190792*^9, 3.743239835225259*^9}, {3.743239957601283*^9,
|
|
3.743239964073461*^9}},ExpressionUUID->"093b63ec-d5d7-429c-a6ae-\
|
|
daee424561d5"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.742921693566469*^9, 3.7429217919516277`*^9},
|
|
3.743221130252604*^9, {3.743221239571553*^9, 3.743221251731104*^9}, {
|
|
3.743221289458893*^9, 3.7432213035428667`*^9}, 3.743223072588331*^9,
|
|
3.7432231612608023`*^9, 3.743223192566586*^9, 3.743229987526679*^9,
|
|
3.743230199018121*^9, {3.743230249889526*^9, 3.743230269081333*^9},
|
|
3.743230332948771*^9, 3.74323039351552*^9, 3.743230425246151*^9,
|
|
3.7432304703532124`*^9, 3.743230503952559*^9, 3.743230609797349*^9,
|
|
3.743230659345324*^9, 3.743232503176585*^9, 3.743239662879141*^9,
|
|
3.7432396964774113`*^9, 3.7432398357846203`*^9, {3.743239959398622*^9,
|
|
3.743239964638369*^9}},ExpressionUUID->"c8bc8a1a-7edb-4bf3-8401-\
|
|
c89b58f107f2"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.742921693566469*^9, 3.7429217919516277`*^9},
|
|
3.743221130252604*^9, {3.743221239571553*^9, 3.743221251731104*^9}, {
|
|
3.743221289458893*^9, 3.7432213035428667`*^9}, 3.743223072588331*^9,
|
|
3.7432231612608023`*^9, 3.743223192566586*^9, 3.743229987526679*^9,
|
|
3.743230199018121*^9, {3.743230249889526*^9, 3.743230269081333*^9},
|
|
3.743230332948771*^9, 3.74323039351552*^9, 3.743230425246151*^9,
|
|
3.7432304703532124`*^9, 3.743230503952559*^9, 3.743230609797349*^9,
|
|
3.743230659345324*^9, 3.743232503176585*^9, 3.743239662879141*^9,
|
|
3.7432396964774113`*^9, 3.7432398357846203`*^9, {3.743239959398622*^9,
|
|
3.743239964660324*^9}},ExpressionUUID->"f48a9ecf-9fbe-47d9-ae87-\
|
|
f8b5af6c5e0b"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.742921693566469*^9, 3.7429217919516277`*^9},
|
|
3.743221130252604*^9, {3.743221239571553*^9, 3.743221251731104*^9}, {
|
|
3.743221289458893*^9, 3.7432213035428667`*^9}, 3.743223072588331*^9,
|
|
3.7432231612608023`*^9, 3.743223192566586*^9, 3.743229987526679*^9,
|
|
3.743230199018121*^9, {3.743230249889526*^9, 3.743230269081333*^9},
|
|
3.743230332948771*^9, 3.74323039351552*^9, 3.743230425246151*^9,
|
|
3.7432304703532124`*^9, 3.743230503952559*^9, 3.743230609797349*^9,
|
|
3.743230659345324*^9, 3.743232503176585*^9, 3.743239662879141*^9,
|
|
3.7432396964774113`*^9, 3.7432398357846203`*^9, {3.743239959398622*^9,
|
|
3.743239964668839*^9}},ExpressionUUID->"ec1755b9-8f51-47c9-9a0f-\
|
|
1629807636d1"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True"}], "}"}]], "Output",
|
|
CellChangeTimes->{{3.742921693566469*^9, 3.7429217919516277`*^9},
|
|
3.743221130252604*^9, {3.743221239571553*^9, 3.743221251731104*^9}, {
|
|
3.743221289458893*^9, 3.7432213035428667`*^9}, 3.743223072588331*^9,
|
|
3.7432231612608023`*^9, 3.743223192566586*^9, 3.743229987526679*^9,
|
|
3.743230199018121*^9, {3.743230249889526*^9, 3.743230269081333*^9},
|
|
3.743230332948771*^9, 3.74323039351552*^9, 3.743230425246151*^9,
|
|
3.7432304703532124`*^9, 3.743230503952559*^9, 3.743230609797349*^9,
|
|
3.743230659345324*^9, 3.743232503176585*^9, 3.743239662879141*^9,
|
|
3.7432396964774113`*^9, 3.7432398357846203`*^9, {3.743239959398622*^9,
|
|
3.7432399646776123`*^9}},ExpressionUUID->"de84db82-7bcd-4321-be05-\
|
|
acdd32c5a02c"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.742921693566469*^9, 3.7429217919516277`*^9},
|
|
3.743221130252604*^9, {3.743221239571553*^9, 3.743221251731104*^9}, {
|
|
3.743221289458893*^9, 3.7432213035428667`*^9}, 3.743223072588331*^9,
|
|
3.7432231612608023`*^9, 3.743223192566586*^9, 3.743229987526679*^9,
|
|
3.743230199018121*^9, {3.743230249889526*^9, 3.743230269081333*^9},
|
|
3.743230332948771*^9, 3.74323039351552*^9, 3.743230425246151*^9,
|
|
3.7432304703532124`*^9, 3.743230503952559*^9, 3.743230609797349*^9,
|
|
3.743230659345324*^9, 3.743232503176585*^9, 3.743239662879141*^9,
|
|
3.7432396964774113`*^9, 3.7432398357846203`*^9, {3.743239959398622*^9,
|
|
3.743239964686699*^9}},ExpressionUUID->"e6a683e2-6c11-4e7d-802c-\
|
|
2b921896631b"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", "\[Pi]"}], "9"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "-",
|
|
RowBox[{
|
|
FractionBox["1",
|
|
RowBox[{" ",
|
|
SqrtBox["5"]}]], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["c", "0"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}]}], ")"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["9", "45"],
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox["9", "15"],
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{"-", "1"}], ")"}], "2"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "+",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}]}], ")"}]}],
|
|
"\[Equal]",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", "\[Pi]"}], "9"], " ",
|
|
RowBox[{"(", " ",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox["3", "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "15"]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "-", " ",
|
|
RowBox[{
|
|
FractionBox["1", "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox["9", "45"],
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox["9", "15"],
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "+",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}]}],
|
|
")"}]}]}], "//", "Simplify"}]], "Input",
|
|
CellChangeTimes->{{3.7432309244892607`*^9, 3.7432310360686903`*^9}, {
|
|
3.743231109097535*^9, 3.743231258697278*^9}, {3.743231364454309*^9,
|
|
3.743231409370471*^9}, {3.743231900965172*^9, 3.743231986117247*^9}, {
|
|
3.7432324923575897`*^9, 3.743232492703197*^9}, {3.74323512483928*^9,
|
|
3.743235190355508*^9}, {3.74323981050996*^9, 3.743239811158902*^9}, {
|
|
3.7432398596065817`*^9, 3.743240075487534*^9}, {3.743240106386077*^9,
|
|
3.743240217956325*^9}, {3.7432406734447002`*^9,
|
|
3.743240698438498*^9}},ExpressionUUID->"5ce35750-7da9-4ff5-b83f-\
|
|
0ae5f5377437"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.743240691995799*^9,
|
|
3.74324069870498*^9}},ExpressionUUID->"7fb01024-0558-4c4e-bc04-\
|
|
f537ce36e159"]
|
|
}, Open ]]
|
|
}, Closed]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[TextData[Cell[BoxData[
|
|
FormBox[
|
|
RowBox[{
|
|
SuperscriptBox["\[InvisiblePrefixScriptBase]", "3"],
|
|
SuperscriptBox["D", "o"]}],
|
|
TraditionalForm]],ExpressionUUID->"428b48f7-9cd0-4f69-b100-8c3380ba5a83"]], \
|
|
"Subsection",
|
|
CellChangeTimes->{{3.743235924912355*^9,
|
|
3.743235950104946*^9}},ExpressionUUID->"59690161-1c60-4593-a2e7-\
|
|
c717480798c8"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "-",
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], ")"}],
|
|
RowBox[{"Sin", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}],
|
|
RowBox[{"Sin", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}],
|
|
RowBox[{"Cos", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Phi]", "1"], "-",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], ")"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
FractionBox[
|
|
RowBox[{"4", " ", "\[Pi]"}], "3"], ")"}], "2"],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "-",
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], ")"}], "2"],
|
|
SuperscriptBox[
|
|
RowBox[{"(", " ",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "1"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",",
|
|
RowBox[{"-", "1"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",",
|
|
RowBox[{"-", "1"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "1"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}], ")"}], "2"]}]}], "//",
|
|
"FullSimplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "1"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",",
|
|
RowBox[{"-", "1"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "\[Equal]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-",
|
|
FractionBox["1",
|
|
RowBox[{"2", " ",
|
|
SqrtBox["\[Pi]"]}]]}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["1",
|
|
RowBox[{"2", " ",
|
|
SqrtBox[
|
|
RowBox[{"5", " ", "\[Pi]"}]]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}]}]}], "//",
|
|
"Simplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "\[Equal]",
|
|
RowBox[{
|
|
FractionBox["1", "96"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"160", " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "-",
|
|
RowBox[{"80", " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{"16", " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], ")"}]}]}], "//",
|
|
"Simplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",",
|
|
RowBox[{"-", "1"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
SqrtBox[
|
|
FractionBox["3",
|
|
RowBox[{"10", " ", "\[Pi]"}]]], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}]}], ",",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "1"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
SqrtBox[
|
|
FractionBox["3",
|
|
RowBox[{"10", " ", "\[Pi]"}]]], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}]}]}], "}"}], "//",
|
|
"Simplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "-",
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], ")"}],
|
|
RowBox[{"Sin", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}],
|
|
RowBox[{"Sin", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}],
|
|
RowBox[{"Cos", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Phi]", "1"], "-",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], ")"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "-",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox["8", "9"], " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "-",
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}],
|
|
RowBox[{"9", " ",
|
|
SqrtBox["5"]}]], "-",
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}],
|
|
RowBox[{"9", " ",
|
|
SqrtBox["5"]}]], "+",
|
|
RowBox[{
|
|
FractionBox["8", "45"], " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["8", "15"], " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["8", "15"], " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}], ")"}]}]}], "//",
|
|
"FullSimplify"}], "\[IndentingNewLine]"}], "Input",
|
|
CellChangeTimes->{{3.742921541073929*^9, 3.7429217915991783`*^9}, {
|
|
3.743221206846005*^9, 3.7432213027031612`*^9}, {3.743223071879881*^9,
|
|
3.7432230721557083`*^9}, {3.743223122804291*^9, 3.743223160854814*^9}, {
|
|
3.743229983868244*^9, 3.743229987103587*^9}, 3.743230196503038*^9, {
|
|
3.743230229246484*^9, 3.743230392876593*^9}, {3.74323042341105*^9,
|
|
3.743230423574142*^9}, {3.74323046932085*^9, 3.74323050342354*^9}, {
|
|
3.743230609148362*^9, 3.743230658741049*^9}, {3.743232501718238*^9,
|
|
3.743232502023597*^9}, {3.743235961240123*^9, 3.743236001680119*^9}, {
|
|
3.7432360560871887`*^9,
|
|
3.743236072427079*^9}},ExpressionUUID->"83dd638d-a3d9-4eac-9812-\
|
|
c6a4cf31efb2"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.743235997619177*^9, 3.7432360158032103`*^9}, {
|
|
3.7432360571012383`*^9,
|
|
3.74323607285853*^9}},ExpressionUUID->"b4e381d7-4a23-4e07-981a-\
|
|
8f2086d6ecb0"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.743235997619177*^9, 3.7432360158032103`*^9}, {
|
|
3.7432360571012383`*^9,
|
|
3.743236072869734*^9}},ExpressionUUID->"c0f052e7-e375-40fb-9cda-\
|
|
e30d1e386bf6"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.743235997619177*^9, 3.7432360158032103`*^9}, {
|
|
3.7432360571012383`*^9,
|
|
3.743236072878709*^9}},ExpressionUUID->"0bae4c27-c7b9-457a-8a0b-\
|
|
94924bb3d300"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{"True", ",", "True"}], "}"}]], "Output",
|
|
CellChangeTimes->{{3.743235997619177*^9, 3.7432360158032103`*^9}, {
|
|
3.7432360571012383`*^9,
|
|
3.7432360728882093`*^9}},ExpressionUUID->"c64341aa-bf6d-4dfd-8f07-\
|
|
5440230a7974"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{{3.743235997619177*^9, 3.7432360158032103`*^9}, {
|
|
3.7432360571012383`*^9,
|
|
3.743236072897498*^9}},ExpressionUUID->"55d747c3-742f-4a1c-84a2-\
|
|
fde40e88cc5e"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], "-",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}], "3"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]"}],
|
|
RowBox[{"3", " ",
|
|
SqrtBox["5"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}]}], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox["8", "9"], " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], "-",
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}]}],
|
|
RowBox[{"9", " ",
|
|
SqrtBox["5"]}]], "-",
|
|
FractionBox[
|
|
RowBox[{"8", " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}],
|
|
RowBox[{"9", " ",
|
|
SqrtBox["5"]}]], "+",
|
|
RowBox[{
|
|
FractionBox["8", "45"], " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["8", "15"], " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["8", "15"], " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}]}], ")"}]}], "==",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox["64", "27"], " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
FractionBox["1",
|
|
SqrtBox[
|
|
RowBox[{"4", "\[Pi]"}]]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], "2"]}], "-",
|
|
RowBox[{
|
|
FractionBox["64", "27"], " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
FractionBox["1",
|
|
SqrtBox[
|
|
RowBox[{"4", "\[Pi]"}]]], " ",
|
|
FractionBox["1",
|
|
SqrtBox[
|
|
RowBox[{"4", "\[Pi]"}]]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], "+",
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"],
|
|
FractionBox["1",
|
|
SqrtBox[
|
|
RowBox[{"4", "\[Pi]"}]]], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}],
|
|
RowBox[{"27", " ",
|
|
SqrtBox["5"]}]], "-",
|
|
RowBox[{
|
|
FractionBox["64", "135"], " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
FractionBox["1",
|
|
SqrtBox[
|
|
RowBox[{"4", "\[Pi]"}]]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "2"]}], "+",
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
FractionBox["1",
|
|
SqrtBox[
|
|
RowBox[{"4", "\[Pi]"}]]], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}],
|
|
RowBox[{"27", " ",
|
|
SqrtBox["5"]}]], "-",
|
|
RowBox[{
|
|
FractionBox["64", "135"], " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
FractionBox["1",
|
|
SqrtBox[
|
|
RowBox[{"4", "\[Pi]"}]]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], "-",
|
|
RowBox[{
|
|
FractionBox["64", "135"], " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], "+",
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "2"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}],
|
|
RowBox[{"135", " ",
|
|
SqrtBox["5"]}]], "-",
|
|
RowBox[{
|
|
FractionBox["64", "135"], " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "2"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], "2"]}], "+",
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], "2"]}],
|
|
RowBox[{"135", " ",
|
|
SqrtBox["5"]}]], "+",
|
|
RowBox[{
|
|
FractionBox["64", "45"], " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}]}], "-",
|
|
RowBox[{
|
|
FractionBox["64", "45"], " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}]}], "+",
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}]}],
|
|
RowBox[{"45", " ",
|
|
SqrtBox["5"]}]], "+",
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}]}],
|
|
RowBox[{"45", " ",
|
|
SqrtBox["5"]}]], "+",
|
|
RowBox[{
|
|
FractionBox["64", "45"], " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], "-",
|
|
RowBox[{
|
|
FractionBox["64", "45"], " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], "+",
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}],
|
|
RowBox[{"45", " ",
|
|
SqrtBox["5"]}]], "+",
|
|
FractionBox[
|
|
RowBox[{"64", " ",
|
|
SuperscriptBox["\[Pi]", "2"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",",
|
|
RowBox[{"-", "2"}]}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "2"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}],
|
|
RowBox[{"45", " ",
|
|
SqrtBox["5"]}]]}]}], "//", "FullSimplify"}],
|
|
"\[IndentingNewLine]"}]], "Input",
|
|
CellChangeTimes->{{3.743236087870112*^9,
|
|
3.743236258450646*^9}},ExpressionUUID->"e4ec2f88-e321-4297-8368-\
|
|
7cf33b0e5d5e"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"2", " ",
|
|
SqrtBox["\[Pi]"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "2"], "+",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"5", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+",
|
|
RowBox[{"2", " ",
|
|
SqrtBox["\[Pi]"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}]}]}], ")"}]}], "-",
|
|
RowBox[{"2", " ",
|
|
SqrtBox["\[Pi]"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "2"]}]}], ")"}]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"1", "-",
|
|
RowBox[{"2", " ",
|
|
SqrtBox["\[Pi]"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}]}]}], ")"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}]}], ")"}]}], "+",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{"5", "+",
|
|
RowBox[{"4", " ",
|
|
SqrtBox["5"], " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}]}], "-",
|
|
RowBox[{"2", " ",
|
|
SqrtBox[
|
|
RowBox[{"5", " ", "\[Pi]"}]], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "+",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], ")"}]}], "+",
|
|
RowBox[{"4", " ", "\[Pi]", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-", "5"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}], "+",
|
|
RowBox[{
|
|
SqrtBox["5"], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}]}]}], ")"}]}]}], ")"}]}]}],
|
|
"\[Equal]", "0"}]], "Output",
|
|
CellChangeTimes->{3.743236150702338*^9,
|
|
3.743242100431136*^9},ExpressionUUID->"468a3fca-bc22-4dbe-ba2e-\
|
|
d09f5efde874"]
|
|
}, Open ]]
|
|
}, Closed]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell["Triplet D state", "Subsection",
|
|
CellChangeTimes->{{3.742903401180684*^9, 3.742903403606084*^9}, {
|
|
3.742918347228277*^9, 3.742918347362217*^9},
|
|
3.7429860324223146`*^9},ExpressionUUID->"eac4bda2-189e-42f0-81dc-\
|
|
51e5ebbd2f4a"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"\[CapitalPhi]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}],
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "\t",
|
|
SuperscriptBox[
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "2"]}], "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}], "\[Infinity]"],
|
|
RowBox[{
|
|
SubscriptBox["c", "\[ScriptL]"],
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Gamma]", "]"}], "]"}], "\t",
|
|
SubscriptBox["c", "\[ScriptL]"]}]}], "=",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]"}], "+", "1"}], "2"],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0", "\[Pi]"],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Gamma]", "]"}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "2"],
|
|
RowBox[{"Sin", "[", "\[Gamma]", "]"}],
|
|
RowBox[{"\[DifferentialD]", "\[Gamma]"}]}]}]}]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.742897993868801*^9, 3.7428981067548847`*^9}, {
|
|
3.742898182660631*^9,
|
|
3.742898271183833*^9}},ExpressionUUID->"17b135d5-7e41-4643-b4bb-\
|
|
f3eea5ce1e51"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"\[Rho]", "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{"2",
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"\[Psi]", "[", "\[Gamma]", "]"}], "2"],
|
|
SuperscriptBox[
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "2"],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}]}], "=",
|
|
RowBox[{"8", "\[Pi]",
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"\[ScriptL]", "=", "0"}], "\[Infinity]"],
|
|
RowBox[{
|
|
FractionBox[
|
|
SubscriptBox["c", "\[ScriptL]"],
|
|
RowBox[{
|
|
RowBox[{"2", "\[ScriptL]"}], "+", "1"}]],
|
|
RowBox[{
|
|
UnderoverscriptBox["\[Sum]",
|
|
RowBox[{"m", "=",
|
|
RowBox[{"-", "\[ScriptL]"}]}], "\[ScriptL]"],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}], "*"], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "2"],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}]}]}]}]}]}]}]}]], "Input",\
|
|
|
|
CellChangeTimes->{{3.742898286664424*^9, 3.7428983914044456`*^9}, {
|
|
3.7429901583001747`*^9,
|
|
3.7429901628375263`*^9}},ExpressionUUID->"14802bea-9955-4893-8c9c-\
|
|
a17bac458ece"],
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"\[CapitalLambda]", "[",
|
|
RowBox[{
|
|
SubscriptBox["\[CapitalOmega]", "1"], ",",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}], "]"}], "2"],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}], "=",
|
|
RowBox[{"\[Integral]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"\[ScriptL]", ",", "m"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
SqrtBox[
|
|
RowBox[{"4", "\[Pi]"}]],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}]}], "-",
|
|
RowBox[{"2", " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}]}], "+",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "2"], "]"}], "2"]}], ")"}],
|
|
RowBox[{"\[DifferentialD]",
|
|
SubscriptBox["\[CapitalOmega]", "2"]}]}]}]}], "\[IndentingNewLine]",
|
|
RowBox[{"\t\t\t\t\t ",
|
|
RowBox[{"=",
|
|
RowBox[{
|
|
RowBox[{
|
|
SqrtBox[
|
|
RowBox[{"4", "\[Pi]"}]],
|
|
SubscriptBox["c", "0"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}], "+",
|
|
RowBox[{"2", " ",
|
|
SqrtBox[
|
|
RowBox[{"5", " ", "\[Pi]"}]], " ",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}], ")"}]}], "+",
|
|
" ",
|
|
RowBox[{"4", "\[Pi]", " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox["1",
|
|
SqrtBox[
|
|
RowBox[{"4", " ", "\[Pi]"}]]],
|
|
SubscriptBox["c", "0"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "7"], " ",
|
|
SqrtBox[
|
|
FractionBox["5", "\[Pi]"]], " ",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"3", " "}],
|
|
RowBox[{"7", " ",
|
|
SqrtBox["\[Pi]"]}]],
|
|
FractionBox[
|
|
SubscriptBox["c", "4"], "9"]}]}], ")"}],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}],
|
|
"2"]}]}]}]}], "\[IndentingNewLine]",
|
|
RowBox[{"\t\t\t\t\t ",
|
|
RowBox[{"=",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", " ",
|
|
SqrtBox["\[Pi]"], " ",
|
|
SubscriptBox["c", "0"]}], "+",
|
|
RowBox[{
|
|
FractionBox["18", "7"], " ",
|
|
SqrtBox[
|
|
FractionBox["\[Pi]", "5"]], " ",
|
|
SubscriptBox["c", "2"]}], "+",
|
|
FractionBox[
|
|
RowBox[{"4", " ",
|
|
SqrtBox["\[Pi]"], " ",
|
|
SubscriptBox["c", "4"]}], "21"]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}], "-",
|
|
RowBox[{"2", " ",
|
|
SqrtBox[
|
|
FractionBox["\[Pi]", "5"]], " ",
|
|
SubscriptBox["c", "2"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}], "+",
|
|
RowBox[{"2", " ",
|
|
SqrtBox["\[Pi]"], " ",
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
SubscriptBox["\[CapitalOmega]", "1"], "]"}], "2"]}]}]}]}]}], "Input",
|
|
CellChangeTimes->{{3.742898559305214*^9, 3.7428985732593737`*^9}, {
|
|
3.7428986183390417`*^9, 3.742898668556341*^9}, {3.742898891156012*^9,
|
|
3.7428989301880617`*^9}, {3.7428993174640627`*^9, 3.742899416229143*^9}, {
|
|
3.7428994864779387`*^9, 3.742899491064481*^9}, 3.7429886359329147`*^9,
|
|
3.7429900484723463`*^9, {3.742990166278675*^9, 3.742990237918317*^9}, {
|
|
3.7429902717689734`*^9, 3.742990293829607*^9}, {3.74299036171*^9,
|
|
3.742990367572699*^9}},ExpressionUUID->"d3a6ec1b-6a01-430d-947f-\
|
|
8f0e2ffa4abc"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{"Simplify", "[",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], "2"]}], ")"}], "2"], "\[Equal]",
|
|
" ",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"16", "\[Pi]"}], "45"],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "-",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], ")"}], "2"]}]}],
|
|
"]"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "\[Equal]",
|
|
RowBox[{
|
|
FractionBox[
|
|
SqrtBox["5"], "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}]}], "//",
|
|
"Simplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"4", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "\[Equal]",
|
|
RowBox[{
|
|
FractionBox["1",
|
|
SqrtBox[
|
|
RowBox[{"4", "\[Pi]"}]]],
|
|
RowBox[{"(",
|
|
FractionBox[
|
|
RowBox[{"3", " "}],
|
|
RowBox[{"16", " ",
|
|
SqrtBox["\[Pi]"]}]], ")"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"12", "\[Pi]", " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "-",
|
|
RowBox[{"30", " ",
|
|
FractionBox[
|
|
RowBox[{"4", "\[Pi]"}], "3"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox["35", "9"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"16", " ", "\[Pi]"}], "5"],
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{"8",
|
|
SqrtBox[
|
|
FractionBox["\[Pi]", "5"]],
|
|
SqrtBox[
|
|
RowBox[{"4", "\[Pi]"}]],
|
|
FractionBox[
|
|
SqrtBox["5"], "2"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], ")"}]}], "+",
|
|
RowBox[{"4", "\[Pi]", " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], ")"}]}]}],
|
|
")"}]}]}], "//", "Simplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox["1",
|
|
SqrtBox[
|
|
RowBox[{"4", "\[Pi]"}]]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["1",
|
|
SqrtBox[
|
|
RowBox[{"5", " ", "\[Pi]"}]]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}]}]}], "//",
|
|
"Simplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox["1",
|
|
SqrtBox[
|
|
RowBox[{"4", " ", "\[Pi]"}]]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "7"], " ",
|
|
SqrtBox[
|
|
FractionBox["5", "\[Pi]"]], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"3", " "}],
|
|
RowBox[{"7", " ",
|
|
SqrtBox["\[Pi]"]}]],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"4", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}]}]}], "//",
|
|
"Simplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "1"], "]"}], "2"], "-",
|
|
SuperscriptBox[
|
|
RowBox[{"Cos", "[",
|
|
SubscriptBox["\[Theta]", "2"], "]"}], "2"]}], ")"}], "2"], "\[Equal]",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ", "\[Pi]"}], "45"],
|
|
RowBox[{"(", " ",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
SqrtBox["5"], "7"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}], ")"}]}], "-", " ",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["3", "7"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"4", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}], "+", " ",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"4", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "2"], ",",
|
|
SubscriptBox["\[Phi]", "2"]}], "]"}]}]}], ")"}]}]}], ")"}]}]}], "//",
|
|
"Simplify"}]}], "Input",
|
|
CellChangeTimes->{{3.742880368692409*^9, 3.7428804029481373`*^9}, {
|
|
3.742880525109131*^9, 3.7428805458700542`*^9}, {3.742898467130229*^9,
|
|
3.7428985242579517`*^9}, {3.7428992114127827`*^9, 3.742899287783554*^9}, {
|
|
3.7429000811947393`*^9, 3.742900096336309*^9}, {3.7429001529365797`*^9,
|
|
3.742900153845666*^9}, {3.7429004278822927`*^9, 3.742900428277691*^9}, {
|
|
3.74298603971874*^9, 3.7429860419785643`*^9}, 3.742986079185611*^9,
|
|
3.7429861263095503`*^9, {3.7429861707391243`*^9, 3.742986176886547*^9}, {
|
|
3.742988127917576*^9, 3.7429881333292313`*^9}, {3.7429884518630743`*^9,
|
|
3.742988466927435*^9}, {3.742988614273793*^9, 3.742988621922674*^9}, {
|
|
3.742988949793998*^9, 3.7429889765908937`*^9}, {3.742989035521098*^9,
|
|
3.742989036038781*^9}, {3.742989066504467*^9, 3.742989077787426*^9}, {
|
|
3.742989120733507*^9, 3.742989125869351*^9}, {3.742989158533863*^9,
|
|
3.742989165084914*^9}, {3.7429892546397333`*^9, 3.742989256945628*^9}, {
|
|
3.74298965374714*^9, 3.742989684099773*^9}, 3.742989723248888*^9,
|
|
3.742989769652746*^9, 3.742990034250306*^9, {3.742990088379957*^9,
|
|
3.742990101236594*^9}, {3.74299030724561*^9, 3.742990327161159*^9}, {
|
|
3.7429907017821703`*^9, 3.74299072239389*^9}, {3.7429908205311613`*^9,
|
|
3.7429908668042183`*^9}, {3.742990911350947*^9, 3.7429909369698267`*^9}, {
|
|
3.742990986407577*^9, 3.742991149240193*^9}, {3.742991181429986*^9,
|
|
3.7429911879128942`*^9}, {3.742991228402446*^9, 3.742991283398488*^9}, {
|
|
3.7429913939451714`*^9, 3.742991452973744*^9}, {3.743012976931136*^9,
|
|
3.743012981788251*^9}, {3.743014002358323*^9, 3.743014005210388*^9}, {
|
|
3.743014104919067*^9, 3.743014159696444*^9}, {3.74301459429853*^9,
|
|
3.743014634843196*^9}, {3.743015160912546*^9, 3.743015175544134*^9}, {
|
|
3.7430158664921703`*^9, 3.7430158941204767`*^9}, {3.743242363536222*^9,
|
|
3.743242389796681*^9}},ExpressionUUID->"9bfbd342-26ab-4960-b0c1-\
|
|
6d30bc401946"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{
|
|
3.742990035044002*^9, {3.742990089298437*^9, 3.742990101821583*^9}, {
|
|
3.74299031120933*^9, 3.742990327878141*^9}, {3.74299070268925*^9,
|
|
3.7429907228016376`*^9}, {3.74299084137978*^9, 3.742990867547271*^9}, {
|
|
3.742990919780897*^9, 3.742990937796235*^9}, {3.742990999884145*^9,
|
|
3.742991032479315*^9}, {3.742991086930072*^9, 3.742991150291108*^9},
|
|
3.742991188683301*^9, {3.7429912342502527`*^9, 3.742991284798403*^9}, {
|
|
3.742991402090814*^9, 3.742991453961009*^9}, 3.743012984577449*^9, {
|
|
3.743014110712698*^9, 3.743014160015524*^9}, {3.7430146058709993`*^9,
|
|
3.7430146353393784`*^9}, {3.743015162920779*^9, 3.743015175881279*^9}, {
|
|
3.743015887754745*^9, 3.743015894566107*^9},
|
|
3.743242390346169*^9},ExpressionUUID->"bad42b6b-febc-423c-b781-\
|
|
8e8f634645b2"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{
|
|
3.742990035044002*^9, {3.742990089298437*^9, 3.742990101821583*^9}, {
|
|
3.74299031120933*^9, 3.742990327878141*^9}, {3.74299070268925*^9,
|
|
3.7429907228016376`*^9}, {3.74299084137978*^9, 3.742990867547271*^9}, {
|
|
3.742990919780897*^9, 3.742990937796235*^9}, {3.742990999884145*^9,
|
|
3.742991032479315*^9}, {3.742991086930072*^9, 3.742991150291108*^9},
|
|
3.742991188683301*^9, {3.7429912342502527`*^9, 3.742991284798403*^9}, {
|
|
3.742991402090814*^9, 3.742991453961009*^9}, 3.743012984577449*^9, {
|
|
3.743014110712698*^9, 3.743014160015524*^9}, {3.7430146058709993`*^9,
|
|
3.7430146353393784`*^9}, {3.743015162920779*^9, 3.743015175881279*^9}, {
|
|
3.743015887754745*^9, 3.743015894566107*^9},
|
|
3.743242390358519*^9},ExpressionUUID->"08268186-e6a0-4d08-92db-\
|
|
7368a97e5b15"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{
|
|
3.742990035044002*^9, {3.742990089298437*^9, 3.742990101821583*^9}, {
|
|
3.74299031120933*^9, 3.742990327878141*^9}, {3.74299070268925*^9,
|
|
3.7429907228016376`*^9}, {3.74299084137978*^9, 3.742990867547271*^9}, {
|
|
3.742990919780897*^9, 3.742990937796235*^9}, {3.742990999884145*^9,
|
|
3.742991032479315*^9}, {3.742991086930072*^9, 3.742991150291108*^9},
|
|
3.742991188683301*^9, {3.7429912342502527`*^9, 3.742991284798403*^9}, {
|
|
3.742991402090814*^9, 3.742991453961009*^9}, 3.743012984577449*^9, {
|
|
3.743014110712698*^9, 3.743014160015524*^9}, {3.7430146058709993`*^9,
|
|
3.7430146353393784`*^9}, {3.743015162920779*^9, 3.743015175881279*^9}, {
|
|
3.743015887754745*^9, 3.743015894566107*^9},
|
|
3.7432423903674*^9},ExpressionUUID->"14e5cd70-74bd-402b-9647-758b00e98438"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{
|
|
3.742990035044002*^9, {3.742990089298437*^9, 3.742990101821583*^9}, {
|
|
3.74299031120933*^9, 3.742990327878141*^9}, {3.74299070268925*^9,
|
|
3.7429907228016376`*^9}, {3.74299084137978*^9, 3.742990867547271*^9}, {
|
|
3.742990919780897*^9, 3.742990937796235*^9}, {3.742990999884145*^9,
|
|
3.742991032479315*^9}, {3.742991086930072*^9, 3.742991150291108*^9},
|
|
3.742991188683301*^9, {3.7429912342502527`*^9, 3.742991284798403*^9}, {
|
|
3.742991402090814*^9, 3.742991453961009*^9}, 3.743012984577449*^9, {
|
|
3.743014110712698*^9, 3.743014160015524*^9}, {3.7430146058709993`*^9,
|
|
3.7430146353393784`*^9}, {3.743015162920779*^9, 3.743015175881279*^9}, {
|
|
3.743015887754745*^9, 3.743015894566107*^9},
|
|
3.7432423903763742`*^9},ExpressionUUID->"a1021d01-c1ea-43ff-815d-\
|
|
85bf1860cda5"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{
|
|
3.742990035044002*^9, {3.742990089298437*^9, 3.742990101821583*^9}, {
|
|
3.74299031120933*^9, 3.742990327878141*^9}, {3.74299070268925*^9,
|
|
3.7429907228016376`*^9}, {3.74299084137978*^9, 3.742990867547271*^9}, {
|
|
3.742990919780897*^9, 3.742990937796235*^9}, {3.742990999884145*^9,
|
|
3.742991032479315*^9}, {3.742991086930072*^9, 3.742991150291108*^9},
|
|
3.742991188683301*^9, {3.7429912342502527`*^9, 3.742991284798403*^9}, {
|
|
3.742991402090814*^9, 3.742991453961009*^9}, 3.743012984577449*^9, {
|
|
3.743014110712698*^9, 3.743014160015524*^9}, {3.7430146058709993`*^9,
|
|
3.7430146353393784`*^9}, {3.743015162920779*^9, 3.743015175881279*^9}, {
|
|
3.743015887754745*^9, 3.743015894566107*^9},
|
|
3.743242390470005*^9},ExpressionUUID->"a6228c72-c3ab-4a4b-a7dd-\
|
|
114c74203722"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{
|
|
3.742990035044002*^9, {3.742990089298437*^9, 3.742990101821583*^9}, {
|
|
3.74299031120933*^9, 3.742990327878141*^9}, {3.74299070268925*^9,
|
|
3.7429907228016376`*^9}, {3.74299084137978*^9, 3.742990867547271*^9}, {
|
|
3.742990919780897*^9, 3.742990937796235*^9}, {3.742990999884145*^9,
|
|
3.742991032479315*^9}, {3.742991086930072*^9, 3.742991150291108*^9},
|
|
3.742991188683301*^9, {3.7429912342502527`*^9, 3.742991284798403*^9}, {
|
|
3.742991402090814*^9, 3.742991453961009*^9}, 3.743012984577449*^9, {
|
|
3.743014110712698*^9, 3.743014160015524*^9}, {3.7430146058709993`*^9,
|
|
3.7430146353393784`*^9}, {3.743015162920779*^9, 3.743015175881279*^9}, {
|
|
3.743015887754745*^9, 3.743015894566107*^9},
|
|
3.743242390489365*^9},ExpressionUUID->"449b7df1-0d75-4d67-925c-\
|
|
350cdef9600b"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"32", " ", "\[Pi]"}], "45"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox[
|
|
SqrtBox["5"], "7"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"]}], ")"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}], "-",
|
|
RowBox[{
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "5"], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox["3", "7"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "4"], "9"]}], " ", ")"}],
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], " ",
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"4", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}]}]}], ")"}]}], "==",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"16", " ", "\[Pi]"}], "45"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
FractionBox[
|
|
SubscriptBox["c", "2"], "7"], "-",
|
|
FractionBox[
|
|
RowBox[{"2", " ",
|
|
SubscriptBox["c", "4"]}], "63"]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"0", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "7"],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "2"], "-",
|
|
FractionBox[
|
|
RowBox[{"5", " ",
|
|
SubscriptBox["c", "4"]}], "9"]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"1", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
SubscriptBox["c", "0"], "-",
|
|
FractionBox[
|
|
RowBox[{"2", " ",
|
|
SubscriptBox["c", "2"]}], "5"], "+",
|
|
FractionBox[
|
|
SubscriptBox["c", "4"], "9"]}], ")"}], " ",
|
|
SuperscriptBox[
|
|
RowBox[{
|
|
SubscriptBox["Y",
|
|
RowBox[{"2", ",", "0"}]], "[",
|
|
RowBox[{
|
|
SubscriptBox["\[Theta]", "1"], ",",
|
|
SubscriptBox["\[Phi]", "1"]}], "]"}], "2"]}]}], ")"}]}]}], "//",
|
|
"Simplify"}]], "Input",
|
|
CellChangeTimes->{{3.743242411599864*^9, 3.743242542176011*^9}, {
|
|
3.7432426464259987`*^9,
|
|
3.743242663769794*^9}},ExpressionUUID->"f27d4a85-2a37-4803-a443-\
|
|
435791839d08"],
|
|
|
|
Cell[BoxData["True"], "Output",
|
|
CellChangeTimes->{
|
|
3.7432425122523003`*^9, 3.743242543096746*^9, {3.7432426562822657`*^9,
|
|
3.7432426685230703`*^9}},ExpressionUUID->"2dc3a301-69c8-4267-acd1-\
|
|
185a7e3220d5"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "n_"], "[", "u_", "]"}], "=",
|
|
SuperscriptBox["u",
|
|
RowBox[{"n", "-", "1"}]]}], ";"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "10"}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"H", "[", "R_", "]"}], "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0",
|
|
RowBox[{"2", "R"}]],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "i"], "[", "u", "]"}],
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox[
|
|
SuperscriptBox["u", "2"],
|
|
RowBox[{"4",
|
|
SuperscriptBox["R", "2"]}]], "-", "1"}], ")"}],
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Psi]", "j", "\[DoublePrime]"], "[", "u",
|
|
"]"}]}], "+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{"7", "u"}],
|
|
RowBox[{"4",
|
|
SuperscriptBox["R", "2"]}]], "-",
|
|
FractionBox["3", "u"]}], ")"}], " ",
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Psi]", "j", "\[Prime]"], "[", "u", "]"}]}],
|
|
"+",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox["1", "u"], "+",
|
|
FractionBox["3",
|
|
SuperscriptBox["R", "2"]]}], ")"}],
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "j"], "[", "u", "]"}]}]}], ")"}], "u",
|
|
RowBox[{"\[DifferentialD]", "u"}]}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"i", ",", "M"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"j", ",", "M"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"S", "[", "R_", "]"}], "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubsuperscriptBox["\[Integral]", "0",
|
|
RowBox[{"2", "R"}]],
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "i"], "[", "u", "]"}],
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "j"], "[", "u", "]"}], "u",
|
|
RowBox[{"\[DifferentialD]", "u"}]}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"i", ",", "M"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"j", ",", "M"}], "}"}]}], "]"}]}], ";"}]}],
|
|
"\[IndentingNewLine]", "]"}], ";"}]}], "Input",
|
|
CellChangeTimes->{{3.742918604620111*^9, 3.7429186131351423`*^9},
|
|
3.742918719955948*^9, {3.74291885295679*^9, 3.742918854648775*^9},
|
|
3.742922362967875*^9, 3.742980439148241*^9, 3.742980540306929*^9, {
|
|
3.742994989188118*^9, 3.742995016518692*^9}, {3.742995150772037*^9,
|
|
3.7429951513978567`*^9}, 3.7429952985264072`*^9, {3.74299538074587*^9,
|
|
3.7429953808123302`*^9}, {3.742996132486848*^9, 3.7429961349036427`*^9},
|
|
3.7429963078815823`*^9, {3.742996660743409*^9, 3.742996660843338*^9}, {
|
|
3.742996945034573*^9, 3.742996945161457*^9}, 3.7430081967857656`*^9,
|
|
3.743009059579871*^9, 3.743009234820531*^9, 3.743009382026333*^9, {
|
|
3.7430094920285807`*^9, 3.74300951455619*^9}, 3.74300961041049*^9,
|
|
3.743009666438663*^9, {3.7430098539824047`*^9, 3.743009854170718*^9},
|
|
3.743009922023739*^9, 3.743011705512869*^9, {3.743012282155789*^9,
|
|
3.74301230752779*^9}, 3.819448341004202*^9, 3.8194484732834682`*^9},
|
|
CellLabel->"In[38]:=",ExpressionUUID->"17d3180a-586b-41af-a83f-6e20a124c592"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{"With", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"M", "=", "10"}], "}"}], ",", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"tab", "=",
|
|
RowBox[{"Table", "[", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"\[Epsilon]", ",", "c"}], "}"}], "=",
|
|
RowBox[{"SortEigensystem", "[",
|
|
RowBox[{"Eigensystem", "[",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"N", "[",
|
|
RowBox[{
|
|
RowBox[{"H", "[", "R", "]"}], ",", "100"}], "]"}], ",",
|
|
RowBox[{"N", "[",
|
|
RowBox[{
|
|
RowBox[{"S", "[", "R", "]"}], ",", "100"}], "]"}]}], "}"}],
|
|
"]"}], "]"}]}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"f", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["\[Psi]", "n"], "[",
|
|
RowBox[{"2", " ", "R", " ",
|
|
RowBox[{"Sin", "[",
|
|
RowBox[{"\[Theta]", "/", "2"}], "]"}]}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"n", ",", "M"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"\[Rho]", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"\[ScriptL]", "+",
|
|
FractionBox["1", "2"]}], ")"}],
|
|
RowBox[{"NIntegrate", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
SubscriptBox["P", "\[ScriptL]"], "[",
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}], "]"}],
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
"c", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
|
|
".", "f"}], ")"}], "2"],
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}], ",",
|
|
RowBox[{"WorkingPrecision", "\[Rule]", "15"}]}], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"\[ScriptL]", ",", "0", ",", "4"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"\[Rho]", "=",
|
|
RowBox[{"Normalize", "[", "\[Rho]", "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"Chop", "[",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"N", "[", "R", "]"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "3", "\[RightDoubleBracket]"}],
|
|
"-",
|
|
RowBox[{
|
|
FractionBox["5", "9"], " ",
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "5",
|
|
"\[RightDoubleBracket]"}]}]}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
|
|
"-",
|
|
RowBox[{
|
|
FractionBox["2", "5"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "3",
|
|
"\[RightDoubleBracket]"}]}], "+",
|
|
RowBox[{
|
|
FractionBox["1", "9"],
|
|
RowBox[{
|
|
"\[Rho]", "\[LeftDoubleBracket]", "1",
|
|
"\[RightDoubleBracket]"}]}]}]}], "}"}], "]"}]}],
|
|
"\[IndentingNewLine]", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"R", ",",
|
|
RowBox[{"-", "20"}], ",", "20"}], "}"}]}], "]"}]}], ";"}]}],
|
|
"\[IndentingNewLine]", "]"}], "\[IndentingNewLine]",
|
|
RowBox[{"ListPlot", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"tab", "\[LeftDoubleBracket]",
|
|
RowBox[{";;", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"1", ",", "2"}], "}"}]}], "\[RightDoubleBracket]"}], ",",
|
|
RowBox[{"tab", "\[LeftDoubleBracket]",
|
|
RowBox[{";;", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"1", ",", "3"}], "}"}]}], "\[RightDoubleBracket]"}]}], "}"}],
|
|
",",
|
|
RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}]}], "Input",
|
|
CellChangeTimes->{
|
|
3.7169719668102694`*^9, 3.725887849338797*^9, {3.725887899762218*^9,
|
|
3.725887922914515*^9}, {3.725887992098515*^9, 3.725888054354484*^9}, {
|
|
3.725888190363358*^9, 3.725888220466589*^9}, {3.725888405954722*^9,
|
|
3.7258884143609447`*^9}, {3.725888474666101*^9, 3.725888479977105*^9}, {
|
|
3.725888867994993*^9, 3.725888870697344*^9}, {3.7258889297858877`*^9,
|
|
3.725888934808717*^9}, {3.725888967938243*^9, 3.725889013634396*^9}, {
|
|
3.725889098059265*^9, 3.725889127921206*^9}, {3.725948058954719*^9,
|
|
3.7259480590574303`*^9}, 3.72594816605788*^9, {3.7259484228037577`*^9,
|
|
3.7259484452333307`*^9}, {3.7428020644337606`*^9,
|
|
3.7428020663834143`*^9}, {3.74280212730392*^9, 3.74280222326132*^9},
|
|
3.742813402384555*^9, {3.7428134755684967`*^9, 3.742813490200959*^9},
|
|
3.742814183560895*^9, {3.742819919975389*^9, 3.742819921001403*^9}, {
|
|
3.7428199815500298`*^9, 3.742819983199623*^9}, {3.742877775652999*^9,
|
|
3.7428779074014883`*^9}, {3.7428779855771227`*^9, 3.742878008161315*^9}, {
|
|
3.7428782383972187`*^9, 3.742878269832116*^9}, {3.742878722461308*^9,
|
|
3.7428787571128817`*^9}, {3.742878822183488*^9, 3.742878822578849*^9}, {
|
|
3.7428788828839493`*^9, 3.7428788901191797`*^9}, {3.74287901611771*^9,
|
|
3.742879142617798*^9}, {3.742879199059029*^9, 3.7428791995390997`*^9},
|
|
3.742901214891993*^9, {3.74290164400101*^9, 3.742901906207686*^9}, {
|
|
3.742901977623595*^9, 3.742902002095676*^9}, {3.742902032247851*^9,
|
|
3.742902129781516*^9}, {3.742902162525971*^9, 3.74290222166597*^9}, {
|
|
3.742902276796481*^9, 3.742902287956953*^9}, {3.74290235927039*^9,
|
|
3.7429024146277122`*^9}, {3.7429024507177353`*^9,
|
|
3.7429025388586197`*^9}, {3.742903006310214*^9, 3.7429030105077744`*^9}, {
|
|
3.742903134891645*^9, 3.742903234602419*^9}, {3.742903317285879*^9,
|
|
3.7429033173754187`*^9}, {3.742903361602311*^9, 3.74290336281636*^9}, {
|
|
3.742905076823636*^9, 3.7429050778905582`*^9}, {3.742918166486006*^9,
|
|
3.742918220012596*^9}, {3.742918311916502*^9, 3.742918313196629*^9}, {
|
|
3.7429183606868353`*^9, 3.742918373040654*^9}, 3.742918421383092*^9, {
|
|
3.742918494233326*^9, 3.742918623848249*^9}, {3.74291880637696*^9,
|
|
3.7429188584054213`*^9}, {3.742918994743949*^9, 3.742919000933652*^9}, {
|
|
3.742919057477284*^9, 3.7429190853953876`*^9}, {3.742919151618346*^9,
|
|
3.742919208160902*^9}, {3.742920743629745*^9, 3.742920743849949*^9},
|
|
3.742922144965681*^9, {3.742922177083435*^9, 3.742922183503256*^9},
|
|
3.742922225061594*^9, 3.742922262893311*^9, {3.742922314745081*^9,
|
|
3.7429223742620287`*^9}, {3.74292246647335*^9, 3.742922597303072*^9}, {
|
|
3.742922649922433*^9, 3.7429226518828707`*^9}, {3.742923296115052*^9,
|
|
3.742923318322493*^9}, {3.742980141599243*^9, 3.74298028080587*^9}, {
|
|
3.742980310806139*^9, 3.7429803255358543`*^9}, {3.742980357754479*^9,
|
|
3.742980398957408*^9}, {3.7429804420837727`*^9, 3.7429804467641287`*^9}, {
|
|
3.742980541432966*^9, 3.742980548122097*^9}, {3.742980578285955*^9,
|
|
3.742980578400919*^9}, {3.7429806326930037`*^9, 3.742980650442853*^9}, {
|
|
3.742980694195736*^9, 3.742980749099784*^9}, {3.742981142831009*^9,
|
|
3.742981146671338*^9}, {3.742995040906142*^9, 3.7429950736953487`*^9}, {
|
|
3.742995103988391*^9, 3.742995134262944*^9}, {3.742995247787807*^9,
|
|
3.742995324266892*^9}, {3.742995360656518*^9, 3.742995384384591*^9}, {
|
|
3.7429954237133417`*^9, 3.742995433990855*^9}, {3.74299547198099*^9,
|
|
3.742995484920415*^9}, {3.742995760731353*^9, 3.7429957673259373`*^9}, {
|
|
3.742995847653798*^9, 3.7429958543557777`*^9}, {3.7429960931764708`*^9,
|
|
3.742996100192951*^9}, {3.742996300021468*^9, 3.742996312749928*^9}, {
|
|
3.742996623983343*^9, 3.742996683485918*^9}, {3.742996763260223*^9,
|
|
3.7429967667513227`*^9}, {3.742996823435986*^9, 3.742996947881322*^9}, {
|
|
3.7429969858904467`*^9, 3.7429969890918093`*^9}, {3.742997154797719*^9,
|
|
3.742997179630937*^9}, {3.742997221183319*^9, 3.7429972234251423`*^9}, {
|
|
3.742997256190982*^9, 3.742997295285985*^9}, {3.742997325738884*^9,
|
|
3.7429973513749123`*^9}, {3.74299738735357*^9, 3.7429974112679663`*^9}, {
|
|
3.742997461552939*^9, 3.7429974669219646`*^9}, {3.743008210683326*^9,
|
|
3.743008225538146*^9}, 3.743009057265111*^9, {3.743009239073036*^9,
|
|
3.7430092656499767`*^9}, {3.743009361125576*^9, 3.743009373039097*^9}, {
|
|
3.7430094955856752`*^9, 3.7430095437002373`*^9}, {3.7430096137618933`*^9,
|
|
3.743009669733102*^9}, {3.743009863885*^9, 3.7430099872406483`*^9}, {
|
|
3.743010046219955*^9, 3.743010048241816*^9}, {3.7430103170795507`*^9,
|
|
3.743010344854659*^9}, {3.743011088494897*^9, 3.7430111264389553`*^9}, {
|
|
3.7430111611489353`*^9, 3.743011161959427*^9}, {3.743011716328226*^9,
|
|
3.7430117899482517`*^9}, {3.743011834479101*^9, 3.743011843089284*^9}, {
|
|
3.743012369035474*^9, 3.7430124950847063`*^9}, {3.7430153810128*^9,
|
|
3.7430155810205812`*^9}, {3.7430156217096233`*^9,
|
|
3.7430156592999067`*^9}, {3.743016498555264*^9, 3.743016521049993*^9}, {
|
|
3.743016567918239*^9, 3.743016589484662*^9}, {3.743017337660697*^9,
|
|
3.7430173705891113`*^9}, {3.743017472981872*^9, 3.7430174949264183`*^9}, {
|
|
3.743049426352824*^9, 3.743049462340137*^9}, {3.743049515767*^9,
|
|
3.743049532564899*^9}, {3.7430495813737097`*^9, 3.743049625292449*^9}, {
|
|
3.743049662050229*^9, 3.743049691793056*^9}, 3.743049918773452*^9, {
|
|
3.743050058713081*^9, 3.743050090033937*^9}, {3.743050142594883*^9,
|
|
3.74305016311656*^9}, {3.7430502085142813`*^9, 3.7430502178348913`*^9},
|
|
3.74305026397199*^9, {3.743050578043778*^9, 3.743050605922763*^9}, {
|
|
3.819448286225428*^9, 3.81944833030002*^9}, 3.8194493548537903`*^9, {
|
|
3.819461124517785*^9, 3.819461125384673*^9}, 3.819461243348475*^9},
|
|
CellLabel->"In[42]:=",ExpressionUUID->"e8a12bd0-24b7-41d6-8141-13207367f442"],
|
|
|
|
Cell[BoxData[
|
|
GraphicsBox[{{}, {{{}, {},
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[
|
|
0.011000000000000001`], AbsoluteThickness[1.6], LineBox[CompressedData["
|
|
|
|
1:eJxTTMoPSmViYGDQBGIQDQEmB156ihVovVxmD+EbHyhne33ujNtKKN/oQL3v
|
|
4l5GtjVQvuEBwzyT1VI266F8gwPefdy+LE0boXy9A79mHD/HcmAzlK9zwGZe
|
|
5tXHudugfK0DFvdcVmYu3wnlaxyw2eHV1d2/F8pXOzC5RP57k8ZBKF/lQHiG
|
|
eFUy3xEoX+lAwU7HN14Tj0P5CgdOv2Zsytx3GsqXOVDLLqb8x+EClC9xYLL+
|
|
zVe79l+C8kUOfL+tfiD27RUoX+BARfCurHKGa1A+x4H3/nfP5x+ByTMcOFnW
|
|
v+XJ1vNQ/of9N781M9y13QeTRwMf7Df8WsbtprpmP1TA4eBygVUfuNdC+RwO
|
|
hu27X9RWzoPyBRzqf11p7rZtgbnPoT6M6dCZptUw9zt0zt1+0/fXDpj/HPR4
|
|
Lj6VuQ4LHwWHyIzZDWsvHoOFjwNX09Wbqsmw8FBxuP010GNJN8z9ag4+d12W
|
|
8a24CAt/h7k3b6XfiL4Mix8HXo6GIrmnMP/rOPxvWXHsnDssfPQcbq6SerC0
|
|
/Tos/h0aNPu7JVbcgKUPh+/Oe/R81tyEpR8HruDJV8Sm34KlL4fmhw9NmbNv
|
|
Q/kmDo84nGaHad2xBwCXwsCN
|
|
"]]},
|
|
{RGBColor[0.880722, 0.611041, 0.142051], PointSize[
|
|
0.011000000000000001`], AbsoluteThickness[1.6], LineBox[CompressedData["
|
|
|
|
1:eJxTTMoPSmViYGAQAWIQDQEmBz79vvD3+6qN+yF84wPzr3H2fl8M4xsdWFnK
|
|
4eo6C8Y3PPAsYO2rXT0wvsEBXrnMglmVML7eAUfjR/cM4mB8nQPhX/1ETc1g
|
|
fK0DywQjdiz/tQHK1ziQbeYTvH8+jK92wPHv1sUfBGB8lQMW1jcuWwatg/KV
|
|
DnCuqpkx03U1lK9wQGXxufP1H5ZC+TIHHOI1vHZOmgHlSxwocZe4dTu9zR7C
|
|
FzmwJmHDa7/8zVC+wIHtxxJu77h0AsrnOPC9Wle/xvkmlM9w4ITSMeeGr0+h
|
|
/A/77Y/xvymye28PAPRxbP0=
|
|
"]], LineBox[CompressedData["
|
|
1:eJxTTMoPSmViYGAQAWIQDQEf7FM2yLbE1Hy0hwo4FH6IOBJh8QHK53CQ2zRP
|
|
VGbWWyhfwOHTVE3btT9eQfkiDh99pq2OXP4CypdwyNnOrcy4+BmUL+MgY554
|
|
o/HhEyhfwaHNkdU4IuIxlK/k8Pa427egfw+hfBWHE/lZepdOP4Dy1RyKy7z+
|
|
W5feh/I1HJba7twR0H0Xytdy4JrSdHbJxdtQvo6DluwJyXLHW1C+noOs5Ct+
|
|
06s3oHwDh41XrnTZdlyH8g0d8les498Ydg3KN3JQmrqwycf2KpRv7HDUrfe5
|
|
t+UVKN/E4SZjT2Cwx2V7ANcnWZY=
|
|
"]]}}, {
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[
|
|
0.011000000000000001`], AbsoluteThickness[1.6]},
|
|
{RGBColor[0.880722, 0.611041, 0.142051], PointSize[
|
|
0.011000000000000001`], AbsoluteThickness[1.6]}}, {
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[
|
|
0.011000000000000001`], AbsoluteThickness[1.6]},
|
|
{RGBColor[0.880722, 0.611041, 0.142051], PointSize[
|
|
0.011000000000000001`], AbsoluteThickness[1.6]}, {}, {}, {}}, {
|
|
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[
|
|
0.011000000000000001`], AbsoluteThickness[1.6]},
|
|
{RGBColor[0.880722, 0.611041, 0.142051], PointSize[
|
|
0.011000000000000001`], AbsoluteThickness[1.6]}, {}, {}, {}}}, {{}, {}}},
|
|
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, Automatic}, {Automatic, Automatic}},
|
|
GridLines->{None, None},
|
|
GridLinesStyle->Directive[
|
|
GrayLevel[0.5, 0.4]],
|
|
ImageSize->{821.2421875, Automatic},
|
|
Method->{
|
|
"OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> True,
|
|
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
|
|
Identity[
|
|
Part[#, 1]],
|
|
Identity[
|
|
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
|
|
Identity[
|
|
Part[#, 1]],
|
|
Identity[
|
|
Part[#, 2]]}& )}},
|
|
PlotRange->{{-20., 20.}, {-0.06901502558410735, 1.092861667707461}},
|
|
PlotRangeClipping->True,
|
|
PlotRangePadding->{{
|
|
Scaled[0.02],
|
|
Scaled[0.02]}, {
|
|
Scaled[0.05],
|
|
Scaled[0.05]}},
|
|
Ticks->{Automatic, Automatic}]], "Output",
|
|
CellChangeTimes->{{3.7430123811424637`*^9, 3.743012408192389*^9}, {
|
|
3.7430124387563047`*^9, 3.743012508045164*^9}, {3.7430154219485817`*^9,
|
|
3.743015452598775*^9}, {3.743015490869273*^9, 3.743015590126574*^9}, {
|
|
3.743015634807576*^9, 3.743015676803303*^9}, 3.743016540493622*^9, {
|
|
3.743016579584977*^9, 3.74301659848284*^9}, 3.743017504154944*^9, {
|
|
3.743049470930752*^9, 3.7430494941500807`*^9}, {3.743049533404334*^9,
|
|
3.743049546355226*^9}, {3.743049615424395*^9, 3.743049644042947*^9},
|
|
3.743049688622527*^9, 3.743049735290845*^9, {3.743050075077178*^9,
|
|
3.743050118654882*^9}, {3.74305015232526*^9, 3.743050173216238*^9},
|
|
3.743050228261497*^9, 3.743050274432351*^9, {3.7430505492426453`*^9,
|
|
3.7430505625451717`*^9}, {3.7430505977198277`*^9, 3.743050624288727*^9},
|
|
3.819448332544907*^9, 3.819448474023838*^9, 3.8194485230467*^9,
|
|
3.819449404013495*^9, 3.819461183333342*^9, 3.819461295735427*^9},
|
|
CellLabel->"Out[43]=",ExpressionUUID->"6cf12868-5980-4ee9-9f5e-473067fd4e9d"]
|
|
}, Open ]]
|
|
}, Closed]]
|
|
}, Open ]]
|
|
}, Open ]]
|
|
},
|
|
WindowSize->{1425, 1395},
|
|
WindowMargins->{{0, Automatic}, {Automatic, 0}},
|
|
FrontEndVersion->"13.0 for Mac OS X x86 (64-bit) (December 2, 2021)",
|
|
StyleDefinitions->"Default.nb",
|
|
ExpressionUUID->"8b8f66d5-74ef-4f00-a943-e92faec4ee0a"
|
|
]
|
|
(* End of Notebook Content *)
|
|
|
|
(* Internal cache information *)
|
|
(*CellTagsOutline
|
|
CellTagsIndex->{}
|
|
*)
|
|
(*CellTagsIndex
|
|
CellTagsIndex->{}
|
|
*)
|
|
(*NotebookFileOutline
|
|
Notebook[{
|
|
Cell[CellGroupData[{
|
|
Cell[580, 22, 157, 3, 98, "Title",ExpressionUUID->"f14a9b83-4155-4933-b4bd-86482283a3f0"],
|
|
Cell[CellGroupData[{
|
|
Cell[762, 29, 635, 13, 68, "Input",ExpressionUUID->"f63df8ff-a805-43cf-b25e-970437446449",
|
|
InitializationCell->True],
|
|
Cell[CellGroupData[{
|
|
Cell[1422, 46, 183, 3, 24, "Print",ExpressionUUID->"5cb064db-9a96-49d8-b73d-03704506f017"],
|
|
Cell[1608, 51, 256, 5, 24, "Print",ExpressionUUID->"a1b2528f-5340-4604-8b03-168c2a162b5a"],
|
|
Cell[1867, 58, 491, 9, 26, "Print",ExpressionUUID->"cd6f07bd-300c-4ba1-83eb-469c1e63eaf6"]
|
|
}, Open ]]
|
|
}, Open ]],
|
|
Cell[2385, 71, 593, 16, 46, "Input",ExpressionUUID->"06b69520-f042-4fc6-9314-22d2e79542d6",
|
|
InitializationCell->True],
|
|
Cell[2981, 89, 549, 16, 46, "Input",ExpressionUUID->"a8c11cd4-a9a5-4079-8595-5294b1fb94c7",
|
|
InitializationCell->True],
|
|
Cell[3533, 107, 484, 12, 49, "Input",ExpressionUUID->"e29c6d12-164d-461c-b102-761d687a35f0",
|
|
InitializationCell->True],
|
|
Cell[4020, 121, 470, 11, 49, "Input",ExpressionUUID->"74769596-3e6e-4ca2-8edd-d3dad7f9f8d1",
|
|
InitializationCell->True],
|
|
Cell[4493, 134, 439, 10, 49, "Input",ExpressionUUID->"1fff622e-e162-45b8-93d8-03e2f95f6a4a",
|
|
InitializationCell->True],
|
|
Cell[4935, 146, 2202, 63, 69, "Input",ExpressionUUID->"7fc2e2a8-1267-4aa2-acf5-d2d12a58563c",
|
|
InitializationCell->True],
|
|
Cell[7140, 211, 296, 8, 49, "Input",ExpressionUUID->"76897437-158e-48b2-bca0-c92679d71862",
|
|
InitializationCell->True],
|
|
Cell[7439, 221, 246, 6, 49, "Input",ExpressionUUID->"751041e2-0753-48c1-aa6c-9f69333e4db7",
|
|
InitializationCell->True],
|
|
Cell[7688, 229, 879, 25, 49, "Input",ExpressionUUID->"f13406bf-d041-4fbb-823f-f514d04fe27c",
|
|
InitializationCell->True],
|
|
Cell[8570, 256, 315, 7, 46, "Input",ExpressionUUID->"183ae429-a997-4f0d-baef-2a20bbc5c8ff",
|
|
InitializationCell->True],
|
|
Cell[8888, 265, 1716, 51, 78, "Input",ExpressionUUID->"2fd619d6-5e78-47b6-adfc-2c3a75428669",
|
|
InitializationCell->True]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[10641, 321, 226, 4, 98, "Title",ExpressionUUID->"c626dffe-68a4-4be1-b83c-a98638c384be"],
|
|
Cell[CellGroupData[{
|
|
Cell[10892, 329, 161, 3, 67, "Section",ExpressionUUID->"e0a5c645-2143-460d-a4e6-085c89e142f8"],
|
|
Cell[CellGroupData[{
|
|
Cell[11078, 336, 3716, 104, 118, "Input",ExpressionUUID->"18ee6744-3e3b-4677-9588-1803214665ac"],
|
|
Cell[14797, 442, 3605, 105, 98, "Output",ExpressionUUID->"cbca8ed1-5d8f-4e61-8033-cf95096b7059"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[18439, 552, 3842, 109, 125, "Input",ExpressionUUID->"ea189845-c47e-4753-ae12-0c29bb7fe966"],
|
|
Cell[22284, 663, 2907, 81, 119, "Output",ExpressionUUID->"92d6db72-9f08-4355-8160-14f066aceceb"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[25228, 749, 2154, 64, 63, "Input",ExpressionUUID->"c2d3be71-50b2-4d02-bc7c-fa8422bb9511"],
|
|
Cell[27385, 815, 943, 29, 56, "Output",ExpressionUUID->"3a86ae5d-84b5-4de4-bf01-e2f7182357aa"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[28365, 849, 2113, 62, 63, "Input",ExpressionUUID->"6d246081-7c23-4031-b117-f6e9dbc0e0a0"],
|
|
Cell[30481, 913, 981, 24, 65, "Output",ExpressionUUID->"3f1ab4cb-673d-4ce6-aaea-91d682381bce"]
|
|
}, Open ]]
|
|
}, Closed]],
|
|
Cell[CellGroupData[{
|
|
Cell[31511, 943, 192, 3, 53, "Section",ExpressionUUID->"f857da23-6512-4a44-801c-0238416ec25a"],
|
|
Cell[31706, 948, 582, 11, 35, "Text",ExpressionUUID->"2556e3c0-3c07-46c8-a4f0-e0d5f873e557"],
|
|
Cell[32291, 961, 468, 14, 46, "Input",ExpressionUUID->"52f037c3-c011-4459-9ec6-6f496c768a58"],
|
|
Cell[32762, 977, 1494, 39, 67, "Input",ExpressionUUID->"e939f164-90ed-4275-8c20-a3c9b35f02a0"],
|
|
Cell[34259, 1018, 1322, 35, 67, "Input",ExpressionUUID->"abec2db9-74cd-44ab-8e15-ec3c2d9acd58"],
|
|
Cell[35584, 1055, 1045, 31, 67, "Input",ExpressionUUID->"6245dfde-4373-46ac-8f56-97c43c57cefd"]
|
|
}, Closed]],
|
|
Cell[CellGroupData[{
|
|
Cell[36666, 1091, 697, 10, 53, "Section",ExpressionUUID->"d36161d9-7065-4d0c-9aa3-9e184ff60f78"],
|
|
Cell[CellGroupData[{
|
|
Cell[37388, 1105, 509, 8, 54, "Subsection",ExpressionUUID->"caba0f41-e4c2-48bd-b7f9-f49d444689e8"],
|
|
Cell[37900, 1115, 1902, 45, 54, "Input",ExpressionUUID->"19db6ad5-bc03-487e-a573-966ce5a1e931"],
|
|
Cell[CellGroupData[{
|
|
Cell[39827, 1164, 1804, 46, 53, "Input",ExpressionUUID->"6cb4dcc6-ee3c-42a3-83e3-235f526f9182"],
|
|
Cell[41634, 1212, 280, 5, 34, "Output",ExpressionUUID->"7a5608ac-da7f-4146-9663-314f8a925eb7"]
|
|
}, Open ]],
|
|
Cell[41929, 1220, 2101, 56, 49, "Input",ExpressionUUID->"4538602f-e656-4a1f-8b53-fef84aa71ecb"],
|
|
Cell[44033, 1278, 6017, 123, 284, "Input",ExpressionUUID->"1fc2dedb-8f1a-403e-a7e1-c8dbd76bc9e5"]
|
|
}, Closed]],
|
|
Cell[CellGroupData[{
|
|
Cell[50087, 1406, 490, 7, 38, "Subsection",ExpressionUUID->"bdb8d3b4-c988-408c-865f-6a4aaefec0cc"],
|
|
Cell[CellGroupData[{
|
|
Cell[50602, 1417, 9360, 179, 332, "Input",ExpressionUUID->"fd4d7d77-fd44-443b-a877-600297ee2a20"],
|
|
Cell[59965, 1598, 1753, 31, 196, "Print",ExpressionUUID->"eddb80e0-8314-4b81-a073-134184dae11a"],
|
|
Cell[61721, 1631, 711, 14, 37, "Output",ExpressionUUID->"77e73b0a-4204-439b-880c-363ddd8df3f0"],
|
|
Cell[62435, 1647, 1780, 45, 242, "Output",ExpressionUUID->"e954db0b-9de5-4b95-884f-97be0d9ee069"]
|
|
}, Open ]],
|
|
Cell[64230, 1695, 248, 5, 30, "Input",ExpressionUUID->"2a334965-e048-4730-b8d2-934066eee580"],
|
|
Cell[64481, 1702, 370, 12, 48, "Input",ExpressionUUID->"7e0bdb5b-809c-478e-a3d8-bbaf3faf9a2a"],
|
|
Cell[64854, 1716, 670, 19, 45, "Input",ExpressionUUID->"efa3f2c4-c56a-4f0d-a231-57f12b695850"],
|
|
Cell[65527, 1737, 419, 12, 54, "Input",ExpressionUUID->"6d2eae8e-6c4d-48f2-a1b2-4de4ecc2600b"],
|
|
Cell[65949, 1751, 499, 14, 48, "Input",ExpressionUUID->"ae82bc8b-92a9-43b2-ac92-6cd163b82739"],
|
|
Cell[66451, 1767, 1953, 45, 98, "Input",ExpressionUUID->"87275d0e-03a0-4d3c-9d6f-87d7d86f1997"],
|
|
Cell[CellGroupData[{
|
|
Cell[68429, 1816, 3013, 81, 63, "Input",ExpressionUUID->"3a93abe4-2ad3-486e-8c6e-7fdc2391862f"],
|
|
Cell[71445, 1899, 1192, 22, 34, "Output",ExpressionUUID->"3f0af36f-5a14-4009-9228-7f92279f21fd"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[72674, 1926, 8927, 172, 325, "Input",ExpressionUUID->"d1b1610f-85af-4346-ac50-e489107603e8"],
|
|
Cell[81604, 2100, 2691, 64, 56, "Output",ExpressionUUID->"d46330e7-34f6-4fd6-87c7-9d62e37f39f0"],
|
|
Cell[84298, 2166, 2830, 58, 240, "Output",ExpressionUUID->"a1eff725-6cd6-4766-9c48-e4596ad8fcd8"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[87165, 2229, 2391, 67, 205, "Input",ExpressionUUID->"312998b8-f34f-4d8f-ada8-529ce8e4fc92"],
|
|
Cell[89559, 2298, 1880, 62, 77, "Output",ExpressionUUID->"732834ed-bb17-43bb-807d-6b18ef0060a2"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[91476, 2365, 6643, 173, 162, "Input",ExpressionUUID->"2016af84-5098-4a00-a783-f0d93f8c9ba3"],
|
|
Cell[98122, 2540, 1495, 25, 60, "Output",ExpressionUUID->"bd9eb2f7-582b-4a68-9544-172d9b5d206c"],
|
|
Cell[99620, 2567, 815, 13, 34, "Output",ExpressionUUID->"202780ab-b52d-489c-a92e-1b0fd0915e99"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[100472, 2585, 1857, 44, 140, "Input",ExpressionUUID->"30e5f6ef-f847-4642-bbeb-30c280b77e0b"],
|
|
Cell[102332, 2631, 767, 15, 60, "Output",ExpressionUUID->"5e69b9d6-c0fe-4adf-b5a6-d354021c664b"]
|
|
}, Open ]]
|
|
}, Closed]],
|
|
Cell[CellGroupData[{
|
|
Cell[103148, 2652, 212, 4, 38, "Subsection",ExpressionUUID->"c866a966-62d2-4aaa-be30-188e454b7735"],
|
|
Cell[103363, 2658, 1830, 66, 53, "Input",ExpressionUUID->"c4a884e6-15b7-471a-9826-860d9af553cf"],
|
|
Cell[105196, 2726, 4796, 151, 192, "Input",ExpressionUUID->"ee948f7b-d70d-4f37-b367-09ca445c478b"],
|
|
Cell[109995, 2879, 1464, 44, 56, "Input",ExpressionUUID->"141f30e2-0cbb-4f96-a17a-38662c6cc740"],
|
|
Cell[111462, 2925, 1505, 42, 54, "Input",ExpressionUUID->"5f15e614-bd85-47be-b20b-e346fe08a2c7"],
|
|
Cell[112970, 2969, 1820, 52, 56, "Input",ExpressionUUID->"95762630-81b3-4910-890e-f8cbb4b3594c"],
|
|
Cell[114793, 3023, 4914, 151, 104, "Input",ExpressionUUID->"d65bd25c-ca2f-407d-9b79-7092dc14020a"],
|
|
Cell[CellGroupData[{
|
|
Cell[119732, 3178, 3637, 118, 100, "Input",ExpressionUUID->"86c4c204-12d5-4cc4-91f3-4ef38f2f1176"],
|
|
Cell[123372, 3298, 403, 6, 34, "Output",ExpressionUUID->"a2be3453-5dee-4d23-b728-7cbc223eac21"],
|
|
Cell[123778, 3306, 405, 6, 34, "Output",ExpressionUUID->"f9680827-b5a0-43a4-8fce-6d063ed22fc4"]
|
|
}, Open ]],
|
|
Cell[124198, 3315, 2969, 102, 102, "Input",ExpressionUUID->"ffcbeb9c-6e95-4df6-bb5b-328b41b21992"],
|
|
Cell[CellGroupData[{
|
|
Cell[127192, 3421, 2044, 57, 48, "Input",ExpressionUUID->"61ee86cb-074d-4ac7-9f61-c1c6b64052ea"],
|
|
Cell[129239, 3480, 453, 12, 48, "Output",ExpressionUUID->"c480bc7f-ce40-4eee-b55d-3f73c76d3e72"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[129729, 3497, 819, 26, 48, "Input",ExpressionUUID->"b6e55c8f-0333-4b09-aed9-bd0241fab7b8"],
|
|
Cell[130551, 3525, 552, 16, 48, "Output",ExpressionUUID->"dacdb030-75e3-4580-b198-bc005365a6e5"]
|
|
}, Open ]],
|
|
Cell[131118, 3544, 1773, 53, 51, "Input",ExpressionUUID->"db51f6a7-4690-40c2-af32-a6f7eab9b126"],
|
|
Cell[132894, 3599, 468, 15, 48, "Input",ExpressionUUID->"67e833cb-794e-46bf-aaaa-f7fedec74084"],
|
|
Cell[CellGroupData[{
|
|
Cell[133387, 3618, 385, 12, 48, "Input",ExpressionUUID->"3ade0751-2e40-483d-aa9f-7c6decd096ba"],
|
|
Cell[133775, 3632, 303, 9, 34, "Output",ExpressionUUID->"e43011ca-1485-4c14-8ef5-e3e5c2853e54"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[134115, 3646, 607, 20, 48, "Input",ExpressionUUID->"1f77c8a4-02f2-4a43-9353-2c6dc0e607c1"],
|
|
Cell[134725, 3668, 305, 9, 34, "Output",ExpressionUUID->"8b84c089-d48f-4520-a0df-2c902ca82399"]
|
|
}, Open ]],
|
|
Cell[135045, 3680, 3775, 112, 185, "Input",ExpressionUUID->"fc6fe6fa-c5e9-41cb-966e-1e14dcc26ff6"],
|
|
Cell[138823, 3794, 7265, 190, 388, "Input",ExpressionUUID->"a06ef68f-50cc-4e7f-bfb8-5863cadce9e2"],
|
|
Cell[CellGroupData[{
|
|
Cell[146113, 3988, 3422, 84, 250, "Input",ExpressionUUID->"6619aa61-41df-4561-afa2-5b697e931325"],
|
|
Cell[149538, 4074, 169524, 2909, 308, "Output",ExpressionUUID->"826737d4-2b6e-4de9-b31d-fe96204e193e"]
|
|
}, Open ]],
|
|
Cell[319077, 6986, 255, 6, 30, "Input",ExpressionUUID->"b5b12c32-af87-4895-806f-bf157bb129aa"],
|
|
Cell[CellGroupData[{
|
|
Cell[319357, 6996, 850, 28, 46, "Input",ExpressionUUID->"cc05efbd-961f-46db-b61a-58c996905985"],
|
|
Cell[320210, 7026, 685, 22, 60, "Output",ExpressionUUID->"8fa408ca-cd50-43f5-b8e3-e8f3a0b3e9c1"]
|
|
}, Open ]],
|
|
Cell[320910, 7051, 448, 13, 30, "Input",ExpressionUUID->"98d3c666-fed4-4e94-8773-702f80e147f2"],
|
|
Cell[321361, 7066, 383, 11, 49, "Input",ExpressionUUID->"7760399b-0d77-4553-9ef6-998865cceadc"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[321781, 7082, 179, 3, 54, "Subsection",ExpressionUUID->"77b56f7c-700c-4596-b77a-642cfae1f22b"],
|
|
Cell[321963, 7087, 5580, 148, 245, "Input",ExpressionUUID->"0096765c-1955-4233-8b61-c68add30afd7"],
|
|
Cell[CellGroupData[{
|
|
Cell[327568, 7239, 3535, 89, 209, "Input",ExpressionUUID->"b5718ede-6400-4124-b4a6-2186a8843623"],
|
|
Cell[331106, 7330, 2508, 57, 251, "Output",ExpressionUUID->"86990887-6b9b-4c25-928a-8a2d9a47fc30"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[333651, 7392, 3733, 92, 256, "Input",ExpressionUUID->"e6212f5c-f61a-44bd-9741-ee94d91faa85"],
|
|
Cell[337387, 7486, 459, 9, 34, "Output",ExpressionUUID->"9dd3881f-824b-4e31-8bf6-7abeadcfec2e"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[337883, 7500, 4812, 107, 255, "Input",ExpressionUUID->"b2ce964b-b1a4-4e17-b745-0e349e4a0a11"],
|
|
Cell[342698, 7609, 304, 5, 34, "Output",ExpressionUUID->"b0ff418f-98de-4bad-842e-e06fcdb95ae7"]
|
|
}, Open ]],
|
|
Cell[343017, 7617, 149, 3, 52, "Input",ExpressionUUID->"d55ebddf-dd3a-4100-b7d6-bf59fb20a73f"],
|
|
Cell[343169, 7622, 4071, 140, 167, "Input",ExpressionUUID->"20962513-a6c6-46ea-aebc-973a60c3f95f"],
|
|
Cell[347243, 7764, 3745, 93, 220, "Input",ExpressionUUID->"d3a32aba-35d9-4b11-8965-8489f6e162bc"],
|
|
Cell[CellGroupData[{
|
|
Cell[351013, 7861, 2386, 60, 121, "Input",ExpressionUUID->"0d9be6fe-c20c-4b13-b4c3-a4f6c73c3a1d"],
|
|
Cell[353402, 7923, 72806, 1305, 284, "Output",ExpressionUUID->"fab28477-49a9-4922-9e62-38257f87c619"]
|
|
}, Open ]],
|
|
Cell[426223, 9231, 149, 3, 52, "Input",ExpressionUUID->"d453d858-8a7b-4124-abfb-9e6f74a501dc"],
|
|
Cell[426375, 9236, 147, 3, 52, "Input",ExpressionUUID->"eead3199-3345-46f2-a4c0-2fec2d348b90"]
|
|
}, Closed]],
|
|
Cell[CellGroupData[{
|
|
Cell[426559, 9244, 163, 3, 38, "Subsection",ExpressionUUID->"d406c2ba-4ab0-44d0-9b6f-c0c1db6c1acf"],
|
|
Cell[426725, 9249, 1505, 42, 54, "Input",ExpressionUUID->"5964132e-935a-46a6-b153-12b5727d94a0"],
|
|
Cell[428233, 9293, 1820, 52, 56, "Input",ExpressionUUID->"9e3ef216-9ad2-4adb-b9e7-96392657d2b3"],
|
|
Cell[430056, 9347, 4737, 148, 104, "Input",ExpressionUUID->"fd5e482a-7176-4bda-b608-c9d284776293"],
|
|
Cell[CellGroupData[{
|
|
Cell[434818, 9499, 3814, 120, 100, "Input",ExpressionUUID->"d44672a8-904c-49d5-a749-404599638355"],
|
|
Cell[438635, 9621, 617, 9, 34, "Output",ExpressionUUID->"f95cdf80-034d-490c-9052-1ab0cd6440d3"],
|
|
Cell[439255, 9632, 617, 9, 34, "Output",ExpressionUUID->"1b714e96-da79-4d94-a1ba-aad82b46c1b7"]
|
|
}, Open ]],
|
|
Cell[439887, 9644, 3409, 116, 102, "Input",ExpressionUUID->"47e6ea8d-fe96-432b-bc8f-37af178f58c4"],
|
|
Cell[CellGroupData[{
|
|
Cell[443321, 9764, 3501, 118, 102, "Input",ExpressionUUID->"41ad596d-10ce-4e99-baba-2ce47459342c"],
|
|
Cell[446825, 9884, 179, 3, 34, "Output",ExpressionUUID->"564d55f1-fbb5-4701-bf39-19b29e089fa9"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[447041, 9892, 4888, 165, 132, "Input",ExpressionUUID->"0539ebc8-55d1-4e61-8059-2b873a109fd0"],
|
|
Cell[451932, 10059, 1039, 31, 34, "Output",ExpressionUUID->"eb2da5a6-57c0-4846-bf3e-a339f3051de0"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[453008, 10095, 6113, 200, 137, "Input",ExpressionUUID->"ba29c20b-dea9-41b8-b3d4-fc57943bb3a3"],
|
|
Cell[459124, 10297, 469, 7, 34, "Output",ExpressionUUID->"a45ecd9f-4177-4783-8c1c-5a81ef2ad1df"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[459630, 10309, 5193, 175, 110, "Input",ExpressionUUID->"5f1d575c-4c3c-4bde-8f8f-240d45244a88"],
|
|
Cell[464826, 10486, 206, 3, 34, "Output",ExpressionUUID->"1f981ff0-2415-481e-9272-8f05a9125627"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[465069, 10494, 2662, 88, 80, "Input",ExpressionUUID->"d0f32758-1361-44ee-bb02-8950288c60b3"],
|
|
Cell[467734, 10584, 957, 29, 34, "Output",ExpressionUUID->"55173617-34ac-4fdc-9406-99bf575c07a4"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[468728, 10618, 3501, 117, 102, "Input",ExpressionUUID->"c1307343-2cfb-4e0b-83cc-02e91fb1c0ed"],
|
|
Cell[472232, 10737, 176, 2, 34, "Output",ExpressionUUID->"3b48e172-c35e-4179-ad01-d64d2ba564df"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[472445, 10744, 3554, 119, 102, "Input",ExpressionUUID->"318015e8-2886-4487-be95-e7f69ff7a94c"],
|
|
Cell[476002, 10865, 156, 3, 34, "Output",ExpressionUUID->"3c0943dd-d696-48fb-95bf-e076fa93c9b0"]
|
|
}, Open ]],
|
|
Cell[476173, 10871, 3033, 103, 102, "Input",ExpressionUUID->"b4079bea-4a03-45f8-9706-9190d1a1a2fd"],
|
|
Cell[CellGroupData[{
|
|
Cell[479231, 10978, 1956, 55, 48, "Input",ExpressionUUID->"523e901d-07d6-4226-ab0a-a0f8b4022ef8"],
|
|
Cell[481190, 11035, 422, 11, 48, "Output",ExpressionUUID->"cdd496d7-6f57-4d4b-9410-784a9d2ec602"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[481649, 11051, 696, 24, 48, "Input",ExpressionUUID->"a2621bef-7c52-4cc5-b04b-4a41d784cd3d"],
|
|
Cell[482348, 11077, 482, 15, 48, "Output",ExpressionUUID->"47b658d6-e43b-40a5-bd62-147a938a1d86"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[482867, 11097, 581, 19, 48, "Input",ExpressionUUID->"ab059271-ba95-494b-97be-904cc891c23e"],
|
|
Cell[483451, 11118, 371, 11, 50, "Output",ExpressionUUID->"8f57ea33-6026-4373-bdf2-c97365a6aff0"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[483859, 11134, 452, 12, 30, "Input",ExpressionUUID->"1423d03d-0009-4a98-923c-6616c220bc62"],
|
|
Cell[484314, 11148, 7116, 137, 239, "Output",ExpressionUUID->"a9257c0c-b5e1-4c1f-b935-f11312fc5f0c"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[491467, 11290, 558, 16, 48, "Input",ExpressionUUID->"7d937c46-315c-4127-85c4-712b14bc01aa"],
|
|
Cell[492028, 11308, 402, 12, 48, "Output",ExpressionUUID->"cd9d35dd-d570-4a5a-8d26-67dfbe5a07bb"]
|
|
}, Open ]],
|
|
Cell[492445, 11323, 513, 17, 48, "Input",ExpressionUUID->"a2ac8ff2-1cae-41e1-a20b-4fbb997dec08"],
|
|
Cell[CellGroupData[{
|
|
Cell[492983, 11344, 448, 14, 46, "Input",ExpressionUUID->"2f20c949-180a-497c-b460-fc41151522d8"],
|
|
Cell[493434, 11360, 275, 8, 48, "Output",ExpressionUUID->"0b25d327-e92b-4494-a4e0-91dc831b2739"]
|
|
}, Open ]],
|
|
Cell[493724, 11371, 191, 6, 48, "Input",ExpressionUUID->"939751eb-557e-4570-ac5e-0177a1ac50cf"],
|
|
Cell[493918, 11379, 1875, 54, 51, "Input",ExpressionUUID->"7f39c9ab-32fa-41ee-a84c-0db48d3fd4ca"],
|
|
Cell[495796, 11435, 468, 15, 48, "Input",ExpressionUUID->"59da42ed-948c-40cc-9a75-afe1a8b88822"],
|
|
Cell[496267, 11452, 4909, 127, 185, "Input",ExpressionUUID->"47cbd7eb-4244-4a5a-b725-eb6c2ae63c11"],
|
|
Cell[CellGroupData[{
|
|
Cell[501201, 11583, 9467, 180, 308, "Input",ExpressionUUID->"54cba639-78de-41b7-b09f-3fb5cc912380"],
|
|
Cell[510671, 11765, 3821, 95, 182, "Output",ExpressionUUID->"278ca01a-9bd3-4962-aa4f-fe7918d70fe0"],
|
|
Cell[514495, 11862, 2875, 61, 247, "Output",ExpressionUUID->"44916109-9e4c-44de-8ffc-11faec7bc38d"]
|
|
}, Open ]]
|
|
}, Closed]],
|
|
Cell[CellGroupData[{
|
|
Cell[517419, 11929, 304, 9, 38, "Subsection",ExpressionUUID->"c3267724-2a1e-46ae-a70a-24dbe2bc9597"],
|
|
Cell[CellGroupData[{
|
|
Cell[517748, 11942, 9486, 298, 329, "Input",ExpressionUUID->"093b63ec-d5d7-429c-a6ae-daee424561d5"],
|
|
Cell[527237, 12242, 759, 11, 34, "Output",ExpressionUUID->"c8bc8a1a-7edb-4bf3-8401-c89b58f107f2"],
|
|
Cell[527999, 12255, 759, 11, 34, "Output",ExpressionUUID->"f48a9ecf-9fbe-47d9-ae87-f8b5af6c5e0b"],
|
|
Cell[528761, 12268, 759, 11, 34, "Output",ExpressionUUID->"ec1755b9-8f51-47c9-9a0f-1629807636d1"],
|
|
Cell[529523, 12281, 809, 13, 34, "Output",ExpressionUUID->"de84db82-7bcd-4321-be05-acdd32c5a02c"],
|
|
Cell[530335, 12296, 759, 11, 34, "Output",ExpressionUUID->"e6a683e2-6c11-4e7d-802c-2b921896631b"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[531131, 12312, 5317, 162, 97, "Input",ExpressionUUID->"5ce35750-7da9-4ff5-b83f-0ae5f5377437"],
|
|
Cell[536451, 12476, 156, 3, 34, "Output",ExpressionUUID->"7fb01024-0558-4c4e-bc04-f537ce36e159"]
|
|
}, Open ]]
|
|
}, Closed]],
|
|
Cell[CellGroupData[{
|
|
Cell[536656, 12485, 357, 9, 38, "Subsection",ExpressionUUID->"59690161-1c60-4593-a2e7-c717480798c8"],
|
|
Cell[CellGroupData[{
|
|
Cell[537038, 12498, 12034, 380, 331, "Input",ExpressionUUID->"83dd638d-a3d9-4eac-9812-c6a4cf31efb2"],
|
|
Cell[549075, 12880, 209, 4, 34, "Output",ExpressionUUID->"b4e381d7-4a23-4e07-981a-8f2086d6ecb0"],
|
|
Cell[549287, 12886, 210, 4, 34, "Output",ExpressionUUID->"c0f052e7-e375-40fb-9cda-e30d1e386bf6"],
|
|
Cell[549500, 12892, 210, 4, 34, "Output",ExpressionUUID->"0bae4c27-c7b9-457a-8a0b-94924bb3d300"],
|
|
Cell[549713, 12898, 260, 6, 34, "Output",ExpressionUUID->"c64341aa-bf6d-4dfd-8f07-5440230a7974"],
|
|
Cell[549976, 12906, 210, 4, 34, "Output",ExpressionUUID->"55d747c3-742f-4a1c-84a2-fde40e88cc5e"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[550223, 12915, 15052, 468, 347, "Input",ExpressionUUID->"e4ec2f88-e321-4297-8368-7cf33b0e5d5e"],
|
|
Cell[565278, 13385, 3774, 117, 61, "Output",ExpressionUUID->"468a3fca-bc22-4dbe-ba2e-d09f5efde874"]
|
|
}, Open ]]
|
|
}, Closed]],
|
|
Cell[CellGroupData[{
|
|
Cell[569101, 13508, 238, 4, 38, "Subsection",ExpressionUUID->"eac4bda2-189e-42f0-81dc-51e5ebbd2f4a"],
|
|
Cell[569342, 13514, 1505, 42, 54, "Input",ExpressionUUID->"17b135d5-7e41-4643-b4bb-f3eea5ce1e51"],
|
|
Cell[570850, 13558, 1851, 52, 56, "Input",ExpressionUUID->"14802bea-9955-4893-8c9c-a17bac458ece"],
|
|
Cell[572704, 13612, 5028, 155, 151, "Input",ExpressionUUID->"d3a6ec1b-6a01-430d-947f-8f0e2ffa4abc"],
|
|
Cell[CellGroupData[{
|
|
Cell[577757, 13771, 12016, 360, 415, "Input",ExpressionUUID->"9bfbd342-26ab-4960-b0c1-6d30bc401946"],
|
|
Cell[589776, 14133, 842, 13, 34, "Output",ExpressionUUID->"bad42b6b-febc-423c-b781-8e8f634645b2"],
|
|
Cell[590621, 14148, 842, 13, 34, "Output",ExpressionUUID->"08268186-e6a0-4d08-92db-7368a97e5b15"],
|
|
Cell[591466, 14163, 838, 12, 34, "Output",ExpressionUUID->"14e5cd70-74bd-402b-9647-758b00e98438"],
|
|
Cell[592307, 14177, 844, 13, 34, "Output",ExpressionUUID->"a1021d01-c1ea-43ff-815d-85bf1860cda5"],
|
|
Cell[593154, 14192, 842, 13, 34, "Output",ExpressionUUID->"a6228c72-c3ab-4a4b-a7dd-114c74203722"],
|
|
Cell[593999, 14207, 842, 13, 34, "Output",ExpressionUUID->"449b7df1-0d75-4d67-925c-350cdef9600b"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[594878, 14225, 3780, 122, 98, "Input",ExpressionUUID->"f27d4a85-2a37-4803-a443-435791839d08"],
|
|
Cell[598661, 14349, 211, 4, 34, "Output",ExpressionUUID->"2dc3a301-69c8-4267-acd1-185a7e3220d5"]
|
|
}, Open ]],
|
|
Cell[598887, 14356, 3620, 91, 172, "Input",ExpressionUUID->"17d3180a-586b-41af-a83f-6e20a124c592"],
|
|
Cell[CellGroupData[{
|
|
Cell[602532, 14451, 9840, 189, 283, "Input",ExpressionUUID->"e8a12bd0-24b7-41d6-8141-13207367f442"],
|
|
Cell[612375, 14642, 4442, 90, 525, "Output",ExpressionUUID->"6cf12868-5980-4ee9-9f5e-473067fd4e9d"]
|
|
}, Open ]]
|
|
}, Closed]]
|
|
}, Open ]]
|
|
}, Open ]]
|
|
}
|
|
]
|
|
*)
|
|
|