summaryrefslogtreecommitdiff
diff options
context:
space:
mode:
authorJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-23 11:24:29 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-23 11:24:29 +0100
commit36c174b5b3ec9a4d5435a27128bc7e1c1fa4f118 (patch)
tree1fd387c455109664a5279965d09d0d98499a92ea
parent63aba3f33f80b56e82c7f8c29cd49fac0002c2f5 (diff)
downloadmma-36c174b5b3ec9a4d5435a27128bc7e1c1fa4f118.tar.gz
mma-36c174b5b3ec9a4d5435a27128bc7e1c1fa4f118.tar.bz2
mma-36c174b5b3ec9a4d5435a27128bc7e1c1fa4f118.zip
Got the basic matching working!
Diffstat
-rw-r--r--new_schofield.nb7584
-rw-r--r--schofield.wl30
2 files changed, 6995 insertions, 619 deletions
diff --git a/new_schofield.nb b/new_schofield.nb
index 7aafe40..b73ca0d 100644
--- a/new_schofield.nb
+++ b/new_schofield.nb
@@ -10,10 +10,10 @@
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
-NotebookDataLength[ 591593, 11657]
-NotebookOptionsPosition[ 577508, 11420]
-NotebookOutlinePosition[ 577901, 11436]
-CellTagsIndexPosition[ 577858, 11433]
+NotebookDataLength[ 939814, 18035]
+NotebookOptionsPosition[ 918520, 17694]
+NotebookOutlinePosition[ 918915, 17710]
+CellTagsIndexPosition[ 918872, 17707]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
@@ -22,8 +22,11 @@ Cell[BoxData[
RowBox[{"Get", "[",
"\"\<~/doc/research/first_order_singularities/mma/schofield.wl\>\"",
"]"}]], "Input",
- CellChangeTimes->{{3.817548726786456*^9, 3.817548838429791*^9}},
- CellLabel->"In[3]:=",ExpressionUUID->"e595a667-7f25-4f98-9f12-a321a236d113"],
+ CellChangeTimes->{{3.817548726786456*^9, 3.817548838429791*^9}, {
+ 3.817579586526174*^9, 3.817579588547625*^9}, {3.8176251109891653`*^9,
+ 3.817625112168749*^9}, {3.8176254615736647`*^9, 3.817625462650483*^9}},
+ CellLabel->
+ "In[149]:=",ExpressionUUID->"e595a667-7f25-4f98-9f12-a321a236d113"],
Cell[CellGroupData[{
@@ -32,575 +35,6846 @@ Cell["Definitions", "Section",
3.817119834596055*^9}},ExpressionUUID->"bb531fce-8a9d-4a5f-8d6a-\
ec66b9fbf698"],
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"h1", "=",
+ RowBox[{"h", "[", "0", "]"}]}], ";"}], "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"F1", "=",
+ RowBox[{"RF", "[", "2", "]"}]}], ";"}], "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"eq1", "=",
+ RowBox[{
+ RowBox[{"eq", "[",
+ RowBox[{"F1", ",", "h1"}], "]"}], "[", "1", "]"}]}], ";"}]}], "Input",
+ CellChangeTimes->{
+ 3.817563268660089*^9, {3.817563829122241*^9, 3.817563846550528*^9}, {
+ 3.817563950998456*^9, 3.817563956525237*^9}, {3.8175645239988813`*^9,
+ 3.817564534320574*^9}, {3.81756485534698*^9, 3.817564862343175*^9}, {
+ 3.817564919676697*^9, 3.8175649235785027`*^9}, {3.817565106996109*^9,
+ 3.8175651474217367`*^9}, {3.8175652415905113`*^9, 3.817565250029232*^9}, {
+ 3.8175657444559927`*^9, 3.8175657689660788`*^9}, 3.8175669120549498`*^9, {
+ 3.8175677716518087`*^9, 3.817567773706285*^9}, {3.817579700926876*^9,
+ 3.817579701354711*^9}, {3.8175810533593073`*^9, 3.817581114447541*^9}, {
+ 3.817581149854197*^9, 3.8175811499220247`*^9}, {3.817581265163169*^9,
+ 3.81758126542041*^9}, {3.81758144220247*^9, 3.8175814490334673`*^9}, {
+ 3.8175815152710047`*^9, 3.817581521148234*^9}, {3.817581712240638*^9,
+ 3.817581717799356*^9}, {3.8175852594077063`*^9, 3.817585266989357*^9}, {
+ 3.817625116141048*^9, 3.817625146387568*^9}, {3.817625823896328*^9,
+ 3.81762584825317*^9}, {3.817626018033968*^9, 3.8176260183177137`*^9}, {
+ 3.817663520836796*^9, 3.817663527972684*^9}, {3.817663582652149*^9,
+ 3.817663582839945*^9}},
+ CellLabel->
+ "In[150]:=",ExpressionUUID->"c239eacb-bd0a-49ce-8667-3aa72e4020c9"],
+
Cell[BoxData[
RowBox[{
- RowBox[{"$Assumptions", "=",
- RowBox[{"{",
- RowBox[{
- RowBox[{"\[Theta]c", ">", "0"}], ",",
- RowBox[{"t\[Infinity]", ">", "0"}], ",",
- RowBox[{
- RowBox[{"gC", "[", "\[Infinity]", "]"}], ">", "0"}], ",",
+ RowBox[{"\[Theta]c1", "=", "1.2"}], ";"}]], "Input",
+ CellChangeTimes->{{3.817585268393762*^9, 3.817585293317271*^9}, {
+ 3.817585486091017*^9, 3.817585494971346*^9}, {3.817585564983135*^9,
+ 3.817585565747403*^9}, {3.817613382923294*^9, 3.817613383138185*^9}, {
+ 3.817613792996088*^9, 3.8176137947992983`*^9}, {3.8176138325298033`*^9,
+ 3.817613832689768*^9}, {3.817613945403081*^9, 3.8176139460305977`*^9}, {
+ 3.817616912295125*^9, 3.8176169290794497`*^9}, {3.8176186151558523`*^9,
+ 3.817618619104945*^9}, {3.817619090418564*^9, 3.81761910673524*^9},
+ 3.817619253736672*^9, {3.8176193746564007`*^9, 3.817619374732581*^9}, {
+ 3.817619426379078*^9, 3.817619430415657*^9}, {3.817619495695971*^9,
+ 3.8176194979719963`*^9}, {3.81761962610084*^9, 3.81761962629879*^9}, {
+ 3.817619675607584*^9, 3.8176196962814493`*^9}, 3.817619789430169*^9,
+ 3.817619991910288*^9, {3.8176200580506697`*^9, 3.8176200588070917`*^9}, {
+ 3.817620109806219*^9, 3.8176201102512617`*^9}, {3.8176207225281963`*^9,
+ 3.81762072275283*^9}, {3.817625744386352*^9, 3.817625748424838*^9}, {
+ 3.817625808751005*^9, 3.817625809099471*^9}, {3.8176290646805687`*^9,
+ 3.817629065099968*^9}, 3.817629131750176*^9, {3.817629190325059*^9,
+ 3.817629190809897*^9}, {3.817629497269574*^9, 3.817629497707655*^9}, {
+ 3.817629563603163*^9, 3.817629563901677*^9}, {3.817637457431973*^9,
+ 3.817637458007321*^9}, {3.817639806034833*^9, 3.81763983029615*^9}, {
+ 3.8176404653824*^9, 3.817640484337888*^9}, {3.817640545505579*^9,
+ 3.817640547534202*^9}, {3.817640702610136*^9, 3.817640702917857*^9}, {
+ 3.8176411385765676`*^9, 3.81764115635804*^9}, {3.8176635991713743`*^9,
+ 3.817663599392414*^9}, {3.8176641062045927`*^9, 3.817664108809791*^9}, {
+ 3.8176642725583572`*^9, 3.817664273275118*^9}, {3.817664462392371*^9,
+ 3.81766446250115*^9}, {3.817664613433975*^9, 3.817664613564913*^9}, {
+ 3.817664802762989*^9, 3.81766483117656*^9}, {3.817664863597609*^9,
+ 3.8176648843718557`*^9}, {3.817664977236157*^9, 3.817665003913262*^9},
+ 3.8176650486087637`*^9, {3.817666520433958*^9, 3.81766652831031*^9}},
+ CellLabel->"In[99]:=",ExpressionUUID->"b0293560-4bfa-4de2-84b0-335927f7dbea"],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"sol1", "=",
+ RowBox[{"FindRoot", "[",
+ RowBox[{
+ RowBox[{"eq1", "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c1"}]}], ",",
+ RowBox[{"{",
RowBox[{
- RowBox[{"gC", "[", "_", "]"}], "\[Element]", "Reals"}], ",",
- RowBox[{"B", ">", "0"}], ",",
- RowBox[{"A", ">", "0"}], ",",
- RowBox[{"\[ScriptCapitalF]1", ">", "0"}], ",",
- RowBox[{"\[ScriptCapitalF]0", "\[Element]", "Reals"}], ",",
- RowBox[{"\[Gamma]", ">", "0"}], ",",
- RowBox[{"\[Theta]i", ">", "0"}], ",",
- RowBox[{"\[Theta]i", "<", "\[Theta]c"}]}], "}"}]}], ";"}]], "Input",
- CellChangeTimes->{{3.817121509075202*^9, 3.81712159405204*^9}, {
- 3.817122146902429*^9, 3.8171221498463*^9}, {3.817123222631443*^9,
- 3.8171232401305323`*^9}, {3.81712327174748*^9, 3.817123302075263*^9}, {
- 3.817123345236269*^9, 3.8171233467245693`*^9}, {3.817123565480311*^9,
- 3.817123582960553*^9}, {3.8171246080192423`*^9, 3.817124610971168*^9}, {
- 3.8172096124512787`*^9, 3.817209616026865*^9}, {3.81721066071721*^9,
- 3.817210665188924*^9}, {3.817211071596877*^9, 3.817211091620666*^9}, {
- 3.817271204530282*^9, 3.817271209927745*^9}, {3.817275283336474*^9,
- 3.8172752836605864`*^9}},
- CellLabel->
- "(WOPR) In[446]:=",ExpressionUUID->"395191f4-75f5-4aa3-87f6-ccf9cbedf73f"],
-
-Cell[CellGroupData[{
-
-Cell[BoxData[
- RowBox[{"Manipulate", "[", "\[IndentingNewLine]",
+ RowBox[{"{",
+ RowBox[{"A", ",",
+ RowBox[{"RandomReal", "[",
+ RowBox[{"{",
+ RowBox[{"0", ",", "3"}], "}"}], "]"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], ",",
+ RowBox[{"RandomReal", "[", "]"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"FC", "[", "0", "]"}], ",",
+ RowBox[{"RandomReal", "[", "]"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"FC", "[", "1", "]"}], ",",
+ RowBox[{"RandomReal", "[", "]"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"FC", "[", "2", "]"}], ",",
+ RowBox[{"RandomReal", "[", "]"}]}], "}"}]}], "}"}], ",",
+ RowBox[{"MaxIterations", "\[Rule]", "500"}]}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.8175612726329412`*^9, 3.81756128486736*^9}, {
+ 3.8175614038617268`*^9, 3.817561415404965*^9}, {3.817561511096093*^9,
+ 3.817561563944231*^9}, {3.81756250196518*^9, 3.817562507914916*^9}, {
+ 3.817562967760625*^9, 3.81756298304041*^9}, 3.817563161460335*^9, {
+ 3.817563206558021*^9, 3.81756320676147*^9}, {3.817563530710863*^9,
+ 3.817563550054001*^9}, {3.817563775700533*^9, 3.817563804069632*^9}, {
+ 3.817563971222761*^9, 3.817564086350409*^9}, {3.817564155680212*^9,
+ 3.8175641623358994`*^9}, {3.81756424029494*^9, 3.817564240399859*^9}, {
+ 3.8175645416987743`*^9, 3.817564542202907*^9}, {3.817564715061411*^9,
+ 3.817564723202471*^9}, {3.8175648450855713`*^9, 3.817564883921851*^9}, {
+ 3.8175650025642157`*^9, 3.817565074155829*^9}, {3.817565217921039*^9,
+ 3.817565230520749*^9}, {3.817565359356901*^9, 3.8175654247402163`*^9}, {
+ 3.817565602697175*^9, 3.817565635407323*^9}, {3.817566059389201*^9,
+ 3.817566077942937*^9}, {3.817566269837482*^9, 3.817566273547044*^9}, {
+ 3.8175663066250553`*^9, 3.817566306784181*^9}, {3.817566684914805*^9,
+ 3.81756668549652*^9}, {3.817566919102108*^9, 3.817566934549343*^9}, {
+ 3.8175696638331223`*^9, 3.817569664744486*^9}, {3.817579706169273*^9,
+ 3.8175797767735577`*^9}, {3.817581067506674*^9, 3.8175810689721537`*^9}, {
+ 3.817581121371869*^9, 3.817581169115347*^9}, {3.817581207766066*^9,
+ 3.817581270669099*^9}, 3.817581309702499*^9, {3.817581355857291*^9,
+ 3.817581356026667*^9}, {3.817581392130506*^9, 3.817581416424316*^9}, {
+ 3.817581457365512*^9, 3.8175814943565397`*^9}, {3.81758152586852*^9,
+ 3.817581526654297*^9}, {3.81758529416886*^9, 3.817585296714147*^9}, {
+ 3.817585561197172*^9, 3.817585562026663*^9}, {3.817618621207481*^9,
+ 3.817618624394899*^9}, {3.817619444974866*^9, 3.817619445137411*^9}, {
+ 3.817619996280697*^9, 3.817620100970377*^9}, {3.8176203511794863`*^9,
+ 3.817620366471381*^9}, {3.817625755050593*^9, 3.817625785196938*^9}, {
+ 3.817625855158732*^9, 3.817625933259389*^9}, {3.817626021714408*^9,
+ 3.8176260359581003`*^9}, {3.8176261569605293`*^9, 3.817626157278273*^9}},
+ CellLabel->
+ "In[153]:=",ExpressionUUID->"3d566693-1b4e-4bc5-b33b-b8036e1e4822"],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"A", "\[Rule]",
+ RowBox[{"-", "4.704112966196344`"}]}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], "\[Rule]", "0.10599424935557819`"}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "0", "]"}], "\[Rule]",
+ RowBox[{"-", "3.0139824654804324`"}]}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "1", "]"}], "\[Rule]",
+ RowBox[{"-", "0.9956839089360535`"}]}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "2", "]"}], "\[Rule]",
+ RowBox[{"-", "0.04568459097897419`"}]}]}], "}"}]], "Output",
+ CellChangeTimes->{
+ 3.817561286441853*^9, 3.817561420490069*^9, 3.817561452135456*^9, {
+ 3.817561512454604*^9, 3.817561517595207*^9}, 3.817561585719215*^9,
+ 3.817563004628446*^9, 3.817563182856628*^9, 3.817563228472159*^9, {
+ 3.817563534906947*^9, 3.817563573064754*^9}, {3.817563797249289*^9,
+ 3.817563825598139*^9}, {3.817563996789044*^9, 3.817564046321703*^9}, {
+ 3.817564078153729*^9, 3.817564103465789*^9}, 3.817564181902115*^9,
+ 3.817564233365617*^9, {3.817564277720583*^9, 3.8175642801348143`*^9},
+ 3.817564315116712*^9, 3.8175645338256474`*^9, {3.817564627325935*^9,
+ 3.8175646522898493`*^9}, {3.817564705276019*^9, 3.817564735465515*^9}, {
+ 3.817564839073145*^9, 3.817564850280691*^9}, 3.817564889679229*^9, {
+ 3.817564994846734*^9, 3.817565091817582*^9}, 3.817565231749591*^9, {
+ 3.817565295003468*^9, 3.817565428068199*^9}, 3.817565500042843*^9, {
+ 3.817565636029861*^9, 3.81756564530912*^9}, 3.817565735768449*^9, {
+ 3.817566053734901*^9, 3.8175660860827293`*^9}, 3.817566141015539*^9,
+ 3.8175662848590927`*^9, 3.817566325612877*^9, {3.817566873920313*^9,
+ 3.817566888279759*^9}, 3.8175669368598824`*^9, 3.8175676424929543`*^9,
+ 3.817567784807679*^9, 3.817569665139393*^9, 3.81757954674091*^9,
+ 3.81757967210157*^9, {3.817579713138091*^9, 3.817579777361397*^9},
+ 3.817579821306189*^9, 3.8175810242250967`*^9, {3.81758111825353*^9,
+ 3.817581144262869*^9}, {3.817581181116104*^9, 3.8175811880013027`*^9}, {
+ 3.8175812210575027`*^9, 3.817581247862958*^9}, {3.81758129685359*^9,
+ 3.8175813628876057`*^9}, {3.8175813942271137`*^9, 3.817581435480754*^9}, {
+ 3.817581471263382*^9, 3.817581496713935*^9}, 3.817581543505228*^9,
+ 3.817581753404653*^9, 3.817582064358006*^9, 3.8175852248573008`*^9, {
+ 3.817585283585939*^9, 3.8175852999095488`*^9}, {3.817585487301776*^9,
+ 3.817585502087878*^9}, 3.8175855671904163`*^9, 3.817613385098051*^9, {
+ 3.817613796159917*^9, 3.817613803142503*^9}, 3.8176138343071117`*^9, {
+ 3.8176139473966227`*^9, 3.817613949416984*^9}, {3.817616913905779*^9,
+ 3.817616930282693*^9}, 3.8176186258104343`*^9, 3.81761872710673*^9, {
+ 3.817619101977674*^9, 3.817619107965846*^9}, 3.817619255028962*^9,
+ 3.8176193759050617`*^9, {3.817619431498866*^9, 3.817619449292502*^9},
+ 3.817619499053896*^9, {3.817619627402491*^9, 3.817619631209499*^9}, {
+ 3.8176196774271812`*^9, 3.8176196990743523`*^9}, 3.817619790930694*^9, {
+ 3.817620004685841*^9, 3.8176201113198757`*^9}, {3.8176203674921637`*^9,
+ 3.8176203774276752`*^9}, {3.817620724033588*^9, 3.817620733528399*^9}, {
+ 3.817625777669826*^9, 3.817625820443478*^9}, {3.817625892508223*^9,
+ 3.81762593562003*^9}, {3.817626153175129*^9, 3.817626158370763*^9}, {
+ 3.817629070037771*^9, 3.817629090362233*^9}, 3.817629133150034*^9,
+ 3.817629194401656*^9, {3.817629503724696*^9, 3.817629507102276*^9}, {
+ 3.817629568997431*^9, 3.817629573075118*^9}, 3.817637461057411*^9, {
+ 3.817639795406546*^9, 3.817639831570113*^9}, {3.8176404678175488`*^9,
+ 3.817640566074553*^9}, {3.817640674521316*^9, 3.817640706720207*^9}, {
+ 3.8176411402417173`*^9, 3.817641207390697*^9}, 3.8176636123222113`*^9,
+ 3.817664109962291*^9, 3.817664274608094*^9, 3.817664463710967*^9,
+ 3.8176646147589073`*^9, 3.817664804500786*^9, 3.817664837913732*^9,
+ 3.817664888223516*^9, {3.817664979000359*^9, 3.817665005249496*^9},
+ 3.817665050841535*^9, 3.817666529326723*^9, 3.817707205358016*^9},
+ CellLabel->
+ "Out[153]=",ExpressionUUID->"f676952c-992f-4ebe-a4d1-30e21dd4d0ca"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Plot", "[",
RowBox[{
- RowBox[{"Plot", "[",
+ RowBox[{"Evaluate", "[",
RowBox[{
RowBox[{
RowBox[{
- RowBox[{"R\[ScriptCapitalM]", "[", "2", "]"}], "[",
- RowBox[{"\[Gamma]", ",", "B", ",", "\[Theta]c", ",", "1"}], "]"}], "[",
- "\[Theta]", "]"}], ",", "\[IndentingNewLine]",
- RowBox[{"{",
- RowBox[{"\[Theta]", ",",
- RowBox[{"-", "20"}], ",", "20"}], "}"}], ",", "\[IndentingNewLine]",
- RowBox[{"Epilog", "\[Rule]",
- RowBox[{"{",
- RowBox[{"Line", "[",
- RowBox[{"{",
- RowBox[{
- RowBox[{"{",
- RowBox[{"\[Theta]c", ",",
- RowBox[{"-", "1000"}]}], "}"}], ",",
- RowBox[{"{",
- RowBox[{"\[Theta]c", ",", "1000"}], "}"}]}], "}"}], "]"}], "}"}]}],
- ",",
- RowBox[{"WorkingPrecision", "\[Rule]", "30"}]}], "]"}],
- "\[IndentingNewLine]", ",",
- RowBox[{"{",
- RowBox[{"\[Gamma]", ",",
- RowBox[{"1", "/", "10"}], ",", "10", ",",
- RowBox[{"1", "/", "10"}]}], "}"}], ",",
- RowBox[{"{",
- RowBox[{"B", ",",
- RowBox[{"1", "/", "10"}], ",", "10", ",",
- RowBox[{"1", "/", "10"}]}], "}"}], ",",
+ RowBox[{
+ RowBox[{"RF", "[", "2", "]"}], "[", "\[Theta]", "]"}], "/.",
+ RowBox[{"B", "->",
+ RowBox[{"ruleB", "[", "g1", "]"}]}]}], "/.", "sol1"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c1"}]}], "]"}], ",",
RowBox[{"{",
- RowBox[{"\[Theta]c", ",",
- RowBox[{"1", "+",
- RowBox[{"1", "/", "10"}]}], ",", "2", ",",
- RowBox[{"1", "/", "100"}]}], "}"}]}], "]"}]], "Input",
- CellChangeTimes->{{3.8175496131650867`*^9, 3.817549762607664*^9}, {
- 3.817550982837791*^9, 3.817551030438055*^9}, {3.8175529357604218`*^9,
- 3.81755293778432*^9}, {3.8175530988827267`*^9, 3.8175531070583982`*^9}, {
- 3.817553402424604*^9, 3.8175534118159523`*^9}, {3.8175536922933187`*^9,
- 3.81755370940517*^9}, {3.81755419838216*^9, 3.817554207237907*^9}, {
- 3.8175542657350683`*^9, 3.817554403122216*^9}, {3.817555063285273*^9,
- 3.8175551707746563`*^9}, {3.817557024056016*^9, 3.817557024895731*^9}, {
- 3.8175573533737717`*^9, 3.817557355637789*^9}},
- CellLabel->"In[6]:=",ExpressionUUID->"389cbfb1-8cc7-458c-9f8c-1fd631f97f2c"],
-
-Cell[BoxData[
- TagBox[
- StyleBox[
- DynamicModuleBox[{Schofield`B$$ = Rational[9, 10], Schofield`\[Gamma]$$ =
- Rational[22, 5], Schofield`\[Theta]c$$ = Rational[179, 100],
- Typeset`show$$ = True, Typeset`bookmarkList$$ = {},
- Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ =
- 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{
- Hold[Schofield`\[Gamma]$$],
- Rational[1, 10], 10,
- Rational[1, 10]}, {
- Hold[Schofield`B$$],
- Rational[1, 10], 10,
- Rational[1, 10]}, {
- Hold[Schofield`\[Theta]c$$],
- Rational[11, 10], 2,
- Rational[1, 100]}}, Typeset`size$$ = {270., {82., 85.33243899140032}},
- Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True},
-
- DynamicBox[Manipulate`ManipulateBoxes[
- 1, StandardForm,
- "Variables" :> {
- Schofield`B$$ = Rational[1, 10], Schofield`\[Gamma]$$ =
- Rational[1, 10], Schofield`\[Theta]c$$ = Rational[11, 10]},
- "ControllerVariables" :> {},
- "OtherVariables" :> {
- Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$,
- Typeset`animator$$, Typeset`animvar$$, Typeset`name$$,
- Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
- Typeset`skipInitDone$$}, "Body" :> Plot[
- Schofield`R\[ScriptCapitalM][2][
- Schofield`\[Gamma]$$, Schofield`B$$, Schofield`\[Theta]c$$, 1][
- Schofield`\[Theta]], {Schofield`\[Theta], -20, 20}, Epilog -> {
-
- Line[{{Schofield`\[Theta]c$$, -1000}, {
- Schofield`\[Theta]c$$, 1000}}]}, WorkingPrecision -> 30],
- "Specifications" :> {{Schofield`\[Gamma]$$,
- Rational[1, 10], 10,
- Rational[1, 10]}, {Schofield`B$$,
- Rational[1, 10], 10,
- Rational[1, 10]}, {Schofield`\[Theta]c$$,
- Rational[11, 10], 2,
- Rational[1, 100]}}, "Options" :> {}, "DefaultOptions" :> {}],
- ImageSizeCache->{307., {134.849609375, 139.150390625}},
- SingleEvaluation->True],
- Deinitialization:>None,
- DynamicModuleValues:>{},
- SynchronousInitialization->True,
- UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
- UnsavedVariables:>{Typeset`initDone$$},
- UntrackedVariables:>{Typeset`size$$}], "Manipulate",
- Deployed->True,
- StripOnInput->False],
- Manipulate`InterpretManipulate[1]]], "Output",
- CellChangeTimes->{{3.8175543100594673`*^9, 3.817554403402668*^9}, {
- 3.817555144679367*^9, 3.817555170954733*^9}, 3.817557025045121*^9, {
- 3.817557353599874*^9, 3.81755735592977*^9}},
- CellLabel->"Out[6]=",ExpressionUUID->"2b3d333d-6106-45b7-8d31-f398af6dca84"]
+ RowBox[{"\[Theta]", ",",
+ RowBox[{"-", "\[Theta]c1"}], ",", "\[Theta]c1"}], "}"}]}],
+ "]"}]], "Input",
+ CellChangeTimes->{{3.8176233124650707`*^9, 3.817623348286018*^9}, {
+ 3.817623414269414*^9, 3.817623458216208*^9}, {3.817623857421668*^9,
+ 3.817623947337986*^9}, {3.8176244336335487`*^9, 3.8176244577469254`*^9}, {
+ 3.817624497193656*^9, 3.817624500892652*^9}, {3.817624532809559*^9,
+ 3.817624535743273*^9}, {3.817624582381755*^9, 3.817624593129384*^9}, {
+ 3.817624645730153*^9, 3.817624809282262*^9}, {3.817626169490147*^9,
+ 3.8176262061761208`*^9}, {3.8176374709933147`*^9, 3.817637472394459*^9}, {
+ 3.8176405306118803`*^9, 3.81764053152619*^9}, {3.8176407139007196`*^9,
+ 3.817640715271174*^9}, {3.817663620966742*^9, 3.8176636222101192`*^9}, {
+ 3.817666515543281*^9, 3.817666525799995*^9}},
+ CellLabel->
+ "In[154]:=",ExpressionUUID->"a4f082dc-c86b-4fae-a5ca-c1981cd9d9cf"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "General", "munfl",
+ "\"\\!\\(\\*RowBox[{\\\"Exp\\\", \\\"[\\\", RowBox[{\\\"-\\\", \
+\\\"17851.66136326923`\\\"}], \\\"]\\\"}]\\) is too small to represent as a \
+normalized machine number; precision may be lost.\"", 2, 154, 144,
+ 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817666517288512*^9, 3.817666530774806*^9},
+ 3.817707207513198*^9},
+ CellLabel->
+ "During evaluation of \
+In[154]:=",ExpressionUUID->"36ce886b-a17b-4e11-a0fa-9283b3f2481b"],
+
+Cell[BoxData[
+ GraphicsBox[{{{}, {},
+ TagBox[
+ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
+ 1.], LineBox[CompressedData["
+1:eJw12nk01N//B/CJEllCPsgehZSIFJFBiDZrRRGJQkglayKiLNl3Zt5KKCFb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+ "]]},
+ Annotation[#, "Charting`Private`Tag$121137#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->{{-1.2, 1.2}, {-0.031083408212676744`, 0.}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.05]}},
+ Ticks->{Automatic, Automatic}]], "Output",
+ CellChangeTimes->{{3.81762333834346*^9, 3.8176233497856483`*^9}, {
+ 3.817623416062337*^9, 3.81762345918757*^9}, {3.817623881680962*^9,
+ 3.817623949604845*^9}, {3.817624440474684*^9, 3.8176244586045856`*^9}, {
+ 3.817624497853997*^9, 3.8176245014514923`*^9}, 3.817624537275628*^9, {
+ 3.817624585218245*^9, 3.817624594015519*^9}, {3.8176246351419277`*^9,
+ 3.8176248099871397`*^9}, {3.817626201171485*^9, 3.817626207195038*^9},
+ 3.817629092963571*^9, 3.817629135304832*^9, 3.817629511298234*^9,
+ 3.817629576664672*^9, {3.8176374666375017`*^9, 3.817637473634259*^9},
+ 3.817639798078849*^9, 3.817639833944018*^9, 3.817640490911343*^9, {
+ 3.817640528768524*^9, 3.817640532508259*^9}, {3.817640698745162*^9,
+ 3.817640716239604*^9}, {3.8176411418589973`*^9, 3.81764114787577*^9}, {
+ 3.817663615159411*^9, 3.817663623606195*^9}, 3.817664111761855*^9,
+ 3.817664276359878*^9, 3.817664465371686*^9, 3.8176646170967903`*^9, {
+ 3.817666511582511*^9, 3.817666531246264*^9}, 3.81770720809378*^9},
+ CellLabel->
+ "Out[154]=",ExpressionUUID->"790a1b14-2979-49a3-9e30-5d496c64e79a"]
}, Open ]],
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"h2", "=",
+ RowBox[{"h", "[", "3", "]"}]}], ";"}], "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"F2", "=",
+ RowBox[{"RF", "[", "2", "]"}]}], ";"}], "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"eq2", "=",
+ RowBox[{
+ RowBox[{"eq", "[",
+ RowBox[{"F2", ",", "h2"}], "]"}], "[", "2", "]"}]}], ";"}]}], "Input",
+ CellChangeTimes->{
+ 3.817563268660089*^9, {3.817563829122241*^9, 3.817563846550528*^9}, {
+ 3.817563950998456*^9, 3.817563956525237*^9}, {3.8175645239988813`*^9,
+ 3.817564534320574*^9}, {3.81756485534698*^9, 3.817564862343175*^9}, {
+ 3.817564919676697*^9, 3.8175649235785027`*^9}, {3.817565106996109*^9,
+ 3.8175651474217367`*^9}, {3.8175652415905113`*^9, 3.817565250029232*^9}, {
+ 3.8175657444559927`*^9, 3.8175657689660788`*^9}, 3.8175669120549498`*^9, {
+ 3.8175677716518087`*^9, 3.817567773706285*^9}, {3.817579700926876*^9,
+ 3.817579701354711*^9}, {3.8175810533593073`*^9, 3.817581114447541*^9}, {
+ 3.817581149854197*^9, 3.8175811499220247`*^9}, {3.817581265163169*^9,
+ 3.81758126542041*^9}, {3.81758144220247*^9, 3.8175814490334673`*^9}, {
+ 3.8175815152710047`*^9, 3.817581521148234*^9}, {3.817581635837187*^9,
+ 3.817581700879589*^9}, {3.817581767691791*^9, 3.817581768673394*^9}, {
+ 3.8175821842992363`*^9, 3.8175821844066353`*^9}, {3.817582286431714*^9,
+ 3.817582297101211*^9}, {3.817582488847374*^9, 3.817582488974349*^9}, {
+ 3.817582803954041*^9, 3.817582804222094*^9}, {3.817618756754203*^9,
+ 3.817618757439868*^9}, {3.81761900296082*^9, 3.817619003035212*^9}, {
+ 3.8176203963382673`*^9, 3.817620396528458*^9}, {3.817626242723531*^9,
+ 3.817626282042306*^9}, {3.81762924164756*^9, 3.8176292443562737`*^9}, {
+ 3.8176636404765043`*^9, 3.817663648770928*^9}, {3.817666003825204*^9,
+ 3.8176660163975077`*^9}},
+ CellLabel->"In[89]:=",ExpressionUUID->"4dc1af41-4bef-447e-a233-c8c033887359"],
+
Cell[CellGroupData[{
Cell[BoxData[
- RowBox[{"Limit", "[",
- RowBox[{
+ RowBox[{"sol2", "=",
+ RowBox[{"FindRoot", "[",
RowBox[{
- RowBox[{
- RowBox[{"R\[ScriptCapitalM]", "[", "2", "]"}], "[",
- RowBox[{"\[Gamma]", ",", "B", ",", "\[Theta]c", ",", "M0"}], "]"}], "[",
- "\[Theta]", "]"}], ",",
- RowBox[{"\[Theta]", "\[Rule]", "\[Infinity]"}]}], "]"}]], "Input",
- CellChangeTimes->{{3.817557366814589*^9, 3.817557383669715*^9}},
- CellLabel->"In[7]:=",ExpressionUUID->"377f0dcd-6050-40b3-be70-41379e9fda93"],
+ RowBox[{"eq2", "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c1"}]}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"A", ",",
+ RowBox[{"A", "/.", "sol1"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], "/.", "sol1"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"FC", "[", "0", "]"}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "0", "]"}], "/.", "sol1"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"FC", "[", "1", "]"}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "1", "]"}], "/.", "sol1"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"FC", "[", "2", "]"}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "2", "]"}], "/.", "sol1"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "1", "]"}], ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "2", "]"}], ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "3", "]"}], ",",
+ RowBox[{"RandomReal", "[", "]"}]}], "}"}]}], "}"}], ",",
+ RowBox[{"MaxIterations", "\[Rule]", "10000"}]}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.8175612726329412`*^9, 3.81756128486736*^9}, {
+ 3.8175614038617268`*^9, 3.817561415404965*^9}, {3.817561511096093*^9,
+ 3.817561563944231*^9}, {3.81756250196518*^9, 3.817562507914916*^9}, {
+ 3.817562967760625*^9, 3.81756298304041*^9}, 3.817563161460335*^9, {
+ 3.817563206558021*^9, 3.81756320676147*^9}, {3.817563530710863*^9,
+ 3.817563550054001*^9}, {3.817563775700533*^9, 3.817563804069632*^9}, {
+ 3.817563971222761*^9, 3.817564086350409*^9}, {3.817564155680212*^9,
+ 3.8175641623358994`*^9}, {3.81756424029494*^9, 3.817564240399859*^9}, {
+ 3.8175645416987743`*^9, 3.817564542202907*^9}, {3.817564715061411*^9,
+ 3.817564723202471*^9}, {3.8175648450855713`*^9, 3.817564883921851*^9}, {
+ 3.8175650025642157`*^9, 3.817565074155829*^9}, {3.817565217921039*^9,
+ 3.817565230520749*^9}, {3.817565359356901*^9, 3.8175654247402163`*^9}, {
+ 3.817565602697175*^9, 3.817565635407323*^9}, {3.817566059389201*^9,
+ 3.817566077942937*^9}, {3.817566269837482*^9, 3.817566273547044*^9}, {
+ 3.8175663066250553`*^9, 3.817566306784181*^9}, {3.817566684914805*^9,
+ 3.81756668549652*^9}, {3.817566919102108*^9, 3.817566934549343*^9}, {
+ 3.8175696638331223`*^9, 3.817569664744486*^9}, {3.817579706169273*^9,
+ 3.8175797767735577`*^9}, {3.817581067506674*^9, 3.8175810689721537`*^9}, {
+ 3.817581121371869*^9, 3.817581169115347*^9}, {3.817581207766066*^9,
+ 3.817581270669099*^9}, 3.817581309702499*^9, {3.817581355857291*^9,
+ 3.817581356026667*^9}, {3.817581392130506*^9, 3.817581416424316*^9}, {
+ 3.817581457365512*^9, 3.8175814943565397`*^9}, {3.81758152586852*^9,
+ 3.817581526654297*^9}, {3.8175819155874557`*^9, 3.81758195123713*^9}, {
+ 3.8175820720836487`*^9, 3.817582073079625*^9}, {3.817582192281794*^9,
+ 3.8175821927535973`*^9}, {3.8175824979646*^9, 3.817582531058486*^9}, {
+ 3.817582601242318*^9, 3.817582616669943*^9}, {3.817582763042087*^9,
+ 3.817582823261053*^9}, {3.817582997786705*^9, 3.817583024595161*^9}, {
+ 3.817584829987904*^9, 3.817584859074748*^9}, {3.81758494165969*^9,
+ 3.81758496226119*^9}, {3.81758499940244*^9, 3.8175849995669928`*^9}, {
+ 3.817585077390765*^9, 3.817585077573927*^9}, {3.817585156651001*^9,
+ 3.817585156823139*^9}, {3.817585322721836*^9, 3.817585349348461*^9}, {
+ 3.817585456385895*^9, 3.817585457280986*^9}, {3.817585513558703*^9,
+ 3.8175855137401114`*^9}, {3.817613675501788*^9, 3.817613676578967*^9}, {
+ 3.8176168804169617`*^9, 3.81761688926372*^9}, {3.817618774003889*^9,
+ 3.817618793385603*^9}, {3.8176190151288853`*^9, 3.817619038205636*^9},
+ 3.8176190698677187`*^9, {3.817619141079945*^9, 3.8176191871342373`*^9}, {
+ 3.817619234638775*^9, 3.817619240400311*^9}, {3.817619299848545*^9,
+ 3.817619332922262*^9}, {3.817619399549685*^9, 3.817619401809965*^9}, {
+ 3.8176196502657223`*^9, 3.817619664950913*^9}, {3.817619740359915*^9,
+ 3.8176197551387*^9}, {3.81761980328899*^9, 3.8176198034943733`*^9}, {
+ 3.817620410694891*^9, 3.817620463869529*^9}, {3.817620674916114*^9,
+ 3.817620678055534*^9}, {3.817620745057685*^9, 3.817620761178657*^9}, {
+ 3.817626286376536*^9, 3.8176263645243196`*^9}, {3.817629112637333*^9,
+ 3.817629115136323*^9}, {3.817629250682312*^9, 3.817629259447815*^9}, {
+ 3.8176294333109083`*^9, 3.817629436163623*^9}, {3.817641032808353*^9,
+ 3.817641033101226*^9}, {3.817664188948728*^9, 3.817664189649652*^9}, {
+ 3.817664815999873*^9, 3.817664819955031*^9}, {3.817665075387652*^9,
+ 3.8176650759521837`*^9}, {3.817665115247237*^9, 3.817665115392807*^9}, {
+ 3.817665186844384*^9, 3.817665187022648*^9}, {3.817665325401506*^9,
+ 3.8176653256436853`*^9}, {3.817665620012444*^9, 3.8176656289311333`*^9}, {
+ 3.817666022150625*^9, 3.817666032733485*^9}, {3.817666540959165*^9,
+ 3.817666542789474*^9}},
+ CellLabel->
+ "In[107]:=",ExpressionUUID->"e74b775a-c745-4f15-9b63-7bb00af5a487"],
-Cell[BoxData["0"], "Output",
- CellChangeTimes->{3.8175573858936357`*^9},
- CellLabel->"Out[7]=",ExpressionUUID->"02602b05-0f8e-4f3a-8e08-cb1c3aa44a3f"]
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"A", "\[Rule]",
+ RowBox[{"-", "0.0002788135841983469`"}]}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], "\[Rule]", "0.3828625584477164`"}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "0", "]"}], "\[Rule]", "0.0003354084116184048`"}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "1", "]"}], "\[Rule]",
+ RowBox[{"-", "0.3498228420875202`"}]}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "2", "]"}], "\[Rule]", "0.23702958720320444`"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "1", "]"}], "\[Rule]",
+ RowBox[{"-", "0.025660834842616474`"}]}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "2", "]"}], "\[Rule]", "0.0008664997125686273`"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "3", "]"}], "\[Rule]",
+ RowBox[{"-", "0.00004770629388813386`"}]}]}], "}"}]], "Output",
+ CellChangeTimes->{
+ 3.817582243098262*^9, {3.817582385638481*^9, 3.817582397851478*^9}, {
+ 3.817582440404005*^9, 3.8175824479120073`*^9}, {3.8175825951659813`*^9,
+ 3.817582624284917*^9}, {3.817582771007656*^9, 3.817582790104224*^9}, {
+ 3.81758295912363*^9, 3.8175829694259653`*^9}, {3.817583027875955*^9,
+ 3.817583190779282*^9}, 3.817584063702273*^9, 3.817584867935519*^9, {
+ 3.8175849339417667`*^9, 3.817584980641724*^9}, 3.817585038615395*^9,
+ 3.817585139927609*^9, 3.8175851869224243`*^9, 3.817585430610086*^9,
+ 3.817585477765168*^9, 3.8175855203843403`*^9, 3.8175855792410593`*^9,
+ 3.817613703655264*^9, {3.817613820666153*^9, 3.817613850447565*^9},
+ 3.817613970041641*^9, {3.817616894358282*^9, 3.817616938169628*^9},
+ 3.817618971174425*^9, 3.8176190263238583`*^9, {3.817619068552326*^9,
+ 3.817619077160112*^9}, {3.81761912964554*^9, 3.817619175572*^9},
+ 3.8176192081695538`*^9, {3.817619251398644*^9, 3.8176192611467113`*^9}, {
+ 3.817619296755875*^9, 3.8176193494538918`*^9}, {3.817619385600893*^9,
+ 3.817619417396243*^9}, 3.817619473822008*^9, 3.817619517658676*^9, {
+ 3.817619647045698*^9, 3.817619702143152*^9}, {3.817619744218728*^9,
+ 3.81761983514673*^9}, {3.8176206689279957`*^9, 3.817620689262381*^9}, {
+ 3.817620739706464*^9, 3.817620790926754*^9}, 3.8176208714846783`*^9,
+ 3.817626520486795*^9, 3.817627350228532*^9, 3.8176277415834227`*^9, {
+ 3.8176291050494337`*^9, 3.81762916583361*^9}, 3.81762919776195*^9, {
+ 3.817629413613976*^9, 3.81762948905116*^9}, {3.817629524644546*^9,
+ 3.81762958732838*^9}, {3.8176374819742413`*^9, 3.8176375106923237`*^9}, {
+ 3.817640096850602*^9, 3.817640121730076*^9}, 3.817640151968046*^9, {
+ 3.817640182770095*^9, 3.817640187935651*^9}, {3.817640906566828*^9,
+ 3.817640920542989*^9}, {3.817640970056382*^9, 3.8176410191014643`*^9}, {
+ 3.8176411254021797`*^9, 3.817641132552412*^9}, 3.817663859128675*^9,
+ 3.81766409610642*^9, 3.817664145086022*^9, {3.817664185171232*^9,
+ 3.817664200765719*^9}, 3.8176642675306892`*^9, 3.81766430138046*^9, {
+ 3.8176643315114822`*^9, 3.817664370422*^9}, {3.817664458382655*^9,
+ 3.817664488432055*^9}, 3.81766452015694*^9, 3.817664552319276*^9,
+ 3.817664596918642*^9, {3.8176646320970383`*^9, 3.81766466707036*^9}, {
+ 3.817664773532157*^9, 3.817664900143231*^9}, {3.8176649709901123`*^9,
+ 3.817665017377138*^9}, 3.81766506372715*^9, 3.817665098250661*^9,
+ 3.817665165135291*^9, 3.817665295970982*^9, 3.817665563376853*^9,
+ 3.817665956408876*^9, 3.817666446270624*^9, {3.817666535892387*^9,
+ 3.817666551982074*^9}},
+ CellLabel->
+ "Out[107]=",ExpressionUUID->"b0bec539-56ed-4897-b80b-cd8dfd2677e2"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
- RowBox[{
- RowBox[{
- RowBox[{"eqLow", "[", "2", "]"}], "[",
+ RowBox[{"GraphicsRow", "[",
+ RowBox[{"{", "\[IndentingNewLine]",
RowBox[{
- RowBox[{
- RowBox[{"f", "[", "\[Theta]i", "]"}], "[", "0", "]"}], ",",
- RowBox[{
- RowBox[{"g", "[",
- RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "0", "]"}]}], "]"}], "[",
- "0", "]"}]], "Input",
- CellChangeTimes->{{3.8175547641765738`*^9, 3.817554807184411*^9}, {
- 3.81755721589187*^9, 3.817557223395288*^9}},
- CellLabel->"In[4]:=",ExpressionUUID->"8c3eb7fb-65d2-4a56-a3e3-0dc6e0518fe6"],
+ RowBox[{"Plot", "[",
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{"h2", "[", "\[Theta]", "]"}], "/.", "sol2"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c1"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]", ",",
+ RowBox[{"-", "\[Theta]c1"}], ",", "\[Theta]c1"}], "}"}]}], "]"}], ",",
+ "\[IndentingNewLine]",
+ RowBox[{"Plot", "[",
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{"F2", "[", "\[Theta]", "]"}], "/.",
+ RowBox[{"B", "\[Rule]",
+ RowBox[{"ruleB", "[", "h2", "]"}]}]}], "/.", "sol2"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c1"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]", ",",
+ RowBox[{"-", "\[Theta]c1"}], ",", "\[Theta]c1"}], "}"}]}], "]"}]}],
+ "\[IndentingNewLine]", "}"}], "]"}]], "Input",
+ CellChangeTimes->{{3.8175672854849167`*^9, 3.8175673108365*^9}, {
+ 3.817567343605356*^9, 3.817567515945986*^9}, {3.817567689779602*^9,
+ 3.8175677001061993`*^9}, {3.817567852209393*^9, 3.8175678553653107`*^9}, {
+ 3.817569677608418*^9, 3.8175696880410147`*^9}, {3.817581502775428*^9,
+ 3.817581583359663*^9}, {3.817582250277421*^9, 3.817582268443882*^9}, {
+ 3.8176137509420633`*^9, 3.817613772032806*^9}, {3.817616947220008*^9,
+ 3.817616967115974*^9}, {3.8176195353257837`*^9, 3.817619546043696*^9}, {
+ 3.817627764775979*^9, 3.8176278238158283`*^9}, {3.817629596792068*^9,
+ 3.817629639260833*^9}, {3.817666456802641*^9, 3.8176664741498337`*^9}, {
+ 3.817667652558447*^9, 3.81766766911417*^9}},
+ CellLabel->
+ "In[132]:=",ExpressionUUID->"48ef1564-45f8-4d3a-b3bc-835e87c4b434"],
Cell[BoxData[
- RowBox[{
- RowBox[{"M0", " ",
- RowBox[{"(",
+ TemplateBox[{
+ "General", "munfl",
+ "\"\\!\\(\\*RowBox[{\\\"Exp\\\", \\\"[\\\", RowBox[{\\\"-\\\", \
+\\\"5449.6971089453045`\\\"}], \\\"]\\\"}]\\) is too small to represent as a \
+normalized machine number; precision may be lost.\"", 2, 132, 142,
+ 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817667666243705*^9, 3.817667670105051*^9}},
+ CellLabel->
+ "During evaluation of \
+In[132]:=",ExpressionUUID->"b51d87d3-de21-4502-b43b-5a537a1c6dc1"],
+
+Cell[BoxData[
+ GraphicsBox[{{}, {InsetBox[
+ GraphicsBox[{{{}, {},
+ TagBox[
+ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
+ Opacity[1.], LineBox[CompressedData["
+1:eJwt2Xs0lN/XAHAqKiGXIipfpVRyKbqgshERQoluRJKEFKISRUVFpZBcIily
+C6kk0sbMIwkRcr/OPDOMa6hU4j2/td6/Zn3WmnXOPufsvc9Z61nheGbfiVl8
+fHyf+Pn4/ve79JCIoobGOBZUcLJPGTl+0FfL2au2YRxddQ5XCpbqoqvA3oD1
+KuOo/+raaa9iSyx4GdWgsGYcd8ZAW2C+A+4XWnZt0dJx7EwsdylMO4u3i5S6
+f8wax9NpSid17wTi9HLjuIKvYxi4LC3YxeYe9vReFdXxGsPp7pVh678+RhlO
+/ZjIk+8YP+xU7quTgxdT21MKO0YxxvrPVg/6DXqIpG/ZLjeKV83OKElsL8LR
+rDbLf7KjWBlsauG/twg9zUTdPkiPoteGI6lNzkV4Lsz7sa74KDK9j30/dr8I
+L83XmWc4ZxSTMvasoegiXLgg9VV8wwjSv6zOfwx7j/p/f//+4D6CpSonf5ZX
+FWN625MQgYRhPHdSb8sN8RKMbvZ/8jN6GDM89vrXyZTg1cYD77n3hnHFu9OX
+F68swcNfRMY+XR9G49MZ70LVS1CYcdHurvsw8grt5ZWsSvBsxt5N0tuHsb9N
+YO+OyBLcepG/d23bEHITEh0KRUtxlW/7lEzjEBbXfb6/Q6oUxbzfSi/4MoQr
+bMOiC5eXYp/76T1DZUNorUstT1YuxTiHloKXGUOokG6uucakFKeNXoZr+w1h
+dfsvI6HrpUhJHdthJjOEt0yOq2uNl2LAiGxgkcQQBtvffnrzTylurmgoUxIe
+QmGRuO+1/GWYctHYeP7MICY6nFxrJlaGwe1qVuXsQZzzdGrZkHIZGiZPu+jm
+DuKuE31zWp3KkFJ5FLXJaBCLxy/8cf5ShgGCNk1PdQfxs9dZ/obGMtzctVBW
+UnsQbzevEdRuJ+Pfu/b4u/IgSixbIPK9j4w/7pqRLTGIFtx1qgtmMdDwnVbJ
+2s4BtL63JXNUnYGUQdPAMp8BrGuPXngznIF52lcaMzwG8GOk+tRUFAMTN6xB
+TZcBjH4daOwWx8ALy85H7D8ygJ/X2M7ZlMJApQkprdt6A6j2XFvRt5CB957a
+hPwVGcBG4wX/ilkMPDLrm3xrKg+TXQNsj29kovFkgJBLEg/9LqvtFtzCxE3D
+qyd+xPLQ8+rFt8naTBRt9fkofoeHkhlrl1fsZGLJy8Ueu715eMdpz3rKmomK
+x6yLCoCHzMSYXbcuMPE7Nlg/bO7H8vMj6/TeMbHce2x11Nd+nP4QmdbwnomP
+1oj9vFfVjx/x8GPHEjJ/uGl0aEk/6v76MXn6IxOTjpZ9C0jrx2zHMR/9RiZa
+/ss54HShH+fq2zqxRsh8L6vXHPPqxww/wXq5cSZOOQ38snPvR6bh9Yr9P5mY
+VqUYc8ChH+tdc0xzp5g4E5/QbGLcj/qRjKrV8ynM1g47tHFJPz5WzQ5dsILC
+68Np61Ql+jHkhcG3EQUKDyeX/1YS7seIq4lvaxQpFBSaFbeKrx9j0x3AX5nC
+oy0XWqX7+nBpR1hA9FYKRS44H5l+24cadO7NCjMK3d/o2X0+0Ifa8edvrvOm
+UNRQx3rX3j6cKVJXiPChMKdBe0+pSR9mmwlcnzhP4di4xo63O/rQp4t+lOpP
+4QV1xeVPFfrw++Ij5iXBJL4coQ6/ES5yhI98rIymUBHmNv7o42Jm9sTB2hgK
+P9bMrj7by0UVrSTmlzgKhYan3js3clFTZKva+0QK7ymPPNpXxEXfX0XnTFMp
+jE+vt1W6wUX0nGg3eE3hdq3a/SmBXIy9ff153xsKOyuqzOT9uCgue84h5C2F
+8n3UdqnTXAzacC85p5DCVMWCZbOsyPxZz8LelVBonP96UYAZF92uSJFyobDf
+8KXwpCEXzQ+rGMUxKFQ+kTE1pMnFEH5vnmM5hXlPH7W3yHGRV3NHPOszhfs1
+Yhv2L+Gi+jFr25EqCn+UPaj6Is7FzqGlGco1FGr23n1PzeFi6Hiz1YNaCj/I
+Bz16yeNg3a5bc/5rpNAhNyBKmc1BFeHiMPVvFPLr+t1+3sHBOZN28rpNFBrY
+e/sn1HIwb9+q87tbKKxMOGF7K5+Dy0UCZxZ1UGg90KTtncvBS6rs5Tzibk0T
+GbsMDm6d5yJV2EniqVf9tiGRg6YCsnEm3RQGrnjyWjaGgzssPdYs6CH7fUYy
+ck4EB9OSVSPLieWFJi2agzm4dJe+kCqLwowDrqplVzgomVws3Uq8OaVdOOsi
+B/ct/TE3iE2hiW7ppyunOWghMRCFNIU+vqE711hz8P53/SszXAr5mFMrxC04
+uMlzqORqH4Wh4mf4/hpzcHHQzBBfP4VJWVbFNds5mBHwWnSYWOkPFV+whYO1
+i4Pn2PEofGOk6Ze8gYMzUUt45cSVvcu2+q7i4E01zs2wAbL+DeGLHeQ4uLfe
+woBD3B3AP7F7CQd7PNrGtw1S6PrZ+6uGBAcXHXkSc5v4xxJO7nJhDq5XLtRo
+Jg50Phg+V5Ds70udcrkhsh+vK09/n6Ex6KfRXgfiB/w7zNp+0/hUd6TxEbG8
+RY4SNU7jPnFz6wbizEcr5ucM0UivulwrOEzhFl4kN4ZLY7lXrPEm4pKtguVX
+e2h0VCn8YEtsGnzhmXsbjSvK/mgEEn/7yrtq00jj/haf9ERiB3m7Y7pfaFxn
+s0u+gHjg9BdQ+kRjss2N2Cpi3yI9uUUMGq9p7JdqJ+af/3rq33sadwVWPOQQ
+37ZRbOPm07h4Ad9/g8RSz2Le1eXSmNMu9eJ/fvJdKKYog8bTmut29hErQ4Bv
+yjMa/3tk1dtJnH97ZH94Io2LSvLCaon1Wo9pXIyhUfDhcd1i4qo1DeLHI2ic
+ZX6NP4X4gM+uUbPbNLqaqdXeIO4tK6jZEkIjSyP4xQlid7H1L+QDadzZnRyn
+Q/zLLiFMyI/GsJOpMRLEVzMXuk5401gnk53WQ/ZT+HeQcedpGg2Cmj9nEj/c
+NaFYcZLGeY4Gsz2JV0Y5C+Qdo1GrUMxyI3FWTzMr/giNLaW2rwbJeW5VMy0L
+tqaR4hmpPiU2q1S7cmg3jd9u+p3hJ26STrbbuZNGv1mzNNNJvjieWLRdZQeN
+pqlpy8yIz/P9nuTbSOYfadS5RvJti9uhy/PX01jbYJouQ/yz8d1sidU0Cmn+
+csok+Xou009UQYZGyRsbG0pIfm+SaotcL0nj1OXeWwbE44HbZDaJ0PhSWOQB
+g9SDl82UgiE/jX92Lc59xaFQvdQ2fc9fNiqnSpWtIv6+vljV5gcb9/C1qNwn
+9XSW/7LWyX42Vu/hSdmSevPImjG/VcfGx87mewpJvapKOzTc/8zGM4YnTAWJ
+h4JKDsVRbLzEbMzcQ+rd/UCQU+Y7NoY2S8bUkH5watZsv+onbLTcorc9to1C
+p4OCKeJebIw6MJayr4HCVQxnJVl3Nmpt9jG1rqeQpfIxZ6UzGwUWZzhZfSX7
+NftmocZhNmYL3PipR/qZffb8Wmt9Er9kSn4f6YeH54j8jZUg8es0JtiRfip7
+5nRgsjAbDY9X8y8ppbClpVogU5CNlMvsgWqk8GDOXbH3f1i4fk7kXuViUs+H
+xRQ7e1moIL3x7ivSvy1zJfeufMXCj0siiwczKWz7uW86LYuF6XsEhHUyKHTe
+EZGplsrCLyt814WmUehfKSa4I5aF4gpzmyRSKExjixQduMLCxFmdqzgJFM4s
+mbf6jikLL9VOfX5wl/Qje6OvkoYsrOYbfRN1m8JFqSFX4nRYWMSpCb4bSvqR
+hkDr840s1Pda1OEVQqHNnlnhZdIs9ChQiZgOIPdx0NTkL1Yv3jw7eljBnUKt
+im2plzt68WHh5r11pyhkil6yEmjqRbfGhwZ+Jylsjf/9QqKyF7PGb6wtdiT3
+c/5PR5XcXlz6bEpk7iEK7XijVY7+vWh5RPNhlgGpBys6qXpRLxpaXR81XkL6
+1YG4TQzRXrSVSawPW0zhxBGLioJ5vTigVHK1UoLCDqd3I0+nevDtv4nd20RI
+fL53dPzYPbg0VSKRx0+hRdzmdsXXPRhrb3Q6iMfEiJ5g6UCrHuy2Z6jHFDBR
+kKOd6bOnBy86z4zZvGGiH29Ex82oB48LHE0Vz2Oi4/ghZ5ttPbioymvAL5OJ
+GgKqb5QVenADf6T48kQmNqz9tq9lrBuTkxawkq4yUfqs4l31iG70CrawyDFm
+oo1l4e7UsG60lN05P9GAidEbzAVkg7tRUaNV7aYuE6W++/jzX+jGnJlDn8w1
+mbjYi3KttetGF9Erh1PWMFHynJORx7pu1OWttLsowES5UQP+/UFdGHjrrmpF
+MQNF+HZw9Ds7MLR6u5ztCgb+/KObebKuA/kfe/0wWcbAzh8GZ28zO1B9Rqti
+szQDcwfM/jRmdKDdU6bzjDAD9zfZip4634FxoR9fOU6WYVy2/5ZwsQ6cjJEf
+dq0pw7V270Pa9NvRVzh3/Pb5MtxZuG3NueetqLdM3vnsh1KUPiXzdElaE8ZP
+qTsIQwm++uckWneyAVe+ys9mNr/HoZDw11NH61D20sMbS+TeYduARdQFpSoU
+PPjHy6z8Nd6aTniRSN4xcQ8Hw+7p5yJ3wuqijT2i/uK3J27hc2y7pmCNFnm4
+Yq+Oo/RIPC57UOTZcD4G9cQKju0uvIpVoMK3/PBDOHWx2/5jVxCIDld3vqrJ
+g2djb+aq5TyCvHeLIiT7P8Dabw8j57s8h2W/6hj3Z5eD3H8Zkbv9ciHP1r92
+zLsKJjaYNphPvoZg99ev8rXrwCtvW9OHEfJSZr5f6ODfABUtj/7+G30PL9dy
+NkSHNEFe/W6FHSolsGKMr+1CUCvUWNwTj88qhdyUgcUud1thQea45cu8UtA5
+9M3yQHwrsMxU+xgFpWBbklm++U0r3Bq6L93JLIXouzZ5Y32tYCnz25TTXgrC
+67NuuVu2we0Ty+INhMvg5/EDmg7/tcNOhegjKi5lUNn44oFRcQfw1y+02r+I
+ASEiL2Yf+tQBlzpm/VoqwwB9wyxP18YOGFBKEe9ezoCi1xl77gx1QMCn8hS7
+NQzIinwuUL+8E07kbVytqs2AO3uf+By93Am8isqjCvYMsKyOsvaBLug//z7f
+OpUBwgJRjBDTLvgnND83PYMBFdsjN8Yc6AJRjZqfv7MZoJd1X6ToTBdYXUk9
+Gf6WAephdym+pC64ufxb3p0KBoSuYsru4uuG642/6r71M8Cttzi0zqEbkt84
+74tYx4TLyZ0ytie7YfaT9H0lKky45ziTxjndDTbTXyr7NzIhv1f341+/bni3
++NgyNW0m8LEYsxUfdEOTd7P0NRMmRLE++ft96oYlPIEFFq5MeM9u9FBQ74HH
+ITfL3VKZUPPs578Xmj0greyZLZDBhB4n6Tua0AOZfMFtcS+YIEgfzNxj1gP+
+9dzp/NdMsKTbuOedeyDtRpFOfhkT2HSPQ1VcD1zQu2TwpYMJItyhfT6ze8H5
+O/O6gxgFW/pj/t6b3ws6snPtVSQpcBjY+SxrYS84fNk5/GMxBXkjsT9YS3uh
+Li1T0W8pBQcnDWP2beqF3Oqt7eaKFCTPT+xQO9ELcz7N6K/dRsHnBbtDTN16
+YY//hqacHRRMiEyonvTsBZXVHsIauhQYSZgEJgb0whO+ZdbKhhQMyv5cKRLd
+CzPtidt55iQeZXMXXnkvqB1tsIg4RoG96m8xwepeOKOU6FB/nIKbG569W1Hf
+C6VaRdMLnSlo2/RH6FBXLxxhze285EpB4I7UFx9/9UKh3jNBOW8Sj/n02LO1
+LDh36Ohw6DWyPs/sAPtQFuzt8Y2eTqJgv43bFdt7LIjcKncjNZmC3dvWBh2K
+ZoFuPZ+wyTMK1AWSr1sls+CB8Vj1tecUCMQ+CDMqZEGDJk+i7AUFGSX+sWo8
+FsgPTjxzeUdBYopWvPIoCxZbSuz7VEhBZOjPR+t+ssAv0y1o9XsK/PefTVKY
+xQbP04ccaz9QYNF3/Lm0LBtaD3WKjDLIfi00fTOzmw018fISNtUU9E3MfTtl
+wYZZRjp2HjUUdLQwC35bs2Gk/vOSq18oKH+q8378GBuCn1S2x9dRELtVncG9
+yAbFJo+LMY0U3F02wmRfYcPC0RXrbn+j4Cp/VnlPMBvGrLx0LzVR4P55dWXb
+fTZ8iwh+YtpCgY69TN2XdDZwrhWJvmkn6zf49rUqhw3iyxPar3VQsGZdZMOn
+N2zovGYz37yTArFx4WZGKRui2N/9GrooYIXwdb1tYcPjTJ2k9F4Kmt2Ku193
+saHkt+UuKxYFVZZ+vS9pNhytvKo/SZwvO0FnfmfD5+JBzU00Od9s7uDj+TRs
++s9/xptLwcu3VLmcGA3iBrTG7D4KWkueJiVI0dDquLfnNrFyvf3+eAUarlXn
+PAnvp8C6fYeqrBINyV49L+fxKLhML50Xu4GGA8yozf7Etb+aiqJ30KC1b1bE
+vgEKfvPlP1hsQMOSbdMn3xCvFIo6E2VCg4jSTKbEIAWmkl67JffSIJObautK
+fG6ZpULEARqm0qIvvCdOWK36T+woDUe2eU7PGyLnoSrcFO5EQ1lz86AF8ehW
+Xq6oGw2446z+fWIZvYrQO540THi2/qsi1jdJdRK+QMOqisLls4fJeVhd1wm7
+TINR5+skDeIHto5LhIJpSElwDz5K/OGE7tjNMBqatEMqrxFzPeSq5kbQwNuc
+6vGUWOzCVEpIDA3Ohz3Pkvc/aAW1XhF4TIy3a+qIHUMLDl1PoSH1Y8KNbuKw
+yGiN2Vk0xK0wiesnfv3onMjVPBr8Pm4VGCLuSNnH5XtH1jcj/JFHLJizofQK
+0qB55GxnL7FagWj8NEWD2Lt5Jo3EB0sHzwVUkXj0A+aVEQdVVppPfSXr9fBZ
+kk6cUZ+29lILDXdmYi6EEte3h8z600XDwdn31jgTT9FO7Rc4NFg2zlq1nXj1
+iH7+r0Ea2pbFuQsTm0/K3/Mdp6GlenrmG9m/8/wzp378piFvbWt7PHGSUMfO
+c3wcOF/YyH+EeGxZ7C9PEQ6c2tIoV0HOa6ni+bpRSQ44F6os8iU2ULPOPCPL
+AfF0CzM54mg9cfvTazigZfzoih3JBzQZ0RxU4cCuP8svTJD86bOqlnDbxAED
+WensYOJtzrfKXfQ4cGJSvjqa5J/TmZNJXCMOSK4MeyVFfPeCoZ+zOQdY9/77
+eo/ka3cov6rTETLeqYC8/+X3/KiuuaxjHLiTkezZziH1llDcc8yFA6Hd6ceB
++HrOxQf2PiTejTJt42wKXhQcONN5iQPHIrrsDIm/lW7ebXeVA67nDETvk3pa
+2/B96nA4B3Ykp49JkfqrmjzlZJPOgSRR9ZR2Uq/CBl8POOdwILAs016U2Cxc
+29T3DQeCDVjT2qS+P69eoB5dygHGN3Pu9TYKKvdlzTS2cGCb7iX9NtIvhBIX
+jdNdHNCsNRBgk35i0u/P+UFzAG8efMYl/abyyp7qxWMcsJZc591VT8GnrOE4
+ayEuWCwW3HKf9Kt5kzZ3T4hxwa0qv/gs6WfGOzHIR4oLH+btkTEl/a6iJdzl
+wUou2GlNGY1WEgtu3NKozYW8uo3OUxSpLwfvuv1uXLj+XKFYtojkY1Yb08mT
+C7+/mwg+J/1316+dBefOcyGfVSShWkD+f2fR46hrXKiTtfVUfkMBVfjGvSGe
+C601VWt52RQwF03O3V/FheeRo3EuTyiY4+Dw9/hXLpw6EZeQ9JjkR2bFsHcz
+F1BFzao+gQKGXmxjJJsLgSeE6tfGUVDmof20fooLnENK86MiKCit8NexUumD
+Xw/H3V2vkvtMU1CI1uiDIznnE/4LJPn/PLzRV7sPSryNg2oCKIgISXaPM+qD
+mGvv7GQukvwxqIjrOdYH+moWu46fIesrkfx1JroPRifEisoPU+CnllDGn9AH
+VW5nb0odpGA4UfFu5FMyPrd/wt6agqYArdVvc/tAUlUptcuCgrRt9lbTlX2Q
+PTq0K8KAnNfbjJzbM31gZCnhxlAm/URx0yU5wX5wu/0yKmsdyb/o4l25wv0Q
+nBa+O5zc70t9ajvqZfrJupZb6smT+1r954Klm/qhR0gp+wB5L9zN1nNJd+mH
+o+dOPTKbZMLXlGb58rp+sPQT+WhezASJSW9DreZ+6HhoZ3jxHRP2mix0zers
+h+02R08kvGFC7bDhq4iBfuD7NRH8lbxnvmx9ZWgvwINP8+SVRhOYUPXpjuuk
+Jg/e91fNmfRnAjWk/1opiQejpn1G6luYMEe3szkhlQeqh1d8u0veWwYRF/+J
+veCB0ER5L1uZCcwtubt+veNBc4aAd4ACE8quLG9h1POAqbB6r4MYEz6IT/6z
+nTsANlXPJQf7GFCw+YVRuMcAOLCP6y16wADRyq/BkecG4FFf45OpcAacODrJ
+eOg3AKOnL27rCmWAxI2dukkhA9Bu+VMqMpC8D5tbNF8mDoC5PRx448YAuUuC
+SvU1A3BoJk2PpcuA6yX2wtJqg/DCyH20k1MGFqYSdYkjg1C9jVqzdkUZtM4+
+xF31cxBET2f7CcmWgdP7x/8ypgbBspOmaIky8FNRUXo7fwhMvE30bswpg9SF
+xte+KAyB7rBprg+3FKbqAzbzHRyCDG/fyJnMUkiz7Y89VjIE6ZstnpWolcIs
+jxLHVfeHQT/8eXvZihJ45nI/YtvDYdizaqGRt0wJGB53LNuXMAxsN2Pb5eIl
+cPPgnJVB6cMQnLvr+lG+EhDdadzTUToMnc/13NcVI8guqbV/ODYM2+57zjzW
+QNAo67IV2j8CpRF4+I/UB/KevrL+woJReBR7RFDqbRHUaLYZ3aocBVdebELi
++XyYdD/i0hj7HarVD6hOvM+BPyyFQoMjY3D51D2NqdwnUHOr3vvZ0THwkC7s
+dPV4Ak/VrqnMcRwDdnpdzNv1T8DsUm8Sw2UMjKM/bRhISYJEiSc39H3HYOvT
+W44+Gx+Dvp6cte79MfitZyE8NhIHoYlLRrd9HAMc1R/4qBUBRw0q0uMrxyB9
+55+78ln3QYN3/vjf6jEYXiJSsUnuPrRvbvpW2DAGp4aBF85/D1SrHxRr9Y7B
+ded1M/KhYfD1r0TY1n9j0O/A4j9z+SqkPikzeMg3DuwhSYPww0Fwychr+ufs
+caDqPTcpbgmEVZF1nvlC4/Dq1MHZZ5suga/SvYObl4yD1sWtfxuSvMCkFiQe
+LB2HlKDpksuWZ+E/35HPE3Lj4LdKu0Vp2g0qSs3h9epxmL/gqa9EniMknJye
+lFw3DnN85AVjxW3BSyQ7z1t5HFblH/2Chftg1ys793q1cRBI+vifOurD/39/
+hP///qjzf/1IiY0=
+ "]]},
+ Annotation[#, "Charting`Private`Tag$15177#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->{{0.5, 0.49999999999994316`}, {0.5000000000000284,
+ 0.5000000000000284}},
+ 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->{{-1.2, 1.2}, {-0.1713538975870725, 0.17135393862514176`}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.05]}},
+ Ticks->{Automatic, Automatic}], {159.94490842698488, -97.50736892665738},
+ ImageScaled[{0.5, 0.5}], {299.89670330059664, 185.72832176506168}],
+ InsetBox[
+ GraphicsBox[{{{}, {},
+ TagBox[
+ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
+ Opacity[1.], LineBox[CompressedData["
+1:eJw12nc8Vf//AHArZaUkhMgIKVRSonqTmYYoSsOoRFb2jIRssrKyChkle3Nf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+ "]]},
+ Annotation[#, "Charting`Private`Tag$15219#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->{{0.5, 0.5}, {0.5000000000000284, 0.5000000000000284}},
+ 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->{{-1.2, 1.2}, {-0.12925956528287175`, 0.}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.05]}},
+ Ticks->{Automatic, Automatic}], {479.8347252809547, -97.50736892665738},
+ ImageScaled[{0.5, 0.5}], {299.8967033005967, 185.72832176506168}]}, {}},
+
+ ImageSize->{
+ UpTo[600],
+ UpTo[223]},
+ PlotRange->{{0, 639.7796337079396}, {-195.01473785331476`, 0}},
+ PlotRangePadding->{6, 5}]], "Output",
+ CellChangeTimes->{
+ 3.8175673122534857`*^9, {3.8175674402281427`*^9, 3.817567489380693*^9},
+ 3.817567520221552*^9, 3.817567705671341*^9, 3.817567793079455*^9,
+ 3.817567857173483*^9, 3.817569690002346*^9, {3.817581574147563*^9,
+ 3.81758158515839*^9}, 3.817582270590219*^9, {3.817582390618846*^9,
+ 3.817582400806323*^9}, 3.817582450685178*^9, 3.817582634245347*^9,
+ 3.817582776393298*^9, {3.817582962930173*^9, 3.817582972201144*^9}, {
+ 3.8175830310073977`*^9, 3.81758319355462*^9}, 3.817584882023147*^9,
+ 3.81758498666595*^9, 3.817585045390573*^9, 3.817585149785573*^9,
+ 3.817585439738227*^9, 3.817585525878573*^9, 3.817585585204454*^9, {
+ 3.8176137655148363`*^9, 3.817613774145886*^9}, 3.8176139295702887`*^9,
+ 3.8176141329700117`*^9, {3.817616943087964*^9, 3.817616969451852*^9},
+ 3.8176192172908077`*^9, 3.81761927371955*^9, 3.817619365966529*^9,
+ 3.817619480892799*^9, {3.817619523373876*^9, 3.817619547918648*^9}, {
+ 3.817627771060638*^9, 3.817627777110018*^9}, {3.817627809877636*^9,
+ 3.8176278273754797`*^9}, 3.817629121373373*^9, 3.817629171350617*^9,
+ 3.81762920273244*^9, {3.817629594110446*^9, 3.8176296424131317`*^9}, {
+ 3.817637486886181*^9, 3.817637516006345*^9}, {3.817640106937131*^9,
+ 3.817640125681921*^9}, 3.817640193215719*^9, {3.817666455601337*^9,
+ 3.817666477542403*^9}, 3.81766655795111*^9, {3.817667657897683*^9,
+ 3.8176676742443247`*^9}},
+ CellLabel->"Out[132]=",ImageCache->GraphicsData["CompressedBitmap", "\<\
+eJztfQl4VdW1/3lcAkrbZ/tqB+2gra2tdrCDQ1tttdaq73V8HV77OqHVKqgg
+4lhnVERFQBxRcVYUVBCRSUDmeQ6QQAhDCIGQhATIRJj2f/32Wb99973se24I
+6fT9X74vaM6wz9prr73mtfZPLr6u2196XHxd90suPv6C3hf36tb9kmuPP//q
+3nIp9W9RlDo+iqL9x0f4fyP/q/9k/ZyAfw66/P/t1YX4T8pcdtll9mo/ezX9
+N/6a7z2Zdevw3rHX/2ajt/M7/yActd87F9v/fNDU7mo2S1ZXmjEzS80zbxea
+/i8vMLc/Ncvc8Og0c+3gqea6h6eam5+YYfo+N9c8+voS89qkYjNtySZTurnO
+7Nm7/3e5Pl1g/7eLaW7ZZ2YXbjZPvbXc3PH0LHOtjHfjY9PN/S/NNyMmrzYl
+m2rNgQMHbnJIvdG9uNfMWVFhgeozdLYFBED1e2GeBWJ12XZzwJgL4+n80f6n
+o/3cglVbzdDRy03vh947yvypz9iowFx89zg7yIgpq+2L+/YfiP4nF+gpvdG0
+e68ZLiBe1m9idIQdKGWuf2SanT4GuCEwwPV6rU7Q+uK4leYv905w794k056/
+agugjs6Pwf6dgi2XzKr1NebxN5aaS/tO6Gjf+HfTc8Bk0/+VBeblCavMhHnr
+zZzCCrtYK0qrzfK1VXa09xaVmTenrrEIxhTd6x3Nlf0nmeffWRHj2JhfOhxb
+WDvYb7/PFJZWmR7yIXnH/l5+30SL9KmLy8ySNdvsR94W6rj3+bkyiXgqf318
+uiktr7MjXBdAw7V6TdBkxs1ZZy4VNHSw73Y23R941zwxcqmZtGCjWSyTwXK9
+M3udue/FeW78B2XSdfW77Sjnxaj6rQ4pRGemyJyFFvTxeKJPy/wB6o6G3R+w
+jxaY/QcOmLLKnWbivA1mwLCF5pK+490XsBhTFpaZ3Xv2Rf+dixIEWqwMZk/s
+4FMkgE76zK7GFvPGe2vMn+8Zb5/petc4M3JqCejaYcIfu7e+h72HfcWxb1QC
+Ebh17E5mh2ABa8hnejw42azbXKdIIQ3v3bffTF64EQSjeO5oaR70BLqSEY9W
+UmvZG++QQa8tAqAdFB9Y9ddld8hcop8FYD6g8OC/IGzCg2Fko3TR29t3NltU
+u9uvLsSe7B0Y8Rp9ZX3FDjsrvvLOrFJgt4suIsis58Ap9paQEaYT/SCe/a8V
+j8tKtlnW4FPwqGkldi7H6pd3NrSYt6avBaVHnPNl/SbYrSPwRz/JOecCy244
+Np7HBn6/h49xc9abrnofPK6hac81geF66XAr1lWDL9jHew2aAhKNSLIgpVuf
+nBnPtu8Es7a8Njo3nu0vdbZgLQ+PWOwgwiwwM0Fz9GmPHmYsKwcHd7O94oFJ
+lkZAuT8KgLdfCQT7kmOPmVX6QYUMbIIEfsuQGaa+qUVnlDnM1fo8+BOfB1/C
+Yhyl98DbgShuqKraxuj78Sy5F4FXsLtu97/rZgCuhHXEE5/R58Bhpi8tB4m4
+54BAQZx94j8DIO7Tma4pq7W7BGC8MrHoPxQ6ECSQyuUUaHVWmcP01OdXb9wO
+1mKfh3RqEZbyIb0npCAyY6q9BzEquy86J57pz5WCgAzsU+IcIkY49on6RfA7
+MCDBpZvgC2NX2tfwxAX41wK2V78pK2Ou1h0DcQ429GG9J6zD0R6YLIihpxuh
+hz61uarebiI8JWzfzujDirTK7Q2WMnFPGJNO5mc6GbwJNsbJQHLJDE7S29U7
+mixL4O3eg98D+i4IYHevfg9KBx696sFJmNlH9PJK2UQX3RWv3UvjV/UMjHCV
+t6fwIa4BtjuHWVi01QEjQ54dz+an+ibuElvYPkLT0Vd0KouKt1ratQxffocL
+kxBsnqi36+vrzZAhQ0yPHj3MNddcY4YPH27279/fQUd++eWXzYMPPkhYzezZ
+s+WqQC/aws6dO+210aNHm5tuuslcccUV5rrrrjOPPfaYqaioKAhMdY9OZ1Fx
+pZuOMMqP6eUZskF4WfSFHoERrlTAsJ/6Ph/LJKgfwtAjDvP4mzGVQocTkvhe
+jKwf64yxYyHH+SFokfL2KUSIUCXXEr93PTPH1Oxo+jxudzCDBw+WDzQ0NJht
+27aZW2+91bz11lsxso4wixcvNtOmTXPIEjyaPXv2mOXLl2MOHfBH/Gxn++zm
+zZtNU1OTHeqZZ56xyJOh5QMHz7tF5wbFEcwYoD07pvAYvfzqu0X2EtiE8IWr
+cmKuoyUAPirb7ON6GfMmnchoirQfEWmiogj5OqwAxbJfvu7hFNoGNxx0p2Ul
+VZ9QMFpaWszWrVvxK3/h3wJTVVVl4aqpqbFglpeXRx30+VmzRAG/9lpFVXxt
+5cqVnI67BgSDcJcuXZqINAhD8nDZVccoDUHvuldpCLSCDfdjvTdv3jxz8803
+W6K+5557zLp16xx4IHx8Zs2aNe7ac889Z69ha3Sw/6bMbbfdZuGQZddNkzLd
+unVz4KUCIF+hIBeKWCKyRY08Vi/PXVlhL4GllG/b9d14lf5LlwGbgsTvKQGn
+6u1spgc9SnBwjIJRUlJiWYD8yl/4t8D06dPHwrVs2TILOng0p7xp0yYLel1d
+XeIqYQtceeWV2AbBVdqtc4MifalysamLN31CL0OzBFPD5SdHLYsp8n2mtLTU
+Lg4gwxcmTJhgevXqZRkafpqbm83rr78OOlOIBT/79tln33jjDdO/f3/7/3v3
+7uWE3nzzTXPjjTeaLVu2RHazQkPZuzdxvborvYg677bPE7IE0L24aNgd94rA
+tYLulQW6aP+pb0IH8mWNML7oDAUYu/0Jb0FjNXXv8QrI3Llz7YrhL06iurra
+AohdFlqVlK4N9uOKFSss8xHiNo888oj561//CrzFq2QptkmnQNUecklI5pMB
+KhVl/Vz9AtYgc7/LMu7YYTGGjfL4448TXDAW4Hzq1KnCQdProELHEcy4cePs
+c5WVlW5a/jp0U2wC1wOGLXBSG0oRod1UuctBK9L8rHgdLtQ3sXkeEiuBlpFs
+tejbug4Y9d35G5wkBxpEKByngLRld6R0aAgC7A4wGzAM4Ed4Ykh6Nus8ttY0
+OEjEpvi0Xqa5A+Yr6uf3PcxlbuuOVqzj5+677zZjx44lYUNyv/TSS0ohBy8G
+gZLFssJKBJgagKHF6GhFAtFZurmOgA4ZucyJVsHsmfE6XOCtwyOvL3ZsTugq
+OkvvwUakwgdfQNnWnc6WoCARxLtFmDFjRqIg4cSxCMqtHRWGMA9/gAc5JyRK
+hrnmoVhzk0eoy2NJ33vvPfsXIXr22WfNU089lRPFRCcg7927t2VfFu12O/5F
+PwiLnHgQLn6cXobO21UJQ1CliD2fW0O2GrwP1ARB4N/Te1uq653uiYGLN25X
+xHaCzmMGDRpkdu3aBdZopyVaTyf9KPC5YMECq/kIiNywRCnYKJkp+C9RGmKm
+TW4ejW4eRRtqjtfLMEi5f+X/L9QRlIgz0JyPknkNS4FnjcdqfIguI+7kP4OH
+x8wBLhlh2hG5sAglex2OoQyUQy1LW+Ri/Z2jo0FYQO3EZdieoqNHn1Js51DI
+iW1g+v7777e3s7CdrX6Ao7cG28+OiXl7n2dmY56f0cvcpXBoijl4geIN/Ekx
+Zn/yMXBiGjwDVkIyptOWDihUjGNCUyEESt9FaXndd2I8/1DvwkNGPE+ct+Fc
+xTM8o7IqjgeJVqErlPntRh0GFhh9AUvWbPusXoYt3/3+d7nbiAlqIMA9tI13
+3nmHGkjE5RJ7yar/oEXBSEdd5BdeeMEUFRVZTXLjxo3mjjvuMEOHDg0xfW55
+X/F/fuyKE/TRwcNjTinEGSlSztM34G7iLho2seg8RQr0DfJX/Ipci9+03yUq
+Rs9Y63x9ssQn6OXpaqHBeBD9kzwb2vItt9xi0dG3b1+rLXfWV0aNGmXuuusu
+0717dx8FuAztErLvhhtusCJJjKEkFHA3gfPL0hImuPhJMdtqG2OZrb63AkDp
+vCRwR0FG/1DvwQDg7sXv5IUbVeRnAtCgXwLqeqoLWkjuczoMmANt0Xues5JB
+Yc4c5lIdBsyW/pw5hRWf10ex/3StFIqIhAz3DCwU2qtwdBD32IDwOHESUxeX
+Rd9KmAQ8t7E/biKI6vN6GcYBN9jcFRVJ8FO/uvtZO1eOgCiI1T9kqwjDiGFQ
+f1mM6wdemh8v4IOT4R50KrAvmfAreoOqwKEppNyeFo0n+oIjjtgCxh6Rr18a
+eP0SfRRhCRLMhi07TvRWl9t8duHmDPg7Wsc5KV/40o8CJITxZi4rj04PfLte
+h4Fo4zQF5YQenIrmg2w9C70d4M/6ALQiRDPwwNOjl39RP0FjXswLXXR122H7
+V/mE/RMPYJoUXeOZRqflBDhljURVeaKTdGi6XkFCwjMvCbxOuBGdwaPwDMiS
+f9HbAgRO9my82NHZCiO88zT5Hntjid1Q9HVZG1fdkFZNX1ERnerQtUvHxyzp
+WxRqIuB4mR74l8avCgF+sT4Kfsu9Litysj4KzU/lgJKo06GsO0HNPHwEju6f
+e1DTqwSltrC0Kvpm4OuEnyQKf63Qxsl6mX4zEGFVbeOfE+AnAwez3L1nH0eg
+So5QhQB8uj+Fjmas+sUwvujWv/Cg594FL90oavc3ckKfcqqD/Df6kg4NJgn/
+uprxIdAv0kfhiqJ2K2yWI8CTTAeTqH8K+nf1Lvg8Zfe4Oet/paDL1J0LH6io
+3tEUfT3w7Z06DFR5iguxbr+sl2F4kOK21DRcnAA9tySi0oK4L+uj9MsIn1MG
+4awaMJ7bNJgCOQIR9Wu9B1URI1HxbGjeE30tAX6qT2Am8vWv6KOkS9k5UQj4
+rvo6nC3E8azlm7+ilxFfpWkg0J7mw592rwFvVXWNv1HQBU/WFuW0oDOfkhP0
+lNsfz7+zIvqqDo3QBzmVrPBFCaDDhU8sCWUTdJ+rL1ldqaCfqXcRZ6ApLVvj
+fxV0RKJJTGA2WBELkv30Dn0ZtEWHlRAI54ZYhmobMVHYl/6kLyEsxqHFtOVL
+lOBCJsqOVZ0rsJGVG5VpDXx1oeWGDMhjuSm1X5tU/NUAfggt5T4CFEIZp3gY
+ICeWfd01MAJBpwP41iEzgRGOQEEDaSDYPtWHPi03EZ+oq9/9B72MNAF+VsTJ
+V3ICnkkX3Lp0mAk+ohDIzLOo9bAtVtbXPKIgh1m+tkpB/rbeBSuhfiYKL6dP
+AgO+l67Z9uXAZ+v0USwZucjKddVf18uI2HHS8pE/JQD+yoRYnYHMF1xz3pTc
+z44pjBTqbymZQImidEJ474BbuVg0DVSUYd6yNZUxh+GH6WBVOdm+Qivk9ZQB
+4Osh4Lm4UFe5Meat3PINj1hJgQLRN334O9oEEcqerTUNFynoYMggOBojcNKf
+nBP09EYSGaMSNs29sdNFAPwxAXSKTQRDBUaCjq3O2KnwJAX9DL0Lu5E8Rpjh
+nxX06romp8bAswguYjUR++lafRnrxrwCIVHCDHlJH4FQXgjm3+ujSJWg8jhl
+Udmp3CPqzBSzKcoCWMjHzVJolYox8ESLcdS0kpMC3yTUZBtYLRHMp+plMhms
+vojxP7jZElauMuAVuAkr1RLhc4T1dH0Du5FACQOnMTh+bpqByOUj7eV2iWfi
+JxD+CVmmtXoNWTQABC6g0xRA7DmG1EdNL/lD4PXfBR4VAuQICIh4SvI3MvGC
+sLh+E8TyF50h6IZuSnBk0bRjv0w7Bi8TYi9B3w7RdKfqf8L83TQyCGLPvt8n
+oIn8Q4mLZhZVJxEjqpW6NXBqW2zpXa44Ak/hWzc8PNlsKNsMt/phxyUZW9EY
+h8Ol7yML4We7ggvFl9Jc1o0ogjQhh5BJhlD0v/ooVp9YFq5BI5pCeMCwhUQR
+dyxgYyaP8MzuehkZEFiSi2550XS/okfHdogH0geZz18b8lUSQ4x/9n7oPcyV
+/GyMZr7BhS3y6kxd58MP4h7pgrhcR/g24Zi/6qqrzKOPPoq4VhRiDVyR4o3b
+fdlDiKFh0i52gXS3KKJ627tQXWp2NDEoXLShxmmrb88s5WfbHgbMH6Owz1kO
+Wa1/P6WOmudEHaPsbmzeY5kNrs9ZURHrfn+DGG0nM378eOtGRiCisbHRPPHE
+E/CH516BlMvzE93JAQyLlgALk1D0U/ZCoNLXOmLy6qv0MjJEuZSry7ZzJ/+9
+90KNgoO9zoTYRcWV1F7pJbVaujHUHNsxJks2h3Dx5MmT3fYA6wSgFRUVQTb3
+W4UQEp1yrWzrTnpcmSwoGI+yFmTMrHh/Q5sSBZAZU35UBt4e5O4RY20PBybH
+OEIT44rIZJyXQMDkisAIoT1RuLaKK9KOgVlOENlEAGzt2rUOET179jTz58/P
+SU5MWOa+fuDl+Wq8pZxwFkWUS0KNGDovTah3529gkmGDcILeGgqFhoJNwVB3
+WwKJyWGW3IuRstmu1vXw3FwX9EG6vdpHztHfligtn6utrbXfRiCcuAV3mj59
+ehrflnv+WicJ1yZpQRgPrWRR75yiIlrA1zJxzcg+dEQxXa/Wywh8cKx3ZpUS
+zYcWQSzQhQuFcEJcleil+il2gvOmbPGCdGLrMgrRlgDt4VD0bxQchgSg6gmr
+IK7BNUiiYq8ormmjI7mCSBWF8xq9THMDvF9k92cCn63WR+FcYDam2Ipn6aN0
+WTz6+hIVQ4ceTPU576RJk9x70OeTOO//KGi+nBZViqDRZpb/RlnoYHxRYz3X
+KLUAh5wQJCWyrG08PJVWFTraEhb6fgQrZ2VdBpqFN56hkzqMeCq0AgQRRVm3
+3AWK2QMPPBCiX6LinVkZKiNRMW/lFiqYRAWdRlTZ8Lu2vPZaRQWUdioLUDXA
+8Y7LSR4p2ILkjs55DXTSySG6Ol06bQirUkWFmIOKCuoSVTeECbIk6EKcwIS5
+6wkTGDynW1XXeIqPjHQITohAi4liBFE9HTt7XRIS6I+WVXDBB/oAYHYItYTq
+nggyCkNo4Da37P2ePsrkxhlLy9XTHNFJifIMz/V2A6nAC3jImn468M0qfRTb
+mq7EdZvrCDV0RXq5RW3PDXXK5Zq+NH6VhrpSjrXDXZUBcpphILR/o1IElpec
+F2uGcMCnEoCm/xw7UNb5bL2McjFcRmREaO/XgRF+pY/6ytqWmgbCzRWQ7UO4
+6bP30+xECjDlA/QEzx8uP/7m0txQp5w598BL8104EwYp3UCymBZk+/av9CX6
+tKC/8CVETwiKSN6v+oCmXBgRn7lZ32DgTS2ZT7rPELb+iv3RM9ZGTLEjk4Tz
+PoTLX+rg1i+q0ZWla7bxdUYk5XsKW8TohZ/RJZbkLXqZrmgoYGIffiLwzW36
+KHxLZPkyAsPZxRtqHOHX1e/+VQLUVKSQgCCjEWoKjedcuMZBzVsqNG5R4oUf
+A5mTViuTvYD6sWMTQN+wZYezgmWbEXQwSw4zclpJCPRfeJNn9EymwfzUmcvi
+LBYZhaAz0OfrZ8vXVt3m0TQ3v/Cs3FCnbBWfTl6TUNJRcJhrwkd+mQAyQ21w
+csnuPtcRQlpBFNPiK5lQMzKjms7teplKCyYkyDwmAWpmBAlncFDD6d1N3dpz
+CityQ53CprOPPTtmhXsd60S3dGFplYLMaC6SqrgXhJncoTQCBkfZgkgeMl0+
+HvhwpfcRlt0tK9l2nj5KI7jP0NlRCO7/1tcRo+R2lzXm6zQqR04tibLgHqH5
+EJoYdadHNwwBCE+3INtPElDwL35J+ACTtESy+irzL3LCmhYVKHD9oV5jwB6O
+ZwWUkX7oejTQRDDdpZfpoVcC/1hO3KaQWsF10IzGdFAB8uoXbpI/18ERoiez
+EeWZ6XnUnBAScyFxByhDLqqJ3a2XaY/C8ymy46MJgJL8ARRTL1dqsih2rYiB
+UO0soWY6CwSqAECowa6458WyV6iZSoLN4QVd7lH6RSIPU4Ftuplc/UgC6MxN
+QNY/QQdN36SqzFvT14ZA/xkfhcGg4uPtmaUsUAPjxSW4xLPgJnsCK5IZ9tXL
+KA4kHYocCoG8VR+FxkMWKXi5QC8zBxO7UbD48wSoKWSBXVlaQj1sYmyvwVGn
+UDNfCPO87mEXIemnl1/RN7DzRIod7QiSsPpuVgGKsCK5h3S6qHhrblhTLmwK
+2mLGMQMRAlE2oMu1IgLBQrEM+ilZAGdcJ2skyNUP58RxyoXH4bxgOjmpHApO
+COKfKgg1nqYkLOVC7zI3viD9Sz7caSfp0NHLI+vizxdL62Ief/JZc2mPm+1r
+yAvN4R2n5/YQygSJBUa7X5tUrFiI8xQ5jW21jaEa8J/qNUY94L3i69ZpqrGU
+ZSVVigWm4VXVprmxCEyLiMS4WRdrrQ56crhTx94c9XbIQd3Wuj+iAtW2+ISw
+by33Srma/OGCnhAefqKzgoFHR7EYWXyd9oXoUFEGHtLiE0l/f9Vrh1PEx/Ar
+bCiqblf27G0mTZ7snve9xySKfAV+W3SG8DqSKKrrmv5LLzMjVS1KSxd2AGKG
+GxkLJwydmKFEQrhMMcMkUYQOKedleCLncGrnUjo0vMcX9xltrw8fMyvk7SIO
+8pXUES+smAAChPKJFywDZZdM4qeBEdhngCkfSLX9EUdV9g1rTkY9ORNDTBHH
+XflQHx0oX5Cqo74+fMISe+3SO0dgf3ObeV7VpNK1dOXaZv0Gm2LA3fJjvcYU
+PXDX0OR/rLD4ybpiB3P+8Ph4VqXOn2nQ4DAMLgsHukvHz0cF8fyPMvUNjfYa
+Aq/Y4DBh8OORQa6asaC/dote81Vazo9eZ/wKXw31liDK2FvinufmONpgRrrs
+oigLCWhrgFtwBwmKiIR8QRl247nhhpvMJTc8bIeAwuL5Nx0CZOJHJsz36rRR
+kCZmtVLggPmqfvDQYsR5hGInCykkG27hEfi+lyxZEloZklPGbiysILBMexMa
+ysRuWi4iw/Ae/XBicCX2kPbs1dt0vXWYufTu0WbAoMHwkHKmbanWqlD4/TQV
+0bTJW9F4wOOtsZ7UhphwovztbO68804rRCFrATGYBPZZmqeEsU7ZgJCi6MHE
+Ot3C/YVdKNY/p2/AmUS9t2hDDRGfGG6JHbJvvPGm6XZlT3PZ5d1Nr5vuSWtF
+bSvcqtBrzNITu8Upf5D1PdOJ75/TR9sY/SXZHizfO/ny3SJfozS+2Fq4cGHO
+SbC1C5UYZKlxErTdVMCclLkOlM42NdKYh/Wyn7UpBtkHEhCHNjR47KHXFjnF
+SbQge00MsohYa2OENndiwPt8lm8xjW369NNP222L7YAyuauvvhqRxSD5UoT7
+anDl9gZizhdNtbuaFXOslPI9/WKuPaqXiQ6Y52Il2JZB9qvEF8uiR00vcTYc
+HB60MkRVZjZpvmgq53SwOtDJVwfsZPH3gAEDuC1AlFCd3TBWztMmo3V0/0tp
+64hRviVrtkVZqKDmpxGEGBWxgoquQZYFoCeNXbTclERsQsrwq8QWomlES74Q
+aGtJBj9AHTJj8DeUcnDLfv362XdCJEPTB6orHUIyfYJL5zUCuRlIStk0YsrL
+x3UUOGUZ5JmxtDyEHC6RH0ESIUF3Czo0WZv83gnp2pbkWGg2H0rrD518/cH+
+QO2ePHkysUzVAfpREnbYewaGkue+ILMZJKxCscOyUH8Lbqmuf0Iv0+oEqmUL
+dsmJoJRTz9Hsix7JA57LetKCjcRO/uBoThWAklIt0Qy6wRYUqZmAmXTWJhQR
++qLo5hAtKxMtcdMnbsQh9lq8rVi9NkhLGELKGxHDsByUdjrGKZmV7Z+sQ+eO
+kebV1aDegS/BYYFHsKk2bNgQ0tXoRNnIDB8YmjuauGg7MlWg2KkSsXY59jZN
+UG9T5ZN6Gekb5KCi9yXhg8VDI6asdviAA53ybk1ZbaiBGHnjc9q9A9US9IbT
+IVC4tirKgnd65lYg46ZTANFOmaTNT0j5phZ9lvBR8DMo38M1lAyEQEx75PY6
+HAkz5ev0vo2ZWZoJZdrHCZw8raPAzUZPiejPoVYO5foovLvE/taaBga7mDEM
+12RD054LE0CeoslRcPeKlUaQuf+R56Egs4GBH22Qbx6lb5CrxWIO/xbYLB38
+HIIJckbybVrS2SnwDz/8sOWf2ECwol999VXo2kwAYQQZv4tXV4Z6r7AAEpXs
+9957rxtJNERV/bpY4+Ltt9/O91UmLCPPIxMlHV1+PlAjV1L61ZABRy2JEUSI
+GrdEsYlOMpkwd/2FjpJ9DzyTokUCMMTIoDeqFDKWNtOlELcifJ9l5dDpmMO0
+atUq+/cBNelba+qckXDPd0P66fuQitCf8G3haZY1imzIzihDhWtj855OgVWN
+80A6WyixUlg9iA3MAs6HoqKiiF+HEYfreb7O5OfctQWxtgOk8Cep1oAMhbJb
+JJVLEWGyro3TGRNq3cfVZi0L1Jq6Xc3MfNiquxW8XgzY2DeqqT2ZTtUZy8rJ
+ag42tDo7Q4s/mAb3NPdTPg8qC+QOxwtLCQOfGZ4Tq83leYH/UpkVxTU3QcR7
+EyJTVtF9BhY4eE6uzzAV8OD+YMnVElxhlsNBp+YK+906isPNGRm1ZN4nUmn4
+OhxrLFITCshaXrQvpk0k8pvLe7BF2NlZhEnLm8/7x+U9HD8y8S7fNZdffrnt
+5MX9vtxr1CUiLqTicHkhLgYOHGj/4meQawiG4y+v/5ncy5vf9KGIZdQfMUtm
+UVHvQWJNaH0ZqkXUlWspCg1fp+aKfhIZ65tppDEQF1q4fG7r01r5XIzxTmb1
+6tXwklgWXlhYaG6//XYo5iz8YCsJuFaF51i13E6Zq4POMVDk/e9gQyKGZIzJ
+9x0mPYcWKp/pTr0Hwotljas3bmdCJQtdNKjLrRdaLgbcEfEXauZyMW0I5qYu
+FztswfdGq3NteW3SiuXbJqe18jlictiwYZaDIr8UtCxC1+zevZsr5vfNfGVi
+UciQau3OyvPFpLXLt8m4dqg+Jx9oaN7DtcOSMjwtgjO0dud5jzKE9/bM0t9w
+HrqkaESStXbMH1NJnLR2+eIDp7XyOfI3YFLZsyv9YYYvxLqYYCHfpC/psKl9
+STd06FAn6UKfYSJxLkmXy8VBNsiWimJVuIIZ5nFBZxUMMvkntDx+4KWufjdT
+4Vfr5oTtJiOc6K9Qynm8xOyO2F0aDoSZM2da/YvLdIQSaA5HwxnJt6lTAFsv
+vvhiRqwBGiGn8k2FwM8xh9GP/hFchSRFdeTIkfb/oV1SUW3tt1k4mlWLcoR+
+IskLwwWknwLGNhcQTIKqiojf3AuYLsNBbIev++FtWVRdvU/pXb/qSPY3FxC5
+8FgJoCR7AdtmQfpIzI5ZTJw40U2FrNHvUjhyWklo7Wg6lpWVWR8mkAtygenY
+uZWf45plFbYcqUOHHERUKxlIQzcflguyeBr2u10oCzGTGrEUbASworSaLzHa
+uGJddZSxPGnVtf/LC6JhiuCpi+NUd22jZufhOVLIX9GhkXWkftHEzoYWkouP
+TMKITqVWiRg8FSyGMLIviVi8hJGdUWHMMDd77oqKYd4OZKY+EtX222Iu+WSZ
+9x59UDIPvwqZziDZDiFYz/UepWdwzMxSntPCVDCkI2XBSlUWnvuWvfteVVgR
+q+fCyAwtndDXQ08tQBUuwnpyJllB2RI8/SABTHpBMMKO+t0E0zc8M8BMkxZm
+MFxHYbYmVFX5Srk+ypRMwYPr6YBUcXIMIarcsKW7LT3y+mL3Ok1a5P3L1OLA
+ccSWyraTkqrLRRtqhisKsZpsOYEPwUu7ST/CDgfYFWxlQGUVrCoE4PcDc1m5
+rvr3Dop9jqtV1TVmwcgSaG1UNUIvwwEL2YbvzFxWPlI/ixkd0M+yvpL1pMhv
+YnsP5gNq2vu5CVBPmJtBHZw0ffOIKWWAnLJnBeEWGvi9oaPg7CCMjpwhUWLf
+1Ech16APwftKeFkGgHQKwutvj9Ez1obgPcd7lDqcbDo2DPE9qArv0fGbMkgv
+/MPMZjjp6RHdUl3PTjS+ss70fwsBP1zklRIIZ+KHR2iNCbI5sxAF8G3GoOEB
+JZlTCl0LBZr+Nd7taK+R0oVuWjvkv+KUu+iU4RzHdSTtyjKzho61QaAVYTek
+Md9+X1ZS9f3AwOfoNabFPPbGEteDiLzi1iEzQ6T2r4K7w3/XRsRdQ18oJWiX
+FApB/vPBfjj0FkeDcB3pbWSorF9AmU9XvUYfA7TzEJmdbf+NI3rUbIo3bmcP
+MMb/IM6EGcaJIsGesSEb+nxvkVCewf6Sz49dEYVsgtAYPK8DzaW8WBLnzOgT
+tkdXfZRREA1afkahaKfMN8Zh4BqFxwK377vvPthKwYREYpiR9ZtitwAxjBBe
+1/S82oTh9LVFxZXuNCJo0HwuJEhzYztdtAtFj93QqF8gcYKNCelxhEERh4ba
+P+MNNun1119vDTwcT/Huu+/abKt0FmnIxood3nTxi4lAkFlWsXh1pSY+6UGN
+nf1RXIEYtJQ9e/erKZMZSxNVgcih0oJYMDtjuhSLB20VHEuP/sa5afhBkqBg
+kL4eOEvh24n/yo0xvxZPGCkxxhooqFQ+xhioBO9g3dyIKauJKbpmwFZ2NbYw
+8gKtm9qxiEciq8UrvhMkElntnpLWKSO/CPQEp34WsoDPZGSlG0LAo84Wo6wz
+RvQ/g7aOyKAt/MzQmkwo98JlX9ERePAIIjcMZqAolg4PIUV+jIY2XJDH6bW2
+p6O9LyMdjQmO2HcIc3Mfg9m5VD3L2NkLwy/sEwZMIFl6mk4zVIwceRBGsLOY
+fo+EcpyBxtVE9gKpY1HxVu46Rq1QmMQOzH7SQUV1PX1+bc9I65JBMfCegbuN
+GDHC9iMAJwL7F8mRGGVSygBDJaRs5I6Y24HMs36zRungIZl6o9g8hJwGNbyd
+wmiIHWYVoayDrZ8ZdULMIUZN+2WiwQcqezOU2MNWGH7ut+wAYgL6MNds+87m
+BEyweIRlfeAkIjZf1Jv0+aB8g/2m2WkdGbfs/EiMwV0nnOdTionDzjrrZNav
+X2+rweCx2759u22Zs3LlyhBtEClzMxvJc6moLa1cVx3lxUjc85Qt9ZFkDAJ+
+Xr+QlbxKzPBxxAuJGT/OLzbrp3X0NqSdETCE5ZBqBt80kCn8KKgoMZLADOlX
+JhZFbGtPssXhDQedic1SGri9XEb0wjJOnhUx8PrLNiNXBbuht7ZkUy2/RIUS
+DOu7ASjP9D7m6aN8XVRbR4AJi1ago6RTkSdikZ71YKOSIVNmWzC/8qChaQ/P
+J8gqgDwrJ9TpmmokK/LIA24lXMsLcmZNG0s7n1FIfLehiHzSGT0mVz04Sc89
+SSsV8BeGIGb3InjNvCxeAs2wEWoBEoDupKOs83MPV1Q8o48+rXkS8PKxNSvr
+elF2fpm+Th8symrFkDnTkR6hpINbi4HZtBX8mgu2e8++z+YGlG1u2MMJwk4w
+yEQ/32HgGjinXF8MtCEgrH5CrdBO6PwXNmrzS7dGTivhCOAkXiF4K6CG8ka9
+WiwxQs02ENDCZVBCzZYi4+eujy7XRxlFQssvmcF3EqAu9dKXanc1X66Pkibn
+rdwS+SCn0gGtdBsQ1SPY85FV6bCmGXMlDpHqTij9FJzC0qrcUKb94VDkuuk1
+Z0FNL4kSsHqkfo2ZxbAfZLsP0ctlXk6ubH1Gn6w7sw8rJBr5TcbXBgxbEIXg
+ZZjYdwCIxOHrZIfwarYCZPil2Q7gyVHLhuij9EKgyojhKz9IIVuGZ6j5xrtM
+I2QIE+RRWsKiFjVBpncMZdAJINNz53fAkbVm3j/8FdxxYlWTKlhHceNj0/Xs
+ynRmrijkQcOdaYBYIYrWKYvK2Hp2XaYa+JncINO/SnSqw4vHeTG+owm6BJnN
+JJHSz86qTAoAZxUOGzo/h1CzcEwfJdS+yla3q7kVUFsP0ECXcsdqnANeM2jh
+AuxyTNaMWnhC7Rd7TV640UJtv8U0Wh64gYjElXqN1e8ihCIfSvvi+3XkpWr5
+4nfFuupH9DJb/Wt3A8LGBYfexGNms9w7oeN82N94nXeAU1VtIwHFUUq4jFO7
+EtD5AR2FYTAU/ci2e1gfpVkKuUogGOrEKXeEF+n0XsAtN7zpgBt6n/GkXX95
+FNg4BHTI+djt10aBmEH2Aacs+thgvUwzGr9icXM1Mgi5fjcnyGAfJh1CDtlY
+Ft/k6/6m8/FziGnNOdr/trW7wr8r0P7x2qvW1zykj9KjgFZO3P5+SrnQNXsD
+82gHpeHQEVDEUBabJoYIA7rtKIZe11v5EnsLdPpJDXlb21LhKIWSaRBgnkIS
+A/Wyr34K0yQlsC83XO0845yHUYD5hPDhC+oe6VPVeuhlhorU1X58JkpaV06f
+v39oazsqEC2IZdMQFZZCtLAWRPVdooVMEKH5nvooUQWNVnTg0NlbxEyWqCFm
+oF2SWqvrmrIw07pGC6HetW3ossAN5B82Jv/Ps3v98LWYdhSr1MHQ6ZlosbJM
+EfveorLcaMmUalfrNTq24RxoN1I5ss1dFz6ks6JmgpkJ6fTXy37IXBima5Tr
+yVE2+aVFrGVv6aPOaARncR4ihHk7QpnZCGltF4aELrMOITm6MHD+fjssUZn7
+66OsORUm4zRE6iVikrjJI+3Xy5s7NfAl2tS+UO6l14h9MSKJAwrlVrRLCDSU
+PZx2Cf+hc2KFmRrw9+tl32khFh11ehgQfHr7zmbOjNIYYcwQVujUqcuUxnyd
+1iUK4LMQ04p2BoH+sofTzuDDCit9MfCHijZ2nz46It2r1Jm8NPmghwpEvQJb
+YUtNQ+iAPSKGdpwKYSKGQhipWIqYkM4ZgxyfLkc7n93e7tUvwEXPNHkxwUjm
+rCHDF3rrNe5VnOp0tA7dTtFZMifcxisbN24MMixGozAjtrOdsbSc7a8pjBXh
+x3moseMcrc8hxurayBVWEBd0fGBpBS/Eha8U9tZH6Vqyffvqd8e7ps1B1E7Z
+iqV9WAZIadgG2iLwAEknAiAk+okaplVCxovOQtT4aWyyQ33UZA30EX1jmNe1
+rnZX8z16GW4m5oAJedI5QSYGaUck+Un4I6asZhJEu0dSCzIiqUiw7d69e5TS
+6COeRa8KQWtQZ2LSD0Q7WzGMnb3uWn2UcQ9YYXmxltlCj60Z2CuS5juU8l2N
+LUQdGy7jXN9r9VF6Q2Kdai+FV7vHVTOjZIh8QJ5A6cKPtx1Du5GY8xVAEaXE
+HBUg9LlOwNxHdRT/kEMhYnYCte1HlIiEuOgYdanMpdUOaVktwj+kj7Y9utrl
+oGYfUDtRFBzCjlU12VzY75U+fFLxdfoNloqhS0ECTj6mo1CtApvZXFXfRy8z
+gIrLdbua6c72Ne5ttY3X6WXWZWjj0A/q99ortIofLBJqhiAO8hANW53Tgaft
+9YkgSjzU0uVFUJwMTH0UkSJUX9zhLQFdxM+PXZEdAoIaI68TS1BhvEa0MZba
+GmXN1FTJpfActFVocklSjq3Vman79Ojl2r0+ncuNlsE+fuwIzLpCAIONQ2XP
+ECE+ysUi41Zi/gjC8ew4z/7B2HmCx6MUG4cRaWW4DzsItxNIhC3a6cTAr6wa
+UcAqIeHMSSRyjI5CVqra+e36KOOVT3uRLLpi0buUmIBu6oIHa6s+qGvZhsgq
+McDNkhcD6d7vMBcIEKLCnI8Q7afzYSAukGCHC/BNMfGiW3U0IhO7YWtNAzHB
+PkXI+btRr1HE41ia0Am5ZH02p+Qu1/KDcB/w41OVOxPgPlbhRhUL+TkSuyBL
+b9HnmXICPsGAL7vDjpuzToE+6LCX0NGzhJuaPeLr8ilOmyUii4q3RglAsyIA
+sSp+cMaycnbs9w+wLd+267uBwW/Sa+yBiPBmCF62U4fDNB3r2MrX01hYnwQv
+C1WY4mKPRa5tZKtQBnrFBk6f/yEryOIVWUEemcBqBay5iB2LTvstAsq0RKiN
+oj4SUJ/GfEDtu59UGoDbjdUeYOZIL+La+kc4CK8gmH71qGwQzohi4oWxK6PQ
+Qb4sMGjxWmZPXbyJrzPejgKpBLSy3A10x8bxr00qJjExLxwtg5iSxpopMcPc
+AQ+U8F3jAsnQKb6El+IdngmxWggvYyPXPzItCV6Wv1Ku4HdZyTYeloK0LFKz
+rDNB9vPDCDKog140WdoQyOylDvONrn7ZrBwhK7b4qXxQx5yNTgbYg8IbI2oS
+dLWAXZ2t10iJ2Fo8pYKmLniTvB86cJhwMzULqBYyIdzQ+Yk7kasJcB+ncMMa
+o5UAugRV02ryjzIReUXQGbrB0QcE3Z6KqUqm7KIQ6GyoDvWGdr5o17fqo1Sj
+5UNRAtxsDYQdRw4wYvJqgsz8LT3klSDTsBG72skbErbVQXY0hc5IJsh0SwNG
+IWyCzIDbdDErfJDtIGwOxcwOldp0vbCpW9eYg7Fag74/GBME1NceRfKFAGU3
+dYRImeY4ZVHZbVkE+ObUNUm4ZaI7PkjzAPxHlOIMtzP3lgBzjneZkrZyeyOP
+AWGWzUUxQ04f5kyAWSYHc1cYLAGm7o08WAW4VdHBdj+w+LM6LIiWQWboa9gm
+DC/QWaMnthMlVd4RdW5q8WpSAAjDCJ0Zze7qiJ1QeRYao77IdmOIsvnI+Qce
+WMwukSj3oGb16rvFDPbBq00uK4Yk60jo2UVTvDv0UXcCsVCMsPwvBj5G9NAy
+wLrIehA9jBVgVEVPa+OC7XlGMbuvMh0MvwuLtjJ8TuDBUoSBEyX+2t6p1+jt
+hIIZwseJOiSSi3iO3uzCzcQoC1+UDj+ZiZK/92GsMVpiHsPEWih8InEjpobA
+tU/eLjYTa09cKtHIpRGPkWHCYNfYMPtC4ItEDzPjoOiK7kf0gHNd5DhXQxZ6
+/j5HBZ+gSIELnJweVC3sPGJeE/PBoILKYmUXM8ONw9bxbNuNKGoII2w6jtQD
+aobzV23h63Q9ojb/H0wtJypiYGlSE0aCCgrrmW3o2zPFG7ezsJrCGbFBeqtK
+vUdF6J6YgBuaBNbtcOAAcZNWJDZl4+bveYAuWSBsZoarhKMwbRSbi/MXG479
+BPyYLzvMs9wZka0QPsjGsALk7IuKK/k6I9Oo31J8tCpi2G6n11KRYNU1fkWP
+Zmoz41NA0taaBnZ8yMp1pIeX1Yr4XVtea2nBfo5YoOPBbkJjiAVmqCDJMQsL
+f9vDZb+oz/vcFCJANHdXJQITh4kCL09YxcY3/gFpgg5GBmgW6lF0nwt8lMIe
+RhI557KSqrv1UVpkEGGKjJCyeZKC7vM8tA6AS+hi/QIDP9AdGpr3kI7Z7hwS
+nsEgHM3gHUObBHeWjUC42Y9LcJUBtx2E3XOxDajJ4H0woq46LpyE1IHnrdzC
+AlUaAMAHT49i3rWqvScEoGXXZMb31FDgfP3j0QSFn8iN6C8p6D6vQGYwfFh/
+1HsQgkzktqdQG+MKbF9XTQVil/DD4cNTXcQU7eiRbetjsEfk2hwWblE7CzQg
+DonD2YSkBE0tzIJuLNmpfb3Lrk9DTUMCqugm4smqOj1W3bNFJlxdolWdryMw
+8wsimAFcxj6h2ohNwBK59i1tjc86hpwQ/uryKlCS2BpskWMCRNEE7tVHKSRg
+gSagiq5KMSkdquaurGCvEhg/FBfj565nL0I/RTWm5C4uCLu5You5fuAY0/W2
+4WbQi1MPLxAbOk4pDlri3crKSieOQ86FBs+MfntmaT99lI56QJ8XNZkuIeBC
+NqB2J4qPbaQuwVpFIukaT//idvfCraZnz6s7mL90uxLceoitRGlbxDV0qlLK
+HqiAFFCkuXVKwBF91GBhLXv3EUecMDZDAo54mgwEMWuzgPGK6nrXxYt7CExr
+U+UutuTzFXYR6XHaSydXGwHnBB5R7ZvTal2YNZz5By0O2cXYlen4Kv2rUBrI
+XkQzYhoOrRWcg+cjwuLhFJ0+DGOGlIFIYRXuwG04PLmFxswsZUf1LMbP6aN3
+GPuBI1upHSiCuwtoU+U0qII5F6jQNOv5+6sQITbIUfs+PzeJLL6mQ0HM0iEI
+Xau5ZZ8esBzLKioMCJBg67CXHGNIOCDgAX2e7nJw7SFPDsVUotYwk3y9ErFR
+kP+ZjJZ0qivWUgzM+/VRnmWAg9MTMPJ1/Sb8nfQFYcNg1mzPTcsWmp98gc3a
+GG5EgDZGRpcMQd93yDu5VO08EVTmUKG5alFRkZXtqPK+44470O8xpKlytyCI
+yeD2W9PXPuAROx2FAuOxuRHyDUUIlECqM9j7QAiPF/CrMbwD/OjGhc89zqw8
+Ii7s00dfHTkxW+tu5ckIOFwebYeR7oq0FXghm5qaQohgOAnSgfE1dLZCvgCx
+sdtPWN7RlIAN9n6EnUOmiAArsPEzvQcHEJU16CrYl0QJDwFHxieTkFmCqtVB
+oYPHGbJjvg0wuKas9kF9lKb66rLtUQLwpyqAyPAmBwWAUKp/ovcgILjbwdoF
+Ne4oJPo5UNRL4P0ioaGjl4eAZ3wUpEi8vDKxaIA+yq/hdHEfeDvIaQrW7MLN
+jmxgA4OH8pQ4SkZsR5FnPBGOURYEWAcECHVZybb06ekMPINKaKKjoBfHOxNQ
+Sjy01UjA8uk6FBpGEGTYsQCZff8xHcIh8+ZM8HU6iMS6YfI+jX5YlWIJhFpH
+HauP0hjEh0s21Q7UR+ldwVnoCaCfoaD7MRSczQEKpjxEDiudhUK5PE3NP9hp
+V2PLQB0pdNxw6HBypmxAEFGsvjapeJA+ykgniiIT4P+WfnXywrRz4nmF/3y9
+hy+wmgOHvIMPcBJi7znRJe8M0svF3tnDwt5C8H9cR9/v6ZkwjdCJhpOgbwQ1
+KAmT+LYORTmqSo1lMed5aGVTXNS9CsbdQZFM6kHFI0upmKOs2WShg9aZQcRA
+KR4VfLDUiK48kSVJwH8nADxamQMP5+o9XweFaIIrmqecgZ0A3XCZDdbnIUPZ
++QCce3eOI9eZOkfHAn7F6CIOgDMsAQhYFvcYbxJ2nDP1cxDjZO1YSjiFz/FA
+IRuAMETwtELvQVEke0P2zgEHUijrscAmK5BxQzDh+bhdZHvG3g6hHO8sHRaB
+Wu5w8MBttY2uDy7om55xiBC0T+JZ1qix4TYZN2d9aO7MlfWdUMhPB45HeXNv
+x9DaoZbcfVdBRG4Llwfhc8hWYghqLF2T+BWu68pXD/NkmG8l3KNXw3Pt2GHF
+vLbNiVEMBI0IaiGabkHi0K3FfFJ1NXzUkT3z+SF7GNwA/xMFWJ3zScB0OQiY
+JUuWWAAACJKv0WtH1oUlRMiCJHriAoyCjAMq9BweVzaQo9o0NlwOK9DIa/kK
+Dkn6cLHQ24W9j0Unu8smCBQ1MRjbXofJxHrFhw/Fp2X/Bm5kbta/g/2E98BM
+xo0b58LtgJ8nTpAlfySAC5ZRULPHr/DUmE7ef6igdbClbAUWKpARWvDAQC4p
+KYnY6hveNQyFc5tQHoH/94qTsw/2yVF/m0UubQmr8Vq+QsyzFXBIMqYqqsaf
+rryMJQkjCPhF02v2SkEyfmaZRCfLvvwfBY2N35Oi5cwkbGP1BYs34BJDAy38
+lU7T2OfOoYIjE5krRweQwhIqdk7Cr9DQia2Anp9/6KGHrPwzTs9LWaanh3a5
+MwySaoxPySSDtgebOydVn0bp8tPvKTFgtWnmUfHcUb+b1g3SyJh2qVqL67uD
+gTMLPzpZfpyTGPJHfpkD2caaEpakjBkzxkoD/MWIOtxi9GjD0YboEg/U8AmC
+hwAgMZ1eBSi5UIIYFs03DcIBFQjd3XJRBr2q+Uqtv5pJHW2PvXfKVYob0rqo
+FcNjR/cjIl6FpVXO24DEAapLUE0heq4JfL61J+Wc1srneOALzknG1KFoQKxC
+XMp7VA8QmKT7Hop6c8teXeBQ0W2BVdCpYMKnABPsC60EiXFrnDOGbQBGD/UO
+OgJEDyorWL4XIoKDq8pTflV5NhG0PckgXYSLv0InPf5AAYNDm0WalBSiINM3
+izAntxQUM1GzXWFmW47aOa2VzzE2jt6k4GzwsyF0DivjC3oPSjIT0bnyLL7y
+p8raCaw8U6YQm4Kf+YuthKejootVRrAJABeKsmRLs6buMHb+4WRStK3m+jz9
+ImxTVnzQ8+ZqFgpsija5JLwpZVt3Rqy1O9RzfE5vxTPEG5ZeD/qMGJFHuh99
+VKjzA4dnYZk/taP0eSQYZpPISa2AIbswWBREV+6RS+7naAZAud+2HBF/fTMt
+l/yl4+frF+FTIIfkFm/Zs+/kHMuPwOfOhhYmWbfhsJ/TW/GMv8pQhXzC5RGg
+xqSTwhDsYUgEztXqHU3RUYFJ/7s+D2WPVIteK2j13prjorNXHj0sQsF2ak/Q
+yKHxwQIFE4H5yIOEcvRJUHsg5MG6QCGEJsPeTPTOo2AAGsoXdHQklZM1x8ta
+DFWPVamHcODPtxLukbFjnbIJEFEgQk6mjBALS+Th6RRGEq+Jnej7FXasr2/G
+oeRQ2PGXEwAhwXBhfEAwx9DCYJ9hHDRt9hcmR58Gf2EsuIw0Alx4zVH6x4bp
+yJnCZPHECTou2mQxQcT6zGXZVqyr3qu3Efe6VmUtaBO55DJ07q7/8eZkPxCN
+ckBjmZCbhBjsgQmIzCNR2RzMOFgF3SHwxHH6HLxhiCHDt8rn4IqBTx1P7FNI
+8DePvI+9hotxLXQ8QRd9BQKXgV3461DHIvOdmBt4hk8qquvpEnBAwZ4FP8ce
+YBQCtgsyB5DGxedQ7oW9gSeM7ieYQEhtoocQ7BALCvU61KGFhILcEN90QgXO
+ynXVk3LPgI5wkIaez+Yggz8TOIChSgclUtlwPLKPfnj+MCs43e2o1DtR5IeT
+ZggOgrtESSjFhXsGaLLHPvVLfwSBQySR44mE+fxcr4FsYCMJ3cpfGKKjVaJQ
+u4qiMwGBghi+KsRMkAOX0q/BqEBrXbBhOzDBhRGP9HixPhxomBZiSYh/hawW
+CkXEOpGShAo2vovEikXFsVd4Su5p/UKvYcci0wsNRzraITpbtgU/O7yWi1dX
+WgsD+/CApwdi1yCpEoSG9+GWlt3eUaGAboIQHCIP9oPcJihSBYfo6nblBywr
+AKlgyRHpQPkJfggvuBUEAuprkGiCg1xSHqng+7LC0VRvuna2PMwXEwC3hRUn
+O6CzLh98bXgf/xWLqLMOiRQMTF24VQy7v65I0gQXLNCHYTQCTtlQgpX0AGBt
+WL7puZfgt94eQ2gUU0P0E7nwgpIYnE52y4KPQkTg6xCDsmqXGuKoV9qRHPxO
+nNB3pI0eoGUSCt2AZlQT4NQBxN1QhABDsFfg/X/Fg19a+27M+zpbEkNICNag
+tVUEL0r2rT4g519x/qFrfmwu61bRPxGY//fuP5wc6gPXzg9cSzp8Pd+1M/55
+Pp++0y/w5PzcgP7937HX/xEQtQpHJvPnhP+76l+N/u3/AWN9G3o=\
+\>", "ImageResolution" -> \
+96.],ExpressionUUID->"4418ccfb-99b7-488d-a161-2678f84be87f"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"ParametricPlot", "[",
+ RowBox[{
+ RowBox[{"Evaluate", "[",
RowBox[{
- FractionBox["1", "\[Pi]"], "+",
- FractionBox[
+ RowBox[{
RowBox[{
- SuperscriptBox["\[ExponentialE]",
- FractionBox["1",
- RowBox[{"2", " ", "B", " ", "\[Theta]c"}]]], " ",
RowBox[{"(",
- RowBox[{"1", "-",
- RowBox[{"2", " ", "B", " ", "\[Theta]c"}], "-",
- RowBox[{"2", " ", "B", " ", "\[Gamma]", " ", "\[Theta]c"}]}], ")"}],
- " ",
- RowBox[{"ExpIntegralEi", "[",
- RowBox[{"-",
- FractionBox["1",
- RowBox[{"2", " ", "B", " ", "\[Theta]c"}]]}], "]"}]}],
- RowBox[{"2", " ", "B", " ", "\[Pi]", " ", "\[Theta]c"}]]}], ")"}]}],
- "+",
- FractionBox[
- RowBox[{
- SuperscriptBox[
- RowBox[{"(",
- RowBox[{
- SuperscriptBox["\[Theta]c", "2"], "-",
- SuperscriptBox["\[Theta]i", "2"]}], ")"}],
- RowBox[{"1", "/", "8"}]], " ",
- RowBox[{
- SuperscriptBox["Gl", "\[Prime]",
- MultilineFunction->None], "[", "0", "]"}]}],
- SuperscriptBox["\[Theta]i",
- RowBox[{"1", "/", "4"}]]]}]], "Output",
+ RowBox[{"R", "\[Function]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"R", " ",
+ RowBox[{"t", "[", "\[Theta]", "]"}]}], ",",
+ RowBox[{
+ SuperscriptBox["R",
+ RowBox[{"\[CapitalDelta]", "[", "2", "]"}]],
+ RowBox[{"h2", "[", "\[Theta]", "]"}]}]}], "}"}]}], ")"}], "/@",
+ RowBox[{"{",
+ RowBox[{"0.25", ",", "0.375", ",", "0.5", ",", "0.75", ",", "1"}],
+ "}"}]}], "/.", "sol2"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c1"}]}], "]"}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]", ",",
+ RowBox[{"-", "\[Theta]c1"}], ",", "\[Theta]c1"}], "}"}]}],
+ "]"}]], "Input",
+ CellChangeTimes->{{3.817632402392982*^9, 3.817632515056671*^9}, {
+ 3.817632566288678*^9, 3.817632585257243*^9}, {3.8176665668940477`*^9,
+ 3.817666597156199*^9}},
+ CellLabel->
+ "In[113]:=",ExpressionUUID->"802f97e2-70b5-4c0e-b977-f8a2e505bb60"],
+
+Cell[BoxData[
+ GraphicsBox[{{{}, {},
+ TagBox[
+ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
+ 1.], FaceForm[Opacity[0.3]], LineBox[CompressedData["
+1:eJxd2nk4Vd/XAHBJZAiZK0WIRGQoMm0yFUKUKck8k1CmzMN1biglhOQrJElk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+ "]]},
+ Annotation[#, "Charting`Private`Tag$13125#1"]& ],
+ TagBox[
+ {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[
+ 1.], FaceForm[Opacity[0.3]], LineBox[CompressedData["
+1:eJxd2nc4le//APASikQpHw1KIoWkJSt3CCW7zAhFIpE9spKVvcd5hGSEBtmS
+t805xz6cg2QVkdFSQul3f//9/cP1uh7Pet/vcT/X5eANRz1rpg0bNtTjH//7
+vT94TrdqfwvKLF9lFV2xqNUg/g4xs7Ugze7oCVEtHlBkKaVc/dGMju03+Ue9
+JAy3+zdPr7c1o493xLI5Fc8Aw9yY2cepGYWGJocmHVeBY2LpY3tamtCFIY+Z
+Ag596E3I2v7RoRH1f9GqXmi1ghDjS9VWaYD2lwdc/CTnCslj7t5OEWXIaOe9
+9bX3D6Hs/JGSR8a5yKqkTDh/MAKy3uR/yWx0RyxiGSf1deMgcvjwaye1LFCy
+kdE0dEyEMO//+JYjs4BHvPXipFcicDQUNTr0ZcGmsw81rIMSIU+xreW02RN4
+rnrm3pW0RJjf3vh0n3M2nO89oNTTmAi7ZlrrrqblwOc211GNXUkw77nNyfX9
+M8hasvQ3KkkCVW61D6czikHXKbNpkZYMJ1WsmTY1FsP8U6YG2ffJIJvwgIM8
+VQx2wZRC3+lkKAwom5A/VgIHPj+9OPM7Gb5kbYptelMCufHGvTr8KXBkWfWP
+BuM1jFpdPnvPKgUUVy136mwph7I7Uc7f5lLge6xy/D6xcriZwuHPv5QCLUqH
+/oxqlgPVqfrJ+T8pAMsjsZoJ5ZAc+1PCniMVDubL1JH5K8C89WG0kXgqRO9L
+PaJwohKesc7FhNqlAte1WTlevWqQnbATujieCuXpbU5KLtXgf2JfkfSnVKjk
+u/PeOrEabD0fNQsspkINY6NBEr0aWv7MlDHWUmFexqEj2aQGvGupxeP/pUHz
+S6WuQ5ZvQCX6MrK4nAYBJsPCt26/haofigcOvEwDYRuLXalhb4Ep4UISc1ka
+HH1dJN347C3kVQmQJ6rT4NimeMF/M29hvWPK8WFLGljFPb6/z7YOft+VH785
+kgaq14uVRm0AJo9dDiRtIcFWsxvcra/qQdvzacKMCQmCtCoX9evqQbjmxpCr
+OQme3HWzmeyoh+Sjwf+t3iRB6+ljEt9m66FXOPn+F3sS1E+Hb58+1ADmmvY7
+QvxI4DG0fuRYSgNIpXE53cwiwa+V9meS9xuBaWRI5tMoCb5mKnNffdQI5R9f
+FCdOkiDGRWS3a0ojzDXFX5CbJkHVU9GVgtJG6Ek2bndZIEGNyIHtC3ON8Lnb
+3TJ+DT9fXX1cz7UmuHOz41PIfwQIikx/4JBphrWbU036agRIb1SamFNrhq0e
+5xas1QlIrPSabDVohm9FEWIOmgTsr/b5es+1Gep9jBZuXSHAlatXNulVMxQd
+WihZuU6ALFtp2H7hFnB2FMvOdSXgeX5H09tTLcAfPj141oMAa8FGJmOlFpjm
+3KDQ6EVAwfPzkQ/NWyB9piIN/Ahw2RXZ+SytBdzmDjebhuHnO2HKdnpbK3zu
+36glSCJgKeFUYMK+VnifWCcmnU7AFtr0+uLRVhguLNJVzSCAdXp8E0m1Fbhy
+0nwuZxOgYn5Ivt6/FUL2O/qsFBCglDNE+xfVCn6bDci9RQSEtdxxlEtvhRJ7
+3zvZLwiYSD/0Oq8KH3fmrxAvIWAoY8Ja81sr5Hvlx09VEsDS6s53918rVPgk
+VgZUE+BJ/kQP29YGvpvnFXa9IUDC2syw7Ggb6Ft43BeqI2D8S3LIO8s28NG4
+PjzbhOOzwm76zrENSLNr5y+2EDAyanKG4dsGdX1qvJmtBHxViP7RmNYGV5kT
+90iRCTDVU86w622DssSKp2xdBKyeXX15fbQNlLf9LNrdTcB1l8eq2nNt4Kl9
++sjBHgLH7Rn7YZZ2aFwXDdzfh+8/TpsqkG4HtQClScoAAUWuC8cCVdrB9ElX
+cS4dr/f1H38M9NqBZ1lr3YtBwJOTzcd/3WmH+PyifVxDBJSPe82wZ7ZD7DPL
+kLl3BOQK/rJpK2qH7xN7XOJHCDCrue4QUNUOl8c7Zk++J2DP3BLXTG87HOR7
+7m0xSoBAkGBR8mg7VMQ8TlnAnneW71Scawf907suuI4RQNM9kxfFTAZ92K/r
+ME7AouIuM4kdZLgt6102gd0VOkai8pOhmevzc60JnB+HUsytRcnQ3tonV449
+ukuuaE2KDDdOpt3gmSSA05TqG61Mhol72YKO2JtW1Bj8OmTYOH/FtxG7bq64
+ssCUDC1GO125PhBw7jTrgZO2ZPCpVN1igB3Qp7at0o0MpCtX5ZKxw1vdAqUD
+yVDelM3Zg22yPdavIpoMjrOpDzd9JGDhVfLGEwQZnL89JiSxVXMfbX2WTwaV
+K3uMDLFvfb2dvq+MDDd7nWs8sC/GnS6LqCfDqid3cxz219B5vd8dZGDLtnDP
+xb7eH+tpOUQGiS8tfa+x49wPCrdNkSFfs2i4GjvSIcPo6HcynP/pFVODfal2
+886wdTKcu018L8Ommptd/cBOAVUXL5YC7F3GmXxyvBS4ecyPnIx98FnnnZhD
+FBhb3nneD/u7xozi+HEKqPjl2pljh6l9yTgmTwGlisfqstjTKZOBHhcpkDRm
+M8GJzabQuPD2KgXYgxwl3+N4LMpEj22wpICVh4BMLjYRoWp0/i6+HmP6zy3s
+bafmDH28KHBo63FfQewLkj6jZcEUkG22fsPA66HwcGVuNo4Cvn+Xq0KwN4rf
+DNiXQYH7a3oex7FDRauJS4UU0Nf4uNyL1/vjEVEbohE/T7SlCjN21REVXuii
+gM9WUZ5EnC9X/TS0xoYpIP594jk/9rCogC7PDwosyYzI7Mf55onaLi6uU2Bu
+0OpHCs7H1bi/s03sVLisaFG1FfvFV96j1oJU2Lm6124C5/fgn7VWSQkqlFfF
+Gitjf1Z15FyRoQIv/7RxJq6HqsRNJH9dKlCSM+NVhnE/TBUaPWdGhdxTtZ0x
+uH52DfdTf9+mgkzw0QP9gwRs4P3w1CqAClpSduyXcb0FelSo7npFBZW1t0e+
+03A92ekyKmuooJCYKr8Ney9xf4dRKxViw147CeJ6VqrwDYx+TwXPNgEVOVzv
+CjRpQ9rWDtBdN6k83EGAVLnmaVPeDnDZ8HSNm0rA9oFvNROCHbDryVH7FdxP
+XLs+NU/KdMAJNQ9GWRsBU/nh1FqbDojQbvw71Yjj4bnnp6hLB0hmFVGeNuB+
+G3q2PcmvAw7pfOi6Vo/z0fzgHcukDpiJpATWvCXA52fR057GDqhcN4eTVfj9
+atPHOPk74VpVVRPXcwK07xzIVjvSCUvXo547FRIQbHSC0/dUJ8xObvjQ+YwA
+0jzTh/eXOkHVz1LBLZcApzVTfw/3Tji9bEn3x/28p3Q+kL27E1pEV1uDY3B/
+4pS3+DvcCTapHBw3ogh4ZlGoPT/dCfW+vyvORhBw4/MHq7r1TvBtTlfpDsHx
+TaTcPiXRBarsc56vfPH1lW/RLSK7wH/6WvcZOwK6d+QO7ErtAgfSOY0CGwJs
+GUyfmp92wdk3Ahr/WRNw/uK+83vedIGskOLIiDkB6fVAjZ/tgijCwIlPn4D1
+rYyLZJVuME3S2mqjQMCcJoudgm43zDxjS3KRw/EP1Xv8yrQbtmReAC9pPJ/G
+LsmGuHTDT7/cP84nCXgs/FyT+Uk38L/Ypb3nMAEe29Cw8lo3GP6k/JDiwPV1
+SFvltkEPtHWNGDTRSGDP27wn5FoPHGC8KFPrIQEXm6F0tkUP7GoQqmntIEH7
+NP3KgF0PFC2KN5a1kIA9UoFZxL8H1iV6v+lU4v2H7wt1z/wemK0OPRqRRoJ9
+62wOfb964ILwycEdeP9yu0IhpHqtB04lbxBb1CfBO/u4mYwNvRBod9ywRZcE
+Z/pjI6zYe6H61k9Fq0skqIhcVn/H3ws7xg5GWUmTYDHH6pX7hV7oCKw2ucdD
+AgXnt5zWsb0wmfDxI1Dx/mpSS8A7qRfG0zkLE1rT4Ea8+fEoUi/syox6bNmQ
+Bjml6yovcnrhKPMr3nm8JXi4ckp/oKoXngzHxL15kgbP473Xmsd7wXhBx1rV
+PQ2KVj1sBI/3gXw2z+yefWkQ7vLtyPKpPnD2vnLvLE8avBb//Iks3Qergpk2
+2lxpMGRufN1WqQ+yjhW9dNiE94dkiWOx+n3wrqp80G4uFaQLy/V87/dB9+Mw
+h2s1qWDw5NTbgZY+WN+957z41VS4u97ceJXSB1x1+Wk1mqlQFe492NvVB2ds
+dRjKaqnwWVLvdCujD7za51jVZFOhvrT0RcpsH0jxnnPcLoCvn4Dy33PQwMah
+SqjkcwroV3uX/9SlwewMz2lpnxT48ScOpAxo8HWM8eOwWwo0O3YOuZnQ4GTx
+jsHtDinA8qFYYfEGDb49ZvuPbp4CK/+OUtpcaHD0y0TWYeUUKNo59Yk/iQb3
+KuqqJ7akgFy2n4IBnQYRK2aKXbHJUPOrXHjXMA36uMcpBY+SoVEpz6znPQ1K
+dkRceRCYDPYNJaA8RYObHmy2Qq7JIGzsqvHfEg0UPjnRZA2TQep7fpjdjn7Y
+9I7OV8iXDO2U9ohu9X6gvzFRyshJwvPxQLihVj+UEG5f/6QngZumxNB73X7w
+3OxLM0xKApWXHrZTRv2gEM2DmEKSQJ29Qm/8Vj9oCNPeHbVJgu9iE2rBgf2w
+wVw+v+VIEpTxfKuNqOqHpjxre7mCROAudCgUru0HFuOSFNesRHD+m5j+Fvph
+4sNIZEFKIihMvIv+1NoPRn6x71lDEuFvul7RoYF+aGF5oh9zIxEEpj40yX/r
+h7VfQ+FDexPha2WSy3eRAVgJzLl9IywBasTFfmmIDUBVeiLXHv8ECLWw9c2V
+GABHw4pWqlsCiLOMp+mcGQBOQRsH4ZsJkKFUwR6jNAAP610nCs4lwOFo1o7n
+pgNwTjlbdeVbPDTaSOGBOwDzJiukBsN4eCJSsqYbj89v+yyZqxUPplYS96SS
+BmDycXVysEo8WF2VFFslDYBd1pkh+VPxUMepN2ufNwBFFWn2wZzxkDLPEfKv
+dgBmOw9aBzTHwbCGheLQzABESB63FpWIA5FnopJhcwPgUujhXyQUBzoBy1Zn
+FgeA/HtnztF9cXAqPzUr/McAnJHO2sm/JQ4udP82F1gfAKdRDxifiIWIMMl/
+v7npkJy6Z3okMRYKM33huhwd9M7HFdl9i4Frpy8Lb1Wgg0G8G3X7SAwMOwsF
+lZ+nw7by7Q+LW2NAbmFFnFkVH5dS7RghYiCZISn2SIcOmj9q1WdVYuBlYNfQ
+CWs67BNy2ENPjYZbJ8n//kbSIcF0L5+AbBS82MARahtDBxeh09eYhKKgwdNk
+My2ODp1xfuTRbVGgc2vvj8xkOlCuFqqGTEQC69nDHgez6CBZH3cxNiwS+l7e
+PdH0mg67l1WSEgci4PvyG4cHdDpcPWJc6X8nHC7wkZmyB+mwc37KeZ9+ODjn
+ENn1w3RQOuF/+LVCONiOx7L8HqWDG89aaM+OcKhgrTXS/oSft/hgaW/lI6Bz
+8JzOWqbDp1rNp7NMj0D0X28d5T8GqJxxbYhJCgXRzAjq890M2DpTo5HgFwqb
+n7J/jNzLgIqyfMt4m1AwphtJq+1nABtrpexDmVAwnzvjkCPMAH6zuKOS70Pg
+S9d3zo2nGfCZsXe15lAICPl4CClrM6B7wsip7EUQ7N8alUDRYcDebrW/LSlB
+kLrxoraOHgOeblE93P8gCNiFXz430GfAwkeT69P6QTCvIvdP6xoDZOyMuif/
+PoT8L0abFm8x4Nve178VNB/C6uST0CkfBnB/3hyXMfsAFiytIqT8GBDccWFN
+nfYALC52vAv2xw4S916qfQBtlyNvHAhkQJrsSrNC7AOIE+/crBDKAHtfz+Vi
+qQfAZ6BXcjSOAdpVG3ZzPQwAzkt2ATVPGVA3U7o37ZQffO762jOfw4Czgzt1
+XJn8IN6h7CB/HgP8TuQ3Xer1BaW1700ezxjg3toU8cHBFwTVNbfyvGBAyO9b
+z2kFPjD31j33SzkDdNonE1/uvw9u410rGytx/Lv6xU8ueAOZz0qLu4oB1H0R
+6cVvvKFvUuW3eA0D8t++Ppph5A23c6a11OsY8Onxhi3n4r0g7W/6ZuFWBlhq
+synEM3tCT22rOW/b/45X0Nr6PKAv6VjV5nYG3Av9N/w7ywPOJL22nSQzYOfw
+pJXmOQ/wJ6d1+3cy4Gu+i0uDmzvs2fI+z6SfAXG12TPvp1zB7r3Uw9hxBhg6
+LeaKNTnBf2bl/GcnGEB/fElCOtEJSr/wrL7Dbqs7SFG0dgLQ9PUU+MCAQ+al
+1zQ2O4HgwseIxCkGKPBqNqLL92BHNe+2o58ZYFCXvqqRexeoNpUtpdhUe6dB
+LrW74HZUpl5+jgETr0oGO2fs4fHUpPeleQZItxn7y4nbw1nFblatRQaEmiXz
+j722g4TgrV6bvuP8+/XBQh9swORmh7YzttFqaXOvhQ1wX3W8PYbte4ZQVWey
+AQOHa+ZlPxhQtPnJh+Mqt0AkpOPmpZ8M4Pt8XK6bYgVua48vFWKLil2/KGFv
+BWUPdZ3YfuF8D4v49mibFbB0Xg9pxJbNHTY4q3MTvilxtx34jdfXctdh+wFL
+aNVeeuOMranP3FHibgmRjlXfm7D33pyKWOK1hM+fpoUtVxiw3ds91cnEAr6/
+GckOWWXAK777cil1ZqBl0Z1HxS59Jp+6vMEMSLw585xrDIgpGBC6omwKrPDj
+XCw2QyTq8p82ExD9Jrbs+4cB8928int7DeH1MrFSir2kthi9g9cQfN3VtGew
+V+OFJVjMDGB4RGfp8l8GTAe4MiZmroJ980vl+9hsnnN8VImrcF7o4vQz7JVP
+D0RLXK9AscYx4X/YJl6du1w36IEGj1eDyDoDhnk+iOuq6oKowYYSLey0/UMP
+xSJ14MX5hkcp2KoZupTi41qg93nVuRo7Y6RN3+CNBshy3Hs19D9TgzSWVS9D
+bxWHIM8/BpTPm9iKX78IAcqnjSSxT5RIszbMqoKTasrEJexulek1XTcVyGk4
+U2eJ/cyyNXhswwXYW8616IG94YPcmG2kEtAEhJ0isTM7CpS/8SpCF7O7Wia2
+dsj0yJwqgq2WTE7F2F92LZ/5aiYP4WcoC4A9zaLB9tVVBjQDO992YndpPu+c
+i5ACXTWOiSHs11xjKx+yT0FqUIjhx/8dTyliHqqWhIOy8gcXsG88f01OfiIG
+CzbHFJaw51+bC3p0C8PqNpOXK9iNwu82Pls9AJfFG53+Yt8JZeSaGuyC0Ubr
+sH/Y0rfzefmsNkJZ74Xv/zPtWFgYV/wnBaqR+at17OQYhznBY9uQsFE5rGGL
+V//LG5Xdixq7VQ8tY5OjpvoTvgiiLFzZX7HVJX11yxuOoAYRvo8z2O7mle/6
+EiSQ8BYLxTHsr05MTT9PnkRUi7FvNOxv1++c+LfvDCo9QfrZii22W1uJhUUa
+jXrHalRhR1tP+21elEUa8o2/8rE/y9rdY2GcQ2tux5eSsFNH2XT+mZ9HCyKD
+FwL/d/xQ9GWvfkUkqFc7Y4+9pfq649eLykiP66zoOWzfPCOlgROqSCu7s00Q
+21G51lspTw1FvMisYsUuqRtfKNp7CXWJ/0og43x5+WQy2XmTBurP8vZ7hn0n
+f02/20MT7YuSrQ3G7ujQuCEyr4Wcu+xPyP0vPz3CZK0+66AHh8Zu78TuTbcI
+DMvRRX1fI3/M4nx+JcC9WnBdD8ktkZjiscM+I6aPfVeQeEbA5i5cL1EvgqRO
+vDFAo7F0xUTsKzwVbczBhsjzVPRDI2wFYmKRpmWELMME+d/hepQeirKxmjRG
+bE5jz9px/VpM735/ic0M/ZpU2u+PHei2/PtnnxlqZ95CnML2CMi5n55+HQkZ
+VRYm435wpH6ec57XAhWfKxRUwf2C6eatQaYiSzQgsY82t4z7ow2/Yz3XDTTR
+vRAei52q9uqJt+sN9Opg1fZ+3I+ks7OiP567iQSYJ1yVcf8y9XR0i+yxQkbN
+DzObvuH+qMI9te+nDfpSytWqjh01y2JMMr6NHK78/dH9lQHbZsZkdtXdRgLZ
+f637vzAApcb9WgmxRcZ+8dktC7g/nmZWj9h9Bwmd3OZ3aZYBBE8LpUzWAR0T
+KNtbMsOAS+63JCYyHND+utq6/7D19M/2bN7kiMrYfvCNTOP5Q2kKVKY6ooqx
+Hye0PzIgR4vrUvWLe4g7VLWOPsqA2U+9NtrnnNFvpnOiYthsQ1Yso3ecUdnd
++lHf9ww4ELMnw5bkjMq5HA7uH2HATPXpbI9lZ9QdbLVNfQjP3386+x1KXNBd
+2Tp/bRoDjp1JOF4n5IaoTx+6hvUxIEggaHr3FTe04c9ACfQyYDl8iP/eAzf0
+1fMg69EeBp5Tm7/sHHVD8zlXeD51MIDVk35BMsUdabQIdW3H89Xw4we28i2e
+6CBf9WWJFgYU9Icf75fyRN2WwzvUm3E9sTNd+2LliYqrmzx8Ghnwz6IxZ0+D
+J4okThR24HmdXy5/7JyXF3op4l2wF8/70uNqFtUz3ijJsm7HXbx/kA6Npeg0
++6LcavRLLpcBcHJFr/SnL3r2OIq+Be83DGK1uLaL+KFQtpjw9Cd4PyIz9afy
+kR/Ku3ekvigdz4eJEaJeyx9Z+ZRb2sbjflxpf4Z+JwAtPJL2s8T7o9ukcSn9
+7w+QvsXlkS/eDOANOnw1iz0QFTeKSvl44f3D4OWvnwQD0Tkx7ffR7gzI7n8f
+Z38lEFVFSKwQ93D/uEL+rl4WiCTD1Wz0rRjAs6n0m6HbQyTmO8mnoo73V7y/
++eOWghB/jcQ06SID/hZwuP3YGoxO3Fx6u6iK53kbha57KBjVrcylxirj9aJx
+PWPSC0b20pF/auUZQGG6znT6VTD670+sd5UEvv9KA9F7OwS9SC/Sld2B49VU
+ThocDEX9ZsKfdbnwvNg541X6JRTxR+yOs9mG8z08uu8RaxjaJXqHPYoNx89Q
+YPTI6TCU4tVQWL+RAfG5MHY8JgwtXD+ZTflGB8XK5VSzC4/QoJKwvW0PHUZU
+AnR2F4WjG49cFm266CCy56/XMIQjcv08WHXg7wGeq1Kp/eFInMlCx7idDvZC
+f4xY18ORavclEYl6Olw/eGL8uU4E6ooXfRHyig4TIm9bD/yMQMIgsOcH/j7g
+Mn358KFsFJI/2BnwJpwON446/inWikKSrjlnA8PoIDVBTRi6EYWK5mnx7EF0
+WEse4+KLiEK/RKT+sd7H9z8mOmj9LgqNtm0ufnmbDmyig/5s96PR6vMxp2ol
+fNxhes6jIgaRhlhFefH3zGyZ5b1n1BgUsUdkyvkcHQT3PnjVNx6DbtD0rISk
+6aBw6KVwOEssGpcwDHE8hq8XVFqbezwW8QXvNM7jpQPH+QCG0sNYFP/SRCb5
+8wDwGs2TmY/EIVOVHJ2yTwOQKXRB/fTJOOT5Zdqu5+MADMFGcwv5OJTja/iM
+aWwAHjxPl3+pE4eoD6ZUtWkDcCl1LEzAKw4ZHy3nfvQGf08259qZkeOQy0/B
+Kb/wAQh0vh58xCYeeeumvokPHYBu3mSn8/fiEbecLz0naAB2C7MK6XvFo68V
+SUNNfgPQ8kCp3zUiHt3S3ciz4DwAcbN7jke9ikcXdzRZzJsMQM+e41ICy/Go
+p/br5YyjA/CyUa+38WEC6qIYFnsfHgB292PrjpEJyPSWhLH+oQH4pHGock9S
+AjqsKurJwo+/V4+LtN7IS0Cez0zndLYPQLralsPU9gS07XdRXuKvflD66G38
+gyMRrTcu3etu6Ie0wS2rifGJyPlIll5wXT/MFv6oyCMloum8zeEyb/rBpFZh
+riw7EXUusq+ml/XDdRO50tbXiSihcHJUO78fFgMgDvoSEWsf/Y11ZD9MS27Y
+wcKdhB6M9zbq6vdDv/8xS1pUEpqy3mDap9sP+cKzlHtJSUiNeU5dV6sf3JYC
+3NkfJyH2yKWj6mr98MIlM/Lk8yQU0TY4LyLTD1O8e0P0KUnIaXEqOIGvHx44
+PZWdYklG9DVuFrFJGgwM9/IKeCcjfyH5EOFRGvC/o7S9f5CMfm/z27F/mAYq
+eVK9yY+S0ZVDGqpsfTSgpTLPrKYmo1LDHUfbG2jQ7zj0ObwyGe3+hGifsmig
+fkfSqf1HMvLJOlbz0owG+/qG5wpvp6DPkw5+dsY0IJcaQbdjCjoy3a4hpE+D
+usGSgi/uKWjr8bbN8Ro0uMsorREITkH3KfO/9OVoIO0mlaj2JAVtPDJS7b+b
+BuLm24zyBlNQnu/lPpPePjjOZteWppyKTPIaVIU7+wBVtS++uJSKprU1WRfb
++yCDTkt+q52KHgjn3vKu7wPtUP0b3ddSEWXY4Lnfqz7wkHpfVeuSivLuNl4+
+E9UHpWrXf9Rmp6KA0zXDJmp9MDC5Veji31TE5TlesqjUB9+6jE6SmdKQuzxf
+f4BCH5g5zkSqbElD7Wr9K5ln+mBfkY6A5M405HtblUI+1AfT/zHiO46koRN9
+J/2p/3ohWnWD/MEraeitqrhMaEUvXJ5UviqRk4bKfc0eB5T0wrr/F17/gjRE
+Vdq7wfN5L9x+obCb8jINXfSQarDIxuc/zWnVqk5DCY9WTuyN7gWlF4VPuLvS
+kN2Vwk5x615wVg0ID/yVhnb5VCz07OiF4KZy1p9KJBTtbnwonKMXbqW+dnmk
+RkKC/0INFTfj65v3jfBqkFBmTeibgj89kDjsTwjqk9Ds8A7nG596oJO/Pf7L
+LRJ6W6+T5lLbA8/UyEXWj0joxkGvnl3WPeAX7/6yjExCSkPv0ufMe2BZ/qD+
+hU4SIvdHFNSb9ECkkUBIVw8J0ZJpD611ekA4uC6gj0FCFFUmeZJcD9garxWl
+TpGQhsFIzasdPaC7Xc+DbwOBXl/cGWnH0QMZL4eYr24iUL1fyuNDm3tgkWG2
+KYSVQEV3uDYdXOmGBCqn5hAHgSiZnKTCrm6485L1k/weAh23YZ3i8eqGkI9N
+A78kCbS5gS/uikM3WPqkVPSfIpBkdufbqJvdcKRS98tzKQI5r66nLmt2g9Pb
+czc05AnUxJRl8ESwG/xMTQXV1AgU4vxuUYPaBcXztFeipgSyVSTl6NV3gQNH
+xNUX1wmUnvJj+Gp5FzBxGEiLWhJodciNrJXZBVPKfyq4bxHIs6LqxW6XLuCG
+29YZjvjvu84mMO/tgr326RKZDwjErbcazs7VBXorrFdqHhLoH9vew9uYu+BA
+usBgdzCBLvA6qW5Z7ITfG56szz4ikFO+73F6QyeU3nmaOBxHoOsZ25/23O6E
+Tuu5p0VZBLpmm9eTZdYJ7NUXReyzCdR1O+3JXb1OeDbgtHQ4h0AHWFKO/ZXr
+BHk3j1sR+QS6Vfp14QdnJ1DfRT/geonfd5p/+/myDngRXG2wqYZAbCshLsPP
+OsCTq7bD5g2BNp3X9HZ63AHvZWbcWmsJZHHnm1NSSAekTfObOgNer7OpbOVG
+HUAYF+sENROIefFz6GnNDrhLeyVd00KgxkFSQbEiPj856+LnVgLlXOZmZIh2
+QHxd3bA0mUA78s2H9f5QQThsKCumk0B8G9NdKr9SIdJF80lyF4GImDPFu6eo
+cHY1vC6lm0Cs6gE7ezupsG+Ndimsl0D+p10D92RSwfhus4/gAIEuniRJ3Uyg
+wpt/BfKr2NFW/NEFoVQ4r6bE2UEnkM8tORHxe1SYC2KeMBvEzzs+sJFNkQq5
+7if2y74jUOTyeYezp6ngeGdQ/is25Tb3tKUIFaIo/65kjhDottHMcuE2KggV
+dVrNvCdQO30+jryBCobsSyaBowQafWl49uMPCnjHkJR4xnB+2lvkbBumQDLj
+zpjwOIFsdNfv8HVSIODunrin2AaxTEikngKO3RrH9k4Q6M+Ru/wSpRSQvXrx
+9SNso30Km0/kUaC7RGv/d2w7G7c/x9MoYPg32/HKJIFObtv5VzSSAvJFYTkv
+sF9y8LIJ+lNAM0b5zYYPBJqwfiDA40yBnhHe1xrY1N16yszWFMg8rB4ah20r
+/MjpiyEFzpofkOnGbog4XERXp0Dv4EgLy0cCdV4W/Vp9jgI+Ku1iZ7BjrRPP
+p0lSQKpSxNYMe8uQVbrrIQqsZir6+GFL5xGbNP6jwMde05up2Pyd0u4H2Cgg
+51/PV4RdrSm/tLhGhkjZsrwKbLYjeb41i2Ro/+X/rwab29SdO3CCDPqb7YWr
+sHtmn79W6SeDkEDDfy+xlXsvXWdpIwNZv703HduBW5OnoZoMyfzUq0HYWi8q
+GJ7PyZCruTPDCvvDk5Bc8UwybOGfKzqHfeJrrd9IHBnqDz324cI+lWp8MyyI
+DPMmrpzD+P3n00yvSHqQYYiv1vwxtunPFq1+WzJwCNc7GGMHFCbpu5qSwSW2
+Q4YT+1o11Wa7Nhls3x+DNzj+pz/avZQ/TYZdfwW/b8A+taF/suMwGe6X6aan
+4vX75PZU0HgPGdb/27p6BNvJwa3Zer0deoYNyadwPqh98zg8/bUdPh5/dPYl
+zp/+zvGEGx/agcL7QO8g9rbEqVjt9naIBuawbzj/an0fCNTXtANv8IlMLewD
+DQ/fiL9oh7mZW6Y5OF/Z9d/sXI1rh/q+E40yOJ/jc7/2mAS1w16XOzZewzi+
+2pFple7tUDr9s6hkCMez5JeG9bV22Fd7iYNj8H/9pOVshWY79GvXCEkwCPTR
+a/XYpvP4enspAxdxPZ0qSJGPE2qHwr971mz6CWQsnzHpu9AGSpq0Q5o9BCJx
+d7MQ4224f633qOL6PSfzq6KM1gZ53EX/ZHB9v/YQaXpf3QYTOsIjHB24/1Xz
+PGQNaYOsyKU7Vm0EyuZe4dni1QbU4YB/R3H/uFHbJ8Vq3wa6u7vZZnG/4dxo
+K/hbtw1Yzhn6Xmkk0E7tg09e87fBo5lXNUO4X8WIVT5N3d4GzIYfRu1wP7M3
+Uj59f1Mb8JwUd/xZTSC9pwr/zsy2Am/Gi65fFbie/9bLB5a1wqVTGlaFxQSy
+blnSd1Nvha0FIw003F93P/tyVuhcK8w8Tdqyhvvv8Xfj+d3HW8Gn5ULevkwC
+hZ7MO8HH0wqSFy5OXCQINJ1bOx8x1gIWry6euJJAII3M3RtbXVrAOOwKz+FA
+HP+RyOyctGY49JE6+sYEz6erts/qwpuBwzkprdeQQHkcntn995vhxyFH3bGr
+BKpSEHdZMmsGr8DhkkktAgUWfAnZJNgMcYevb3mkhPtV2qSHeUETVHDMPdU7
+guMz5enPWd4I0wm2dl0LJOTr8Hhrfm4jvJ1kfzE+S0Le0ksRcsmNsCLSUf0Z
+z+d90dK2Rh6NINh3V2z6PQlxnOdLtpRphB9rAcreeN4/rtOuLqltgF6vpc88
+RSTkethG+FJ9PaRs69DabkFC8X7JPoXF9aDznvc/yWt4/1FjubD5ST0s1HE2
+qxmQUMI76r7KB/Vwtudi13W8H6ltWyyaVqoHMe2drmLSJGQTPnqS5xGAWWNE
+2zlOErIoKNejPnoL+1keVMmXpaFnEVUyvS7VIJaUet/gUyqSXr785N3VajjT
+05Q+Mp6KxCV00NiZavC5o2p9bTgVKa8X7u9broKgoi0zSp2pCIkU2t26XwXv
+ZROTq1+nIiU8oC89qISxOLeCCz6pKJ67OG85tBy2HddQobClIl3JAfpyQAnE
+2OnfMuZMQeoCj8jRZiXw97xGqQZLCrrda97AL1sCT1yCuM7+SUYbPdzqD/0o
+hgvJxV+/ziYjarfin26rYljfOHhypTkZxTq+7deLegnx1ksZJl7YjXqK9VsK
+4ZzXbxejd0ko9jTzXHV3FmxKCYr78zARBTSIsRvJWiJNH/br0ZlxaMS9QGir
+21Nkp5WhGh8fifYWycWyi5chv70Hgu5IBCGmSfsBPdM6FEeTv1zq746+Hyg2
+o4TXIcU9tnu2imE/inNUr65DGvOX356luyHmSQlJq/8Ayaw2eHOJuyGjbJrQ
+eg8gtZgBn6oBF8T8enJh6mk9ajFmO7oo4ITKfwqd/8TfiHx0BpkKj9kgFv2j
+GUVnGhFnmvrVIK9byJDy57yrZiNaKop7urnFGrEvb9fn9m1EkeoKImzXrFCE
+0WLFg5FGNPEz+sxyoCXilPe1PJbehFh+mgv/CjJE4WvOHFJlTWhc37O3ZYcB
+2tJ79o9SRxNKGRocnn58FW2vkyi0/dOEjsqgMb4yXaSQ1Ys+mzajv7Lf1V8V
+qyEa1/kdPG7NaCmixeoGXEA2Sb4iF6Ka0W9zp+zKDkVETFoLvnrbjAjb336x
+rWfRmcLtm+cGmhF7peoS69AJ1B8aLim22IwUtTrlA3tF0P37tAxH1hZko89n
+tUbnRf/v/33l/w+vow4j
+ "]]},
+ Annotation[#, "Charting`Private`Tag$13125#2"]& ],
+ TagBox[
+ {RGBColor[0.560181, 0.691569, 0.194885], AbsoluteThickness[1.6], Opacity[
+ 1.], FaceForm[Opacity[0.3]], LineBox[CompressedData["
+1:eJxd2nk4lN/bAHBJiWyh9C2JslVEqUg4CVnShiRFsiVlV0T2LUX27LLMzINk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+ "]]},
+ Annotation[#, "Charting`Private`Tag$13125#3"]& ],
+ TagBox[
+ {RGBColor[0.922526, 0.385626, 0.209179], AbsoluteThickness[1.6], Opacity[
+ 1.], FaceForm[Opacity[0.3]], LineBox[CompressedData["
+1:eJxd2nc4le//AHClFAlpF58ispVoGd0io7KzI4SMihCizIaZzFIk2XuP8whv
+VITseY59OOcoI6VIid/9/ff3D9fr8lzPuO/3uq8L33VnPduNTExMdfjH/37/
+93hGl/RfH6pp/b3IxedXrZHwj7yJtQ8pdOyx9A2RhvObS1v0F3uRV/p70weP
+lcG+dwt9rakX/StpLLjncwUGLEw2PXDpRZniO3tdb1uDhFji2P6PPejhbJPw
+bU036IpJ5ppy6kZzrqYp3tsfwhOTi4TNyw7kfMeGY+1pNDwf8/B2CfuAzNMU
+lUdPp0CZonBxiEk5SlZ5Pc0Ukg3J7zK/vWl4gtSjHmZ/aCiEcMrREhe1Ivi5
+pUhSpKYEgr338CyHF8Eje3aR3sYSYK/PbXDqLgLv4alez84SyDjf9FHGvBi+
+BFtfyJ4sgVmuhtSDriWg48X7qoy1FHZNN9bqvywDxahPI7f1S2H23naXuyMk
+SLr4pv7OVCmocqtNyiTVwf7d3vPT82VwQsV2I3NDHRj807RxXi4D2ZgA9mZa
+HTwVswyaWy+DHP+yCXmJeiDbz5M7ucrhWzJz5Pt39ZDeGdslfaIchJdVVzUG
+GqCZOWbnLbdyOP/HaqfO1o/A7vtDoeBbOfyIVI4+KPYRemPqs8SXy+Gj0pHV
+Uc2PkHP4MCNlrRxgeThSM+Yj2Bu6TXpsrwC+zLO1zbyNsEaMr1aLVkDEwXjh
+c1JN4NBX1dRgXQGcV7/I7dVrBuc8m/s1HRVQntjkouTWDEjscuSB/gqo5Lk5
+YhvbDIMdf746D1dA1cAGw7j+ZtDUifBg/lIBs2edPj83bYGx2ZCt7Rsq4UOB
+UvsRq1YQHUAiP6Qqwd+UInjDvg3u7h/85xteCYJ2lrvig9vAuctanBFVCSIl
+uWcastqgylDxk9qLSpBgjuZfn26DrYeWNX68rQSbqNf3Dzq0g+5oXf5sRSWo
+XitSGrXrgLdSp754jlXCNvPr3I2FndDfG4m+i5LgkVblvEFtJ0xHc0zxHCPB
+29vudtTPncDMbrVbSZoEjTISkt+/dEKa+gd+LzkS1NFDuehHusCyQ5/l1WUS
+eJLXhCVedIFQ8d7xTEcSLK18yjp+vxt4K1gd/qaSYOGNMrd+SDeUH0msNs0k
+wTM3oX13X3SDvH0klOaQgJQqupJd2g1qssyDesUkqBI6xDU30w1vZCddVGrx
++9XWRXVe7QH3Gubz//pJwC9En2Q/2wufRpT3AjMBZzYoTcyo9YJnZoRYBAsB
+sZVe1EbDXiD92/bPgJWA/4gHC3fu9kKl2Y2RDg4C7nJ2ycYV9oJinlD1rf0E
+yLKWBv8n2Acz9mGnNSQIyMv8/L5Gug946LJtmccIsOVv2Gii1AdT1g6nV6UI
+yM5TDH9o0Qe05iPPnp0iwG1XeFvWyz5wvaDqbokI4JcyY5XZ3g+Kqefs8rQJ
++BkjHRhzsB8uq/z4FadLwNYe+tq8SD/sluu+c+8KASz0ceZXqv1Q/JxTStiI
+ABWLI/J1fv1wns9ys/Q1ApTSyD3rT/shpf/KoSkLAoI/3nSWS+yHuXtOUhFW
+BEwkHinJIPVD5zjPhTYbAshJE7aa3/uB61GU5rIjAZsbPXhur/dDpOac3p1b
+BNxrZvQHbx8AWbNAM+ptAiRtzY3KRAaA28s+sPgOAePfnj8ZshqAVwk5yqvu
+eH1W2MyGnAdAZOpKnIInAcOjpicHfAbA3dJy2fMeAQvnIhYbXg6AzGTtjwFv
+Asz0lJMcuwZglcvx+wU/Av6c/lNwbXQApr5tu6/gT8A1t9eq2jMD4Ovyifl4
+AAHuM1lsRzcPQoZQzF7mh/j54z207DODUHo17KbVEwJy785JBKoMwrIZzw7R
+ILzf1xZXDfUGoQ26YRb77YkPx5ZuDoKKUpWCZQgB5eNe02xvBiGWaBtdDyMg
+nX/Jril3ELxMJxbiwwkwr7rm5E8aBJOcU3vEnxKwf+Yn53QXfn4+8UYxgoDD
+j/hzn48OQlyVC0sD9qyrfNv5mUGwF/F/rPCMgB7dkxlPN5Fhfriyiz+SgPnz
+u8wld5DBJvP223Ds9qCxV628ZDgyFh2xgO125IWFrSgZrt91eqUVRcDoLrnc
+v6fIkJyo1piBzWHW6hOhTIaAbtudK9jMK2oDvDpk+NzH9VAlmoDamaLKbDMy
+GOVG7gnHVpBhOXTCgQz/EiU6PmP7d6ttr3QnQ/DZ4wVbYggIbXQPPBNIhlT9
+iTJ5bFOuSN+KCDK0sYRO3cSeK3y+QSqBDDr5bufisFXTQ7ZlZZKB/yvjPQn7
+xoJ94sEyMnxLPe7Rj60eJVMWVkcG6uZ4w3nshaBZvd+fyfDJz/4GUyzez97I
+e1ZkMvR/nM1gx47y4BNsopGhpNN5/07scKckY5EfZDAbkYf/+WL1lp3Ba2QQ
+uP3mJQd2q4W5/iQbBZ6qTGYzY+8yecMjt5cC2nf0v//Az+PLarv57AgF5OSQ
+yzD2D43p8+PHKHD2zIJoHXaw2rckCXkKiCiUHUrCpr+gBnqqU2DEelDHA5v1
+XMNcjT4F2NhyQB17/mzEGJMVBc50edzejZ0QpmqseJsCJUnhV4fxem6XnjF6
+4EUB54SzYa+xLxx/MFr2mALcMp//GWOfe7gy8yWKAr37Yso4sDeIW/sfTMLX
+K4wU1eL9CxIlEi7mUGAXeWXRHntKWNQuoYECp1Knr+TheCAJq+yFdgoMRpq6
+qWDr+2pojVEo8M5tdHQQxxdF9LDu7kUKVHlfezOP4+8ealKfX6OAleSgjxv2
+n6h/X96zDUHhew36Dxy/+Qt7RWz5h2D613+mEzi+B1f/Nh6XHIJH11bsdLC/
+qjpzrJwdAlbFT5uqcD6QYplf+ekOwa5ctPAgFNfDeIFRBfMhYJq7cb4f588u
+Sm/rb/sheLrP/6goNtPeyVQb/yEYUQwursf5FuhZobqrcAj2tf6bK3yE88lR
+d6CyagioyXUbRnH+Hki4v8O4cQj21t0vZcFWqvAJjBgZgmfR1F9qON/P9Zwx
+6tk2DG+Hy/eH+hBwqlxTxmzvMORkPlB8+oAArr7vVRP8w+BlpMsZdh+/Xzvj
+A/XsMJSVSOd4eBFAywxtrbYbhpvZ+r+34/r0597+X6Juw/DpwoaHdDdcb4NO
+f4rzHYZYv3EgXHE8WvDdtIobholMTQMdXN8e/MpN7WwYhuiCZ9znbuLvq04c
+4+AdAZ61kZ88lgRo3zyUoiY8AtOKI3Jvcf19bCzF4SM9AjsePb542JyAV7Mb
+J0cujoDB+6UaDlMCXP6a+Xl6jIDhHpdj+bied5bOBrJ1jABfoYThdxVcnzjk
+Lf9RRsCvgcL1V5mALMsc7Vn6CBwby6xZO0/A9a+TNrVrI6CvoP5zUQGvb2yL
+vbTkKMzZKWx6fhLfX/lGv2X4KBzKHhOoOkJAx470vl3xo+CeltVszUeAw8BG
+xofUUeg+onV/yyECFNUPKu5/Nwrnyqa3KRwgILEOWqO/jEJHzMMdVlwErG0b
+UG9WGYMZcoRwxF8SzGhudjynOwZW4pG25N8k4ArSe11oNgZynV4t/y2RgGXs
+ouwTtzGoLu/hjl8gwWvBPM1Nb8fg/mu9tgs03P+3I4ry3zFYQ0z2wW0kmD+i
+rWJvOA55uqunP7wkwa29H/Y/uToOnCtaz6Ofk4CT1ehMiuU4zPQNbjeLIcEn
+ev+VPsdxeL31jNZ4OAnYws9tEsJ7t5hDyBX44fnDJ//SvcxxqLkmucXKhgQH
+11idupfGwas7yFAczy/2FeeeEH/HoV0dJVoeJcHQrajpJKYJqJ5oEo7kJ8HJ
+3sgwG7YJCDzPwTNxgAQV4cuXhngnII73U8ylbfh902wKPS5MgIv1jW0KM5Vw
+zrWGwzZyAoyE9ynlZOL5iqp12DtuAqSfHfo2k1IJ16Mtjj19NQFCw/+pCidV
+Qlrpmkp+2gSsJD5YiYythIcr0gZ9pAno7Nyawx9QCXnR3n8/jE+AwuEffeom
+lZD7x9OO/xgVDn889ih/cyWEun0XXpamgqaC1U51pkooEf/KaD5DBer2juCR
+PxVAtjC55qBEhcimPxIr3yrAv1lSItKACuxyY88XyRVwJqdcz+c+FXYzC0Qs
+5VWA4Vvpmr6PVFA7+dVbSbsCbq99aNBvoYIGS3CtycUKIIV6D3a1U+FY9We9
+W8oV8PW4nkzjABUuiLy++/B0BdSVlua/+EKF9brMTq9D+P4xKHOEfRK8I189
+Dp4vBwPCu/yX7iTu5webZUPKYXE1Ck4ZTkKb1q9iCCyHD85tZHfTSfjddv+o
+4oNy2DxZdG7++iRQopiqpJ3LYWVdpKXJbRISa7cCTb8ccnfSGLxxk8DF10H1
+OFQOcim+5wz7J8E9YTzHtLgMqpbKBXdRJsFxNfdXW04ZNChlmHeOTMLbDYWx
+CmllcKu+GJRpk/C++X7fjhdlIGhyV2PPz0mYkNn3NOJBGZz6kRnsuGMKmJ8J
+iFNUy+BTy6ewjktTwG6ssvBhsBT3x0OhRlpToNfuW/2xqxTcNSXJI7pTYCen
+wPG+pRRUCjwdaMZTUH3BR720uhQusVXojd+YAv1uf2XH5FL4ITah9jhwCjY8
+bSuUtiuFst3fq8NIU3C0SvEy+lEC3DlOOYLVU2CaRV048bUEXP/FJtbAFID+
+GMFPLYFzE0MRjMYpYJGdrVnqKsF9XS/3SN8UxHZ4NN4pLoHDtMn38t+nYPHM
+9oQC5xJYqIxz+yFEA6Ppt44WX4qhSlxsSUOMBhTndcuh8WIIsnTwSZekQZGj
+9Lsrg8Ugvnn8pc5JGvyVk0s921QMSUoVbM+UaCDsmehNSSuGoxEsn/PMaHC5
+rXe7q0UxNNidwg2XBtvmjVm34HPfW6Hiv7rRNHz+YZbJay4CMxvJO6fiaKAY
+ru6qVV8ENvrHxf68okHk90vHQ4uKoJZD78utDBrUkGfGRyOK4MUs+5P1ahp8
+rugIXbtUBBQNy/PkaRrwvzngphJYCEJZoseDZ2jwfdt20aE7haDjv2xzcp4G
+nq9vut20KATpzPjk0EUa1F2ntdyXL4QLHb8tDq/RYGMb/8zVpQIICz6+/pub
+DqnftaZ4HAog540PXJOjQ5KV93XiUj5clbksuO0cHb4LpggJns4HiqvAo3JF
+OhT1pLKHHckHubkV8U2qdIg94KemspoHzweOi4Xo0EFas2DFLT8PCgLbyVK2
+dKgtqNlfy5EHN040r/8Lp4Nj2YnMI205kM/EHuTwjA5aTy3bhkg5UH/PdEtP
+FB1EarSTItJyQOfGgcU3z+lAXqPqTt3PAZbTRz35kukgf4jZW0c0B7oLbku9
+L6HDsXj15GNPsuHH8jungH46XEl0mxKSzYILPM0bUwbpsIPnotUbwSxwTUtI
+qaPQoVmU6zz3jixwGI/c/HuUDgYWu2W/MjKhgqXaWJuB7ej9xDouE/rZd8sk
+L9NByMtOwu9bBoiud9W27GFAWk8BzTM5HUTfhLXm7WPAkd7mHuuwdNiSyjYV
+foABmrdNcy57pINJv/EZtf8YEN6cwMepkQ4WMyed0gQZMJdCz7ddToNv7T84
+Nsgw4O2+4Gl9zTQQeOApoKzNAOebm9RNllLgv21PY1p0GJB5b1u7PDUF4jeo
+a+vo4b/n7j7L254CbIIFeYYGDNA+MNHam54Csypy61pXGeDCc/DCIYMUyPxm
+zDx/gwGtN5p8BErfwh/q2yDaAwaYzdlxb72dDHNWNmGnfBlwz9p7KMI4GSzV
+Pw899mOAovy5Ze4LydB0Ofz6oUAG3L8ZL7PzYDJEibdtORfEAL/sVM3pqDfA
+Y6hXLBLFAONKkQF39STguOjoX5WKvz/Uj2e6OAG+ti90zqYxoPFyoNfAowSI
+dirj481gwM2zbM/qjRJA6e+P955ZDIhQ7Gd58u8V8F/S3LY7nwF2ApmHutRf
+wUyNR/q3cgZI79fL9hyNB/fx9pUNlQzIV7hbsKc4Hpp5bLS4SQxYS5z7XfQw
+HrqpKr/FqxiQUHYkYEA4HuzT6FqXahkw22lqMOf6Al7+S9wi2MiA3k3575VZ
+nkNndaPF3iYGFLOuoYTBOOiOkyBt+cSAop+kiPmcODgZV+JAbcb7p0I0BmvH
+gV/zyw6/NgYsxLHGh8fHwv6tIxmmvQz4q9/iRRaJAceRUw8jxxkg/Np1Z+PF
+SNhjXs57eoIBt603SJD+w2f2b7v/DGGHupoc12Y8A9D0uXd4kgEc4jpM/2Sf
+Af/cVFgsjQHqSw11B6hPYQexd7vIVwa8Cwm0uHksDFrtKj+WYpfnywQxkUPB
+XeRsnfwM3u/jpWeiAkPhNY3qfXGWAS0D9a7pfSFw+nwHi9Y8Xq+c6f5X94Mh
+5vE2L+YfDHCT37v2sfExmFp/1nbFPjwg+fjAncfAre9sP4Ytenrowc39j8HQ
+6apF2SID5pNyljfeegRCTz5bX/zFAMLpdCHrjofg/vf1xRzs/fZbtJWrAqHs
+oa4L6xIDOufGu72sA2Fz27UnDdgHR27XjZQHwHcl7qZDvxkg332kKdDUHxq1
+f75zxbbOdzuYzuwP4c6kH++xjyk8jwgx8YOvDLqg1QoDfLzTan//84Ef74ZT
+nvxhwPtPApcSVe+DlmVHRit2G/toDBHvDa/2ps1y/GXAiG2JW/dXL2CBRYVI
+7A6HUw7LEfdA9LvYss8qA/oEffR3DLhDyXLCSik2h3H0JS9xd/DxUNOexjY7
+fWF8JOAuUIZ1fl7+x4CUX5ZGr8Xd4NaHAuX72GfzFZx/B7iCooA6PQu7tO5V
+jM6ACxRpSAiuY7cLv3P6HXAHNHZ71QutYX+iVkYWOIOoIVOxFvbniIOPxUyc
+IF+xPuQFtuHxui69gpug9/WPK4H9Mmtn7ZixI8iy3ykkY4ulbfS0Z3aALhI7
+/+51Boz6PxJ2Mr4B/soyxsexA/2YImY22oKL6ouJi9ipp7++tM23hrT6k7VW
+2J8TKwKHja7DgXLOeU9sl0aKr85GK+g5LOgSjr156EXIQxMLaN/kofYGm6l3
+bbdVgRlss9roUoS9zaqPU5bZFEJPtswBdv0blikOYyPQDGyracOWHPFZH8vT
+B1019gky9qaoox35G/Qg/tEToyls6+JBv+95WsAnK88397/70dx9Ag0v4jld
+4txP7HiX1TucTBfgz3bTghXsXrdg+xNXFOCyeIPLP+x3oZeUzmecgNEG2+B1
+7JKimjAZ2iEo67rw43/mZP/AofR6M2o1tihc+9/6RBN3ZOtFkaBxOfzFzvo7
+yx65/Qxq6FA9soytbzn7GJmfR8mwk7KAfWOpUrGsVBXVC/FMTWPPX9xgLsim
+gQS3Wp4fwz6ido/pYpEOarUc+96DvbzLKPvB1SuoVOrVr0ZsCUsp+XwWQzTq
+HalBwh54fVCDUmyMNOQbljKxz9wUvcVsfhX9dT/2Mw67KNr1mPDWa2hOaPBC
+IPaF4Ee70kwsEb9e9fQt7KWwDR5ShVZIj/O0qAJ2zJjcU2VTG6SV0tbEj/12
+A2d/U6EtCst/Q2LBjoqCbPXNdqhdfCmm+X/xdZ6+FxU5oN5kb98s7OU7bipl
+m2+ig09lqx9jJxxnFxC8egu5tt+SksOuCI88sLLZGQUcGbPfiX3VqoWaL3EH
+dS+EL37B8Rw3/jXVbPAOkvv5amM0dtbE4dViCVcknuS/pR3nS0gjD9vZwbto
+NLL/fCz2PyVde40od3RPOuKhMXb8rYtVVy95IKtgft4hnI/Vb/wLbld7IlaX
+saxPOH+3Svxhu5rsjZaoSv/5YQ+py8peMrmPPm3amiCNLTIppybD/QAJGFfm
+PMf1wOJKkPPvhz6oSCGHXwXXC/NsmedJ0v6oT/Jgz8wyA3JGnGrXn/mjiY65
+0EjsJouoFvNZf1TIR+LqxfXIY9uei1zpAejwpom7yrh+iX/o/62x5yEy/vDw
+zfvvDDz3xn7f/fsx+lbK2XgJm+zsI6Og/wQ5Xfm32LHAgIxXviqWRU/Q4ZR/
+tr3fcD4cuxb+0j4ImfhGp3ycY0BtanpT/2AwEjix3ffiF1y/BIiPt0hhSOJw
+2YHiaVz/nb82qe8KR//VVtfuwX6u9Trw0J1wVMa6yDNMZ8AMn9hwtdBTVDG2
+KKU9hfv3IyfZ8ucRiDtItbZ/FMf3WZvqRiIS/d6oICqGrST1TOjeVCQqu103
+6jOC68GWDe1HOaNQOacT33/DDDjBFV103yYKdTy22X6JjOsd57UtzJzR6LZs
+rZ92DwP46ot7AqxjUGvqw7vB3Qww0FvOYI6IQUyrfcXQheP3ytKFQFIMWrjH
+xyLSyQDL0xs/um+PRbNpV3YzPjOAe+ER18nKWKTxUaCdC/fXSHO9Qg6254iP
+h7gs+ZEBAZzfqCYyz1GHFWXHpQ94PW6M3Hl77TkqIt57PmhgwOmyV36Cpc9R
+eIJUzmfcr1kFdqYxmb1ABULe2Qdwv3eh2dFW8+JRnFXtjtt4flCyDD81fDkB
+pRNoSS6dAa8vB3gKeiWgrNdP+7fieUNi4zM7h4wEFMT6LDTxLQOCj+pLTTAl
+oow7wnW5iQx4NXbc9Vl5IrJ5UG7lEI3nkzMhY6O8SWgu5IyvFZ6P8kLq4za7
+JyMDy8vD37wZwONHhGiEJaOiBtFTD7wY8OgAi1rk22SkIKY9EuGB1w9NbONo
+T0akMMmVhDt4Hph9pEQ9+hYdD1WzM7DB/f/1hYdfBt4iMR8qj8olBjSrXDPV
+P52KeKsk6a/UcX1MniR/1EhFUtY/a+ZVGXBuXJwkfT0V1a7MxEcqM8Bm1cR/
+09NUdOtM+Gq1PAMEGnRbvKipaM9qpDdJEtcryR9JheFpKD8xV1d2BwMmVySF
+xEbTUa+54FddTgYkG/PcPryYjnjD9kXZbcf9wT09fMfWDLRL9CbbU1acnzWL
+agypDPTCqz6nbgOez5wd5SwfZ6C5aydSWr7TIYvzk/sjsUw0qCR4y6ETz/MU
+zQted7PQ9RC3ebt2OlSy/bEIDMpCzXWzYPOZDspG4beCXmUh8Y2WOiaf8Pyd
+teny47ospNpxUUiyjg7nhUigzZ6N2qNF858U0kFl9EYiT2o2EoTD+xfx+WAP
+o6rdty0HyfO1+b8LpYOs4GTk+lgOOn437XRgMB0YO0zI93/koNzZnmi2R3SI
+3jL97cbeXLQkdGqd5T4dWk6W9bNY5aLRpi1FBfZ0eCJWl+a4mIv+5I25EEp0
+MDW5eTB3Vz56RWYR3YvPM6MHrznsF85HYfuFaK4K+PyxJrUcIJePrvfo2Qic
+oYOhQkn9+ev5aFzS6ImzBB0CIl4m3i/MRzyPd5pk7KUDPJKEXvUCFF1gevb5
+Vxr4ndFyWfcoRGYqaTplDBosiTG/yQ8pRPe+0R07p2hg+njoiUFiIUrzMcra
+OEaDD5b6d6PrC1FrAE1Vu4cGQi82i4xvLkImIuXcIe9o4NFjK3dXuwi5/eKn
++YbSYCK/ruzoeBHy1o1/Fx1EA7JL/k2f6SLELefTn/aIBlFzVyW6ForQQkUc
++b0vDQ7IaLQ4byhGN3Q37J5zpcFifZpcCH8xUt/x3nLWlAYzf9Yfi9kUo87q
+hctJIjQ4w72Vk59WjNpbjIq8j9IgzTGTumeuGJndkDQxOEKDg8s1YVt/FaOj
+qqL3NvPS4ONCkRF1Uwm6l2U2o8NFg2Af4yxngRK0/XduRuzSFLzJ9q76dr0E
+rTX8vNNRPwXUMfV93iMlyFU4We9x7RQYyoVeH58qQfSMLaFn303BZxNFZ+XZ
+EtQ2z/YnsWwKNCPGmtf/lKCYHOqoduYU/MhvMNbdV4pYuvvf2YZPwX4ts0eG
+eqUoYLyrQddgCkwjYvRH35cimi2TWbfuFHCySC+SW0qR2qaZS7paUzB5WuZI
+d1cpYgv/KXJJbQpuOSpLkcZKUVjT4KzQWXz9yg+K6d9S5DJPexzDMwXVzFu4
+VqTKUP9f7s1i1EmwP5RlE5FYhvwE5J8Ijk6Cxe3mhMzUMvR7u++O/yiTMMgn
+8aw6pwxdOaKhyto9Ccr921LJpDJUarRD5FP9JPyMtr443luG9jFQDyN5Evz/
+8k3yspejB8kSVQXmk/Dg4/yMhmc5+kp18nU0mQQR+5tLZJ9yJEz/pCFgMAkb
+Wvb7X39UjrYda9oSrTEJ/8S8WG9ElaP7LbNLBnKT0KygCadyy9EG4WHCb98k
+JG+05/o3Uo4yfC53m3ZRocJqjJdLsQKZZtSrCrZR4W14CW+qSgWia2uyzH+i
+Aqdx3T+pyxUoQDD9hncdFYhTvsbKhhWohWKY51tIBWMLSS2ZWxUo43bD5ZNP
+qbD423ha80UF8pepopiqUcGxN07X4GsF4rw3XjyvRAXpXOK21bcK5CHP0+t/
+jgrhm7fKOvysQJ/UelfenKTCHbFjIzfXKpCPvWpL8xF8feDaEQXuSiTVfcKv
+dX0CXAaZ7DjOVqIaVfGzQRUTcNDqj53Vw0pU7mP+2r94Aj6qhcidD65ErUoH
+mO7lTcDRIsnGg08rkbrnqXrLlAnQ6VNdqXteiWJCVqQORExA07R/Smt2JXK8
+ktMmbjsBaz/zLcfbK9GuBxVznTsmYLDF68WfXSQU4WFyJJR9AhTiVsol9pMQ
+/3qQ0fktE1BV66BzlZeE3lQFvcteHQe7nubv6YIk9IWyw/U6YxxS/lmU/j5J
+QjV1Oi/dqsfhjlnsy2gDErrO59W5y3Ycqg4porBIElIiDyXOWIyD8N398h0x
+JNTcG5ZdZzoOJl5qpzlekFDP856HtjrjIOfWyu/zmoRaVDfKv5Ibh62y6en/
+5ZCQhuFwVeGOcbj6/ecu5wYSKlHfGe7IPg783x6oX/9IQnW+L14f2TIOtcd4
+rHU+kVDuTU5mvpUxaDImq/G24/u94XiV0z4GZdlfMrzIJHTMjoW222sMVpc2
+ecl9I6Et9TxRV5zGgEtaxGX4OwkdT2mreWo9Bowm67P3fpKQ65+1+GXNMVDn
+s5FJXiGh9xuTDd/yj8HK3vi8YmYCPXEdmtdoHYVzNz7fIO8hkMP5V2l6daPA
+nnap/Oh+AiW+WKTol4/CAvVgjdNBAv0huzdrvRmFPG7OxflDBLpXQcrf5zYK
+nVW5nYXC+Pr20zGbDoxCYpPw3hNnCcSt9yeUjXMUdlvfeXBYjkDrrAeObt80
+CuoSwwSrAoEu7HVR3To/AvmmlMrPigRyyfQ51l8/AixGsQm71Al0LYkrtdN+
+BMbLKEM5BgS66pDRmWw+Ap825QuqGhGo3f7l29t6IxD4MOPEsDGBDm1+IfFP
+bgRM5gcif18l0I3ShblFjhFwqoSzP6zw99JxWpUNwyxTw4HpWwRiXXniRska
+humW7X8lnQjErKjp7fJ6GGT9IOSOM4Esb353iXsyDIPPxfMnXQhUdzqetdx4
+GJ6a8U+HeBBo0/zXIBnNYUjJjdyb4UmghsFX2UXnhyHqx4GZ6nsESrvMPZAk
+OgzXf133ongTaEemBUVvdQjWuGY4+nwJxLMh0a1yYQhyy63kGv0IlPDsZNE+
+2hDYZBAbSvwJxHLJf2dX2xA4pv809AokkJ/M3cD9b4agR3h5vfExgdRPvDpl
+HTMEqRH9A+FPCBRhwxuRHTQE5r9vIs0gAj24ISckfmcIzFozSTXB+H3H+zaw
+nh+CsKKVY+ZhBApfVnQ6LTMEYi38UpvCCdRiz023EhoCvmNH69Kw7Y2nl3O2
+D8FwulZA91MCfeqfjWpmGoIHvxSKLCIINFpgdHpqkQKX2RNv0LGP3bJM206h
+wLWP8tbjzwhkp7t2k6eNAkNXNTKuRBLIMHIjEqqjgGCKjWMd9qrwbV7JUgps
+mZ3NPxpFIOOD57ZIZVDg3pSG8xNsRzv31WMvKdD4dDZvDPvE9p3/RMMpEH9e
+xvZENIEK2Pey8vtRgLs4/Lkv9oRtwOHdrvh5U9fQB+zWfXrKm2wpoKqw6xpz
+DI5vwRCXb0YUMHLd810Ouz7saG7/JQoMx3Qs3cZuuyy6QChQ4CFrzu2X2JG2
+sYovj1NgOZpLvxZ7K9km8e4RCkypOWUNY5/JSGDW2EOB/+IlHX5i87ad8TjE
+SoGcyzWxm2MJRGjK/5z/S4a+wCciXNiswhk+VfNk0KxYEtyFzW3mwR04QQbZ
+Su/gHdidX/JKVHrJoFrop70VW7nr4rXNTWQgDrt5/cb3d+LW3F1PkCGe3rCJ
+iq2VXzFwL48MSTIj3z5gT759ki7+hgzeL46ffYsttVDtOxxFBtJPsTEPbOl4
+E+vgR2T4HXpuXAV79qXZleOeZPjxfUCWA9vs10etXgcyhB+wn+vA6+efE2dw
+14wMS1oWS6HYV4lWOy5tMtSckNRH2DJTjgXyMmSoN9i7NRbvjzRTL/XzUTI8
+S9h1VQab4Z7Kb7KfDCxJhatteL9dnNw/2K4NArkuWHAOx4fad8+j9IVBGCvP
+y3bF7m0bj7k+OQibdsh6fMfxtD2WFqn9aRCMAyypFBx/1T4Bh+uqBmFIjuqr
+gn2o/uE78fxBUM9MMs/G8cpm8G7nn6hBeFSTOGSG4zs6faHT9NEgTI43e+aF
+4vXVDn9Z6TEIfhlbdX6F4PUsXtKwvToI3N/iClyD/1dPPp6u0BwE17puqUyc
+P1NefySYFQeBtevf116cX9LZL+SjBAah7OT674M4/0zkk6g+cwMgnk03Ng4g
+0Cvujs0J4wOQz5fRaofzV+HsUkVZzwDY7qFedMH5XeIp9H6EGIAxjVFrVx9c
+/4jdD1meDADfHosZcS8CpXCv7N7qNQACJZ4v2HH9uF7dfYrl1gAYREqp0HG9
+4djgwP9bFz8vIzk56C6BdmrzvS3hHQCNmMMnA3G9eiZWmRrPNQDPS361SuF6
+dstYWeY+8wAMmKaYDuF6p5d6bv3kl36cfymmPI44n//VyQeW9UPz2vH3BjYE
+sv3408D9Uj8E5q0eTcf1dV/Wt9MCCv2wNyAzexHX32ND45kdx/ph2rKVS16f
+QEEnMqR4dveDn2lRUJUOgejp1bNhY32wL8B86fZFAmm82beh0a0PrDektObj
+ftA5HJ6S9rIXfFUDtoTsJpCrvkNWbWgvzL9XKRnmJlAG+72U3vu9QI7V2yTC
+RSDSOXG3n+a9ICtrGJ/LRqDA7G9PmPl7QX062tB4HffHl1RPi+we+BIeP6HF
+ICEO2j0/jvJuYOuw/ZleTEI+Tq+3ZaZ3Q1nL98JtBSTkfeZnmNzzbrgrwzXl
+gPvzwYgzDsae3bDHUb2IM5WE2BV5nlud7QbIfFnEFEtCr2u1ieLqLshnL9jh
+eZeE7h61E7xY1wnNxS6uucdIKNr3+YOcok44nJzVfUIMzx9VVnNb3nbCsZSk
+jyVHSShmqPVgZUAn5J8Nv5aI55HqpvlculInbM2YOL1nGwnZhY6e2B3SAWHh
+xrapU5XIMrtcrzWkDcR4xzIORFeirDDS2S63ZsjQ0WWc7K9AZ5Yvvx3Sbwb+
+OOm3Kp0VSFxSB42dbAbqw4dJWi0VSHkt57/u5U/QbehroVFbgZBQjuON+5+g
+KNppbCm9AinhBn0xoAnUFwtWWe5WoGjuoozloI/Am2k9zb6tAuke7+tf9q+H
+b31RNt4C5ejS4ZDmCPN60BU1/y3BU47suyzqeWXroezdNRPyTjy/errXHVms
+g0gxO9+9zOWoteP8aodNHagTRjJSE2Uo0rmmV+9pLXx+7aVNTsBu0Dtft7UK
+BHRbjH6yYctsmiE6iqDR70Dr3s4S5F8vxmYs64Jmbh3w5RUpQsMe2QLb3EtR
+fI1fn490DjqQKxfJJv4B5a/HfUwOSEEbqbf69MzakYO5tUDu21j041CReUto
+Oxormclg1ccOiXK+RLSj7LTLsYossWgTVfK4zZ4OdNSWO/20YwwyTukRWOvs
+QJ4B1QaXjkejTSXUOVpqJ+LbKXtj3eEZKv8loMjg7Ua8sTezpM4/RpsNRJJy
+T3ajkK6UiPWER8ioZVXxrmY32mhgkuuz9BCxLXMZcPt0ox8Sce6hOYEozHi+
+ImC4GzGZPGqlcfgjDnkfK4nEHsTp+GX1XJQ7Cv3ryn6qrAdVnYi6PCJ/F23t
+Or2q9LkHGUj9dR9iuCKuWskch9UedN2CQ25Z7g46l9yFvpr1otf79hw1ImxR
+D6fijt3uvWh5hBT/jMUa2cX5CF142ouM43POBOlZogSqLX9hTS86+T7Uy67N
+AJ3M4doy09eL7ng9Xus010G9QaHHxeZ70eWk0YI7Ayro/v2eJGeWPhS+/jXM
+ffgk+n//7yv/f5B+QxQ=
+ "]]},
+ Annotation[#, "Charting`Private`Tag$13125#4"]& ],
+ TagBox[
+ {RGBColor[0.528488, 0.470624, 0.701351], AbsoluteThickness[1.6], Opacity[
+ 1.], FaceForm[Opacity[0.3]], LineBox[CompressedData["
+1:eJxd2nk8VN/7AHBJyVYoSyVJi8oWKls5KUIk6SNRJCGRKBWJKNnJEhFZQ0hC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+ "]]},
+ Annotation[#, "Charting`Private`Tag$13125#5"]& ]}, {}},
+ Axes->{True, True},
+ AxesLabel->{None, None},
+ AxesOrigin->{0, 0},
+ DisplayFunction->Identity,
+ FrameLabel->{{None, None}, {None, None}},
+ FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
+ GridLinesStyle->Directive[
+ GrayLevel[0.5, 0.4]],
+ ImagePadding->All,
+ Method->{
+ "DefaultGraphicsInteraction" -> {
+ "Version" -> 1.2, "TrackMousePosition" -> {True, False},
+ "Effects" -> {
+ "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
+ "Droplines" -> {
+ "freeformCursorMode" -> True,
+ "placement" -> {"x" -> "All", "y" -> "None"}}}}, "ScalingFunctions" ->
+ None},
+ PlotRange->{{-0.9999999658982575,
+ 0.43999999999999995`}, {-0.17135389760223926`, 0.17135393862080836`}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.05],
+ Scaled[0.05]}, {
+ Scaled[0.05],
+ Scaled[0.05]}},
+ Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{
- 3.817554807406887*^9, {3.817557206327607*^9, 3.81755724215594*^9},
- 3.8175573305621147`*^9},
- CellLabel->"Out[4]=",ExpressionUUID->"e44b7486-110d-476c-b94b-28e4b600a40c"]
+ 3.817632448065246*^9, {3.817632480017908*^9, 3.817632515983914*^9}, {
+ 3.8176325673566847`*^9, 3.817632586442404*^9}, 3.817640197146964*^9, {
+ 3.817666564989592*^9, 3.817666601422195*^9}},
+ CellLabel->"Out[113]=",ImageCache->GraphicsData["CompressedBitmap", "\<\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\
+\>", "ImageResolution" -> \
+96.],ExpressionUUID->"1387cad6-2910-4d95-bb16-fccb91fd6a76"]
}, Open ]],
-Cell[BoxData[{
- RowBox[{
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"ListPlot", "[",
RowBox[{
- RowBox[{"eqLow", "[", "n_", "]"}], "[", "m_", "]"}], ":=",
- RowBox[{"SeriesCoefficient", "[", "\[IndentingNewLine]",
- RowBox[{
+ RowBox[{"Table", "[",
RowBox[{
- RowBox[{"R\[ScriptCapitalM]", "[", "\[Theta]", "]"}], "+",
RowBox[{
- SuperscriptBox[
- RowBox[{
- RowBox[{"f", "[", "n", "]"}], "[", "\[Theta]", "]"}], "\[Beta]"],
RowBox[{
- RowBox[{"Gl", "'"}], "[",
RowBox[{
- RowBox[{
- RowBox[{"g", "[", "n", "]"}], "[", "\[Theta]", "]"}],
- SuperscriptBox[
+ RowBox[{"{",
RowBox[{
- RowBox[{"f", "[", "n", "]"}], "[", "\[Theta]", "]"}],
- RowBox[{"-", "\[CapitalDelta]"}]]}], "]"}]}]}], ",",
- "\[IndentingNewLine]",
- RowBox[{"{",
- RowBox[{"\[Theta]", ",", "\[Theta]c", ",", "m"}], "}"}], ",",
- RowBox[{"Assumptions", "\[Rule]",
- RowBox[{"Join", "[",
- RowBox[{"$Assumptions", ",",
- RowBox[{"{",
+ RowBox[{
+ RowBox[{"t", "[", "\[Theta]", "]"}],
+ SuperscriptBox[
+ RowBox[{"h2", "[", "\[Theta]", "]"}],
+ RowBox[{
+ RowBox[{"-", "1"}], "/",
+ RowBox[{"\[CapitalDelta]", "[", "2", "]"}]}]]}], ",",
+ RowBox[{
+ SuperscriptBox[
+ RowBox[{"h2", "[", "\[Theta]", "]"}],
+ RowBox[{
+ RowBox[{"-", "2"}], "/",
+ RowBox[{"\[CapitalDelta]", "[", "2", "]"}]}]],
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"F2", "[", "\[Theta]", "]"}], "-",
+ RowBox[{
+ FractionBox[
+ SuperscriptBox[
+ RowBox[{"t", "[", "\[Theta]", "]"}], "2"],
+ RowBox[{"8", "\[Pi]"}]],
+ RowBox[{"Log", "[",
+ SuperscriptBox[
+ RowBox[{"t", "[", "\[Theta]", "]"}], "2"], "]"}]}]}],
+ ")"}]}]}], "}"}], "/.",
+ RowBox[{"B", "\[Rule]",
+ RowBox[{"ruleB", "[", "h2", "]"}]}]}], "/.", "sol2"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c1"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]", ",", "0.001", ",",
+ RowBox[{"\[Theta]c1", "-", "0.001"}], ",", "0.001"}], "}"}]}], "]"}],
+ ",",
+ RowBox[{"Joined", "\[Rule]", "True"}], ",",
+ RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input",
+ CellChangeTimes->{{3.8176326022950163`*^9, 3.8176326467232037`*^9}, {
+ 3.817632683971553*^9, 3.817632789027328*^9}, {3.81763283674572*^9,
+ 3.8176328368685007`*^9}, {3.817632877796402*^9, 3.817632918098442*^9}, {
+ 3.8176329487995663`*^9, 3.8176329657972403`*^9}, {3.817633013987247*^9,
+ 3.817633015478447*^9}, {3.817633052086051*^9, 3.81763311811401*^9}, {
+ 3.817666615617567*^9, 3.817666635940769*^9}, {3.8176667213758173`*^9,
+ 3.817666760396441*^9}, {3.8176668540479193`*^9, 3.817666907718935*^9}},
+ CellLabel->
+ "In[120]:=",ExpressionUUID->"4c6fe8ab-4f6a-4b57-92a5-c94e403d041d"],
+
+Cell[BoxData[
+ GraphicsBox[{{}, {{}, {},
+ {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.004583333333333334],
+ AbsoluteThickness[1.6], LineBox[CompressedData["
+1:eJwVV3c4kG8XtvcmqxJKUiqppCEZlSINSUlIRtGQQkZL1g9Fg8yyQsgIScb9
+mMnee++99/x8f73Xud4z7nOe93nPfYsYPLpiREVBQdFPTUHx/2dg68+08IBL
+5MS5IKb4dxo4dublxJ3pMwScD+75xhrgKe3FE1X2isR5TtwpWskM9FablWVT
+5UnN5RLD9JrHGNUINZDedYLMTrjQx81aYqZ3rkvO4yhxrxAXdmewxVCEbBel
+6xGSxXqltp79BY4LhdG2DR4mt81DimLpXiP1VNBzhU+HCJ9/ppAU5RsUH5en
+uvr0ILn46uLh+XlHSIlMPnz0XJqUZ5iH3h12xvWOEqv0iAOE9V9bWn2zK3oW
+Vk9XD0oRPWPX5//9c0PsSyvfOQUpovSrbT012QOe1x1GOLT2Ez611n+fgt7B
+7cu231Zn95HbR0UviCl6QZy2Z+/PS3vJcqf9jZeH3uPALQEF2UeSRKX57PCA
+2AecdC/L2xW8h/QXH3c25/2IbeWHDot37iY3Any2bqf7hMrwiFk5qd3E6bXD
+ZZbZT+hY1movdJcgpOJzsEy3N1puj9EZTe0ilmpHvGIqfHD9ddW5HoNdxDUp
+u/RJ5mcY+paFKbWIkzGVfec/f/fFG9UzvmG3xMlVux2Xt3r74WyDzF7Fvp1E
+MOlZIMsrfzD5mwlYWe4kGf/SDM1MA2CkK9gRzbSThEhrPZK/GgibHX+/3fom
+RmbVigXfyQUhO5j7s+BpMRKVuO2ezs4vOCFpmWs7uIMs3+FgjGf7iuwrSVdF
+P+wgZV20um5zXxHTd5QTJ3cQyqr/lBYfBsN8ZO9m+vHtRF7R66dlVzC8Luzp
+TA3dTqLYJC9laIYgBvVHvG9sJw7GL+vKCkPwQPSY913u7WRtsa0/7ngo7CXE
+7lJUiJK3ipkcunGhYFTid9nvKUpO+Bj8axUOw9OF6p8ll0TJTpdn1vs/hmHX
+Lw+JnzyiJJPt4aOrtOHgGTugktkkQj4qpc1esA6H8OP4I2WhIsQ6akl+62A4
+PB/dC/97X4Rc+kBrlav9DTUnn794JytCOn5U/FQo+Qa+U2+zGelEiMSZy7R+
+chHwSWdXEq0VJuveSo+L4iLQpqngnPNNmGzZ0TVety0Smp9WP9VZC5N/Q2/N
+4RWJNfqWFlVVYRJZc7fRkTIKNgcZODiFhcmJkW76XRZRkOtN55Ic2UbiHypW
+fu+KgoLVP+PP/tvI7gouamaN76jnDu8+q7qNCMZ8uaOW+x2WV94Jbl8TIsTw
+ys+HB6PhxcepyJEkRHgubY2yCIvGO8FhnoV7QuTuXNH8de4YmNluTc4TFSLZ
+wtfURd/EYEgpy/1261YStENGo3wqBmoflI+l+20lkqsRUfoGsfipxGwLra2E
+x3NkuK4yFq5nyllu8W0ltm7vU6QVfqDJfjbqTcMWsl8u1O9pwg/oyZsObA/Y
+QoSiusWDtsXhVNmk7H69LeTmTvqR2HdxiP2UX/p5xxYS3NP0IHw1Dra7dD9c
+Gt5MPt6zPuB4Px5eFheELiRtJjLGpqlqzfHgf8Me/dp+M5F8/ejk+o4E0Kum
+03Sf2UwUBjpX1XQSENnwws2YazOZU7Wu9fyYALrKms1U7YJEkXXb+t+iBPBk
+GWyKjRUkzis6SbOUiThu/ljlpp0gWTK7LiFwNBHSu6em6VQFyYT5kI+0eSL2
+BtBkRWwWJPp3YqQUIxMhUDv1Q3pUgEx8W5dQaUvEZUu/nWEQIP1521OUN/0E
+//aDnRMfBMj12SPUsmo/8Vj75QCPiQCxXTuvLPrmJ7qOyH1iOCFA6nwNI6n/
+/IRB2LRjPqcAqT3rqd0y8ROvKimCTw/wk5d/Ot1ixZNAHzDM/Ab8ZCTFxfCp
+bhJuRE5KPvvMT0y8i7gOeSchqaY0ZJs5P7l5W4AMFychPu7nqafn+ImhK4dP
+AFUymIQseR5v5ycZx15nKh1Nxu7y7huca3yEzeKZbs+jZNzgU3l+qXHDjjwd
+/DwiGdcNWfl3p/CRwWOvv7O3JuPZS48xv/d8JMiXK9ifOwUcYgujAQ/5iBWn
+zHeh8ylgD7+7W1KNj9jaOAwGvEpBiAlN65ndfOSm85gjV2oKTlgrGQww8BHr
+mdovDqMpeL9NTZZ1gJfkP127MbL9F14Lmqwm/uUlYcaBDRe1f4E59r+H1ZG8
+5J2+1okfXr+QfnbG6KErL3nzn3oEzd9f2P+gp/HlPV7Smb/lyLXVX6h0uN5M
+o8pLitNa2EIPpmLQo+fTkiQvCQiTvDBwLxURST7ndNl5yRS7NKdEcCpOfxnS
+2Du1idy+G2RjWJeKlj9FO4xqN5Fl/R/h/iy/keT/RZE6bRO5piSdUKz4G6z+
+Riq0QZvIK8H3afPPfmOUr7Xn7utN5FZ2QatQ/G/c8kxs3GO8iRhVmx5V6P0N
+5fG0JVXVTSTP4eeA7uY09Pme2PtXahMZ03hC/+xyGg5Yy5kE8G4iOkQs0cMl
+DZuja+IKVniIcnY/RVBmGrTOvxU4281DCpVecn6fTsPRyuJiwSIesuSss5og
+8Qc6v48vyCfykN1GgW3Jen9wZ1ipPdmXh7j/x1Se7P0Hr2Nfl1m/4iHt77cP
+JBT/wYsP54Rd7vKQECE+pe+U6Xirtu945yUeYlL5byHoSDq4Wz3eOx7lIZLH
+6kU8H6QjiVIo5JEoD/FM/lhnH5aOA288poKZecjsYbb9Jo3pqN3DIcA3y03M
+WLiU1NkzwCzO+rOijZuoee7aLX06A+ZeqYYlhdxEL8d/mcsuAxQrfzoZkrhJ
+/bBF2URCBjbn9XY5BnET760v0or7MiAyWr9b3pWb7Pl5oTpsSyaOPE5xlHnC
+TV5lyUrbXMmE7L/m3Hu63GTV+taIqmsmzrv559af4yYMXqF8W7IysTY5Zvzy
+MDfZ7/T73+B0Jr6fUPTVE+EmUkOC/CkSWWAI333OmpWbHA/j5H+hl4Xc3n0W
++YtcxE/wZ5uydxaeHvTgOtfHRZ6YdbxiLM6CxKO1/ZTVXGTE8RJ3CQVwxM+t
+bgRchF3ZJdpDBjDRVOVn/sFF8pybtVXvA5SP5Flv+nMRcthaliEUeKssWN3s
+wkVeqVzXyq0HJGh533pYbuTviDLKoiP4Ef33zv07XETqEt1VfxGC2sAZR9vL
+XOSWmeMryxMEz4bubf8lz0WaeMpnLmoRKNHXWgnt4yIe7i/+SFgQpK4Epf/c
+wkVEGviaqd4S2K3lSFswcxF+WVb95kiCv1dSRHSWOMmcU9aVpBwC0VdHqh4N
+cpKILzYZbq0EbT9PfIht4CRaebYRtxcIVtX+JXEWcpK4tREBWe5sbP1U4/El
+lZP8fDa0jW1fNi483mN9JZKTKLXYZ3erZOPPkasVkp85iVBMEH3anQ1/kyeL
+ki6cpMtbZvnti2wU6B3QumLNScoqRL4Z+GXDci34cqAJJzEz3s12JDkbr3jF
+rzJd5yRHXVnkmcuz8TrboDRAhZPcbbU81T6YjXk73v2XjnISp3LazUk0OYim
+4xrbuZuTfKm9UO+8LQfHabc6bNvMSdQzK59rH8uB7JUuo6MsnERxip5vn2YO
++ilbeJ+ucpC53BsxlOY5KGQ5tal8jIN0ft+uVOuWA4eA0e5zHRyE3TmlL+pb
+DijGtBl6KjnI7r4rX+xJDkrr3zAF5W7EKx60uNScA8GShqdPUzhI6EkH0x1z
+OaB5uq/mXiQHudap57nAkYuWfz9S7f04SHhNx0DJnlx8S85LiHXnIF+D2F6G
+nMlFvRCfxuJzDvKptv+G1e1c8DmaHzIw5yA+t/Vfq9rn4s5kykifAQcZj7q9
+Kvw5F55PGja5aHIQnqKi2rnEXEhN/FVVVOEgbWXmXKUluZgzNJbkP85BbrQL
+pYf152LpPzsthn0cxPeJT70tVR40q6MecolwEE9Hz0dXtuYhvezWJhkeDlKb
+/tttt2weShtLJizoOYhOaKoUtUYeJHTIxfez7MSkbNe9lgd5UHqpW/CghZ2c
+5wg+/ss1D311A362uezE/ktUvFdYHvp7aUVTo9nJ11P5JWZZeYh5Y5sm+oGd
+/LMx9z/bmIfQed6sDBt20pS4RXjHTB6SvoZ7Od5mJ9t0DxlRsucjYUvNJ5tz
+7IReQvBxu0Q+YikkDwQcYCfyAhKqWcr5cF+aLxsQYCcFqclLQXr5KLKVbbpN
+xU7iDjO6vLDNh2Xph2zaYTaS5GU2r+edD+dvCnPV1WzEMlVAQzEhH8Wb6EaK
+M9hIS+z5ELHifIxP8wuMfmMjddH7Bhn78iEYumVOxpONuCmPHxinKMDgcfa1
+qGdsBC7xDrWbC2C1XS5O0YCNlG/16MqQKYDX8EFnajU20mkWcP3b5QLMBaTQ
+Dx9mI+E/R4ff3S9Ai1rsr4VtbOTF3rdhNi4FWOIVEpBkYiPsB144G4UWwFRT
+JNVxhpXInkPAlcwCzMtUClK1s5Lka+eGTjUUQDxQsSLsHyvhi2W3kZouQLW8
+jdG9ZFZyYDfFRRG2v5gWv2V65SsrkdahfsIt8Rf3dBLMdd1Yyc6PK8N0yn/x
+pZOG5a0lK1mjKCLLun+xPPOzslWflahUKy9M2vyF/H/l1y+psZIjFxT8Bj/9
+xSeK7cd6jrCSD53vorvi/6JPVJjDbzsrKVRdkG4t+ou76s1WD9lZCf13paON
+vX/h20HJYrjMQmK8pPPqKApxoa7yoU0/CzGQdGiq3VyIpmDOU3HVLKTm4rBD
+nUwhBPcziFIRFsLnJZrXcLkQz3dZ/n4ay0KctRvCW+4XgufGf1G0fizEkzlt
+T5dLIfLU2n2TnTbiaR7oDYYW4hP/0wOvLViIeK7vmanMQny5FLzZTI+F7J9p
+6V9pKMQDCU4qCzUW8p973TnGmUL45WZ7eR9lIYv1Qk/42P9BJnjmae1OFlL9
+WdVUfPc/aMrtvXWAh4VYsI4fPnr6H+gbJRajKFmIHLdvi5r+PxzUbl08Ps5M
+9PdXGRrY/UP3rXucQy3M5EykWK2Nzz9cuMs//bOImZR94Dv0MfEfrsle1/D5
+zUwOj0u4xpX8Q/uJ5P6PEcwkKbG5vrj/HzJ2VxjHfGImbY1REsNURfj008C1
+xYGZNL1hcmQRKkK+phSt+GNmcnTJanT/0SLo3qD77KbHTFz+3r6vebUI7+pS
+FujUmUnt3+P0zx8VIaCfrS/gBDOpOvokL8KtCJ8nmjef28NMUsqfRFd9K4I2
+dasWmyAzYSQRoMguQtCt3OvDDMxEoM6C6UBLEUYp9ra1zzORSw4n3t+ZL4LT
+neCo4T4mcnDISNuXqxjvj7rasNUxkVsL6vfL9xZD5Np+bpV8JiJ0X7OU4Vwx
+DoRlyPomM5HxgZo3yobFOCy1P24tjIkU0Yr7OLwsRsg1bVm7j0zkmE4YU65/
+MTKnOwNZ3zARzc9f+2l/FeNqqkxoigUTMXJ4dFC1shjfnT+wPzFgIs58RjMf
+Ropxdnom9vQVJkL1rkKqlb4ENPnblPYqMhG3uxTjEttL0OjzMUBCmolov1E4
+bHOyBNucPV4dE93wF21nLL5RgrfTaxl6XEzkwKrok22WJfin+WmLHxUTOX1J
+09rKqwR1W6LM+qYYyQbX2FIRUwK5CGXrs92MJEbi6z3JvyVQUhBmzahmJHck
+Txm6d5WAQsl/WSmPkdD96eIaXS1BmcRvzvZkRkJrUGh3WaAU2eWi295+YyRr
+jge+/T5UisqY7TMXfBjJ6du3vEUvleKiSOhtERdGorPN7YqnWSlUW4WP0j9j
+JOptM11rzqVIVEhXW7/LSLrQqPY4tBTvW0UfMWozksCZJz59maXwmQp8IqbK
+SDr+rubrNpaCjp5in8YJRhIUk9DZOFOKg46JFh/2MpItyvnjWhxl4Lodxtst
+xEiinjyZa9hTBpeGy+PKHIxkwWhqWedsGbT3ZFelUjKSuIBndD0GZdB5YPf5
++DQDcZs9vuXhizIE3nrHU9HDQJLxWGnZrwwXz/0nYlnHQH5lqDu4p5Th1qKt
+z+5CBuInRd8uVFmG9e/jqhNpDCRhuEwvZaQMASzjggUxDOSBZiPTRYZyqGss
+tcQEMRB+6xt9w9vLwXuG6X6IJwMxoHNYcJcvx93bb0MjXjOQ1UdOZ/ffLMff
+VaOb6U8YyFSnd2OtVTnevhp43G7EQLiv9Sa//FAORe/GbK7rDGRv4Ld2ybjy
+DT1+X1zzPAORM2TQb/1Xji+bFF5GnNjoR0X+xPvecoT/NIig289Amofl5MIp
+KqA9edrWUoSBqJVbe71mq4CJ7t+GKW4GwifQ56+/pQI6VRLBL+gYSGJgiJ7C
+7goc7+aJ51+kJ0bHczu3y1bgzK2PPWSYnggP3tnBcKYCLLmcwtZt9EQ1MXD3
+mEYF9Gp0FI5X0hObdOf52tsVUNgSvIs1j57sv3T8HR5V4JmT4a+RX/TkQ2v1
+ZPTzCmTPvitu/E5POFbuifm6V+DmuO65mkB6smLBJ+niV4EV2QecLZ705JDc
+HMOzyAq0ukfTTjrQk4i3wjBNqUD5WV0Gbit60lGdcFkvtwKye8VWFO7RE2+S
+natZWYH+LRO5z3XoCc/5h/zq7RV43EqlVHCRnuQkVF5RGd3A1zels1mJnri9
+obdSXq7A7P6IWXsZenIsfI+TImMlNjNdmRySoCfjqtpvFPkqIThnc8hoKz15
+yJ7wRFmsEmddxsKGOeiJRfe5GyoHK1F3tmTHCxp6wiBy+oi6QiUaQm0DtyzQ
+kdz/wHHtYiU6q6InCobpCK9a/YDerUo8q71G/7ydjrymj8kxM6sE6x1ScLKa
+jpRX3AixsanE8+FHm1j+0pFzMtSu/7lUgvLzwaaeP3SkQ+mvTYB3JR6qCq0U
+xtGRKy4FNvFhlYhIcTb4HUpHdHhE3fMTN/Bp0c3+9KEj+a7LCa2oxE3fZwG/
+3eiIE4fl2HxpJbhaF+X+vaAj1fcSz/C0VELna19ejwUdOTJYnSE9VAldjyZ+
+ZhM64vuc4qrGQiW+fYsXPXGTjsgl32S3oqsCr/HzYuuLdKQ1g2nKn6cKxkOf
+VzKV6Ijng4Pr2aJVOLDV8yub7EY/Z1aODktV4VXf3i/3JOmItbXHN175KvzR
+tekqE6YjcR3Mp5UvVGGYJuHayU10pEogbPPTm1XQXFDpTWWkI8+e2klG3KvC
+kcPTz46v0RJFCtg2WVchtebTSuEULSl+58vI6VyFyYvnb+r30xKf1IMt5z5V
+YS7f6BVlCy2pas6YdQytQofyQ63YClpydfftGzkJVSCbtpXo59OS22HqTFSo
+giWzSZHQH1riuCWZWbm0Cgo1Jif74miJqXK2vmtzFWTVLXlSw2hJTEQES/lg
+FdTbeI6+96UlX+K9ufgXqiBctOL79C0t2ZlALO/QVePUJ26R2w60xKpT+2gi
+TzX23XyUdc2alrTf9dWn3F6NtGOaupr3aYnXzbgxjQPVGIqXHdO5TUsMc6r6
+ouSrob7+5+aDa7TkXdAJNQr1agQHRX9yVt3AM7BdVFunGo3+VC5Rp2jJiaBs
+s1+m1TBjHxKuPkxLmn9flNxkU40e96RLdHtoid1JRhMrl2p8cGuhURSmJTeP
+797W5F2Nt90sks6baMnzonGtU+HViFDkTali2qjP78vz/Wc1Qr9OvxOnoCV/
+jA2u82RXQ/t3YZTjLA2h5fDc6VBejRmPzsnBIRpi4q7nMNVaDZa2xBtaHTTk
+oDnvI6ORanTG1pSX1NKQXzbz401L1VDJZFY+X0xDqt3OMmgw1uCbgHxEOaEh
+KYlq6aV8NQjxte/T+UVDbPeos6jurEG24fzMZAwN6TL5tFZ0qAZRTvQ570Jo
+yDjLPe8LSjU4ZyZx8uBnGuK/xFtTdbkGH21Xb7R70JBH6kOZ2vo1oA48S/fR
+gYacNJG61vuwBlnFYwfVn9GQzIEjwRbPa3A1ZqWa4yENOYZLX6k8arBlU1B9
+0x0aIr695Jq3fw0kE7dKxd6gIYOBK/92f69BrvtomeNFGnKZQWYlJ7UG138E
+fjM8TUN0fUsnbhXUgCu5+ZvqcRrS0yQQs1xTg8yHdtlHD9CQzRkW+wK7ayBu
+c39onzgNuel24IX8VA2omrK49mylIX8WE4J6KWrBEBoiuY+bhoSLX/B6x14L
+Hw+D3bKMNCToy50bx4Rq8TnkwZrKOjXJuaGxMiBZi/wGtQD9WWriU2hv73+8
+FgeyIqdfDFMT9yqFVvXzteDnV1oK66QmqU20onQ3arHwliK0vJ6aPM3dq05M
+atFxqa2VsoyacE9tM3puVQuK/LngY3nUxOKKsqmcUy1uSb5qs/lDTVK0aW5T
+fKoFrpT8hwRqMsBWrFYQWovMYyo+zJHU5AcN7QHPxFrMF9vN3wqiJh3Gwpw3
+SS10HRhDfn2kJhcWPSYkymuRLBTnvMmNmlzbklG13FqLGa1TgbavqElQhXB6
+xUgtVt4m1PZaURPyZ/+PqOUN/M8ZxLUeUJPlnXqxb5jqkDxl6lh2h5rUsYhn
+3BaoA/Ub7i5VbWoyzkXZobirDhHy1w6VX6ImHz/c3Sx+pA4XHn19dP0sNbEM
+aHrMdqYON888ce2Xoya287V9C1fr8Dj4wRP7Q9Tk6r7m53136tD9R0GMbw81
+Of/f/WP1FnWQnkj7kCqykZ+XTbj4dR3OPU1NuMVPTdriTkvneNUhj1P6KSM7
+NTGf9X+a8bUOS/1Hqv7QUpPXep+H0uLqMC0xiscrVOSgTMHnP5l1kGxzl943
+TUUi/ZNfZpXUQfXrnW0Tg1QE/01+y2+ug82tRrvUDioy287KVjFUhzRhEznH
+eirCeiswvXWxDqPFATeulVGRocgDP8cY6pHUIViwN5+KXL5iOEvFX49ZpcBn
+TBlUJKOlxFVQvB561CPGIz+piOQfWvPDMvW4u3nIufo7FRnRiInTOF2Poyfd
+yhBMRZ6w6qhYXq2HfED1wcTPG/4qv0/536mHdWRHbOQ7KqJvYhCQY1GPJ31t
++8OcqMhC9drNsdf1WE5iSwqzpyJ3KQ45b31fj9dsuZLfn1CR9/ejt14KroeA
+we2PSaZU5NN3lp3O8fU4fvV2a85tKpJ6iz4MWfXg9lKjrL9ORbRVzvmulNbD
+9WPW7PhFKlJ6+g2jXGs9auwNE1nPUhFljbtLr0bq8bdhZbfUSSpS8OHHw8Ll
+eoQ81rqhdZiKbLrIZMrN3ABXIc2DbySpSMT6kYnbgg3w/tgfn7SdinxWm6JJ
+lmjAM2nOggFBKvKNaz6G8WgDopt77otyURERE7pBA5UGHCVOAfqMVIQ6sAvQ
+aoDIIfFzYRRUpFbp0iFhkwZsf83yYGiekqQc5j3vaNUApT+ua4fHKYnt+1Wa
+EacG/PBcm3HqoyR+uZV3tbwbcGp7x9mmVkqi9p++TUH4Br7WuDHpWkriNmNz
+7GhyA84pLXd4llASJfOJ+PjcDXzFhryTuRt2nm+rRHUDClP8nK+lUxIbgfN/
+I7saENN5TYL8pCQzq63mElMNyPtmMrc3mpII3JNqi6NsxEDkt96vIZQkFdu4
+ZTkb8SJlYWyTHyVRaPDgzhduhGngNSYvL0oyuKbdrSnVCEOa3P1srpSkZvGR
+85B8I+JVLmp5vaQkF1iTKd5cbMS9K4I2vNaUZHWd89o2vUaIPrn0NvghJRHc
+Zu2Gh42Yk9/jsc+YkqQrVofcedEIzgeTD8gtSrJQyR/M/K4Rn77P7b6mSUku
+/T3xX2pQI0bsAtLH1ShJU7LMbZMfjXAXusD/VpmShBRSSG7ObATjLaej+05Q
+kr6Kz6NVJY2IfFzEV32QkjieWv7+rqURst1xMXZ7KIncwb1G6iONMLlTOSq+
+nZJstZDezrXSiNs/WurqBSlJgzXXQCNzE1oNXfTcuSiJuGV96rfNTbCb/fhK
+kWnjPDTf+VjuaYKTRYX0KiUluZFzxvXc8SawW/M+Sl+kINkS3O9FVJtgRKe6
+7/kkBckjDCmr2k2ovq97T3GQgrS4yi+0mjahQlhNgLmTgmhcrdLNsW2Cebjg
+kfoGCpJW1DYS7daEPSbN6REVFMT4gVPEZ/8mMERFB9sUUhC+wEFP1+gmrGnF
+t10kFMTC78CP53+aULAi+EjiNwUJ93Smsi5qQuNHCVW6BAoy/Inn09OmJvRY
+itzvi6Qg6glMxlZDTdA9plH87ysF2dXmb2+/1IT3AQIGCZ8pSA/PUrMzUzMa
+tRsl/D0pSPA5fVdvwWbsF6Pc4uKygf8pg3PU7mZQPmOUtn5JQRQ+b3wMx5px
+1fmpkak1BTmfJeDcfL4ZIkJl8fqPKMgmRob3y9rNYH0Xw6RtQkF4fiiubTNr
+hrp7zKNrehRkfYm7SsWuGf18Vg2aWhTE6s4/Div3Zgjeyzh5/SIFWbRLyooM
+aMauMtnAW2cpSCr1zo7WmGac+xw3ZCRPscFnrG34M5rRsTK4/fERCnJWldpT
+q6QZ1PRE4eV+CtLsJCYW0NIMCUu2k17iFIRlv/yp7pFmiEWkc4VvoyCMwsk9
++1ebof3qV9ofPgpy2GaY9zVrC3Zpz0nWsG/MK/Jic93WFnh32RpP0FMQubvq
+Mgf2teAwk5o+OwUF0a+4Lul1sgWuDdO7DCbWYXqxO3tavQWU5keXojvW4Zti
+tHxTrwXGh77vWqxYR4bszdbCRy2Yu/AxSi17HU9tFO8fe9UCRxeth98S13HM
+NSg2wasF/aJGD6lD15E4NBm6J6QFv38cCzL+sI4/wYUaMYkt+FhnNF7msI4S
+ibjc/TktCFZ8c+PEk3WIuEnP/65qQfidkxVxd9bBcmlw6kx3C1TUL6vsvLqO
+I3730hunW7Dk5fgrVHkdNPzqmo9pWkHDHM++4/A6GvgP57NuagV9XopKtNg6
+3FwIe7xYK2Zz3a8d5l1HxYz3UU2ZVhwbPrAvn24dbwJ0z1KcbYV+8a+8G/Nr
+UDf+K5egtZHvlQz7dP8aBmZeiRjdbcV21yaq9w1rKA2RnxeyaUXm18ZPB/+t
+IdglPbf1v1bU+ln/aUpbA5wT3EP8W5FxjPaec/QaOs63aZjGtCKNq8NbJmAN
+8ZcYRGQzWkF5w0Jm2H0NGsOz80ylG/Zf6VPh9ms4eN6itau1FWNPwqNuP1hD
++Au1Ooy1IivhmtF23TW4vNbqD1lvxdWeHrNB9TXwHTXd9B9HGyjuziUmya8h
+7oWekaVIGy4bntzrILXhv4O3xVi6DfJxdtVXRdbguWz+4pZSG2zDn/nv4VrD
+hcZrl29cbQMfK/MzOuo1hAb9vKFt1Aa/aW6D3ulVVMo+CdS3agOPy0v1wp5V
+6Ca6C913aQMWlA/G166Cevd0j71vGyK1jen8C1YR3h8+8+F7G0pfTGS6pq7C
+VCv4StyfNlysW7poF7WKZJ5B6vLiNmy/HPnzsd8qFMadWWdb2pAkJ9pi5raK
+fZNOT4XH2sAsEZpzz24Vh43m5C6vt2ETTHTM7q+ioGXkoQtHO0RjMr+a31rF
+MRkHllyRdvx4tuBgo74K+rDqzTQH22H41GrFSX4VNHFUoeeV23Hn7VcqH6lV
+/FE4HO6j2Q4fmV737yKr+BrnLT5g3A5nlZx3hGsVzxKvHJB/1o4d3X8om6lX
+UWLztSDgv3ZQXdJpXphZAVdC0siqfztce05wCfatwNi+OMooth1BPcuBJ+tX
+UO0hTlGd2Q4NIwUL48INezPrwunydvTsz3J9n7aC4bl876yOdlSG76lH9Aqk
+nILbTky1Q+6r6tXJgI33ffNmHZQdeH59YE7s7QpM4aT0jakDRao1KbderKB4
+MXLhPncHpAWHXHwfraBiK/u7I1s6EP+QxbBOfwVfOB7S0Yp1wLpLTIHvygr2
+89sa1u7twM3OXbw3lVbwrW0oOkqmAxskuynk0Ar+WNq2vJDvwI3vzW+GxVYg
+od27rKXSAQELHyZZvhXssB5iPnS5Aw89Lxm5MKzgr4QqO7d2B15Mi7g3Li7D
+Q7mYYdZgA2+2xJN9w8uo4jqw3GjWgRMH3/E4tyxDT+f0YPbTDiy8sDfuKF1G
+093q2tjnHbiWuUtfDsvQpf6e6+/cAb3y0oXAhGXwvvBJcffsQJXyD/H1kGUk
+pjyMe+m7UU+RvefOx+UNnUKfaBXSAXJXUazYcRkMfkeIeXQHZP4EdB2yWoZn
+dVPbg6QO2DhYcYeYLKN/vJT9YUYHxOQOxbPfWMZ0yoTm4/wOlNmf+PHq/DKY
+34klW5d1QLlqhWbm+DI+O17e+7q+A+VJAz/u7V1G8wWdvLcdHfhlaPO1U2gZ
+keek7IMGO5DdsrfyJscGXpc/WglTHWiPdzvWQLkM7cKhGwXLHWCcE6i+Nr2E
+l85JTu00nWA/aPahvmcJp2YZ25ZZO/H7JLe5dt0Syun6jDbzdSJbMvZO+98l
+pD1SFD4p3Amlw7WGxmlLSInewmEo0YmhQGmz8eglvF15KvtWuhOmQQ8e2gYu
+bewx9cC0450QUT9kTP9uCT8p408OKnfik8fR8z4vl8Bw9avoFvVOqPce4hJ/
+vAQp6j2qV7Q6EW7flZJmsATW1/rp7vqd8Jmn2qt+dQnHRC5bFd7bqGd481HP
+6SXQbOV8yfCkEzt3pjy1P7IEi8+pDar2nShvaD3EK7GESyG6zh+cOjf0R2Rk
+ouASTsttd29514mVPf156ixLaLwjNiTh2wkBE2vH0dVF+NK7RtiGdCIr4HDb
+2/FF7BN4nFsW3YlYeeqi/Z2LeOnOqLwzuRMXn+fLV1ctolvr+Z7XmZ0w2Gp0
+5FneIuQclu3bCzqRb14WJfRrEQe2/jquUNEJ2WOT7gWRi9BW7zKNaOyEli9p
+eOS3iA9XfrOyd3fCflzaRdB9ESwOT8TtRjpRWK3gWWC/iLyrV9KHZjshNj04
+8OThIr4a+5TcWu+E9fpuD1H9RdTbOerWMHThty/946rLi5BxMnyqztWFA0ec
+PN8oLcI6/DVnyeYupG+KbT98eBHhUruPXhDrAvsWlxuDOxdh+Cd+rHJfF7b+
+2z4bxL8IGw6Tw9qyXXi89UO0BtMiWJWjOPoUuhDg1POYaWUBR3+UvbFU7UJk
+3n6lnNEFGI/LfmDQ7EJYmxuvXfsC/q6qyH/V7cImavaeQ5ULaN1m+O7o3S74
+WteHjecsoHd2yqH+cRcsHCjVY5IXYPv8trCNXRdENGObTCIWsLJpm6mQUxe4
+5xcUxHw36jl9ufP3XReOSDHZd/+3gIFlTY6nvl3IekLzOtRuAdqCeLIjtAuk
+iPWcwYMFUMxee98Q04XlrAslonoL4Bb4ct8rpQv2p0epei4t4Mh7fkY1dMH8
+O2/vN8UFiA1dMGX+14USq1nTu4c28h3597Gsqgs7jH557Nm5gAw+gf+8W7qg
+peiiOM63gNt/yi/o93VBr9XHMYlxAQrdDr37JrrAOsmj+mx5HpPjxRqUS12o
+ZpN+Jzc6D6OWs4H11N2w+m/bGer2eZCzn3MSWbvRpMdu9q9iHgI2ukWefN0o
+FD8065kzj1OGp1Mfi3Tj7QJpuZY8j7C4eQ+tPd1o0BwUEIrY8E/ecVHhcDcu
+CHaG936eB9xfUu6X74a6QYvlj//mUcOCSOFz3fhixe5kabcRXx10mlejG3Sp
+cUVyD+ahf6apjf1WNyicxk7S6c1jk7+MNatJN87to24quzSPz/XPuNgfd+NF
+vfCnz4rzMOkwTeax60aksZ2R/qF5pD1p0hdy6kbqgzNnJHbO4+ZBv82Snt1g
+25Syb4pvHulR9gNyft1Ypl3iTWecR9c53WKNsG4wap6df7M8B8sXmwsf/OiG
+7f2yv2qjc8gM9+5yT+3G+zm82tQ+h0jen0Jx2d3o/asq2FYxh9Z92q9qirvx
+4V+wR0TOHHIv2DGv13bDoXuk/GHyHHza6PL2dnTDrk+nRSZiDuY6Uz/0hzb6
+sdoSvfZ5Dg+0jpR+nulG1rTmgYL/5vDHplqseq0bv4ylTd/azSHGozCdi7EH
+SyaNalcfzKHv+ZaP17h7sIf5caWg3hyeGjbGf9nag2eFWyc6Ls2h14mVd1i8
+B0+MqUIiFOdgd7P433HpHgR3y7eYHZqD3GeJcq8TPRDXn/WT2jkHSQml3UNn
+eiBPf6pqhm8OJspH2s9e7kH8wrHnvxnncM5QYur7zR5ISq9/sFueRdhlBRMO
+4x58eBbGfHJ0FhXiMYp25j0QUTjRvt42C0rtz65Dtj344t9Mm10xi1O/j8np
+OvVAlfe99eucWeQ+LTOs8+xBR8I9SYXkDX8JL2oN/x7opz/aQhExi86m7K01
+4T2oz42Wz/o8iwnK6NQb8T1Yfr7tnd1/s3Dz+FjbndaDXzHl60fsZrHQU2pn
+kdeDMNo/HtP3Z/F7LjaOtrwHF7c3ScbpzuLtwf8sghp74HBnV4PJpVnE+qL4
+aE8PbtT4OQsrzmImKTGraawHhzcLSzUcnAXd9/yLrxZ7kKLzveSd2Czuyxi/
+2U3TC/0dwleV+WaR9odKt5Ftw1Yzy1pgmEXKUfYeD4FeDPc8oI5dmsH92zSC
+p3f0Inkz/WbdkRmc99SjodrfC4ntXKtsbTOQrw2NzD3aCw8B45Cs8hkUrF1l
+cFPu3biXtev3s2dA6UO5R/NiL7gvS3EIJs0gbkCWR0y7F1Su8kX54TO4xOpV
+uGjYizjjf2LmPjPgGwhWq37UixuSnoICrjMY3s/0LdG2F3/NLgQTmxnoPXlU
+98mpF9cn0+OMzWYQvdWm196rF2tRb+WYb83gnV1N3b2AXsy9MVeOU5+BHDkY
+fzOiF/d0WdMvnprBGSb1J1cSe9HUQ+83fmAGOnfbxdUzemFgs1b7dvsMdrVF
+Var/7UU1v9u93ZtmIH7P3PJqVS/ey59UzaebgQotJb9eay+0y6IsdBemgcTd
+WQ8HeoGxy/Wzg9MIt8y5/2a6Fx/m083dm6fx1TB0V9BaLxYu3ZHZVjoNq7Dv
+c+mMfXhwPWtbYtY0Qu5nNLfz9MFZWW6HQsI0qnjyWhiE+/CU4fzx8pBp6LLH
+r8ns6cP9Iyo6Nz9OI3nK/IypTB8y+z+96HWcxk97qrRQhT4Uejv7PbCaxpzP
+7Zsdan34RvcgfNpkGsI330tvv96HmN3vfaxvTIOKz1/J7E4fotYPmSyen0bG
+pf8+/n7Yh1GLj6w2J6bRU/RYnNm2D1xKHa/m9k7D2NWM5o5TH152nv39eNs0
+PCs+7idefcjXGI8e4phGgzRrnGhgH4J4Zi7epprGH7d1R7fIPuTOmH2pnZ6C
+MbVv2vzPPlgvG7492zuFG5sZL5tm9aH0TC93at0UliLdLnX960Pc8NCuHYVT
+WGi4kalX2wf/WrPcd2lTyD2eFtjV0QehCM2muegNO2ti2nSkDwyf3hrqBE7B
+NflC4cJ8HzTPT1zH2ym01Ilu86DuR27B5bhtL6eQd65wdQd7P6Rln998bj6F
+a18C7uUK9iO85ZBWw+0pWNWum5js7Mdi2wFfKY0peBncWuOQ7sf1Qzs2OStP
+YX6vqDSR68dpm595DYencPdzNoPluX48LbMJ2iU+hVPPkl32a/ZDKoXVx5J/
+CsFiNsnj+v1wHp4PB+NG/xYfP6Xc7weDym9CtzwJjkSPva+f9UPJO6/9/Mgk
+rqdMO15x7EfdfdcF99ZJdNbqBEt49UOGy4iyqGwStqO3negC+8F2IXGChkzC
+VCf06GDkRrxSWsaJxI33jLk5lUn9CLmSdfNx6CTKDB7uJOiHwNBcbujHSYTp
+XjVNLu5HssG74QrHSWTb7f4UV98PiobwwmXLSXRkx3yP6+7HCYqLl7ebTOJ3
+tm9C8ng/6Gl87M5en8Twp9Q4styPSE1rubvnJpHZWv29in4AIy49Hk7HJuFQ
+kBU5xD2A2B25el/3TGKO4mIcg/AAsh1GYlK2TGJzvn6upOQAIgL2mhSyTmJX
+Re3INdkB+HSccalfm8CUgbeUi/IAzrCPUHaPT+DAKY9PmZcGwE+XVzLUMQGf
+6FihJZ0BDH2+2zpWOYE7BmM1J+4N4JaescR4zgTmQtUznSwHEPz+RMRw0gTa
+t1W01rweQFmFzrme8AmA0u7E7ncDyFjdzdDoPYHSLp12J/8BqDCu1v9zngBD
+sWtJf8QApPIF435ZT4Bfko/pUtIANJIzX369O4GeFrEvWRjAsyYORccbE4jl
+aXh3sGQAL9ylhgzPT6Db6FpXXMMA2I/tfqBwfAKRv8u+SPUOIPn0CgQkJ5Cj
+/LTo9+QAdAu960e3TEDX/aXZ2bUBmN6pi8pknYDUpX2uLUyDaOHbcplrdRza
+H3J3PuMbhOiPRZ/gtnGUObpcENwxCEOnbyw7yTh2Ov+lypUaxCijXkBoyDj2
+8tepWcgN4lmosiTvm3GU1DFJ7zo/iNKzGlGvDMcR8jDnd8+1QVBvMl7oPD2O
+vx90+yPvDMKt/jDtMfFx2E6dzntsvuEfdD3VlWEczXt7NBWfD8JBWWG+dHAM
++kXfQwXcBvGGSv4HY/EYHHayJM77DOLhtH328dgxrN13cmkJG0RQMOUWw7dj
+uOLySbIwYRA1rnHhDg/HEM+eGfEncxAWEfJKny+OQVXRZSWpaBBUM+fbQ6TG
+0Dz68lBy/SDujsvrh3KOIeKOrGZ6z4b/ZpMfvlOjcDM+Y/RvchCNLzt/OFaP
+wk9A2axtbRAh4lEqxsmj+DZa/mCJeQgtQe6Gct6juPLO48lWgaENPXhwgNFq
+FNRlwm/O7hyC0Jutf4qvjeLs+yNhzw4OgaYmiDgcGYVM2sumhFND+Bne2rmP
+fxSDLLH7Jy4MoZ6nmbpiYQSyok++y9wcQoPHXRbjxhGonPZUd7w7BKN9kp0T
+aSPQ1MsSa7Qcwi6lrybm/iPQbck+fPjNEF59Z3XqsR1Bk6euk6/XELTkvYUu
+3ByBqq/OZuovQ6BSFROIPj6CIgWXtacxQ9ja9fzG8uYR3OuPPTz2ewjG6vvz
+Tq0M42n1l78PC4bw1NxPzrZlGMZCB9LnqodgITz8PTJjGBkex/icO4fw3kNk
+tDBwGDZmn7q2jG/g86YfbrUfhoaZ4I70lY16uw679OkMw9Y2ukufaRjd3mzf
+uk4MQyBohxgb/zDuD+WKV20Zxqk806kcsWHsPXlpKnkj7kGY/uWXB4eRSW/T
+79aygcNxWEVJYRjipqWDGhlD6BSYame7OIzeV9+a2QOHEHJRZ2vXRp1r30W+
+ZtkNYbcgN0Om6TCi/knw6m/M0U+JIvLrs2Ec9b4vOnNsYy5H2CjdnIexu0z3
+m63gEHyKxbfafxrGI8djr6YXByHBKEtlFTqMTVfWPuo2DkJ4UiLVOmEY8Z/u
+Z6f/HoTHqQHF11nDoAhnGmTyHQS/9K3YDyXDSKYVHla1HoS2nMVSTNMw9n9J
+iXyxcQ9EatgPlQ4M43bbp7XQw4OQ3LpVf25uGJ5jZ8p/8wwiKfalkzjtCCZr
+uRcxPQCtY5tj9LlHcPIr5c3fVQP4cLWyPkRkBKM21dUhiQPw5nzNNbx/BKcb
+GBTtvQaglElncOLkCGb/a3lz9tEALB2Pl3qrjcCqWsmaWn0AZltntee1R1D4
+enQxfuO/KPaAluv2vRGQpVODaswDeCdxbLHKegT5526JNg32I+qZDt8F5xHU
+7OJ30Crc2AseUk/KP42gjna1Jy+iH/uOWXJrh41AiEZNXNRpYy+9714bSRzB
+tqWFHY/u9GPJdN8JVzKCTWbRaTEK/TgyT1m1p3wE/+x/k/pt/XA7S/23vnUE
+Owb3bJpe7QOpLhfxGBlB2HDG+9XmPqgurwyoLI/g4+4qjvm0Phxy4NvOxjSK
+zoCX99s/b/AIxrC65o17E23k9OKX5cbefyPA9FN8FNx/1IXtNfpQHDqU6yUz
+isq4id1SBzbileyYnp0eRQa7hHUVWx/SK3b0mFwdxYDkrVaDkV7IRxzS0r8z
+itAw38Od/3rRbzJ877bFKBJEPbQuRPaiRcte1Oz1KAwkPAQjHXsxFs7i8txr
+FF7Znppjt3thnPQzyPfrKK4d2t8uKt+LE3qW9zPiRmGbFvpWeUsvNsmqLg5k
+juKiSLaMxgYvNvwlcF6odBS7bNbi1et6cPdesqFOyyjWv5uWyST14JBQi3rY
+8ChMOROMmb16MLcmxza9NApfHq4LJfd78DHaIkqVaQy6P8w0bc5t8G7lVdEf
+AmPgnNyrwbWzB7dtz7/hkxjDnve6Ap+peuDkFF/mJjsGc00fW/r2bhhtvcdE
+rzKGDM91lTvp3Thr5H/cQ2sMzP9dvRb9uRsmZaomgiZjSOxvfdLypBt3J+59
+SLQaQyHbY4vFi91Q1crLvuw8hqdWD0UpJbvhfYZlacl7DH0r0Jim74b842r5
+H9/GICVVX1ve3YXub26f76aMQc8rxtpnQ5evP3xFuzd/DFxFv+nPBnRtzL/9
+7VLNGPYOrmh0WnVBdPnHocqeMbi/mZMwutKFD2ZFqwkzY/BsDr1WtbcLyXHD
+I34049BfsovYxdiFVK8vtB484wjKtuo16emEn7yyqsuOcejNULR7ohMFLhzZ
+7ofGYX5k/Vawfyf2UTCY+imPQ5OhWNLPshO3xdZUEq6OY3eM1CbbS51QMvio
+X7Gxx5jZH3Qo7umEMd3BpMWn48iJ2qM1TduJyl2cSpJO44hXclRw7+iAndUu
+rrve4/AoXDBmSu+A+fAR0R/fxjG6aPHO3LsD163I0+WUcRzeqfgi81EHHByp
+mDUKxpFdxr8yca4Dx6yWe5PqxnFQmamUaUcH6JcM6IT6x5H7kMNs00o70i9E
+3X8/P45fz8lUR3w7tvy0ZqGnmYBWiEWq9Z12mM87055nmYCqvujJRt52PNmh
+HPKeZwLpX54w0Ra1oUfkbHvrBg+4rPLjy5J9G7wGl7P2iU3AtSPJLm1/G44U
+B8s77p1A8AK1iEJXK3y+Kuu3HZ4Ak3ssy/tPrageyNsmd3ICHMfPpUedacX9
+9mL74DMTKHi2Eumy0AI30zJLhosTmHG5p7Y3ugVbqJkYLbUmsHAvTtjvZgt2
+vHI41Kc3gevfbwUUsbSgtHh99uYGzymge3YgO7MZei+ZVevMJxBPZ3zN/mEz
+LIzGpDRtJuCuO2m3LNQMdPwIb3g9ATWFk1wny5vAK8MYpu82AT63PBell00w
+/m21a/TDBLzyVM4x729Ceo3wgRcBG/k4a7M/tTViaqXrN/cGL/s4kKjd/rYR
+vI/OpP+IncDFn7p2QycakVT/4qBaygZvk3f7L2W4AZUlxlvGMycQxs88KO/f
+gNxt9uY+BRPoCK1fdlVpgCR1i4Ri+QTkRNZEvObqMU4lrzhVP4GzroFpV8Pr
+oVI88zNig0e67moQqrtcj9MZ7U/1BifAuLc2hnu9Dp5nzF9tmZrA8siP3yyx
+dZBhCy5tXZqABbtpALleB5qKEY0w6kmwvZqN3EdbBydaDaYHLJOwPMgndS2x
+FuFKKv3HNk1C/I/JG5lbtQi8mNLBIjQJlpCz42UMtTjXOz7ctXMSH4Jqs4SS
+a9AhkbyasX+DJzv2HBPTq4Fi/lamANlJfGSZ/N7JWIO9gcE0zxUm4XWF75JG
+cjWMd1B2GJyfxC9Jhkc2utWgVFN7p6YxibwTa6c1GKqRNlxGcUxnEtSFPzk7
+EqvAlcGya4/RJLguX2HZdrMKfbm/prc9nMSmKfMH7DRV4JMJucJvPYnXlmv3
+EmIrYZP0W5rn1SR2SB47RKlZicc9c6+4/5uE+ouIZYrVCvToXJPg/TAJG5mV
+kbjwCvil5/NuCZhE6put0kxqFdCfETgoFj6JSQPOnu195Vj8uW584Mckwnd6
+h7gdLAdFzrDfqV+TeK/c2XbmVRki9Jh+XsEkVD7O1l8rKYWD8d5PJoWTqM32
+y/nNV4p7+9K2v6ycBGOYfJmpQQl203op+jVNQuBfz3az2GK83LxSkdI9uXEf
+p3tTZ4ugkfn5R82GjjoQJSp18WQR3kYeTJmd3dBFdZp8+53/IfxMeg7/+iRy
+rtt91ywtBGcob7wcwxRiLU1HCXcheuMZLxtyTqHLinQ9vPEX44TjuYfgFPIn
+M17f+lKAP9+P0v7aPoW3MlvT3bry4SK3+LtDcgpyHXPWM2L5YPiyYsgiM4XA
+F+/9fO/m4XjpbJWs/BS4rsovPo3Oxdlqg39GKlPYKnz4rstwDv5+V2f+eHkK
+TeP68aV7cqA6w3SdaG/YI/Kep82yoXKz03T0zhT0tidh5DvBya3pSwIPpsD3
+KKL9dTnwgi8z7bTVFLqpnd1fnstC/da6q+YbOleEjyqzNDsDRSMnnvi5TsE/
+61GAiWw6PFWbUsj7KcRoCB5X+ZEGoxX/X73+U2g/1h5oKvwb4iVh9AzhG/lF
+/v749/4XkhT1pcV/TKHNP/CMPmUK7gzc/qX4awoenK/2SDxKQqgRFYM2ppA6
+8Ix5W3MiXqinvLu/oduFC6hfnTidgGHhsVCbyin8Kj4usKD9A1vGHru/appC
+YYH/iQTxaISW1dm86t7Q5RlqvD4TEQiMLnN6NjIFlwK/7V9SwuDi7hthMjsF
++8W+xAyrYCR/t/iutjaFeLUb6cUm/hvnWyO6k34aswtFopubPmJJJ1xzin0a
+YvqNnF9c3aDftpcmnn8a/t1PKo762W7wQmmqGyLT+B/esTLP
+ "]],
+ LineBox[CompressedData["
+1:eJwVlHc0140Xx2VEKUUZUWbKiIbiobgfo6UUSulJWdE0GpSohJSUZDSUnjw0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+ "]]}}, {{}, {}}},
+ 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->{{-66.43192903964376,
+ 21.162242658677417`}, {-1.988814814026506, 0}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.02]}},
+ Ticks->{Automatic, Automatic}]], "Output",
+ CellChangeTimes->{{3.817637498101*^9, 3.817637523899531*^9},
+ 3.817640201425125*^9, 3.8176403703128757`*^9, 3.8176666395171747`*^9, {
+ 3.817666742407874*^9, 3.817666765580124*^9}, {3.817666863393943*^9,
+ 3.817666920031568*^9}},
+ CellLabel->
+ "Out[120]=",ExpressionUUID->"348377e3-5d2e-45e0-83a1-0bb162fca9ec"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"ListPlot", "[",
+ RowBox[{
+ RowBox[{"Table", "[",
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{
RowBox[{
- RowBox[{"\[Theta]", "<", "\[Theta]c"}], ",",
- RowBox[{"\[Theta]", ">", "\[Theta]i"}]}], "}"}]}], "]"}]}]}],
- "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]",
- RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{
+ RowBox[{"h2", "[", "\[Theta]", "]"}],
+ SuperscriptBox[
+ RowBox[{"t", "[", "\[Theta]", "]"}],
+ RowBox[{"-",
+ RowBox[{"\[CapitalDelta]", "[", "2", "]"}]}]]}], ",",
+ RowBox[{
+ RowBox[{"-",
+ RowBox[{
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"Transpose", "[",
+ RowBox[{"Inverse", "[",
+ RowBox[{
+ RowBox[{"D", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"R", " ",
+ RowBox[{"t", "[", "\[Theta]p", "]"}]}], ",",
+ RowBox[{
+ SuperscriptBox["R",
+ RowBox[{"\[CapitalDelta]", "[", "2", "]"}]],
+ RowBox[{"h2", "[", "\[Theta]p", "]"}]}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"R", ",", "\[Theta]p"}], "}"}], "}"}]}], "]"}], "/.",
+ RowBox[{"\[Theta]p", "\[Rule]", "\[Theta]"}]}], "]"}],
+ "]"}], ".",
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"D", "[",
+ RowBox[{
+ RowBox[{
+ SuperscriptBox["R", "2"],
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"F2", "[", "\[Theta]p", "]"}], "+",
+ RowBox[{
+ SuperscriptBox[
+ RowBox[{"t", "[", "\[Theta]p", "]"}], "2"],
+ RowBox[{
+ RowBox[{"Log", "[",
+ SuperscriptBox["R", "2"], "]"}], "/",
+ RowBox[{"(",
+ RowBox[{"8", "\[Pi]"}], ")"}]}]}]}], ")"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"R", ",", "\[Theta]p"}], "}"}], "}"}]}], "]"}], "/.",
+ RowBox[{"\[Theta]p", "\[Rule]", "\[Theta]"}]}], ")"}]}],
+ ")"}], "[",
+ RowBox[{"[", "2", "]"}], "]"}]}], "/",
+ SuperscriptBox[
+ RowBox[{"(",
+ RowBox[{"R", " ",
+ RowBox[{"t", "[", "\[Theta]", "]"}]}], ")"}],
+ RowBox[{"1", "/", "8"}]]}]}], "}"}], "/.",
+ RowBox[{"B", "\[Rule]",
+ RowBox[{"ruleB", "[", "h2", "]"}]}]}], "/.", "sol2"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c1"}]}], "/.",
+ RowBox[{"R", "\[Rule]", "1"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]", ",", "1", ",", "\[Theta]c1", ",", "0.01"}], "}"}]}],
+ "]"}], ",",
+ RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}]], "Input",
+ CellChangeTimes->{{3.8176326022950163`*^9, 3.8176326467232037`*^9}, {
+ 3.817632683971553*^9, 3.817632789027328*^9}, {3.81763283674572*^9,
+ 3.8176328368685007`*^9}, {3.817632877796402*^9, 3.817632918098442*^9}, {
+ 3.8176329487995663`*^9, 3.8176329657972403`*^9}, {3.817633013987247*^9,
+ 3.817633015478447*^9}, {3.817633052086051*^9, 3.81763311811401*^9}, {
+ 3.817637857064962*^9, 3.81763799340449*^9}, {3.817638044949687*^9,
+ 3.817638084808195*^9}, {3.817638153127841*^9, 3.817638168358132*^9}, {
+ 3.817638399473373*^9, 3.817638412536726*^9}, {3.81763844666143*^9,
+ 3.8176384666464853`*^9}, {3.817638593096958*^9, 3.817638600437099*^9}, {
+ 3.817638794437633*^9, 3.817638799137588*^9}, {3.81766678228234*^9,
+ 3.817666782527095*^9}, {3.817666937000008*^9, 3.817667042110792*^9}, {
+ 3.817667191974594*^9, 3.817667193333255*^9}},
+ CellLabel->
+ "In[126]:=",ExpressionUUID->"3fee7ec2-e0c4-4420-8192-c46efe85e265"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "Power", "infy",
+ "\"Infinite expression \\!\\(\\*FractionBox[\\\"1\\\", \
+SuperscriptBox[\\\"0.`\\\", RowBox[{\\\"15\\\", \\\"/\\\", \\\"8\\\"}]]]\\) \
+encountered.\"", 2, 126, 106, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, 3.81764020582121*^9,
+ 3.817640383596977*^9, {3.817667009401268*^9, 3.8176670429767323`*^9},
+ 3.817667193780019*^9},
+ CellLabel->
+ "During evaluation of \
+In[126]:=",ExpressionUUID->"216842f7-6b1f-4b0e-80ad-7561735930ba"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "Power", "infy",
+ "\"Infinite expression \\!\\(\\*FractionBox[\\\"1\\\", \\\"0.`\\\"]\\) \
+encountered.\"", 2, 126, 107, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, 3.81764020582121*^9,
+ 3.817640383596977*^9, {3.817667009401268*^9, 3.8176670429767323`*^9},
+ 3.8176671938444023`*^9},
+ CellLabel->
+ "During evaluation of \
+In[126]:=",ExpressionUUID->"19c5d1c8-bbcd-4f5b-83f4-3116397aae1d"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "Power", "infy",
+ "\"Infinite expression \\!\\(\\*FractionBox[\\\"1\\\", \\\"0.`\\\"]\\) \
+encountered.\"", 2, 126, 108, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, 3.81764020582121*^9,
+ 3.817640383596977*^9, {3.817667009401268*^9, 3.8176670429767323`*^9},
+ 3.817667194427414*^9},
+ CellLabel->
+ "During evaluation of \
+In[126]:=",ExpressionUUID->"bf3fa7a1-a10c-4f34-b799-15feb6fd9a94"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "General", "stop",
+ "\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"Power\\\", \\\"::\\\", \
+\\\"infy\\\"}], \\\"MessageName\\\"]\\) will be suppressed during this \
+calculation.\"", 2, 126, 109, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, 3.81764020582121*^9,
+ 3.817640383596977*^9, {3.817667009401268*^9, 3.8176670429767323`*^9},
+ 3.817667194492173*^9},
+ CellLabel->
+ "During evaluation of \
+In[126]:=",ExpressionUUID->"8301d9c6-5667-4e0e-babc-34891d14958b"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "Infinity", "indet",
+ "\"Indeterminate expression \
+\\!\\(\\*SuperscriptBox[\\\"\[ExponentialE]\\\", \\\"ComplexInfinity\\\"]\\) \
+encountered.\"", 2, 126, 110, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, 3.81764020582121*^9,
+ 3.817640383596977*^9, {3.817667009401268*^9, 3.8176670429767323`*^9},
+ 3.8176671945907*^9},
+ CellLabel->
+ "During evaluation of \
+In[126]:=",ExpressionUUID->"ccae7427-68ca-4f65-9f6d-4dd2dc4b639d"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "Infinity", "indet",
+ "\"Indeterminate expression \
+\\!\\(\\*SuperscriptBox[\\\"\[ExponentialE]\\\", \\\"ComplexInfinity\\\"]\\) \
+encountered.\"", 2, 126, 111, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, 3.81764020582121*^9,
+ 3.817640383596977*^9, {3.817667009401268*^9, 3.8176670429767323`*^9},
+ 3.81766719464719*^9},
+ CellLabel->
+ "During evaluation of \
+In[126]:=",ExpressionUUID->"cfcfd305-6369-4d0d-ab91-323656281a2e"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "Infinity", "indet",
+ "\"Indeterminate expression \
+\\!\\(\\*SuperscriptBox[\\\"\[ExponentialE]\\\", \\\"ComplexInfinity\\\"]\\) \
+encountered.\"", 2, 126, 112, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, 3.81764020582121*^9,
+ 3.817640383596977*^9, {3.817667009401268*^9, 3.8176670429767323`*^9},
+ 3.817667194702935*^9},
+ CellLabel->
+ "During evaluation of \
+In[126]:=",ExpressionUUID->"ddee7f30-4b8d-49f3-a238-e8df9057bfed"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "General", "stop",
+ "\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"Infinity\\\", \
+\\\"::\\\", \\\"indet\\\"}], \\\"MessageName\\\"]\\) will be suppressed \
+during this calculation.\"", 2, 126, 113, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, 3.81764020582121*^9,
+ 3.817640383596977*^9, {3.817667009401268*^9, 3.8176670429767323`*^9},
+ 3.817667194761594*^9},
+ CellLabel->
+ "During evaluation of \
+In[126]:=",ExpressionUUID->"456dde30-b84b-4cba-9cea-4c2b7080bc35"],
+
+Cell[BoxData[
+ GraphicsBox[{{}, {{}, {},
+ {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.012833333333333334`],
+ AbsoluteThickness[1.6], LineBox[CompressedData["
+1:eJwBQQG+/iFib1JlAgAAABMAAAACAAAAXyvpKMz9Y0C3QrnA1uv8P4duXZXX
+ukRATsZLEVmq+j/FNok+tV8yQAOXrRW2e/k/7JgdMwI9JEDgdVDnWrb4P/OO
++rInDxlAj0txbxUo+D8Z7FlFLawQQCQ4FoVhu/c/1pSFi4JEB0CwfSt4G2X3
+PyVK9yBJxgBA0W4S7MYe9z/hq0CKo7z4P+NUHMNL5PY/oJ6RF3OD8j+aBFX0
+67L2P4wniWVN9Os/raIla7uI9j8DwhD7ZSvlP/Acw5pUZPY/Sy3Y1o353z/S
+YpwBrET2PyVjsO366tc/RZN7kfQo9j+E8fo0go/RP/XATtiNEPY/VdhPqeb1
+yD+Yob8N+Pr1PzvEy3qJwMA/ayjL08vn9T8MgJn33R20PzdIJ1y01vU/VAtC
+Nc44oj9iCJYia8f1P7PGnD4=
+ "]]}}, {{}, {}}},
+ AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
+ Axes->{True, True},
+ AxesLabel->{None, None},
+ AxesOrigin->{0, 1.3363866177721921`},
+ 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, 25.0053870624539}, {1.3363866177721921`,
+ 1.8075778511303449`}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.05]}},
+ Ticks->{Automatic, Automatic}]], "Output",
+ CellChangeTimes->{{3.817637498101*^9, 3.817637523899531*^9},
+ 3.8176379865886707`*^9, {3.817638080223015*^9, 3.817638097089458*^9}, {
+ 3.817638411035137*^9, 3.817638418380022*^9}, {3.817638453141902*^9,
+ 3.817638469864127*^9}, 3.817638603759224*^9, 3.817638801668243*^9,
+ 3.8176402094564*^9, 3.817640385397132*^9, {3.817667011743911*^9,
+ 3.8176670445182667`*^9}, 3.817667195320567*^9},
+ CellLabel->
+ "Out[126]=",ExpressionUUID->"f0d61600-5eb6-4f8a-9c60-ac80b53c708a"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"ListPlot", "[",
RowBox[{
- RowBox[{"eqHigh", "[", "n_", "]"}], "[", "m_", "]"}], ":=",
- RowBox[{"SeriesCoefficient", "[", "\[IndentingNewLine]",
- RowBox[{
+ RowBox[{"Table", "[",
RowBox[{
- RowBox[{"R\[ScriptCapitalM]", "[", "\[Theta]", "]"}], "+",
RowBox[{
- SuperscriptBox[
- RowBox[{"(",
- RowBox[{"-",
- RowBox[{
- RowBox[{"f", "[", "n", "]"}], "[", "\[Theta]", "]"}]}], ")"}],
- "\[Beta]"],
RowBox[{
- RowBox[{"Gh", "'"}], "[",
RowBox[{
RowBox[{
- RowBox[{"g", "[", "n", "]"}], "[", "\[Theta]", "]"}],
- SuperscriptBox[
- RowBox[{"(",
- RowBox[{"-",
+ RowBox[{
+ RowBox[{"{",
RowBox[{
- RowBox[{"f", "[", "n", "]"}], "[", "\[Theta]", "]"}]}], ")"}],
- RowBox[{"-", "\[CapitalDelta]"}]]}], "]"}]}]}], ",",
- "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"h2", "[", "\[Theta]", "]"}],
+ SuperscriptBox[
+ RowBox[{"t", "[", "\[Theta]", "]"}],
+ RowBox[{"-",
+ RowBox[{"\[CapitalDelta]", "[", "2", "]"}]}]]}], ",",
+ RowBox[{
+ RowBox[{"-",
+ RowBox[{
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"Transpose", "[",
+ RowBox[{"Inverse", "[",
+ RowBox[{"D", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"R", " ",
+ RowBox[{"t", "[", "\[Theta]p", "]"}]}], ",",
+ RowBox[{
+ SuperscriptBox["R",
+ RowBox[{"\[CapitalDelta]", "[", "2", "]"}]],
+ RowBox[{"h2", "[", "\[Theta]p", "]"}]}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"R", ",", "\[Theta]p"}], "}"}], "}"}]}], "]"}],
+ "]"}], "]"}], ".",
+ RowBox[{"D", "[",
+ RowBox[{
+ RowBox[{
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"Transpose", "[",
+ RowBox[{"Inverse", "[",
+ RowBox[{"D", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"R", " ",
+ RowBox[{"t", "[", "\[Theta]p", "]"}]}], ",",
+ RowBox[{
+ SuperscriptBox["R",
+ RowBox[{"\[CapitalDelta]", "[", "2", "]"}]],
+ RowBox[{"h2", "[", "\[Theta]p", "]"}]}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"R", ",", "\[Theta]p"}], "}"}], "}"}]}], "]"}],
+ "]"}], "]"}], ".",
+ RowBox[{"D", "[",
+ RowBox[{
+ RowBox[{
+ SuperscriptBox["R", "2"],
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"F2", "[", "\[Theta]p", "]"}], "+",
+ RowBox[{
+ SuperscriptBox[
+ RowBox[{"t", "[", "\[Theta]p", "]"}], "2"],
+ RowBox[{
+ RowBox[{"Log", "[",
+ SuperscriptBox["R", "2"], "]"}], "/",
+ RowBox[{"(",
+ RowBox[{"8", "\[Pi]"}], ")"}]}]}]}], ")"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"R", ",", "\[Theta]p"}], "}"}], "}"}]}], "]"}]}],
+ ")"}], "[",
+ RowBox[{"[", "2", "]"}], "]"}], ",",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"R", ",", "\[Theta]p"}], "}"}], "}"}]}], "]"}]}],
+ ")"}], "[",
+ RowBox[{"[", "2", "]"}], "]"}]}],
+ SuperscriptBox[
+ RowBox[{"(",
+ RowBox[{"R", " ",
+ RowBox[{"t", "[", "\[Theta]p", "]"}]}], ")"}],
+ RowBox[{"7", "/", "4"}]]}]}], "}"}], "/.",
+ RowBox[{"\[Theta]p", "\[Rule]", "\[Theta]"}]}], "/.",
+ RowBox[{"B", "\[Rule]",
+ RowBox[{"ruleB", "[", "h2", "]"}]}]}], "/.", "sol2"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c1"}]}], "/.",
+ RowBox[{"R", "\[Rule]", "1"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]", ",", "1", ",", "\[Theta]c1", ",", "0.01"}], "}"}]}],
+ "]"}], ",",
+ RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}]], "Input",
+ CellChangeTimes->{{3.8176326022950163`*^9, 3.8176326467232037`*^9}, {
+ 3.817632683971553*^9, 3.817632789027328*^9}, {3.81763283674572*^9,
+ 3.8176328368685007`*^9}, {3.817632877796402*^9, 3.817632918098442*^9}, {
+ 3.8176329487995663`*^9, 3.8176329657972403`*^9}, {3.817633013987247*^9,
+ 3.817633015478447*^9}, {3.817633052086051*^9, 3.81763311811401*^9}, {
+ 3.817637857064962*^9, 3.81763799340449*^9}, {3.817638044949687*^9,
+ 3.817638084808195*^9}, {3.817638153127841*^9, 3.817638168358132*^9}, {
+ 3.817638399473373*^9, 3.817638412536726*^9}, {3.81763844666143*^9,
+ 3.8176384666464853`*^9}, {3.817638593096958*^9, 3.817638600437099*^9}, {
+ 3.817638794437633*^9, 3.817638799137588*^9}, {3.817638894386457*^9,
+ 3.817638959881351*^9}, {3.81763900605718*^9, 3.817639007860661*^9},
+ 3.8176391897006083`*^9, {3.817639366190852*^9, 3.817639373670949*^9}, {
+ 3.817639408490509*^9, 3.817639409929799*^9}, {3.817639455026854*^9,
+ 3.817639465324203*^9}, {3.817640238475677*^9, 3.8176402389305267`*^9}, {
+ 3.817640391548546*^9, 3.817640391871228*^9}, {3.8176672347145987`*^9,
+ 3.817667293531107*^9}, {3.817667331524941*^9, 3.817667335774218*^9}},
+ CellLabel->
+ "In[129]:=",ExpressionUUID->"0c28b27c-3e81-49ce-9293-512f19f95aeb"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "Power", "infy",
+ "\"Infinite expression \\!\\(\\*FractionBox[\\\"1\\\", \
+SuperscriptBox[\\\"0.`\\\", RowBox[{\\\"15\\\", \\\"/\\\", \\\"8\\\"}]]]\\) \
+encountered.\"", 2, 129, 130, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, {3.8176389311200447`*^9,
+ 3.817638961027931*^9}, 3.8176393754003963`*^9, {3.8176394554804564`*^9,
+ 3.817639466763811*^9}, {3.8176402126638117`*^9, 3.817640239353836*^9},
+ 3.817640392303451*^9, {3.817667279098195*^9, 3.817667294232696*^9},
+ 3.817667336609736*^9},
+ CellLabel->
+ "During evaluation of \
+In[129]:=",ExpressionUUID->"b34a59d2-df83-4bcc-8877-f7287b9c6b63"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "Power", "infy",
+ "\"Infinite expression \\!\\(\\*FractionBox[\\\"1\\\", \\\"0.`\\\"]\\) \
+encountered.\"", 2, 129, 131, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, {3.8176389311200447`*^9,
+ 3.817638961027931*^9}, 3.8176393754003963`*^9, {3.8176394554804564`*^9,
+ 3.817639466763811*^9}, {3.8176402126638117`*^9, 3.817640239353836*^9},
+ 3.817640392303451*^9, {3.817667279098195*^9, 3.817667294232696*^9},
+ 3.8176673396722183`*^9},
+ CellLabel->
+ "During evaluation of \
+In[129]:=",ExpressionUUID->"f90bbc2c-a921-4f2e-80fc-1fe79d36f5ed"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "Infinity", "indet",
+ "\"Indeterminate expression \
+\\!\\(\\*SuperscriptBox[\\\"\[ExponentialE]\\\", \\\"ComplexInfinity\\\"]\\) \
+encountered.\"", 2, 129, 132, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, {3.8176389311200447`*^9,
+ 3.817638961027931*^9}, 3.8176393754003963`*^9, {3.8176394554804564`*^9,
+ 3.817639466763811*^9}, {3.8176402126638117`*^9, 3.817640239353836*^9},
+ 3.817640392303451*^9, {3.817667279098195*^9, 3.817667294232696*^9},
+ 3.817667339725185*^9},
+ CellLabel->
+ "During evaluation of \
+In[129]:=",ExpressionUUID->"0c5f9a46-bb7f-4f2b-873b-5f8374387e5b"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "Power", "infy",
+ "\"Infinite expression \\!\\(\\*FractionBox[\\\"1\\\", \\\"0.`\\\"]\\) \
+encountered.\"", 2, 129, 133, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, {3.8176389311200447`*^9,
+ 3.817638961027931*^9}, 3.8176393754003963`*^9, {3.8176394554804564`*^9,
+ 3.817639466763811*^9}, {3.8176402126638117`*^9, 3.817640239353836*^9},
+ 3.817640392303451*^9, {3.817667279098195*^9, 3.817667294232696*^9},
+ 3.817667339779063*^9},
+ CellLabel->
+ "During evaluation of \
+In[129]:=",ExpressionUUID->"9152de73-1d17-4288-821f-53b3ff3cd6a3"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "General", "stop",
+ "\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"Power\\\", \\\"::\\\", \
+\\\"infy\\\"}], \\\"MessageName\\\"]\\) will be suppressed during this \
+calculation.\"", 2, 129, 134, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, {3.8176389311200447`*^9,
+ 3.817638961027931*^9}, 3.8176393754003963`*^9, {3.8176394554804564`*^9,
+ 3.817639466763811*^9}, {3.8176402126638117`*^9, 3.817640239353836*^9},
+ 3.817640392303451*^9, {3.817667279098195*^9, 3.817667294232696*^9},
+ 3.8176673398380413`*^9},
+ CellLabel->
+ "During evaluation of \
+In[129]:=",ExpressionUUID->"da8de725-4d35-4371-8f8b-200846f7fadc"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "Infinity", "indet",
+ "\"Indeterminate expression \
+\\!\\(\\*SuperscriptBox[\\\"\[ExponentialE]\\\", \\\"ComplexInfinity\\\"]\\) \
+encountered.\"", 2, 129, 135, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, {3.8176389311200447`*^9,
+ 3.817638961027931*^9}, 3.8176393754003963`*^9, {3.8176394554804564`*^9,
+ 3.817639466763811*^9}, {3.8176402126638117`*^9, 3.817640239353836*^9},
+ 3.817640392303451*^9, {3.817667279098195*^9, 3.817667294232696*^9},
+ 3.817667339891858*^9},
+ CellLabel->
+ "During evaluation of \
+In[129]:=",ExpressionUUID->"77c72bca-73bf-4da0-8420-b2d771db650c"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "Infinity", "indet",
+ "\"Indeterminate expression \
+\\!\\(\\*SuperscriptBox[\\\"\[ExponentialE]\\\", \\\"ComplexInfinity\\\"]\\) \
+encountered.\"", 2, 129, 136, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, {3.8176389311200447`*^9,
+ 3.817638961027931*^9}, 3.8176393754003963`*^9, {3.8176394554804564`*^9,
+ 3.817639466763811*^9}, {3.8176402126638117`*^9, 3.817640239353836*^9},
+ 3.817640392303451*^9, {3.817667279098195*^9, 3.817667294232696*^9},
+ 3.817667339978014*^9},
+ CellLabel->
+ "During evaluation of \
+In[129]:=",ExpressionUUID->"0ab865cc-63da-43d9-be96-488dae3c11a7"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "General", "stop",
+ "\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"Infinity\\\", \
+\\\"::\\\", \\\"indet\\\"}], \\\"MessageName\\\"]\\) will be suppressed \
+during this calculation.\"", 2, 129, 137, 25019439459511732134, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{{3.817638449730116*^9, 3.817638467379733*^9},
+ 3.817638601228196*^9, 3.817638799584732*^9, {3.8176389311200447`*^9,
+ 3.817638961027931*^9}, 3.8176393754003963`*^9, {3.8176394554804564`*^9,
+ 3.817639466763811*^9}, {3.8176402126638117`*^9, 3.817640239353836*^9},
+ 3.817640392303451*^9, {3.817667279098195*^9, 3.817667294232696*^9},
+ 3.817667340071809*^9},
+ CellLabel->
+ "During evaluation of \
+In[129]:=",ExpressionUUID->"d6d0804b-e464-4f31-9989-db903712ce18"],
+
+Cell[BoxData[
+ GraphicsBox[{{}, {{}, {},
+ {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.012833333333333334`],
+ AbsoluteThickness[1.6], LineBox[CompressedData["
+1:eJwBQQG+/iFib1JlAgAAABMAAAACAAAAXyvpKMz9Y0DTbqmRxAFHP4duXZXX
+ukRAO6YZ8mUCYz/FNok+tV8yQAsGLqnC/HI/7JgdMwI9JEDfJY01st1+P/OO
++rInDxlAm9WAac1ohj8Z7FlFLawQQGJo6wwlTI4/1pSFi4JEB0B9iR9ISX+T
+PyVK9yBJxgBAmoJLhfc0mD/hq0CKo7z4P+dDMRynPZ0/oJ6RF3OD8j/dLgSX
+nEihP4wniWVN9Os/x4zHOl4UpD8DwhD7ZSvlP2+323gr/6Y/Sy3Y1o353z+f
+1U1+nwaqPyVjsO366tc/Mw8Nk+EorT+E8fo0go/RP0iJ88FYMrA/VdhPqeb1
+yD++YNy8v9yxPzvEy3qJwMA/5XpMo8qTsz8MgJn33R20P14+RbouWLU/VAtC
+Nc44oj8zvgeScSu3P3GfkeQ=
+ "]]}}, {{}, {}}},
+ 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, 25.0053870624539}, {0, 0.09050664725486328}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.02],
+ Scaled[0.05]}},
+ Ticks->{Automatic, Automatic}]], "Output",
+ CellChangeTimes->{{3.817637498101*^9, 3.817637523899531*^9},
+ 3.8176379865886707`*^9, {3.817638080223015*^9, 3.817638097089458*^9}, {
+ 3.817638411035137*^9, 3.817638418380022*^9}, {3.817638453141902*^9,
+ 3.817638469864127*^9}, 3.817638603759224*^9, 3.817638801668243*^9, {
+ 3.817638950488543*^9, 3.8176389801125393`*^9}, 3.817639384560536*^9, {
+ 3.8176394648201838`*^9, 3.817639475564313*^9}, {3.817640221335127*^9,
+ 3.817640248053196*^9}, 3.817640401002247*^9, {3.81766728274492*^9,
+ 3.817667297661644*^9}, 3.8176673405798473`*^9},
+ CellLabel->
+ "Out[129]=",ExpressionUUID->"1007ec09-f8b7-4f86-9778-7ddc0fddb31f"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"g3", "=",
+ RowBox[{"g", "[", "4", "]"}]}], ";"}], "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"F3", "=",
+ RowBox[{"RF", "[", "2", "]"}]}], ";"}], "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"eq3", "=",
+ RowBox[{
+ RowBox[{"eq", "[",
+ RowBox[{"F3", ",", "g3"}], "]"}], "[", "3", "]"}]}], ";"}]}], "Input",
+ CellChangeTimes->{
+ 3.817563268660089*^9, {3.817563829122241*^9, 3.817563846550528*^9}, {
+ 3.817563950998456*^9, 3.817563956525237*^9}, {3.8175645239988813`*^9,
+ 3.817564534320574*^9}, {3.81756485534698*^9, 3.817564862343175*^9}, {
+ 3.817564919676697*^9, 3.8175649235785027`*^9}, {3.817565106996109*^9,
+ 3.8175651474217367`*^9}, {3.8175652415905113`*^9, 3.817565250029232*^9}, {
+ 3.8175657444559927`*^9, 3.8175657689660788`*^9}, 3.8175669120549498`*^9, {
+ 3.8175677716518087`*^9, 3.817567773706285*^9}, {3.817579700926876*^9,
+ 3.817579701354711*^9}, {3.8175810533593073`*^9, 3.817581114447541*^9}, {
+ 3.817581149854197*^9, 3.8175811499220247`*^9}, {3.817581265163169*^9,
+ 3.81758126542041*^9}, {3.81758144220247*^9, 3.8175814490334673`*^9}, {
+ 3.8175815152710047`*^9, 3.817581521148234*^9}, {3.817581635837187*^9,
+ 3.817581700879589*^9}, {3.817581767691791*^9, 3.817581768673394*^9}, {
+ 3.8175821842992363`*^9, 3.8175821844066353`*^9}, {3.817582286431714*^9,
+ 3.817582297101211*^9}, {3.817582488847374*^9, 3.817582488974349*^9}, {
+ 3.817582803954041*^9, 3.817582804222094*^9}, {3.817618756754203*^9,
+ 3.817618757439868*^9}, {3.81761900296082*^9, 3.817619003035212*^9}, {
+ 3.8176203963382673`*^9, 3.817620396528458*^9}, {3.817626242723531*^9,
+ 3.817626282042306*^9}, {3.817627870666265*^9, 3.817627904779098*^9}, {
+ 3.817629704809123*^9, 3.8176297360288*^9}},
+ CellLabel->
+ "In[150]:=",ExpressionUUID->"78606265-f50f-49dc-888d-33550f059b83"],
+
+Cell[BoxData["$Aborted"], "Output",
+ CellChangeTimes->{3.817632399208988*^9, 3.817637443451262*^9},
+ CellLabel->
+ "Out[152]=",ExpressionUUID->"0e837164-3793-49da-bdd0-d4f51cfcde79"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"sol3", "=",
+ RowBox[{"FindRoot", "[",
+ RowBox[{"eq3", ",",
RowBox[{"{",
- RowBox[{"\[Theta]", ",", "0", ",", "m"}], "}"}], ",",
- RowBox[{"Assumptions", "\[Rule]",
- RowBox[{"Join", "[",
- RowBox[{"$Assumptions", ",",
- RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"A", ",",
+ RowBox[{"A", "/.", "sol2"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], ",",
RowBox[{
- RowBox[{"\[Theta]", ">", "0"}], ",",
- RowBox[{"\[Theta]", "<", "\[Theta]i"}]}], "}"}]}], "]"}]}]}],
- "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]",
- RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], "/.", "sol2"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"FC", "[", "0", "]"}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "0", "]"}], "/.", "sol2"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"FC", "[", "1", "]"}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "1", "]"}], "/.", "sol2"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"FC", "[", "2", "]"}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "2", "]"}], "/.", "sol2"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "1", "]"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "1", "]"}], "/.", "sol2"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "2", "]"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "2", "]"}], "/.", "sol2"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]c", ",",
+ RowBox[{"\[Theta]c", "/.", "sol2"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "3", "]"}], ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "4", "]"}], ",", "0"}], "}"}]}], "}"}], ",",
+ RowBox[{"MaxIterations", "\[Rule]", "500"}]}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.8175612726329412`*^9, 3.81756128486736*^9}, {
+ 3.8175614038617268`*^9, 3.817561415404965*^9}, {3.817561511096093*^9,
+ 3.817561563944231*^9}, {3.81756250196518*^9, 3.817562507914916*^9}, {
+ 3.817562967760625*^9, 3.81756298304041*^9}, 3.817563161460335*^9, {
+ 3.817563206558021*^9, 3.81756320676147*^9}, {3.817563530710863*^9,
+ 3.817563550054001*^9}, {3.817563775700533*^9, 3.817563804069632*^9}, {
+ 3.817563971222761*^9, 3.817564086350409*^9}, {3.817564155680212*^9,
+ 3.8175641623358994`*^9}, {3.81756424029494*^9, 3.817564240399859*^9}, {
+ 3.8175645416987743`*^9, 3.817564542202907*^9}, {3.817564715061411*^9,
+ 3.817564723202471*^9}, {3.8175648450855713`*^9, 3.817564883921851*^9}, {
+ 3.8175650025642157`*^9, 3.817565074155829*^9}, {3.817565217921039*^9,
+ 3.817565230520749*^9}, {3.817565359356901*^9, 3.8175654247402163`*^9}, {
+ 3.817565602697175*^9, 3.817565635407323*^9}, {3.817566059389201*^9,
+ 3.817566077942937*^9}, {3.817566269837482*^9, 3.817566273547044*^9}, {
+ 3.8175663066250553`*^9, 3.817566306784181*^9}, {3.817566684914805*^9,
+ 3.81756668549652*^9}, {3.817566919102108*^9, 3.817566934549343*^9}, {
+ 3.8175696638331223`*^9, 3.817569664744486*^9}, {3.817579706169273*^9,
+ 3.8175797767735577`*^9}, {3.817581067506674*^9, 3.8175810689721537`*^9}, {
+ 3.817581121371869*^9, 3.817581169115347*^9}, {3.817581207766066*^9,
+ 3.817581270669099*^9}, 3.817581309702499*^9, {3.817581355857291*^9,
+ 3.817581356026667*^9}, {3.817581392130506*^9, 3.817581416424316*^9}, {
+ 3.817581457365512*^9, 3.8175814943565397`*^9}, {3.81758152586852*^9,
+ 3.817581526654297*^9}, {3.8175819155874557`*^9, 3.81758195123713*^9}, {
+ 3.8175820720836487`*^9, 3.817582073079625*^9}, {3.817582192281794*^9,
+ 3.8175821927535973`*^9}, {3.8175824979646*^9, 3.817582531058486*^9}, {
+ 3.817582601242318*^9, 3.817582616669943*^9}, {3.817582763042087*^9,
+ 3.817582823261053*^9}, {3.817582997786705*^9, 3.817583024595161*^9}, {
+ 3.817584829987904*^9, 3.817584859074748*^9}, {3.81758494165969*^9,
+ 3.81758496226119*^9}, {3.81758499940244*^9, 3.8175849995669928`*^9}, {
+ 3.817585077390765*^9, 3.817585077573927*^9}, {3.817585156651001*^9,
+ 3.817585156823139*^9}, {3.817585322721836*^9, 3.817585349348461*^9}, {
+ 3.817585456385895*^9, 3.817585457280986*^9}, {3.817585513558703*^9,
+ 3.8175855137401114`*^9}, {3.817613675501788*^9, 3.817613676578967*^9}, {
+ 3.8176168804169617`*^9, 3.81761688926372*^9}, {3.817618774003889*^9,
+ 3.817618793385603*^9}, {3.8176190151288853`*^9, 3.817619038205636*^9},
+ 3.8176190698677187`*^9, {3.817619141079945*^9, 3.8176191871342373`*^9}, {
+ 3.817619234638775*^9, 3.817619240400311*^9}, {3.817619299848545*^9,
+ 3.817619332922262*^9}, {3.817619399549685*^9, 3.817619401809965*^9}, {
+ 3.8176196502657223`*^9, 3.817619664950913*^9}, {3.817619740359915*^9,
+ 3.8176197551387*^9}, {3.81761980328899*^9, 3.8176198034943733`*^9}, {
+ 3.817620410694891*^9, 3.817620463869529*^9}, {3.817620674916114*^9,
+ 3.817620678055534*^9}, {3.817620745057685*^9, 3.817620761178657*^9}, {
+ 3.817626286376536*^9, 3.8176263645243196`*^9}, {3.817627920512431*^9,
+ 3.817627961648692*^9}, {3.8176289379929667`*^9, 3.8176289382553997`*^9}, {
+ 3.817628977854362*^9, 3.817628981182324*^9}, 3.81762904026398*^9, {
+ 3.817629751676261*^9,
+ 3.8176297825415983`*^9}},ExpressionUUID->"396a3ca5-637b-4194-943d-\
+7ec379bcf47e"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "FindRoot", "cvmit",
+ "\"Failed to converge to the requested accuracy or precision within \\!\\(\
+\\*RowBox[{\\\"500\\\"}]\\) iterations.\"", 2, 81, 32, 25019190250911170972,
+ "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{3.817628956297529*^9, 3.817629002758065*^9,
+ 3.817629055942992*^9},
+ CellLabel->
+ "During evaluation of \
+In[81]:=",ExpressionUUID->"9a92db76-2a3a-4c87-9b65-03195ab7f92a"],
+
+Cell[BoxData[
+ RowBox[{"{",
RowBox[{
- RowBox[{"eqMid", "[", "n_", "]"}], "[", "m_", "]"}], ":=",
- RowBox[{"SeriesCoefficient", "[", "\[IndentingNewLine]",
+ RowBox[{"A", "\[Rule]",
+ RowBox[{"-", "42.9483737001412`"}]}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], "\[Rule]",
+ RowBox[{"-", "2.867404604750972`"}]}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "0", "]"}], "\[Rule]", "19.25519435922342`"}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "1", "]"}], "\[Rule]", "84.12814075220349`"}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "2", "]"}], "\[Rule]",
+ RowBox[{"-", "144.60347357786114`"}]}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "1", "]"}], "\[Rule]",
+ RowBox[{"-", "43.371259927071165`"}]}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "2", "]"}], "\[Rule]", "98.30234397173395`"}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "3", "]"}], "\[Rule]", "142.15608968941217`"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "3", "]"}], "\[Rule]",
+ RowBox[{"-", "51.32768903768098`"}]}], ",",
+ RowBox[{
+ RowBox[{"FC", "[", "4", "]"}], "\[Rule]",
+ RowBox[{"-", "43.63797646409232`"}]}]}], "}"}]], "Output",
+ CellChangeTimes->{
+ 3.817582243098262*^9, {3.817582385638481*^9, 3.817582397851478*^9}, {
+ 3.817582440404005*^9, 3.8175824479120073`*^9}, {3.8175825951659813`*^9,
+ 3.817582624284917*^9}, {3.817582771007656*^9, 3.817582790104224*^9}, {
+ 3.81758295912363*^9, 3.8175829694259653`*^9}, {3.817583027875955*^9,
+ 3.817583190779282*^9}, 3.817584063702273*^9, 3.817584867935519*^9, {
+ 3.8175849339417667`*^9, 3.817584980641724*^9}, 3.817585038615395*^9,
+ 3.817585139927609*^9, 3.8175851869224243`*^9, 3.817585430610086*^9,
+ 3.817585477765168*^9, 3.8175855203843403`*^9, 3.8175855792410593`*^9,
+ 3.817613703655264*^9, {3.817613820666153*^9, 3.817613850447565*^9},
+ 3.817613970041641*^9, {3.817616894358282*^9, 3.817616938169628*^9},
+ 3.817618971174425*^9, 3.8176190263238583`*^9, {3.817619068552326*^9,
+ 3.817619077160112*^9}, {3.81761912964554*^9, 3.817619175572*^9},
+ 3.8176192081695538`*^9, {3.817619251398644*^9, 3.8176192611467113`*^9}, {
+ 3.817619296755875*^9, 3.8176193494538918`*^9}, {3.817619385600893*^9,
+ 3.817619417396243*^9}, 3.817619473822008*^9, 3.817619517658676*^9, {
+ 3.817619647045698*^9, 3.817619702143152*^9}, {3.817619744218728*^9,
+ 3.81761983514673*^9}, {3.8176206689279957`*^9, 3.817620689262381*^9}, {
+ 3.817620739706464*^9, 3.817620790926754*^9}, 3.8176208714846783`*^9,
+ 3.817626520486795*^9, 3.817627350228532*^9, 3.8176277415834227`*^9,
+ 3.817628956472193*^9, 3.817629002825632*^9, 3.817629056020689*^9},
+ CellLabel->"Out[81]=",ExpressionUUID->"e97932be-a01b-4712-8761-1702066ed336"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"GraphicsRow", "[",
+ RowBox[{"{", "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"Plot", "[",
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{"g2", "[", "\[Theta]", "]"}], "/.", "sol2"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c1"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]", ",", "0", ",", "\[Theta]c1"}], "}"}]}], "]"}], ",",
+ "\[IndentingNewLine]",
+ RowBox[{"Plot", "[",
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{"F2", "[", "\[Theta]", "]"}], "/.",
+ RowBox[{"B", "\[Rule]",
+ RowBox[{"ruleB", "[", "g2", "]"}]}]}], "/.", "sol2"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c1"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]", ",", "0", ",", "\[Theta]c1"}], "}"}]}], "]"}]}],
+ "\[IndentingNewLine]", "}"}], "]"}]], "Input",
+ CellChangeTimes->{{3.8175672854849167`*^9, 3.8175673108365*^9}, {
+ 3.817567343605356*^9, 3.817567515945986*^9}, {3.817567689779602*^9,
+ 3.8175677001061993`*^9}, {3.817567852209393*^9, 3.8175678553653107`*^9}, {
+ 3.817569677608418*^9, 3.8175696880410147`*^9}, {3.817581502775428*^9,
+ 3.817581583359663*^9}, {3.817582250277421*^9, 3.817582268443882*^9}, {
+ 3.8176137509420633`*^9, 3.817613772032806*^9}, {3.817616947220008*^9,
+ 3.817616967115974*^9}, {3.8176195353257837`*^9, 3.817619546043696*^9}, {
+ 3.817627764775979*^9, 3.8176278238158283`*^9}},
+ CellLabel->"In[75]:=",ExpressionUUID->"050da7fc-1308-4d49-81b4-1f4efc54c09a"],
+
+Cell[BoxData[
+ GraphicsBox[{{}, {InsetBox[
+ GraphicsBox[{{{}, {},
+ TagBox[
+ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
+ Opacity[1.], LineBox[CompressedData["
+1:eJwV1nk4VG0bAHDbzClJ8pZQlkKvLUoowv2kQpRkqci+lpSQkIqilxRZI2uh
+EoUKlaUsUySEkew1M2cGkRkULdL3fH/N9bvmOuc85z73tt7d39pLgI+Pbz0/
+H9//f78Laj8wFDhsVD0jxlfpHmykmrI2W3WtDjQpXR1ZzLGBRnQ7fUF6D+zf
+0Ob/IccDEtLd09jSdjC1/KXP65wg+Na4a9WAtBe8NeiW78yJgvtHKmx6pINh
+Y9ah0/K5KRBZ4BfUJX0F2OWNlmfyCuBri5lgp3Qa7K1PaXlX+BR8t+leWbp4
+F+gzoQxKEg2k+p2GLQ6Vw/tzHvlezR3gvaR5tD65ElbnvGv+G90D6WzNFXRU
+Ax5d235V7RoAe4u3zV9N6iE3+pb7mZ5P0Hfu3E20sQncrXPdfoqyYB9r0VH1
+x2swCIgeKdrLgUodPqsbt1ogb9zP6pX/OIi5XOpqDHoH217adrrxfwXXwIiI
+AJkO+C5xM2zAkAfWLkXJg46dMG254aKX4Ax85XU+9Grugkj/CM0C/m9weX6b
+0yMpOujl+Flrff0OieMjto6xPXC4orL8pNgPkAz1bznE+wAq1nuqhHR+QVa4
+Ubco+gjrF4fPW+xYgHTf/QoaD/ugK6czfvPpRUjoyBRexjcALUPtEfeM+NAf
+GWW9A6cH4WyH7fLfh/gRZ2kea6R/CM64qWy65y6AWn1tFdXVRkBg6+djbtaC
+6N9nex9+zvgEWvx9I8WmQghqjbxUQj7D7S0BggfWUpDyif1asbIM2LddhrHQ
+S0HVSmLnndczwHv9j9Ff/RS0/3P3a21FBrjcvbxjfoiCAu2O2DNUGODkbUT7
+wqSgOvCI1NdhwP0PZw3rpijIelVYx6QFA/arL+sTpVJReF2h78EwBog0yc45
+bqWijhUL+dI9DKCJz631iaUic9MJn/peBqxsf+9Ei6Oi5osD6t79DNjlYjgq
+F09F9V+fVz0eYcBwmHF7VxIVPXkX3Go2zgB18YU2+SwqSo/hTp9dZIBYTBLd
+9xEVuf5lIroyE7aQu5qKOqloSLebEqbGBAk9UaP2biqyP9XQKqvBBCedXyxu
+DxVZD+fZ+m5lwt6tjx5p9lPR7hrHY/xGTLD6Wyd3i0FFyiG9NzRtmNCnQHsu
+PkNF01NvR65dYELn2prUzJUE2n3PNNA3kglpdtrJJf8QKMPpNWVvFBMqq1+b
+Vq8mELTVq1OvMkG882VvpxSB4h88OxeZyoQDO2Y9mesJpOJ5VyK4hAnKb7XM
+b24hkFt/pKVzPxNSvGwj9A4QqCJxkWEwxAQph4yjf60ItMTsfPDaT0x4NlLR
+1mhNoLKqkOw+Ej9Pet1x40ME+pNy6os1jwkBERp+ik4EumXp+J8pwQIriVNF
+gb4E6mra9nKzDgsO7XU/uTmKQM6Wj8b4t7OAdeTVQl40gb70bfiHrs8C7bua
+Esv/I5DA1PJjwYgFdjEmrE+xBNKWJFdWW7BAR35Xq08Cfl+/RK9d7izY4To3
+8TeDQIrzlMRVXiyYHCooNM0k0ONL4dVsHxbQxoI+Xs8iUOtN7xWxJ1mQkxJ7
+f0UugRbqDV60hbJgZ8HXD3P5BHJdPS5y6AYLbrzvv2H+kECTec7b/k1mQUY5
+7czxRwQKU+1x+5HKgnsflWhXSgmUDK+qMjNZ4Dx2PLeqnEC042mun+7i89oy
+lX5WEOjflzsrjtWyYHHVcBFfHY6n2bMRvVcsCEzwa/iOjejqS5c1suCK80qd
+sZcEOjK2xvlRMwuMGtpVXtcTKE58ipjpZkGMUIyGC41AU96ZR8PHWeAYUNcl
+/o5AnqcM+NdNskBKYzz/PfZg8Mi92ikWKPxSkI5rI1BL9IaZP7MsEPFtnJ9v
+J9Cd/OLYyEX8/4EUh2edBJIs3qexnp+Er9YbTd26CJTweIreIEjC3eo39CXd
+BDpXryUnuJSE36LarVZ0AtmOVFde+YcE444pCdoHHE+249GNEiQsXSrFdegl
+0M6vi3zNkiTI57m6cbE1Foz3LZElYVrPbuXKPpw/0u+Yccok6A7ujNs2QKAa
+u8EViYYkaGhfNxAbIZCW04XKzYiEgKxnzpHYRZ5yR7uMSSgYPrxiCjs1yOOe
+uBkJQ4fXSDV+ItCppAmDNGsSOgz/q97HIBCZEc/UsSPhV6C5wQPso7c1Y3sP
+k3DAs81EkEkgs7Ig+honEqRGt86WYW9o/30804cEowNtaRMsnE89OSt2+JLw
+Q+zZXm2SQCuGoHLQj4R2Wm3kOeyFL1F8MoH4vO37g/9iB84o3as7Q4K3w5kt
+RmwCjf1stnAOIeGlxeTJc9gfloik550nQfissNcE9j6xUgMUQUJ0iqWsPIdA
+jWusmJ8vkTA1Imdnjb1dbibmUjSOp0LHksvYpRtTN22IIeHzpQfby7AVNXTp
+jVdJWB0sQPZjZ+n0hXpcJ0G7Q0VYYJRAsbvX0QqTSNj/RJlmjt37bt/2i6kk
+6N/R/HkSW8HmwsPD6SQsuaumnYB9euCR/JZMEpIz4EwJ9ku3kVThHBK86AnP
+X2MvGxddSuaRoKdqyDeMfeQ0XKjLJyGSe8p8GvvevP/0zbskfJs1uykwRqDZ
+i7e9TheRIBHDY4phI2pX/94SEupCrmmuw06I57dUKCXh9ioUrog9uEqrcaGc
+BKa6zmsVbOVsd93epySkiCWLqGOfVUgpLqsiYW/SRSs17KbiJtmrL0hIE1BI
+/BdbTOtbsnstCSX6Ra3y2M4vFAmDV/h7JW/7K4FdguzCVzeS8H30l7ow9o/m
+K9wpGgm7s9bZ/MLnNzlQ5dHSTEJecvPpUeyUXs7HO604nnr/XunC/uy0Zl94
+OwnLI31uPMfWYJvW23aSkDRSkZCNHe4Xqq1BJ0HaxuDyBeyW2aIiopeEMA+1
+40exJcL71zH6SLguU26si+0hIJxUPUjC6zU/l4til1/Vp6SOkFAWoNPKxN9z
+UexE2EkGCTd7Us9WYFtkZH01IUmYDTIVj8LOkGtzkx/F+SR6MdsSe6vGJnP6
+JAnDpEHYEM6vyEqnlw+5OP72Kq252B0GCVr/zZCgtN2d6ox9zIIrrfeDBNVn
+MYZ0nL9V3XI3xH+TsPH3kO5VbEEHK8HJPySozR6QNMDOPfZ4IleQDRYB3okZ
+uD4muAyXUCob+qRClIyxt4eI9xxcyobQ2oi8MVxP9CtBtUIr2HA6xB7UsZcU
+6MT7SrNhvDhQMuEzgQ6pevPvlmGDiVjUK1nsgsc3g2Xk2eB6+eieh7iejern
+nTqV2MAuOfylDtd70PALDd0t+P6yu6NrhghU7/klf4U2G2b7D4tsxRadlF4z
+rssGTweVk/cHcb/4Ff43y4ANrTPLqv7D/WVkjVEnvxkbfMplrORw/1m9LutV
+sTkbhCv2e8V+xPUo/6PUZj8b6ku+V07hflWj/CT+rjUbYh4dJJ7i/paht9Fi
+rxMb7mzqtpfG/c/mqOibxEA2PP1gYeCB+2mcy4lKvWA2TPhsb8rD/bbRo6WQ
+GcIG449e5/txP97sdzlK+wIbFl+ZRO1uxee9MIf6YthQIZxG//EG50vuSI1c
+DhvUNR8LDrwi0N/8HSUteWxo6c/zG8fzQPd+RmZAPhuqTCX//n9e3C2zDmu6
+zwb9trhcai2BLte/0fV5wgax6u7nlOcEMmSWPi5tZoNIT9LouTICPVGKuG84
+g+O9O6nMMBv3uz/0Tf3f8PUPghjzeD4m9yhXnJlnQ568gHnZLRzvqO76kgU2
+2Lw6Xrc6Hc9bhtKAFMGByN3+6xuScL5kt4nMreXAloCwyCQ8n6v/kQ4s3cOB
+ttTBltWnCKQ6cerHXjMOOG5oFjrrR6DMxqaLbHMOqMnf8aXj+R8ecPLaOisO
+5FHKnlzxIZDB+/rCOAcOpL3RU21xxf0nzuejtz8H/tL1j9PwftHEX2kgd4sD
+tlEmfenaBBK2z0iazeLA1EcllwAtAlmXh3OaczmQqD542XQzrldn48TThRy4
+vMYub1wN9+ua96yGMg6c7E/dQFHA8Tz7Jc7zDQesnz6m3BIjUPEXuf4Hsxzw
+/S4irDWO96udghoX5/B5DA9czeVQ0fZbnMvWPzkw25CURZB4PzR9pP57kQO1
+6utC349QEVmoH7lPeBQKV+YK6+J9TsbF7l+u/CgU7Tzg4fySihLpccHalqPQ
+Y/opRjqRihruZ+7psxqF5YKV9/fh/XImvHj1eZtRWFk/9SYc7592iq2VTUdG
+gZKgJtgVTUXSwUvnrD1G4e273acPh1FRgUTs2YDQUfi4J2hZjxsVVdlfCSnN
+H4UzDovktc1UNPgpIkx5fhQ8fheMfadRELlVVpLyaxQKVjEXpRsoaDKmtoqx
+MArLCJ8EgzoKWtD8OZspMAZjiSyp4EoKWhcZeGq56Bj8PGo8WnOXghzlvTxm
+FMcgdawq+vYVChpxNd9faz0GCi2zR5qNKYjJWLXeqnQMGFk6NtlPhFDPk0/6
+C+VjsLQ7XEyrVAi9iSq2LXo6BkcoYW20B0KoWAnF8r0Ygy0V+saM20Io8PgJ
+bnnTGOyyuLZ5LkEICU431K3sHwP+gXthib5CSJHP34EuOA4mqwlKnJwQ8pZ9
+m3LIfhzGwqcVyyIFkbJKIE2A/wuIG2Xr7lEWQPdUajKYVV+g3shkuiGaD93x
+VNh+x3UC6Mze4Eulf8A+TS08RXIScuUMnx9p+QmWqcrn1dongTiabhNM+w71
+7bvN8oO/gvhHm2Ll6WngLvA936c+BTcUn4z73p2ALO+hmQ+9U3D4gkz97C48
+x3MfTghd5EJ01/BTVe1B0HeRPTsQyYX23s7Ymj8DMC2XyFcexQXNJWnZJ5sH
+wPlO0OqjV7lwWNzeUffoAGwv1IfHqVzwex1h4hrdD18ftCQ7lXBByvNchMnw
+RzhUSepV9XFBYkWK5nhxD4icPUS7NsiFtXYqLaJhPdCk22LpNsIFS5fwOkfT
+Htj8vMRDhORCvPhUcSBJh2U1gfHuXC5U53wQi5eng6tr5GlCkAf+cZ6h5be7
+YJW3KO2pFA+0NN9XPo9uBzJ62IS6lgfZT3ZM8ba0Q0XBw7dH1vFgYd6k7vyn
+NrBjmL//I8sDo2sKtYk72uCmY8yAqSIP5saMUyrnW0HShm96UIMHNU94IpaR
+LbAOzcgI7ebBxheMotsfmmDSueH2oT08cOCZN61JaILaC4kKD0x4sGUmm8Y1
+aQKnGg0Vy708WFuSq0170Qi5uie0Myzx/TpmmMKFDSC/iTRXt+fBph823xgS
+r0BJujfE9hQPJvc8rPI/+AyezIjbd/jzQPMTvfBFRxUYvTugbxbAg1iZ0+mS
++6vgyPm3CzvO8MBrRXah9P5KuD5Se0nhHA+qGd3IxuEpfMsvuDZzhQet0nO9
+/nZlcCn8s59fDA/4gsTO9AeVgqitjCUnlgeSQtvSbqY+AmVKutjANR5kWlC/
+rx4uAUefuLSGJB4425LBQXFFQFMLyEvM4UG6qkMhn30+HBQqjRTOw9erhycz
+c+7AyNAXt+jbPPhjK/vNmH0bfsR7KoYW8OCfXZ8EVs3ngjrv8AOXB/h96i6a
+LVy/BS9aUuP6i3ngKblhyU7IAJM7XSdsHvJg/rJ3dencTXC1ttAwLeOBK3lB
+Z21wKqRWGD3VqMTfp2xT6wO3G7A+Pjy1qIoHYWpc4rdUPJR6PQ/e8Bzbw6Zx
+figOWiS0tkvU8OChec6EfNR/sBCqVPenngcnzLp0Puefh6sH3XNDGnnwzWeN
+QVV9KEio5kVMN/Fg58/SwFvfzsDmQUlj9hsehFAlx98YnoC6p3YKLi08KNj2
+qp6n6gnm15OF+t/ywPpLwdzAVQfo9XzPtn7Hg+jCtMFHmubgYSjS3NaGz7M5
+NF9P9bjR/wBE/bQ/
+ "]]},
+ Annotation[#, "Charting`Private`Tag$20069#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->{{11.532844387755102`, 0.4999999999998863}, {
+ 4.997223543150454, 0.5000000000000426}},
+ 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->{{0, 1.05}, {0., 2.9883652669978544`}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.05]}},
+ Ticks->{Automatic, Automatic}], {161.0393860624662, -96.9918078848933},
+ ImageScaled[{0.5, 0.5}], {302.0639437331956, 184.7463007331301}],
+ InsetBox[
+ GraphicsBox[{{{}, {},
+ TagBox[
+ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
+ Opacity[1.], LineBox[CompressedData["
+1:eJwV1nk8FP8fB/B1pJIYOSqVFEXuJCnHW5eQVK74opIjpAMhObuQK+SIKEdy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+ "]]},
+ Annotation[#, "Charting`Private`Tag$20111#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->{{7.849808673469387, 0.49999999999994316`}, {
+ 4.997223543150454, 0.5000000000000426}},
+ 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->{{0, 1.05}, {-4.253794809211212, 0.}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.05]}},
+ Ticks->{Automatic, Automatic}], {481.27664033025576, -96.9918078848933},
+ ImageScaled[{0.5, 0.5}], {298.3809080189099, 184.7463007331301}]}, {}},
+ ImageSize->{
+ UpTo[600],
+ UpTo[223]},
+ PlotRange->{{0, 640.4745085355792}, {-193.9836157697866, 0}},
+ PlotRangePadding->{6, 5}]], "Output",
+ CellChangeTimes->{
+ 3.8175673122534857`*^9, {3.8175674402281427`*^9, 3.817567489380693*^9},
+ 3.817567520221552*^9, 3.817567705671341*^9, 3.817567793079455*^9,
+ 3.817567857173483*^9, 3.817569690002346*^9, {3.817581574147563*^9,
+ 3.81758158515839*^9}, 3.817582270590219*^9, {3.817582390618846*^9,
+ 3.817582400806323*^9}, 3.817582450685178*^9, 3.817582634245347*^9,
+ 3.817582776393298*^9, {3.817582962930173*^9, 3.817582972201144*^9}, {
+ 3.8175830310073977`*^9, 3.81758319355462*^9}, 3.817584882023147*^9,
+ 3.81758498666595*^9, 3.817585045390573*^9, 3.817585149785573*^9,
+ 3.817585439738227*^9, 3.817585525878573*^9, 3.817585585204454*^9, {
+ 3.8176137655148363`*^9, 3.817613774145886*^9}, 3.8176139295702887`*^9,
+ 3.8176141329700117`*^9, {3.817616943087964*^9, 3.817616969451852*^9},
+ 3.8176192172908077`*^9, 3.81761927371955*^9, 3.817619365966529*^9,
+ 3.817619480892799*^9, {3.817619523373876*^9, 3.817619547918648*^9}, {
+ 3.817627771060638*^9, 3.817627777110018*^9}, {3.817627809877636*^9,
+ 3.8176278273754797`*^9}},
+ CellLabel->"Out[75]=",ImageCache->GraphicsData["CompressedBitmap", "\<\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\
+\>", "ImageResolution" -> \
+96.],ExpressionUUID->"1e95a096-656a-4bd0-bdc9-09d9c739bf1f"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"g3", "=",
+ RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "5", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"eq3", "=",
RowBox[{
RowBox[{
- RowBox[{"R\[ScriptCapitalM]", "[", "\[Theta]", "]"}], "-",
+ RowBox[{"eq", "[", "2", "]"}], "[",
+ RowBox[{"f", ",", "g3"}], "]"}], "[", "2", "]"}]}], ";"}]}], "Input",
+ CellChangeTimes->{
+ 3.817563268660089*^9, {3.817563829122241*^9, 3.817563846550528*^9}, {
+ 3.817563950998456*^9, 3.817563956525237*^9}, {3.8175645239988813`*^9,
+ 3.817564534320574*^9}, {3.81756485534698*^9, 3.817564862343175*^9}, {
+ 3.817564919676697*^9, 3.8175649235785027`*^9}, {3.817565106996109*^9,
+ 3.8175651474217367`*^9}, {3.8175652415905113`*^9, 3.817565250029232*^9}, {
+ 3.8175657444559927`*^9, 3.8175657689660788`*^9}, 3.8175669120549498`*^9, {
+ 3.8175677716518087`*^9, 3.817567773706285*^9}, {3.817579700926876*^9,
+ 3.817579701354711*^9}, {3.8175810533593073`*^9, 3.817581114447541*^9}, {
+ 3.817581149854197*^9, 3.8175811499220247`*^9}, {3.817581265163169*^9,
+ 3.81758126542041*^9}, {3.81758144220247*^9, 3.8175814490334673`*^9}, {
+ 3.8175815152710047`*^9, 3.817581521148234*^9}, {3.817581635837187*^9,
+ 3.817581700879589*^9}, {3.817581767691791*^9, 3.817581768673394*^9}, {
+ 3.8175821842992363`*^9, 3.8175821844066353`*^9}, {3.817582286431714*^9,
+ 3.817582297101211*^9}, {3.817582488847374*^9, 3.817582488974349*^9}, {
+ 3.817582803954041*^9, 3.817582804222094*^9}, {3.817583220813534*^9,
+ 3.817583241460207*^9}},
+ CellLabel->"In[58]:=",ExpressionUUID->"56a2c377-648a-4b5e-a0b8-a978c95c7038"],
+
+Cell[BoxData["$Aborted"], "Output",
+ CellChangeTimes->{3.817617526623535*^9},
+ CellLabel->"Out[59]=",ExpressionUUID->"1fb128c6-9917-495f-aa57-47ef430806ec"]
+}, Open ]],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"\[Theta]c3", "=", "1.1"}], ";"}]], "Input",
+ CellChangeTimes->{{3.817582396116788*^9, 3.8175824049054317`*^9}, {
+ 3.8175824459508343`*^9, 3.817582446508223*^9}, {3.817582967426021*^9,
+ 3.817582967790391*^9}, {3.817583034373005*^9, 3.8175831892051573`*^9}, {
+ 3.8175832454786386`*^9, 3.8175832457485743`*^9}, {3.817583916075033*^9,
+ 3.817584052070888*^9}, {3.817584106508939*^9, 3.817584316547625*^9}, {
+ 3.817584353610593*^9, 3.817584391778722*^9}, {3.817584436606126*^9,
+ 3.8175844576427193`*^9}, {3.817616997942698*^9,
+ 3.817616998293277*^9}},ExpressionUUID->"01a65f9d-ccec-4ee5-a3eb-\
+41b72a14e214"],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"sol3", "=",
+ RowBox[{"FindRoot", "[",
+ RowBox[{
+ RowBox[{"eq3", "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c3"}]}], ",",
+ RowBox[{"{",
RowBox[{
- FractionBox[
- SuperscriptBox[
+ RowBox[{"{",
+ RowBox[{"M0", ",",
+ RowBox[{"M0", "/.", "i3"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], ",",
RowBox[{
- RowBox[{"g", "[", "n", "]"}], "[", "\[Theta]", "]"}],
- RowBox[{"1", "/", "\[Delta]"}]], "\[CapitalDelta]"],
- RowBox[{"(",
+ RowBox[{"gC", "[", "0", "]"}], "/.", "i3"}]}], "}"}], ",",
+ RowBox[{"{",
RowBox[{
+ RowBox[{"gC", "[", "1", "]"}], ",",
RowBox[{
- RowBox[{"\[Eta]", " ",
- RowBox[{
- RowBox[{"\[CapitalPhi]", "'"}], "[", "\[Eta]", "]"}]}], "-",
- RowBox[{
- RowBox[{"(",
- RowBox[{"2", "-", "\[Alpha]"}], ")"}],
- RowBox[{"\[CapitalPhi]", "[", "\[Eta]", "]"}]}]}], "/.",
- RowBox[{"\[Eta]", "\[Rule]",
- RowBox[{
- RowBox[{
- RowBox[{"f", "[", "n", "]"}], "[", "\[Theta]", "]"}], " ",
- SuperscriptBox[
- RowBox[{
- RowBox[{"g", "[", "n", "]"}], "[", "\[Theta]", "]"}],
- RowBox[{
- RowBox[{"-", "1"}], "/", "\[CapitalDelta]"}]]}]}]}], ")"}]}]}],
- "\[IndentingNewLine]", ",",
- RowBox[{"{",
- RowBox[{"\[Theta]", ",", "\[Theta]i", ",", "m"}], "}"}], ",",
- RowBox[{"Assumptions", "\[Rule]",
- RowBox[{"Join", "[",
- RowBox[{"$Assumptions", ",",
- RowBox[{"{",
+ RowBox[{"gC", "[", "1", "]"}], "/.", "i3"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "2", "]"}], ",",
RowBox[{
- RowBox[{"\[Theta]", ">", "0"}], ",",
- RowBox[{"\[Theta]", "<", "\[Theta]c"}]}], "}"}]}], "]"}]}]}],
- "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]",
- RowBox[{
+ RowBox[{"gC", "[", "2", "]"}], "/.", "i3"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "3", "]"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "3", "]"}], "/.", "i3"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "4", "]"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "4", "]"}], "/.", "i3"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "5", "]"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "5", "]"}], "/.", "i3"}]}], "}"}]}], "}"}], ",",
+ RowBox[{"MaxIterations", "\[Rule]", "500"}]}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.8175612726329412`*^9, 3.81756128486736*^9}, {
+ 3.8175614038617268`*^9, 3.817561415404965*^9}, {3.817561511096093*^9,
+ 3.817561563944231*^9}, {3.81756250196518*^9, 3.817562507914916*^9}, {
+ 3.817562967760625*^9, 3.81756298304041*^9}, 3.817563161460335*^9, {
+ 3.817563206558021*^9, 3.81756320676147*^9}, {3.817563530710863*^9,
+ 3.817563550054001*^9}, {3.817563775700533*^9, 3.817563804069632*^9}, {
+ 3.817563971222761*^9, 3.817564086350409*^9}, {3.817564155680212*^9,
+ 3.8175641623358994`*^9}, {3.81756424029494*^9, 3.817564240399859*^9}, {
+ 3.8175645416987743`*^9, 3.817564542202907*^9}, {3.817564715061411*^9,
+ 3.817564723202471*^9}, {3.8175648450855713`*^9, 3.817564883921851*^9}, {
+ 3.8175650025642157`*^9, 3.817565074155829*^9}, {3.817565217921039*^9,
+ 3.817565230520749*^9}, {3.817565359356901*^9, 3.8175654247402163`*^9}, {
+ 3.817565602697175*^9, 3.817565635407323*^9}, {3.817566059389201*^9,
+ 3.817566077942937*^9}, {3.817566269837482*^9, 3.817566273547044*^9}, {
+ 3.8175663066250553`*^9, 3.817566306784181*^9}, {3.817566684914805*^9,
+ 3.81756668549652*^9}, {3.817566919102108*^9, 3.817566934549343*^9}, {
+ 3.8175696638331223`*^9, 3.817569664744486*^9}, {3.817579706169273*^9,
+ 3.8175797767735577`*^9}, {3.817581067506674*^9, 3.8175810689721537`*^9}, {
+ 3.817581121371869*^9, 3.817581169115347*^9}, {3.817581207766066*^9,
+ 3.817581270669099*^9}, 3.817581309702499*^9, {3.817581355857291*^9,
+ 3.817581356026667*^9}, {3.817581392130506*^9, 3.817581416424316*^9}, {
+ 3.817581457365512*^9, 3.8175814943565397`*^9}, {3.81758152586852*^9,
+ 3.817581526654297*^9}, {3.8175819155874557`*^9, 3.81758195123713*^9}, {
+ 3.8175820720836487`*^9, 3.817582073079625*^9}, {3.817582192281794*^9,
+ 3.8175821927535973`*^9}, {3.8175824979646*^9, 3.817582531058486*^9}, {
+ 3.817582601242318*^9, 3.817582616669943*^9}, {3.817582763042087*^9,
+ 3.817582823261053*^9}, {3.817582997786705*^9, 3.817583024595161*^9}, {
+ 3.817583292451758*^9, 3.817583331793063*^9}, {3.817583896782114*^9,
+ 3.817583910986412*^9}, {3.817584041997362*^9, 3.817584044193297*^9}, {
+ 3.8175840763191137`*^9, 3.817584118869596*^9}},
+ CellLabel->
+ "In[298]:=",ExpressionUUID->"13e955ed-c66f-412e-a56a-086a5a7c388a"],
+
+Cell[BoxData[
+ RowBox[{"{",
RowBox[{
- RowBox[{"eqMeta", "[", "n_", "]"}], "[", "m_", "]"}], ":=",
- RowBox[{"SeriesCoefficient", "[", "\[IndentingNewLine]",
+ RowBox[{"M0", "\[Rule]", "3014.019240300801`"}], ",",
RowBox[{
- RowBox[{
- RowBox[{"I\[ScriptCapitalF]", "[",
- RowBox[{"1", "/", "\[Theta]inv"}], "]"}], "-",
+ RowBox[{"gC", "[", "0", "]"}], "\[Rule]", "0.27741409131351474`"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "1", "]"}], "\[Rule]",
+ RowBox[{"-", "1.856234758162671`"}]}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "2", "]"}], "\[Rule]", "6.954527958205154`"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "3", "]"}], "\[Rule]",
+ RowBox[{"-", "10.34980326553876`"}]}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "4", "]"}], "\[Rule]", "6.847008239280345`"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "5", "]"}], "\[Rule]",
+ RowBox[{"-", "1.7260540506222146`"}]}]}], "}"}]], "Output",
+ CellChangeTimes->{
+ 3.817582243098262*^9, {3.817582385638481*^9, 3.817582397851478*^9}, {
+ 3.817582440404005*^9, 3.8175824479120073`*^9}, {3.8175825951659813`*^9,
+ 3.817582624284917*^9}, {3.817582771007656*^9, 3.817582790104224*^9}, {
+ 3.81758295912363*^9, 3.8175829694259653`*^9}, {3.817583027875955*^9,
+ 3.817583190779282*^9}, {3.817583867855484*^9, 3.8175840591469297`*^9}, {
+ 3.8175840938584213`*^9, 3.8175843180703287`*^9}, {3.817584358052533*^9,
+ 3.817584394362668*^9}, {3.817584439591468*^9, 3.81758445968953*^9}},
+ CellLabel->
+ "Out[298]=",ExpressionUUID->"666b440f-efe1-40df-97a3-a6ba5f6b502f"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"GraphicsRow", "[",
+ RowBox[{"{", "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"Plot", "[",
RowBox[{
- SuperscriptBox[
- RowBox[{"(",
- RowBox[{"-", " ",
- RowBox[{
- RowBox[{"g", "[", "n", "]"}], "[",
- RowBox[{"1", "/", "\[Theta]inv"}], "]"}]}], ")"}],
+ RowBox[{
RowBox[{
- RowBox[{"(",
- RowBox[{"2", "-", "\[Alpha]"}], ")"}], "/", "\[CapitalDelta]"}]],
- RowBox[{"Dmeta", "[",
+ RowBox[{"g3", "[", "\[Theta]", "]"}], "/.", "sol3"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c3"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]", ",", "0", ",", "\[Theta]c3"}], "}"}]}], "]"}], ",",
+ "\[IndentingNewLine]",
+ RowBox[{"Plot", "[",
+ RowBox[{
+ RowBox[{
RowBox[{
RowBox[{
- RowBox[{"f", "[", "n", "]"}], "[",
- RowBox[{"1", "/", "\[Theta]inv"}], "]"}],
+ RowBox[{
+ RowBox[{
+ RowBox[{"R\[ScriptCapitalM]", "[", "2", "]"}], "[",
+ RowBox[{"B", ",", "\[Theta]c3", ",", "M0"}], "]"}], "[",
+ "\[Theta]", "]"}], "/.",
+ RowBox[{"B", "->",
+ RowBox[{
+ RowBox[{"ruleB", "[", "2", "]"}], "[",
+ RowBox[{"f", ",", "g3"}], "]"}]}]}], "/.", "sol3"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "\[Theta]c3"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]", ",", "0", ",", "\[Theta]c3"}], "}"}]}], "]"}]}],
+ "\[IndentingNewLine]", "}"}], "]"}]], "Input",
+ CellChangeTimes->{{3.8175672854849167`*^9, 3.8175673108365*^9}, {
+ 3.817567343605356*^9, 3.817567515945986*^9}, {3.817567689779602*^9,
+ 3.8175677001061993`*^9}, {3.817567852209393*^9, 3.8175678553653107`*^9}, {
+ 3.817569677608418*^9, 3.8175696880410147`*^9}, {3.817581502775428*^9,
+ 3.817581583359663*^9}, {3.817582250277421*^9, 3.817582268443882*^9}, {
+ 3.8175837859410753`*^9, 3.817583808939587*^9}},
+ CellLabel->
+ "In[299]:=",ExpressionUUID->"cf100fe8-27c6-4a2c-b65e-370cdc76ab54"],
+
+Cell[BoxData[
+ GraphicsBox[{{}, {InsetBox[
+ GraphicsBox[{{{}, {},
+ TagBox[
+ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
+ Opacity[1.], LineBox[CompressedData["
+1:eJwV13c8Vf8fB/ASKSpCtO2GSlak5IVIQySSrazwlZCKhhJFKqmUkjLvteeV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+ "]]},
+ Annotation[#, "Charting`Private`Tag$26662#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->{{17.858577806122444`, 0.49999999999994316`}, {
+ 5.192699455966533, 0.5000000000000284}},
+ 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->{{0, 1.154}, {0., 0.07870593117729505}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.05]}},
+ Ticks->{Automatic, Automatic}], {161.02493916317803, -95.0011368476809},
+ ImageScaled[{0.5, 0.5}], {301.9382030546833, 180.95454637653503}],
+ InsetBox[
+ GraphicsBox[{{{}, {},
+ TagBox[
+ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
+ Opacity[1.], LineBox[CompressedData["
+1:eJwVkHk01XkYxq9RERpEtDDIvncvHZR6IkvdOqZsDRNJiBbUiEhKGGUbRVdT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+ "]]},
+ Annotation[#, "Charting`Private`Tag$26704#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->{{17.332429846938776`, 0.5000000000000568}, {
+ 5.192699455966533, 0.5000000000000284}},
+ 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->{{0, 1.154}, {-1.0627443133427263`, 1.0987766597698887`}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.05]}},
+ Ticks->{Automatic, Automatic}], {482.8117435099423, -95.0011368476809},
+ ImageScaled[{0.5, 0.5}], {301.41205509549974, 180.95454637653503}]}, {}},
+
+ ImageSize->{
+ UpTo[600],
+ UpTo[223]},
+ PlotRange->{{0, 643.5736086935285}, {-190.0022736953618, 0}},
+ PlotRangePadding->{6, 5}]], "Output",
+ CellChangeTimes->{
+ 3.8175673122534857`*^9, {3.8175674402281427`*^9, 3.817567489380693*^9},
+ 3.817567520221552*^9, 3.817567705671341*^9, 3.817567793079455*^9,
+ 3.817567857173483*^9, 3.817569690002346*^9, {3.817581574147563*^9,
+ 3.81758158515839*^9}, 3.817582270590219*^9, {3.817582390618846*^9,
+ 3.817582400806323*^9}, 3.817582450685178*^9, 3.817582634245347*^9,
+ 3.817582776393298*^9, {3.817582962930173*^9, 3.817582972201144*^9}, {
+ 3.8175830310073977`*^9, 3.81758319355462*^9}, 3.817583875298687*^9, {
+ 3.817583922931497*^9, 3.817584004935768*^9}, {3.817584099181155*^9,
+ 3.817584321798046*^9}, {3.817584372034237*^9, 3.817584397850472*^9}, {
+ 3.817584449443131*^9, 3.8175844632363253`*^9}},
+ CellLabel->
+ "Out[299]=",ExpressionUUID->"5ba21607-6804-4676-bd54-9ca50ed7e210"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"test1", "=",
+ RowBox[{"Integrate", "[",
+ RowBox[{
+ FractionBox[
+ RowBox[{
+ RowBox[{"g1", "''"}], "[", "\[Theta]", "]"}],
+ SuperscriptBox[
+ RowBox[{"(",
+ RowBox[{"1", "+",
SuperscriptBox[
- RowBox[{"(",
- RowBox[{"-", " ",
- RowBox[{
- RowBox[{"g", "[", "n", "]"}], "[",
- RowBox[{"1", "/", "\[Theta]inv"}], "]"}]}], ")"}],
RowBox[{
- RowBox[{"-", "1"}], "/", "\[CapitalDelta]"}]]}], "]"}]}]}],
- "\[IndentingNewLine]", ",",
+ RowBox[{"g1", "'"}], "[", "\[Theta]", "]"}], "2"]}], ")"}],
+ RowBox[{"3", "/", "2"}]]], ",", "\[Theta]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.817584512468288*^9, 3.817584556777507*^9}, {
+ 3.8175845874229794`*^9, 3.817584598290722*^9}, {3.8175846841114597`*^9,
+ 3.81758470116075*^9}, {3.817584771036125*^9, 3.817584772363957*^9}, {
+ 3.817585237332501*^9, 3.817585238467779*^9}, {3.8175856895510893`*^9,
+ 3.8175856906752253`*^9}, {3.817613345155766*^9, 3.8176133469126177`*^9}},
+ CellLabel->"In[4]:=",ExpressionUUID->"b69f87e3-927b-4524-9686-1a17f2c879bb"],
+
+Cell[BoxData[
+ FractionBox[
+ RowBox[{
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "3"}], " ",
+ SuperscriptBox["\[Theta]", "2"]}], "+",
+ SuperscriptBox["\[Theta]c", "2"]}], ")"}], " ",
+ RowBox[{"gC", "[", "0", "]"}]}],
+ RowBox[{
+ SuperscriptBox["\[Theta]c", "2"], " ",
+ SqrtBox[
+ RowBox[{"1", "+",
+ FractionBox[
+ RowBox[{
+ SuperscriptBox[
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "3"}], " ",
+ SuperscriptBox["\[Theta]", "2"]}], "+",
+ SuperscriptBox["\[Theta]c", "2"]}], ")"}], "2"], " ",
+ SuperscriptBox[
+ RowBox[{"gC", "[", "0", "]"}], "2"]}],
+ SuperscriptBox["\[Theta]c", "4"]]}]]}]]], "Output",
+ CellChangeTimes->{{3.817584537926284*^9, 3.817584558482575*^9}, {
+ 3.817584681776753*^9, 3.817584701794977*^9}, 3.817584776620221*^9,
+ 3.817585240635579*^9, 3.8175856951701927`*^9, 3.817613349497088*^9},
+ CellLabel->"Out[4]=",ExpressionUUID->"fca5aade-1849-4879-95d9-c83dd6b84d7b"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"test2", "=",
+ RowBox[{"Integrate", "[",
+ RowBox[{
+ RowBox[{"g2", "[", "\[Theta]", "]"}], ",",
RowBox[{"{",
- RowBox[{"\[Theta]inv", ",", "0", ",", "m"}], "}"}], ",",
- RowBox[{"Assumptions", "\[Rule]",
- RowBox[{"Join", "[",
- RowBox[{"$Assumptions", ",",
- RowBox[{"{",
- RowBox[{
- RowBox[{"\[Theta]inv", ">", "0"}], ",",
- RowBox[{"\[Theta]inv", "<",
- RowBox[{"1", "/", "\[Theta]c"}]}]}], "}"}]}], "]"}]}]}],
- "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]",
+ RowBox[{"\[Theta]", ",", "0", ",", "\[Theta]c"}], "}"}]}],
+ "]"}]}]], "Input",
+ CellChangeTimes->{{3.817585638733982*^9, 3.817585654272316*^9}, {
+ 3.817585696967054*^9, 3.817585697075837*^9}},
+ CellLabel->
+ "In[370]:=",ExpressionUUID->"76d49acb-b5e2-4974-82cf-c376b2e9bf83"],
+
+Cell[BoxData[
RowBox[{
- RowBox[{"eqB", "[", "n_", "]"}], ":=",
RowBox[{
- FractionBox["\[Pi]",
- RowBox[{"2", " ", "1.3578383417066"}]], " ",
+ FractionBox["1", "4"], " ",
+ SuperscriptBox["\[Theta]c", "2"], " ",
+ RowBox[{"gC", "[", "0", "]"}]}], "+",
+ RowBox[{
+ FractionBox["1", "12"], " ",
+ SuperscriptBox["\[Theta]c", "4"], " ",
+ RowBox[{"gC", "[", "1", "]"}]}], "+",
+ RowBox[{
+ FractionBox["1", "24"], " ",
+ SuperscriptBox["\[Theta]c", "6"], " ",
+ RowBox[{"gC", "[", "2", "]"}]}], "+",
+ RowBox[{
+ FractionBox["1", "40"], " ",
+ SuperscriptBox["\[Theta]c", "8"], " ",
+ RowBox[{"gC", "[", "3", "]"}]}]}]], "Output",
+ CellChangeTimes->{3.817585659088111*^9, 3.817585703537512*^9},
+ CellLabel->
+ "Out[370]=",ExpressionUUID->"abc7d2c8-0464-4233-a249-6655f54c6cae"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"D", "[",
+ RowBox[{
+ RowBox[{
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"(",
+ RowBox[{"test1", "/.",
+ RowBox[{"\[Theta]", "\[Rule]", "\[Theta]c"}]}], ")"}], "-",
+ RowBox[{"(",
+ RowBox[{"test1", "/.",
+ RowBox[{"\[Theta]", "\[Rule]", "0"}]}], ")"}]}], ")"}], "/",
+ "\[Theta]c"}], ",", "\[Theta]c"}], "]"}], "//", "Simplify"}]], "Input",
+ CellChangeTimes->{{3.817584702838284*^9, 3.817584748931059*^9}, {
+ 3.81758479119285*^9, 3.8175847990853453`*^9}, {3.8175856683615837`*^9,
+ 3.817585674761424*^9}, {3.817613353375083*^9, 3.817613353885504*^9}},
+ CellLabel->"In[5]:=",ExpressionUUID->"06ec162d-d4ce-41ef-aa36-5c655ac7865a"],
+
+Cell[BoxData[
+ FractionBox[
+ RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], " ",
RowBox[{"(",
RowBox[{
- RowBox[{"\[CapitalDelta]", " ",
+ FractionBox["1",
+ SqrtBox[
+ RowBox[{"1", "+",
+ SuperscriptBox[
+ RowBox[{"gC", "[", "0", "]"}], "2"]}]]], "+",
+ FractionBox["2",
+ SqrtBox[
+ RowBox[{"1", "+",
+ RowBox[{"4", " ",
+ SuperscriptBox[
+ RowBox[{"gC", "[", "0", "]"}], "2"]}]}]]]}], ")"}]}],
+ SuperscriptBox["\[Theta]c", "2"]]], "Output",
+ CellChangeTimes->{{3.817584717925565*^9, 3.817584749355122*^9}, {
+ 3.817584781653911*^9, 3.817584799951426*^9}, 3.817585243063086*^9,
+ 3.817585675459407*^9, 3.81758571432295*^9, 3.817613355851296*^9},
+ CellLabel->"Out[5]=",ExpressionUUID->"4f58f171-276d-4b8b-a439-52aa6e0e19fa"]
+}, Open ]],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"eq2", "=",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
RowBox[{
- RowBox[{"g", "[", "n", "]"}], "[", "\[Theta]c", "]"}],
- SuperscriptBox[
- RowBox[{
- RowBox[{"f", "[", "n", "]"}], "[", "\[Theta]c", "]"}],
RowBox[{
- RowBox[{"-", "\[CapitalDelta]"}], "-", "1"}]],
+ RowBox[{"eqLow", "[", "2", "]"}], "[",
+ RowBox[{"f", ",",
+ RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "0", "]"}]}], "]"}],
+ "[", "0", "]"}], ",",
RowBox[{
RowBox[{
- RowBox[{"f", "[", "n", "]"}], "'"}], "[", "\[Theta]c", "]"}]}], "-",
- RowBox[{
+ RowBox[{"eqHigh", "[", "2", "]"}], "[",
+ RowBox[{"f", ",",
+ RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "0", "]"}]}], "]"}],
+ "[", "1", "]"}]}], "}"}], "/.",
+ RowBox[{"rules", "[",
+ RowBox[{"f", ",",
RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "0", "]"}]}], "]"}]}]}],
+ ";"}]], "Input",
+ CellChangeTimes->{{3.817566966465438*^9, 3.817566988369422*^9}},
+ CellLabel->"In[81]:=",ExpressionUUID->"14d51596-0d76-499e-9baa-e7be6425156e"],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"sol2", "=",
+ RowBox[{"FindRoot", "[",
+ RowBox[{
+ RowBox[{"eq2", "/.",
+ RowBox[{"{",
+ RowBox[{"\[Theta]c", "\[Rule]", "1.3"}], "}"}]}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"M0", ",",
+ RowBox[{"M0", "/.", "sol1"}]}], "}"}], ",",
+ RowBox[{"{",
RowBox[{
- RowBox[{"g", "[", "n", "]"}], "'"}], "[", "\[Theta]c", "]"}],
- SuperscriptBox[
- RowBox[{
- RowBox[{"f", "[", "n", "]"}], "[", "\[Theta]c", "]"}],
- RowBox[{"-", "\[CapitalDelta]"}]]}]}], ")"}]}]}]}], "Input",
- CellChangeTimes->{{3.817122561958515*^9, 3.817122595430499*^9}, {
- 3.8171226412071457`*^9, 3.817122654383555*^9}, {3.817122684808043*^9,
- 3.817122893980072*^9}, {3.8171229823734827`*^9, 3.817123013558132*^9}, {
- 3.817124148403132*^9, 3.817124164362879*^9}, 3.817124570570879*^9,
- 3.81712461824366*^9, {3.817124882096373*^9, 3.817124904954482*^9}, {
- 3.817125021810815*^9, 3.817125026171056*^9}, {3.817125056291629*^9,
- 3.817125062179249*^9}, {3.8171251399727*^9, 3.8171252034061813`*^9}, {
- 3.8171272990345707`*^9, 3.817127305730093*^9}, {3.81712793122969*^9,
- 3.817127935645309*^9}, {3.817196911039874*^9, 3.8171969748088827`*^9}, {
- 3.817197722814756*^9, 3.8171977381903067`*^9}, {3.8171977809682837`*^9,
- 3.817197825063862*^9}, {3.8171979540210543`*^9, 3.8171979962111807`*^9}, {
- 3.817198723032823*^9, 3.817198738800659*^9}, {3.817198786617443*^9,
- 3.817198842450691*^9}, {3.817200387324769*^9, 3.817200391268491*^9}, {
- 3.817209494881345*^9, 3.817209739781746*^9}, {3.817209870543663*^9,
- 3.817209873007422*^9}, {3.817210066331233*^9, 3.817210077563465*^9}, {
- 3.817210203677601*^9, 3.817210214085437*^9}, {3.817210686686688*^9,
- 3.8172109359308043`*^9}, {3.8172110570612993`*^9, 3.817211067132907*^9}, {
- 3.8172111388865967`*^9, 3.817211161790626*^9}, {3.8172115612695913`*^9,
- 3.8172115624854527`*^9}, 3.8172121773284616`*^9, {3.817212401044241*^9,
- 3.81721240169213*^9}, {3.8172126942254143`*^9, 3.817212733676169*^9}, {
- 3.8172128432044477`*^9, 3.817212850900301*^9}, {3.817213122273017*^9,
- 3.817213125505207*^9}, {3.817213504392342*^9, 3.817213522176297*^9},
- 3.817214109954194*^9, {3.817214983818109*^9, 3.817214986450067*^9}, {
- 3.8172173960165873`*^9, 3.817217426058158*^9}, {3.817218919892474*^9,
- 3.817218934448584*^9}, {3.817218984339595*^9, 3.817218988675902*^9}, {
- 3.817219056474732*^9, 3.817219056918*^9}, {3.817270667311324*^9,
- 3.817270696028246*^9}, {3.817271226342354*^9, 3.817271252979103*^9}, {
- 3.8172769069026337`*^9, 3.817276953348996*^9}, {3.8172775487711554`*^9,
- 3.817277647805482*^9}, 3.8172803779817553`*^9, {3.817280418228038*^9,
- 3.8172804267347317`*^9}, {3.817282016179366*^9, 3.817282092169364*^9},
- 3.817282209641667*^9, 3.817283240977447*^9, 3.817283291741331*^9},
- CellLabel->
- "(WOPR) In[798]:=",ExpressionUUID->"77a88da0-5b31-458a-9ed8-0b34545e511d"],
+ RowBox[{"gC", "[", "0", "]"}], ",", "1"}], "}"}]}], "}"}], ",",
+ RowBox[{"MaxIterations", "\[Rule]", "5000"}]}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.8175612726329412`*^9, 3.81756128486736*^9}, {
+ 3.8175614038617268`*^9, 3.817561415404965*^9}, {3.817561511096093*^9,
+ 3.817561563944231*^9}, {3.81756250196518*^9, 3.817562507914916*^9}, {
+ 3.817562967760625*^9, 3.81756298304041*^9}, 3.817563161460335*^9, {
+ 3.817563206558021*^9, 3.81756320676147*^9}, {3.817563530710863*^9,
+ 3.817563550054001*^9}, {3.817563775700533*^9, 3.817563804069632*^9}, {
+ 3.817563971222761*^9, 3.817564086350409*^9}, {3.817564155680212*^9,
+ 3.8175641623358994`*^9}, {3.81756424029494*^9, 3.817564240399859*^9}, {
+ 3.8175645416987743`*^9, 3.817564542202907*^9}, {3.817564715061411*^9,
+ 3.817564723202471*^9}, {3.8175648450855713`*^9, 3.817564883921851*^9}, {
+ 3.8175650025642157`*^9, 3.817565074155829*^9}, {3.817565217921039*^9,
+ 3.817565230520749*^9}, {3.817565359356901*^9, 3.8175654247402163`*^9}, {
+ 3.817565602697175*^9, 3.817565635407323*^9}, {3.817566059389201*^9,
+ 3.817566077942937*^9}, {3.817566269837482*^9, 3.817566273547044*^9}, {
+ 3.8175663066250553`*^9, 3.817566306784181*^9}, {3.817566684914805*^9,
+ 3.81756668549652*^9}, {3.817566919102108*^9, 3.817566934549343*^9}, {
+ 3.817567023284172*^9, 3.817567067932376*^9}, {3.817569671239231*^9,
+ 3.817569671464748*^9}},
+ CellLabel->"In[82]:=",ExpressionUUID->"0fdc6db7-418c-44d4-b217-8c6a47dbf54f"],
-Cell[BoxData[{
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"M0", "\[Rule]", "2.5096411192928767`"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], "\[Rule]", "0.21232864452555533`"}]}],
+ "}"}]], "Output",
+ CellChangeTimes->{
+ 3.817561286441853*^9, 3.817561420490069*^9, 3.817561452135456*^9, {
+ 3.817561512454604*^9, 3.817561517595207*^9}, 3.817561585719215*^9,
+ 3.817563004628446*^9, 3.817563182856628*^9, 3.817563228472159*^9, {
+ 3.817563534906947*^9, 3.817563573064754*^9}, {3.817563797249289*^9,
+ 3.817563825598139*^9}, {3.817563996789044*^9, 3.817564046321703*^9}, {
+ 3.817564078153729*^9, 3.817564103465789*^9}, 3.817564181902115*^9,
+ 3.817564233365617*^9, {3.817564277720583*^9, 3.8175642801348143`*^9},
+ 3.817564315116712*^9, 3.8175645338256474`*^9, {3.817564627325935*^9,
+ 3.8175646522898493`*^9}, {3.817564705276019*^9, 3.817564735465515*^9}, {
+ 3.817564839073145*^9, 3.817564850280691*^9}, 3.817564889679229*^9, {
+ 3.817564994846734*^9, 3.817565091817582*^9}, 3.817565231749591*^9, {
+ 3.817565295003468*^9, 3.817565428068199*^9}, 3.817565500042843*^9, {
+ 3.817565636029861*^9, 3.81756564530912*^9}, 3.817565735768449*^9, {
+ 3.817566053734901*^9, 3.8175660860827293`*^9}, 3.817566141015539*^9,
+ 3.8175662848590927`*^9, 3.817566325612877*^9, {3.817566873920313*^9,
+ 3.817566888279759*^9}, 3.8175669368598824`*^9, {3.817567045496682*^9,
+ 3.817567071548258*^9}, 3.8175676612529373`*^9, 3.8175677905056353`*^9,
+ 3.817569682355029*^9},
+ CellLabel->"Out[82]=",ExpressionUUID->"67408372-ed4a-4c44-8e4a-095d1f5a7f3d"]
+}, Open ]],
+
+Cell[BoxData[
RowBox[{
- RowBox[{"\[CapitalPhi]Rules", "=",
- RowBox[{"MapIndexed", "[",
- RowBox[{
+ RowBox[{"eq3", "=",
+ RowBox[{
+ RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{
- RowBox[{
- RowBox[{"Derivative", "[",
- RowBox[{
- RowBox[{"#2", "[",
- RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], "]"}], "[",
- "\[CapitalPhi]", "]"}], "[", "0", "]"}], "\[Rule]",
- RowBox[{"#1",
- RowBox[{
- RowBox[{"(",
- RowBox[{
- RowBox[{"#2", "[",
- RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], ")"}], "!"}]}]}],
- "&"}], ",",
- RowBox[{"{",
+ RowBox[{"eqLow", "[", "2", "]"}], "[",
+ RowBox[{"f", ",",
+ RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "2", "]"}]}], "]"}],
+ "[", "0", "]"}], ",",
RowBox[{
- RowBox[{"-", "1.197733383797993"}], ",",
- RowBox[{"-", "0.318810124891"}], ",", "0.110886196683", ",",
- "0.01642689465", ",",
RowBox[{
- RowBox[{"-", "2.639978"}], " ",
- SuperscriptBox["10",
- RowBox[{"-", "4"}]]}], ",",
+ RowBox[{"eqHigh", "[", "2", "]"}], "[",
+ RowBox[{"f", ",",
+ RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "2", "]"}]}], "]"}],
+ "[", "1", "]"}], ",",
+ RowBox[{
RowBox[{
- RowBox[{"-", "5.140526"}], " ",
- SuperscriptBox["10",
- RowBox[{"-", "4"}]]}], ",",
- RowBox[{"2.08856", " ",
- SuperscriptBox["10",
- RowBox[{"-", "4"}]]}], ",",
+ RowBox[{"eqMid", "[", "2", "]"}], "[",
+ RowBox[{"f", ",",
+ RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "2", "]"}]}], "]"}],
+ "[", "0", "]"}], ",",
+ RowBox[{
RowBox[{
- RowBox[{"-", "4.4819"}], " ",
- SuperscriptBox["10",
- RowBox[{"-", "5"}]]}]}], "}"}]}], "]"}]}],
- ";"}], "\[IndentingNewLine]",
+ RowBox[{"eqLow", "[", "2", "]"}], "[",
+ RowBox[{"f", ",",
+ RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "2", "]"}]}], "]"}],
+ "[", "1", "]"}]}], "}"}], "/.",
+ RowBox[{"rules", "[",
+ RowBox[{"f", ",",
+ RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "2", "]"}]}], "]"}]}]}],
+ ";"}]], "Input",
+ CellChangeTimes->{{3.817566966465438*^9, 3.817566988369422*^9}, {
+ 3.817567083496526*^9, 3.8175671002682753`*^9}, {3.817567232980145*^9,
+ 3.817567237450404*^9}, {3.817567395420353*^9, 3.8175673955203133`*^9}, {
+ 3.817570287418523*^9, 3.817570318305339*^9}},
+ CellLabel->
+ "In[112]:=",ExpressionUUID->"85e42c53-eadd-4f1a-85ea-31722ac3808d"],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{
+ RowBox[{"eqMid", "[", "2", "]"}], "[",
+ RowBox[{"f", ",",
+ RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "0", "]"}]}], "]"}], "[",
+ "0", "]"}]], "Input",
+ CellChangeTimes->{{3.817578043607004*^9, 3.817578057099272*^9}},
+ CellLabel->
+ "In[114]:=",ExpressionUUID->"94b7d8f3-1de1-4724-9998-f9046cf18d08"],
+
+Cell[BoxData[
RowBox[{
- RowBox[{"GlRules", "=",
- RowBox[{"MapIndexed", "[",
+ RowBox[{"(",
+ RowBox[{
RowBox[{
+ RowBox[{"-", "15"}], " ",
+ SuperscriptBox["\[ExponentialE]",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"-", "1"}], "+", "\[Theta]c"}], ")"}]}]]], " ", "M0", " ",
+ SuperscriptBox["\[Theta]c",
+ RowBox[{"2", "/", "15"}]], " ",
+ RowBox[{"ExpIntegralEi", "[",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{"1", "-", "\[Theta]c"}], ")"}]}]], "]"}]}], "-",
+ RowBox[{"15", " ", "B", " ",
+ SuperscriptBox["\[ExponentialE]",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"-", "1"}], "+", "\[Theta]c"}], ")"}]}]]], " ", "M0", " ",
+ SuperscriptBox["\[Theta]c",
+ RowBox[{"2", "/", "15"}]], " ",
+ RowBox[{"ExpIntegralEi", "[",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{"1", "-", "\[Theta]c"}], ")"}]}]], "]"}]}], "-",
+ RowBox[{"15", " ",
+ SuperscriptBox["\[ExponentialE]",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"-", "1"}], "+", "\[Theta]c"}], ")"}]}]]], " ", "M0", " ",
+ SuperscriptBox["\[Theta]c",
+ RowBox[{"17", "/", "15"}]], " ",
+ RowBox[{"ExpIntegralEi", "[",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{"1", "-", "\[Theta]c"}], ")"}]}]], "]"}]}], "+",
+ RowBox[{"15", " ", "B", " ",
+ SuperscriptBox["\[ExponentialE]",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"-", "1"}], "+", "\[Theta]c"}], ")"}]}]]], " ", "M0", " ",
+ SuperscriptBox["\[Theta]c",
+ RowBox[{"32", "/", "15"}]], " ",
+ RowBox[{"ExpIntegralEi", "[",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{"1", "-", "\[Theta]c"}], ")"}]}]], "]"}]}], "-",
+ RowBox[{"15", " ",
+ SuperscriptBox["\[ExponentialE]",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{"1", "+", "\[Theta]c"}], ")"}]}]]], " ", "M0", " ",
+ SuperscriptBox["\[Theta]c",
+ RowBox[{"2", "/", "15"}]], " ",
+ RowBox[{"ExpIntegralEi", "[",
+ RowBox[{"-",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{"1", "+", "\[Theta]c"}], ")"}]}]]}], "]"}]}], "+",
+ RowBox[{"15", " ", "B", " ",
+ SuperscriptBox["\[ExponentialE]",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{"1", "+", "\[Theta]c"}], ")"}]}]]], " ", "M0", " ",
+ SuperscriptBox["\[Theta]c",
+ RowBox[{"2", "/", "15"}]], " ",
+ RowBox[{"ExpIntegralEi", "[",
+ RowBox[{"-",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{"1", "+", "\[Theta]c"}], ")"}]}]]}], "]"}]}], "+",
+ RowBox[{"15", " ",
+ SuperscriptBox["\[ExponentialE]",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{"1", "+", "\[Theta]c"}], ")"}]}]]], " ", "M0", " ",
+ SuperscriptBox["\[Theta]c",
+ RowBox[{"17", "/", "15"}]], " ",
+ RowBox[{"ExpIntegralEi", "[",
+ RowBox[{"-",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{"1", "+", "\[Theta]c"}], ")"}]}]]}], "]"}]}], "-",
+ RowBox[{"15", " ", "B", " ",
+ SuperscriptBox["\[ExponentialE]",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{"1", "+", "\[Theta]c"}], ")"}]}]]], " ", "M0", " ",
+ SuperscriptBox["\[Theta]c",
+ RowBox[{"32", "/", "15"}]], " ",
+ RowBox[{"ExpIntegralEi", "[",
+ RowBox[{"-",
+ FractionBox["1",
+ RowBox[{"B", " ",
+ RowBox[{"(",
+ RowBox[{"1", "+", "\[Theta]c"}], ")"}]}]]}], "]"}]}], "-",
+ RowBox[{"16", " ", "\[Pi]", " ",
+ SuperscriptBox[
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"-", "1"}], "+",
+ SuperscriptBox["\[Theta]c", "2"]}], ")"}],
+ RowBox[{"1", "/", "15"}]], " ",
+ SuperscriptBox[
+ RowBox[{"gC", "[", "0", "]"}],
+ RowBox[{"1", "/", "15"}]], " ",
+ RowBox[{"\[CapitalPhi]", "[", "0", "]"}]}], "+",
+ RowBox[{"16", " ", "\[Pi]", " ",
+ SuperscriptBox["\[Theta]c", "2"], " ",
+ SuperscriptBox[
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"-", "1"}], "+",
+ SuperscriptBox["\[Theta]c", "2"]}], ")"}],
+ RowBox[{"1", "/", "15"}]], " ",
+ SuperscriptBox[
+ RowBox[{"gC", "[", "0", "]"}],
+ RowBox[{"1", "/", "15"}]], " ",
+ RowBox[{"\[CapitalPhi]", "[", "0", "]"}]}]}], ")"}], "/",
+ RowBox[{"(",
+ RowBox[{"15", " ", "\[Pi]", " ",
+ RowBox[{"(",
RowBox[{
- RowBox[{
+ RowBox[{"-", "1"}], "+", "\[Theta]c"}], ")"}], " ",
+ SuperscriptBox["\[Theta]c",
+ RowBox[{"2", "/", "15"}]], " ",
+ RowBox[{"(",
+ RowBox[{"1", "+", "\[Theta]c"}], ")"}]}], ")"}]}]], "Output",
+ CellChangeTimes->{3.817578074909642*^9},
+ CellLabel->
+ "Out[114]=",ExpressionUUID->"c8797d01-60d9-4367-bada-270d874abd6f"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"sol3", "=",
+ RowBox[{"FindRoot", "[",
+ RowBox[{
+ RowBox[{"eq3", "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "1.3"}]}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"M0", ",",
+ RowBox[{"M0", "/.", "sol2"}]}], "}"}], ",",
+ RowBox[{"{",
RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], ",",
RowBox[{
- RowBox[{"Derivative", "[",
- RowBox[{
- RowBox[{"#2", "[",
- RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], "]"}], "[", "Gl",
- "]"}], "[", "0", "]"}], "\[Rule]",
- RowBox[{"#1",
+ RowBox[{"gC", "[", "0", "]"}], "/.", "sol2"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "1", "]"}], ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"gC", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",",
+ RowBox[{"MaxIterations", "\[Rule]", "5000"}]}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.8175612726329412`*^9, 3.81756128486736*^9}, {
+ 3.8175614038617268`*^9, 3.817561415404965*^9}, {3.817561511096093*^9,
+ 3.817561563944231*^9}, {3.81756250196518*^9, 3.817562507914916*^9}, {
+ 3.817562967760625*^9, 3.81756298304041*^9}, 3.817563161460335*^9, {
+ 3.817563206558021*^9, 3.81756320676147*^9}, {3.817563530710863*^9,
+ 3.817563550054001*^9}, {3.817563775700533*^9, 3.817563804069632*^9}, {
+ 3.817563971222761*^9, 3.817564086350409*^9}, {3.817564155680212*^9,
+ 3.8175641623358994`*^9}, {3.81756424029494*^9, 3.817564240399859*^9}, {
+ 3.8175645416987743`*^9, 3.817564542202907*^9}, {3.817564715061411*^9,
+ 3.817564723202471*^9}, {3.8175648450855713`*^9, 3.817564883921851*^9}, {
+ 3.8175650025642157`*^9, 3.817565074155829*^9}, {3.817565217921039*^9,
+ 3.817565230520749*^9}, {3.817565359356901*^9, 3.8175654247402163`*^9}, {
+ 3.817565602697175*^9, 3.817565635407323*^9}, {3.817566059389201*^9,
+ 3.817566077942937*^9}, {3.817566269837482*^9, 3.817566273547044*^9}, {
+ 3.8175663066250553`*^9, 3.817566306784181*^9}, {3.817566684914805*^9,
+ 3.81756668549652*^9}, {3.817566919102108*^9, 3.817566934549343*^9}, {
+ 3.817567023284172*^9, 3.817567067932376*^9}, {3.8175671317703943`*^9,
+ 3.8175671596579437`*^9}, {3.817567241410817*^9, 3.8175672504997997`*^9}, {
+ 3.817568075647451*^9, 3.817568078380481*^9}, {3.817568594743252*^9,
+ 3.8175686239095984`*^9}, {3.817569779755021*^9, 3.817569779981715*^9},
+ 3.817569957333053*^9, {3.81757027719392*^9, 3.817570284741372*^9}, {
+ 3.817570386012393*^9, 3.8175704096934767`*^9}, {3.817570564684226*^9,
+ 3.817570567677744*^9}},
+ CellLabel->
+ "In[113]:=",ExpressionUUID->"f170d041-00ce-4e11-b3a8-0bd59dad2b6c"],
+
+Cell[BoxData[
+ TemplateBox[{
+ "FindRoot", "lstol",
+ "\"The line search decreased the step size to within tolerance specified \
+by AccuracyGoal and PrecisionGoal but was unable to find a sufficient \
+decrease in the merit function. You may need more than \
+\\!\\(\\*RowBox[{\\\"MachinePrecision\\\"}]\\) digits of working precision to \
+meet these tolerances.\"", 2, 113, 52, 25018801182717762080, "Local"},
+ "MessageTemplate"]], "Message", "MSG",
+ CellChangeTimes->{
+ 3.8175681074212227`*^9, {3.817568602720385*^9, 3.817568624745062*^9},
+ 3.817569911216564*^9, 3.817570012763472*^9, 3.817570103749761*^9, {
+ 3.8175703802086477`*^9, 3.817570411997117*^9}, 3.81757046521631*^9, {
+ 3.8175705207912827`*^9, 3.817570554229301*^9}, 3.817570599134549*^9,
+ 3.817578033326234*^9},
+ CellLabel->
+ "During evaluation of \
+In[113]:=",ExpressionUUID->"4eacc95f-2370-4f5b-b81d-114beebccca0"],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"M0", "\[Rule]", "26314.657975676913`"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "0", "]"}], "\[Rule]", "0.26058817076147406`"}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "1", "]"}], "\[Rule]",
+ RowBox[{"-", "0.05055607081397803`"}]}], ",",
+ RowBox[{
+ RowBox[{"gC", "[", "2", "]"}], "\[Rule]",
+ RowBox[{"-", "0.06098078955322251`"}]}]}], "}"}]], "Output",
+ CellChangeTimes->{
+ 3.817561286441853*^9, 3.817561420490069*^9, 3.817561452135456*^9, {
+ 3.817561512454604*^9, 3.817561517595207*^9}, 3.817561585719215*^9,
+ 3.817563004628446*^9, 3.817563182856628*^9, 3.817563228472159*^9, {
+ 3.817563534906947*^9, 3.817563573064754*^9}, {3.817563797249289*^9,
+ 3.817563825598139*^9}, {3.817563996789044*^9, 3.817564046321703*^9}, {
+ 3.817564078153729*^9, 3.817564103465789*^9}, 3.817564181902115*^9,
+ 3.817564233365617*^9, {3.817564277720583*^9, 3.8175642801348143`*^9},
+ 3.817564315116712*^9, 3.8175645338256474`*^9, {3.817564627325935*^9,
+ 3.8175646522898493`*^9}, {3.817564705276019*^9, 3.817564735465515*^9}, {
+ 3.817564839073145*^9, 3.817564850280691*^9}, 3.817564889679229*^9, {
+ 3.817564994846734*^9, 3.817565091817582*^9}, 3.817565231749591*^9, {
+ 3.817565295003468*^9, 3.817565428068199*^9}, 3.817565500042843*^9, {
+ 3.817565636029861*^9, 3.81756564530912*^9}, 3.817565735768449*^9, {
+ 3.817566053734901*^9, 3.8175660860827293`*^9}, 3.817566141015539*^9,
+ 3.8175662848590927`*^9, 3.817566325612877*^9, {3.817566873920313*^9,
+ 3.817566888279759*^9}, 3.8175669368598824`*^9, {3.817567045496682*^9,
+ 3.817567071548258*^9}, 3.817567145762271*^9, 3.817567226729545*^9,
+ 3.8175672805471077`*^9, {3.817567723233759*^9, 3.8175677300193787`*^9}, {
+ 3.817568079036153*^9, 3.8175681074809437`*^9}, {3.817568602782158*^9,
+ 3.817568624803339*^9}, 3.817569911341571*^9, 3.8175700128165197`*^9,
+ 3.817570103832847*^9, {3.817570380409218*^9, 3.817570412059435*^9},
+ 3.8175704652714357`*^9, {3.817570520846631*^9, 3.817570554281905*^9},
+ 3.81757059925739*^9, 3.817578033441112*^9},
+ CellLabel->
+ "Out[113]=",ExpressionUUID->"37349b20-07d0-4012-90ce-068c376209b0"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"GraphicsRow", "[",
+ RowBox[{"{", "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"Plot", "[",
+ RowBox[{
+ RowBox[{
+ RowBox[{
RowBox[{
- RowBox[{"(",
- RowBox[{
- RowBox[{"#2", "[",
- RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], ")"}], "!"}]}]}],
- "&"}], ",",
- RowBox[{"{",
- RowBox[{"0", ",",
- RowBox[{"-", "1.3578383417066"}], ",",
- RowBox[{"-", "0.048953289720"}], ",", "0.038863932", ",",
- RowBox[{"-", "0.068362119"}], ",", "0.18388370", ",",
- RowBox[{"-", "0.6591714"}], ",", "2.937665", ",",
- RowBox[{"-", "15.61"}]}], "}"}]}], "]"}]}],
- ";"}], "\[IndentingNewLine]",
- RowBox[{
- RowBox[{"GhRules", "=",
- RowBox[{"MapIndexed", "[",
- RowBox[{
+ RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "1", "]"}], "[",
+ "\[Theta]", "]"}], "/.", "sol3"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "1.1"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]", ",", "0", ",", "1.2"}], "}"}]}], "]"}], ",",
+ "\[IndentingNewLine]",
+ RowBox[{"Plot", "[",
RowBox[{
RowBox[{
RowBox[{
RowBox[{
- RowBox[{"Derivative", "[",
+ RowBox[{
RowBox[{
- RowBox[{"#2", "[",
- RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], "]"}], "[", "Gh",
- "]"}], "[", "0", "]"}], "\[Rule]",
- RowBox[{"#1",
- RowBox[{
- RowBox[{"(",
+ RowBox[{"R\[ScriptCapitalM]", "[", "2", "]"}], "[",
+ RowBox[{"B", ",", "\[Theta]c", ",", "M0"}], "]"}], "[", "\[Theta]",
+ "]"}], "/.",
+ RowBox[{"B", "->",
RowBox[{
- RowBox[{"#2", "[",
- RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], ")"}], "!"}]}]}],
- "&"}], ",",
- RowBox[{"{",
- RowBox[{"0", ",", "0", ",",
- RowBox[{"-", "1.8452280782328"}], ",", "0", ",", "8.333711750", ",",
- "0", ",",
- RowBox[{"-", "95.16896"}], ",", "0", ",", "1457.62", ",", "0", ",",
- RowBox[{"-", "25891"}]}], "}"}]}], "]"}]}],
- ";"}], "\[IndentingNewLine]",
+ RowBox[{"ruleB", "[", "2", "]"}], "[",
+ RowBox[{"f", ",",
+ RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "1", "]"}]}],
+ "]"}]}]}], "/.", "sol3"}], "/.",
+ RowBox[{"\[Theta]c", "\[Rule]", "1.1"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"\[Theta]", ",", "0", ",", "1.2"}], "}"}]}], "]"}]}],
+ "\[IndentingNewLine]", "}"}], "]"}]], "Input",
+ CellChangeTimes->{{3.8175672854849167`*^9, 3.8175673108365*^9}, {
+ 3.817567343605356*^9, 3.817567515945986*^9}},
+ CellLabel->"In[35]:=",ExpressionUUID->"dcf13cfd-3c9b-4f00-914a-62dd8441c54a"],
+
+Cell[BoxData[
+ GraphicsBox[{{}, {InsetBox[
+ GraphicsBox[{{{}, {},
+ TagBox[
+ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
+ Opacity[1.], LineBox[CompressedData["
+1:eJwV13k8VN8bB3DJUlKWyJotWm2hRPjYZ1IKoSKVLUSoVFoQyVZJfFtshZgZ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+ "]]},
+ Annotation[#, "Charting`Private`Tag$7941#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->{{17.867187499999996`, 0.9218750000000568}, {
+ 2.2657316720620315`, 6.630348647931953}},
+ 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->{{0, 1.2}, {-0.0007438034570260118, 0.04726807745466031}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.05]}},
+ Ticks->{Automatic, Automatic}], {159.24628325886667, -95.39577399785357},
+ ImageScaled[{0.5, 0.5}], {298.4017682929922, 181.70623618638774}],
+ InsetBox[
+ GraphicsBox[{{{}, {},
+ TagBox[
+ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
+ Opacity[1.], LineBox[CompressedData["
+1:eJwV13k8lF8XAHDabC2SrRKRflQqlbXotEgiLUJEe1F2ES1ERdEiWiiMZmQp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+ "]]},
+ Annotation[#, "Charting`Private`Tag$7983#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->{{23.669189453125, 1.0402832031251137`}, {
+ 2.2657316720620315`, 6.630348647931953}},
+ 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->{{0, 1.2}, {-0.07096644650747613, 0.016819129352618336`}},
+ PlotRangeClipping->True,
+ PlotRangePadding->{{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.05]}},
+ Ticks->{Automatic, Automatic}], {480.6990548547251, -95.39577399785357},
+ ImageScaled[{0.5, 0.5}], {304.32217844924224, 181.70623618638774}]}, {}},
+ ImageSize->{
+ UpTo[600],
+ UpTo[223]},
+ PlotRange->{{0, 642.9055431917168}, {-190.79154799570713`, 0}},
+ PlotRangePadding->{6, 5}]], "Output",
+ CellChangeTimes->{
+ 3.8175673122534857`*^9, {3.8175674402281427`*^9, 3.817567489380693*^9},
+ 3.817567520221552*^9},
+ CellLabel->"Out[35]=",ExpressionUUID->"9615b190-9c6f-4136-8ec8-38b48777afc1"]
+}, Open ]],
+
+Cell[BoxData[
+ RowBox[{"Series", "["}]], "Input",
+ CellChangeTimes->{{3.817563126277214*^9,
+ 3.817563127135446*^9}},ExpressionUUID->"c97fd2a9-8030-48bd-ac54-\
+60cfef08006d"],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
RowBox[{
- RowBox[{"DmetaRules", "=", "\[IndentingNewLine]",
- RowBox[{
+ RowBox[{
+ RowBox[{"eqLow", "[", "2", "]"}], "[",
+ RowBox[{"f", ",",
RowBox[{
- RowBox[{
+ RowBox[{"g", "[",
+ RowBox[{"gC", ",", "\[Theta]c"}], "]"}], "[", "0", "]"}]}], "]"}], "[",
+ "1", "]"}]], "Input",
+ CellChangeTimes->{{3.8175547641765738`*^9, 3.817554807184411*^9}, {
+ 3.81755721589187*^9, 3.817557223395288*^9}, {3.817559009520914*^9,
+ 3.817559010159284*^9}, {3.817559981019719*^9, 3.817559982058178*^9}, {
+ 3.817560014463335*^9, 3.817560020731222*^9}, {3.8175601114074917`*^9,
+ 3.817560121907399*^9}, {3.8175601564439993`*^9, 3.817560156604797*^9}},
+ CellLabel->"In[23]:=",ExpressionUUID->"8c3eb7fb-65d2-4a56-a3e3-0dc6e0518fe6"],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"M0", " ",
+ RowBox[{"(",
+ RowBox[{
+ FractionBox[
+ RowBox[{"2", " ", "B"}], "\[Pi]"], "+",
+ FractionBox[
RowBox[{
RowBox[{
- RowBox[{"Derivative", "[", "#", "]"}], "[", "Dmeta", "]"}], "[", "0",
- "]"}], "\[Rule]",
- RowBox[{"If", "[",
+ RowBox[{"-", "2"}], " ", "B", " ", "\[Theta]c"}], "+",
+ RowBox[{"4", " ",
+ SuperscriptBox["B", "2"], " ",
+ SuperscriptBox["\[Theta]c", "2"]}], "-",
RowBox[{
- RowBox[{"#", "\[NotEqual]", "2"}], ",",
- RowBox[{
- RowBox[{"Sin", "[",
- RowBox[{"8", "\[Pi]",
- RowBox[{
- RowBox[{"(",
- RowBox[{"2", "-", "#"}], ")"}], "/", "15"}]}], "]"}],
- RowBox[{
- RowBox[{
- RowBox[{"Derivative", "[", "#", "]"}], "[", "\[CapitalPhi]", "]"}],
- "[", "0", "]"}]}], ",",
- RowBox[{"2", "/", "15"}]}], "]"}]}], "&"}], "/@",
- RowBox[{"Range", "[",
- RowBox[{"0", ",", "5"}], "]"}]}]}], ";"}]}], "Input",
- CellChangeTimes->{{3.8171238506222553`*^9, 3.817123981055841*^9}, {
- 3.817124021016416*^9, 3.8171240795775967`*^9}, {3.8171241841479683`*^9,
- 3.817124191819606*^9}, {3.81712424202855*^9, 3.8171243317581472`*^9}, {
- 3.817124763670149*^9, 3.8171247637578783`*^9}, {3.817124806239091*^9,
- 3.81712480629488*^9}, {3.817125233990562*^9, 3.817125241366708*^9}, {
- 3.8171253924669952`*^9, 3.817125393009253*^9}, {3.817125426242784*^9,
- 3.817125508131061*^9}, {3.817125668253682*^9, 3.817125720078556*^9}, {
- 3.81712575752703*^9, 3.817125884277041*^9}, {3.817126017709049*^9,
- 3.8171260243875713`*^9}, {3.817127284274146*^9, 3.817127295450204*^9},
- 3.8172038927147207`*^9, 3.8172039519957237`*^9, 3.817211900243198*^9, {
- 3.8172119490120792`*^9, 3.817211969444298*^9}, {3.817216957447488*^9,
- 3.817216958531187*^9}, {3.817268003369576*^9, 3.817268019019158*^9}, {
- 3.817283853841984*^9, 3.81728388518631*^9}},
- CellLabel->
- "(WOPR) In[843]:=",ExpressionUUID->"1f309ab1-20a0-46cc-93fe-35aed54ccb3d"],
+ SuperscriptBox["\[ExponentialE]",
+ FractionBox["1",
+ RowBox[{"2", " ", "B", " ", "\[Theta]c"}]]], " ",
+ RowBox[{"ExpIntegralEi", "[",
+ RowBox[{"-",
+ FractionBox["1",
+ RowBox[{"2", " ", "B", " ", "\[Theta]c"}]]}], "]"}]}]}],
+ RowBox[{"8", " ",
+ SuperscriptBox["B", "2"], " ", "\[Pi]", " ",
+ SuperscriptBox["\[Theta]c", "3"]}]]}], ")"}]}], "+",
+ FractionBox[
+ RowBox[{"\[Theta]c", " ",
+ RowBox[{
+ SuperscriptBox["Gl", "\[Prime]",
+ MultilineFunction->None], "[", "0", "]"}]}],
+ RowBox[{"4", " ",
+ SuperscriptBox[
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"-", "1"}], "+",
+ SuperscriptBox["\[Theta]c", "2"]}], ")"}],
+ RowBox[{"7", "/", "8"}]]}]], "-",
+ FractionBox[
+ RowBox[{"2", " ",
+ RowBox[{"gC", "[", "0", "]"}], " ",
+ RowBox[{
+ SuperscriptBox["Gl", "\[Prime]\[Prime]",
+ MultilineFunction->None], "[", "0", "]"}]}],
+ SuperscriptBox[
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"-", "1"}], "+",
+ SuperscriptBox["\[Theta]c", "2"]}], ")"}],
+ RowBox[{"7", "/", "4"}]]]}]], "Output",
+ CellChangeTimes->{
+ 3.817554807406887*^9, {3.817557206327607*^9, 3.81755724215594*^9},
+ 3.8175573305621147`*^9, {3.817558987862504*^9, 3.817559032227151*^9}, {
+ 3.817559982370636*^9, 3.817560072538178*^9}, {3.817560113038806*^9,
+ 3.817560122398291*^9}, 3.817560163463731*^9},
+ CellLabel->"Out[23]=",ExpressionUUID->"ceff9452-e2f4-44ad-af83-bc7a4c209dad"]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData["GlRules"], "Input",
+ CellChangeTimes->{{3.817560532494705*^9, 3.817560541783863*^9}},
+ CellLabel->"In[26]:=",ExpressionUUID->"58cf9ad2-3d46-4b16-9024-9b17cba6f917"],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{
+ RowBox[{"Gl", "[", "0", "]"}], "\[Rule]", "0"}], ",",
+ RowBox[{
+ RowBox[{
+ SuperscriptBox["Gl", "\[Prime]",
+ MultilineFunction->None], "[", "0", "]"}], "\[Rule]",
+ RowBox[{"-", "1.3578383417066`"}]}], ",",
+ RowBox[{
+ RowBox[{
+ SuperscriptBox["Gl", "\[Prime]\[Prime]",
+ MultilineFunction->None], "[", "0", "]"}], "\[Rule]",
+ RowBox[{"-", "0.09790657944`"}]}], ",",
+ RowBox[{
+ RowBox[{
+ SuperscriptBox["Gl",
+ TagBox[
+ RowBox[{"(", "3", ")"}],
+ Derivative],
+ MultilineFunction->None], "[", "0", "]"}], "\[Rule]", "0.233183592`"}],
+ ",",
+ RowBox[{
+ RowBox[{
+ SuperscriptBox["Gl",
+ TagBox[
+ RowBox[{"(", "4", ")"}],
+ Derivative],
+ MultilineFunction->None], "[", "0", "]"}], "\[Rule]",
+ RowBox[{"-", "1.640690856`"}]}], ",",
+ RowBox[{
+ RowBox[{
+ SuperscriptBox["Gl",
+ TagBox[
+ RowBox[{"(", "5", ")"}],
+ Derivative],
+ MultilineFunction->None], "[", "0", "]"}], "\[Rule]", "22.066044`"}],
+ ",",
+ RowBox[{
+ RowBox[{
+ SuperscriptBox["Gl",
+ TagBox[
+ RowBox[{"(", "6", ")"}],
+ Derivative],
+ MultilineFunction->None], "[", "0", "]"}], "\[Rule]",
+ RowBox[{"-", "474.60340799999994`"}]}], ",",
+ RowBox[{
+ RowBox[{
+ SuperscriptBox["Gl",
+ TagBox[
+ RowBox[{"(", "7", ")"}],
+ Derivative],
+ MultilineFunction->None], "[", "0", "]"}], "\[Rule]", "14805.8316`"}],
+ ",",
+ RowBox[{
+ RowBox[{
+ SuperscriptBox["Gl",
+ TagBox[
+ RowBox[{"(", "8", ")"}],
+ Derivative],
+ MultilineFunction->None], "[", "0", "]"}], "\[Rule]",
+ RowBox[{"-", "629395.2`"}]}]}], "}"}]], "Output",
+ CellChangeTimes->{{3.8175605351665916`*^9, 3.817560542255609*^9}},
+ CellLabel->"Out[26]=",ExpressionUUID->"f406ab24-bd3a-4e22-988c-3ba0cf63a667"]
+}, Open ]],
Cell[BoxData[
RowBox[{
@@ -11418,9 +17692,9 @@ Cell[BoxData[
}, Open ]]
}, Open ]]
},
-WindowSize->{957, 1062},
+WindowSize->{1005, 792},
WindowMargins->{{Automatic, 1.5}, {1.5, Automatic}},
-FrontEndVersion->"12.1 for Linux x86 (64-bit) (June 19, 2020)",
+FrontEndVersion->"12.1 for Linux ARM (32-bit) (August 18, 2020)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"6f6c570c-dfc0-4320-bdc7-0f1de62bb24c"
]
@@ -11435,228 +17709,332 @@ CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
-Cell[558, 20, 270, 5, 24, "Input",ExpressionUUID->"e595a667-7f25-4f98-9f12-a321a236d113"],
+Cell[558, 20, 423, 8, 29, "Input",ExpressionUUID->"e595a667-7f25-4f98-9f12-a321a236d113"],
+Cell[CellGroupData[{
+Cell[1006, 32, 156, 3, 68, "Section",ExpressionUUID->"bb531fce-8a9d-4a5f-8d6a-ec66b9fbf698"],
+Cell[1165, 37, 1602, 30, 71, "Input",ExpressionUUID->"c239eacb-bd0a-49ce-8667-3aa72e4020c9"],
+Cell[2770, 69, 2216, 31, 29, "Input",ExpressionUUID->"b0293560-4bfa-4de2-84b0-335927f7dbea"],
+Cell[CellGroupData[{
+Cell[5011, 104, 3208, 60, 51, "Input",ExpressionUUID->"3d566693-1b4e-4bc5-b33b-b8036e1e4822"],
+Cell[8222, 166, 4077, 65, 33, "Output",ExpressionUUID->"f676952c-992f-4ebe-a4d1-30e21dd4d0ca"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[12336, 236, 1289, 27, 29, "Input",ExpressionUUID->"a4f082dc-c86b-4fae-a5ca-c1981cd9d9cf"],
+Cell[13628, 265, 539, 12, 22, "Message",ExpressionUUID->"36ce886b-a17b-4e11-a0fa-9283b3f2481b"],
+Cell[14170, 279, 13223, 234, 239, "Output",ExpressionUUID->"790a1b14-2979-49a3-9e30-5d496c64e79a"]
+}, Open ]],
+Cell[27408, 516, 1897, 33, 71, "Input",ExpressionUUID->"4dc1af41-4bef-447e-a233-c8c033887359"],
+Cell[CellGroupData[{
+Cell[29330, 553, 5250, 95, 51, "Input",ExpressionUUID->"e74b775a-c745-4f15-9b63-7bb00af5a487"],
+Cell[34583, 650, 3504, 60, 55, "Output",ExpressionUUID->"b0bec539-56ed-4897-b80b-cd8dfd2677e2"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[38124, 715, 1736, 38, 92, "Input",ExpressionUUID->"48ef1564-45f8-4d3a-b3bc-835e87c4b434"],
+Cell[39863, 755, 514, 11, 22, "Message",ExpressionUUID->"b51d87d3-de21-4502-b43b-5a537a1c6dc1"],
+Cell[40380, 768, 49252, 840, 205, 26205, 464, "CachedBoxData", "BoxData", "Output",ExpressionUUID->"4418ccfb-99b7-488d-a161-2678f84be87f"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[89669, 1613, 1089, 29, 54, "Input",ExpressionUUID->"802f97e2-70b5-4c0e-b977-f8a2e505bb60"],
+Cell[90761, 1644, 98820, 1642, 103, 73870, 1232, "CachedBoxData", "BoxData", "Output",ExpressionUUID->"1387cad6-2910-4d95-bb16-fccb91fd6a76"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[189618, 3291, 2147, 52, 79, "Input",ExpressionUUID->"4c6fe8ab-4f6a-4b57-92a5-c94e403d041d"],
+Cell[191768, 3345, 26505, 453, 241, "Output",ExpressionUUID->"348377e3-5d2e-45e0-83a1-0bb162fca9ec"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[218310, 3803, 3898, 89, 144, "Input",ExpressionUUID->"3fee7ec2-e0c4-4420-8192-c46efe85e265"],
+Cell[222211, 3894, 630, 13, 40, "Message",ExpressionUUID->"216842f7-6b1f-4b0e-80ad-7561735930ba"],
+Cell[222844, 3909, 570, 12, 39, "Message",ExpressionUUID->"19c5d1c8-bbcd-4f5b-83f4-3116397aae1d"],
+Cell[223417, 3923, 568, 12, 39, "Message",ExpressionUUID->"bf3fa7a1-a10c-4f34-b799-15feb6fd9a94"],
+Cell[223988, 3937, 646, 13, 22, "Message",ExpressionUUID->"8301d9c6-5667-4e0e-babc-34891d14958b"],
+Cell[224637, 3952, 606, 13, 24, "Message",ExpressionUUID->"ccae7427-68ca-4f65-9f6d-4dd2dc4b639d"],
+Cell[225246, 3967, 607, 13, 24, "Message",ExpressionUUID->"cfcfd305-6369-4d0d-ab91-323656281a2e"],
+Cell[225856, 3982, 608, 13, 24, "Message",ExpressionUUID->"ddee7f30-4b8d-49f3-a238-e8df9057bfed"],
+Cell[226467, 3997, 650, 13, 22, "Message",ExpressionUUID->"456dde30-b84b-4cba-9cea-4c2b7080bc35"],
+Cell[227120, 4012, 2149, 51, 237, "Output",ExpressionUUID->"f0d61600-5eb6-4f8a-9c60-ac80b53c708a"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[229306, 4068, 5214, 116, 167, "Input",ExpressionUUID->"0c28b27c-3e81-49ce-9293-512f19f95aeb"],
+Cell[234523, 4186, 783, 15, 40, "Message",ExpressionUUID->"b34a59d2-df83-4bcc-8877-f7287b9c6b63"],
+Cell[235309, 4203, 723, 14, 39, "Message",ExpressionUUID->"f90bbc2c-a921-4f2e-80fc-1fe79d36f5ed"],
+Cell[236035, 4219, 761, 15, 24, "Message",ExpressionUUID->"0c5f9a46-bb7f-4f2b-873b-5f8374387e5b"],
+Cell[236799, 4236, 721, 14, 39, "Message",ExpressionUUID->"9152de73-1d17-4288-821f-53b3ff3cd6a3"],
+Cell[237523, 4252, 801, 15, 22, "Message",ExpressionUUID->"da8de725-4d35-4371-8f8b-200846f7fadc"],
+Cell[238327, 4269, 761, 15, 24, "Message",ExpressionUUID->"77c72bca-73bf-4da0-8420-b2d771db650c"],
+Cell[239091, 4286, 761, 15, 24, "Message",ExpressionUUID->"0ab865cc-63da-43d9-be96-488dae3c11a7"],
+Cell[239855, 4303, 803, 15, 22, "Message",ExpressionUUID->"d6d0804b-e464-4f31-9989-db903712ce18"],
+Cell[240661, 4320, 2259, 52, 240, "Output",ExpressionUUID->"1007ec09-f8b7-4f86-9778-7ddc0fddb31f"]
+}, Open ]],
Cell[CellGroupData[{
-Cell[853, 29, 156, 3, 50, "Section",ExpressionUUID->"bb531fce-8a9d-4a5f-8d6a-ec66b9fbf698"],
-Cell[1012, 34, 1380, 28, 24, "Input",ExpressionUUID->"395191f4-75f5-4aa3-87f6-ccf9cbedf73f"],
+Cell[242957, 4377, 1844, 33, 71, "Input",ExpressionUUID->"78606265-f50f-49dc-888d-33550f059b83"],
+Cell[244804, 4412, 182, 3, 33, "Output",ExpressionUUID->"0e837164-3793-49da-bdd0-d4f51cfcde79"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[245023, 4420, 5046, 96, 71, "Input",ExpressionUUID->"396a3ca5-637b-4194-943d-7ec379bcf47e"],
+Cell[250072, 4518, 457, 11, 22, "Message",ExpressionUUID->"9a92db76-2a3a-4c87-9b65-03195ab7f92a"],
+Cell[250532, 4531, 2580, 49, 55, "Output",ExpressionUUID->"e97932be-a01b-4712-8761-1702066ed336"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[253149, 4585, 1521, 33, 92, "Input",ExpressionUUID->"050da7fc-1308-4d49-81b4-1f4efc54c09a"],
+Cell[254673, 4620, 32862, 572, 167, 17770, 325, "CachedBoxData", "BoxData", "Output",ExpressionUUID->"1e95a096-656a-4bd0-bdc9-09d9c739bf1f"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[287572, 5197, 1598, 30, 50, "Input",ExpressionUUID->"56a2c377-648a-4b5e-a0b8-a978c95c7038"],
+Cell[289173, 5229, 156, 2, 32, "Output",ExpressionUUID->"1fb128c6-9917-495f-aa57-47ef430806ec"]
+}, Open ]],
+Cell[289344, 5234, 648, 11, 28, "Input",ExpressionUUID->"01a65f9d-ccec-4ee5-a3eb-41b72a14e214"],
+Cell[CellGroupData[{
+Cell[290017, 5249, 3637, 73, 53, "Input",ExpressionUUID->"13e955ed-c66f-412e-a56a-086a5a7c388a"],
+Cell[293657, 5324, 1324, 28, 32, "Output",ExpressionUUID->"666b440f-efe1-40df-97a3-a6ba5f6b502f"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[295018, 5357, 1593, 38, 89, "Input",ExpressionUUID->"cf100fe8-27c6-4a2c-b65e-370cdc76ab54"],
+Cell[296614, 5397, 19249, 349, 200, "Output",ExpressionUUID->"5ba21607-6804-4676-bd54-9ca50ed7e210"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[315900, 5751, 854, 19, 52, "Input",ExpressionUUID->"b69f87e3-927b-4524-9686-1a17f2c879bb"],
+Cell[316757, 5772, 1027, 29, 77, "Output",ExpressionUUID->"fca5aade-1849-4879-95d9-c83dd6b84d7b"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[317821, 5806, 429, 11, 28, "Input",ExpressionUUID->"76d49acb-b5e2-4974-82cf-c376b2e9bf83"],
+Cell[318253, 5819, 692, 20, 50, "Output",ExpressionUUID->"abc7d2c8-0464-4233-a249-6655f54c6cae"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[318982, 5844, 718, 17, 28, "Input",ExpressionUUID->"06ec162d-d4ce-41ef-aa36-5c655ac7865a"],
+Cell[319703, 5863, 766, 21, 72, "Output",ExpressionUUID->"4f58f171-276d-4b8b-a439-52aa6e0e19fa"]
+}, Open ]],
+Cell[320484, 5887, 961, 29, 31, "Input",ExpressionUUID->"14d51596-0d76-499e-9baa-e7be6425156e"],
+Cell[CellGroupData[{
+Cell[321470, 5920, 1844, 34, 31, "Input",ExpressionUUID->"0fdc6db7-418c-44d4-b217-8c6a47dbf54f"],
+Cell[323317, 5956, 1564, 26, 32, "Output",ExpressionUUID->"67408372-ed4a-4c44-8e4a-095d1f5a7f3d"]
+}, Open ]],
+Cell[324896, 5985, 1686, 49, 51, "Input",ExpressionUUID->"85e42c53-eadd-4f1a-85ea-31722ac3808d"],
+Cell[CellGroupData[{
+Cell[326607, 6038, 388, 11, 28, "Input",ExpressionUUID->"94b7d8f3-1de1-4724-9998-f9046cf18d08"],
+Cell[326998, 6051, 5181, 151, 181, "Output",ExpressionUUID->"c8797d01-60d9-4367-bada-270d874abd6f"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[332216, 6207, 2463, 47, 31, "Input",ExpressionUUID->"f170d041-00ce-4e11-b3a8-0bd59dad2b6c"],
+Cell[334682, 6256, 893, 17, 43, "Message",ExpressionUUID->"4eacc95f-2370-4f5b-b81d-114beebccca0"],
+Cell[335578, 6275, 2172, 37, 33, "Output",ExpressionUUID->"37349b20-07d0-4012-90ce-068c376209b0"]
+}, Open ]],
Cell[CellGroupData[{
-Cell[2417, 66, 2007, 47, 92, "Input",ExpressionUUID->"389cbfb1-8cc7-458c-9f8c-1fd631f97f2c"],
-Cell[4427, 115, 2664, 57, 288, "Output",ExpressionUUID->"2b3d333d-6106-45b7-8d31-f398af6dca84"]
+Cell[337787, 6317, 1517, 41, 93, "Input",ExpressionUUID->"dcf13cfd-3c9b-4f00-914a-62dd8441c54a"],
+Cell[339307, 6360, 19961, 361, 200, "Output",ExpressionUUID->"9615b190-9c6f-4136-8ec8-38b48777afc1"]
}, Open ]],
+Cell[359283, 6724, 175, 4, 29, "Input",ExpressionUUID->"c97fd2a9-8030-48bd-ac54-60cfef08006d"],
Cell[CellGroupData[{
-Cell[7128, 177, 453, 10, 22, "Input",ExpressionUUID->"377f0dcd-6050-40b3-be70-41379e9fda93"],
-Cell[7584, 189, 150, 2, 25, "Output",ExpressionUUID->"02602b05-0f8e-4f3a-8e08-cb1c3aa44a3f"]
+Cell[359483, 6732, 677, 14, 29, "Input",ExpressionUUID->"8c3eb7fb-65d2-4a56-a3e3-0dc6e0518fe6"],
+Cell[360163, 6748, 1893, 54, 78, "Output",ExpressionUUID->"ceff9452-e2f4-44ad-af83-bc7a4c209dad"]
}, Open ]],
Cell[CellGroupData[{
-Cell[7771, 196, 502, 13, 24, "Input",ExpressionUUID->"8c3eb7fb-65d2-4a56-a3e3-0dc6e0518fe6"],
-Cell[8276, 211, 1300, 38, 62, "Output",ExpressionUUID->"e44b7486-110d-476c-b94b-28e4b600a40c"]
+Cell[362093, 6807, 178, 2, 29, "Input",ExpressionUUID->"58cf9ad2-3d46-4b16-9024-9b17cba6f917"],
+Cell[362274, 6811, 1904, 64, 57, "Output",ExpressionUUID->"f406ab24-bd3a-4e22-988c-3ba0cf63a667"]
}, Open ]],
-Cell[9591, 252, 8663, 212, 332, "Input",ExpressionUUID->"77a88da0-5b31-458a-9ed8-0b34545e511d"],
-Cell[18257, 466, 4921, 136, 144, "Input",ExpressionUUID->"1f309ab1-20a0-46cc-93fe-35aed54ccb3d"],
-Cell[23181, 604, 233, 5, 22, "Input",ExpressionUUID->"e7fef682-ee6e-4d26-962a-6946f28d5999"],
-Cell[23417, 611, 2312, 53, 56, "Input",ExpressionUUID->"2f5b927d-f164-4051-b8ca-bad9a5ba3b97"],
+Cell[364193, 6878, 233, 5, 29, "Input",ExpressionUUID->"e7fef682-ee6e-4d26-962a-6946f28d5999"],
+Cell[364429, 6885, 2312, 53, 73, "Input",ExpressionUUID->"2f5b927d-f164-4051-b8ca-bad9a5ba3b97"],
Cell[CellGroupData[{
-Cell[25754, 668, 4764, 78, 41, "Input",ExpressionUUID->"630fc9c9-229c-4372-8a16-eac1f2d98690"],
-Cell[30521, 748, 632, 12, 31, "Message",ExpressionUUID->"20e41565-1936-405a-9504-d530fdcc8152"],
-Cell[31156, 762, 1499, 29, 44, "Output",ExpressionUUID->"319eb113-9321-48fc-ad65-5700453ef613"]
+Cell[366766, 6942, 4764, 78, 53, "Input",ExpressionUUID->"630fc9c9-229c-4372-8a16-eac1f2d98690"],
+Cell[371533, 7022, 632, 12, 43, "Message",ExpressionUUID->"20e41565-1936-405a-9504-d530fdcc8152"],
+Cell[372168, 7036, 1499, 29, 77, "Output",ExpressionUUID->"319eb113-9321-48fc-ad65-5700453ef613"]
}, Open ]],
-Cell[32670, 794, 461, 14, 22, "Input",ExpressionUUID->"ea36fa2d-8c46-4383-be61-eff682dedb14"],
+Cell[373682, 7068, 461, 14, 28, "Input",ExpressionUUID->"ea36fa2d-8c46-4383-be61-eff682dedb14"],
Cell[CellGroupData[{
-Cell[33156, 812, 452, 12, 22, "Input",ExpressionUUID->"5823df11-0739-494d-bf1b-44bf2a14cb2b"],
-Cell[33611, 826, 278, 4, 25, "Output",ExpressionUUID->"cf69a3b6-a533-4dea-b33c-8d65e371fe08"]
+Cell[374168, 7086, 452, 12, 28, "Input",ExpressionUUID->"5823df11-0739-494d-bf1b-44bf2a14cb2b"],
+Cell[374623, 7100, 278, 4, 33, "Output",ExpressionUUID->"cf69a3b6-a533-4dea-b33c-8d65e371fe08"]
}, Open ]],
Cell[CellGroupData[{
-Cell[33926, 835, 1740, 46, 71, "Input",ExpressionUUID->"2a7b9f00-b942-4f1e-89df-1d3081b1fc6a"],
-Cell[35669, 883, 21020, 380, 153, "Output",ExpressionUUID->"155c39dd-ec1d-4900-9cbf-4fc4b876ac75"]
+Cell[374938, 7109, 1740, 46, 92, "Input",ExpressionUUID->"2a7b9f00-b942-4f1e-89df-1d3081b1fc6a"],
+Cell[376681, 7157, 21020, 380, 204, "Output",ExpressionUUID->"155c39dd-ec1d-4900-9cbf-4fc4b876ac75"]
}, Open ]],
Cell[CellGroupData[{
-Cell[56726, 1268, 966, 27, 24, "Input",ExpressionUUID->"da645597-b6a8-4dfc-83c5-3cec31d750f9"],
-Cell[57695, 1297, 469, 10, 25, "Output",ExpressionUUID->"f27b02e6-f3db-42e2-b534-43e5409fe36c"]
+Cell[397738, 7542, 966, 27, 31, "Input",ExpressionUUID->"da645597-b6a8-4dfc-83c5-3cec31d750f9"],
+Cell[398707, 7571, 469, 10, 33, "Output",ExpressionUUID->"f27b02e6-f3db-42e2-b534-43e5409fe36c"]
}, Open ]],
Cell[CellGroupData[{
-Cell[58201, 1312, 1847, 47, 73, "Input",ExpressionUUID->"b03f723e-24d4-4097-8ca2-9b1145403bfb"],
-Cell[60051, 1361, 519, 11, 19, "Message",ExpressionUUID->"1ff6b3ff-f0d9-48ea-95df-10584520bc02"],
-Cell[60573, 1374, 519, 11, 19, "Message",ExpressionUUID->"82682d18-f80c-4d23-8675-d31ca1576f0e"],
-Cell[61095, 1387, 521, 11, 19, "Message",ExpressionUUID->"164319c1-a2e0-427a-9f70-94e763f48d8e"],
-Cell[61619, 1400, 486, 10, 19, "Message",ExpressionUUID->"5d8fc41c-1820-4591-bdb1-29d65ed68611"],
-Cell[62108, 1412, 25289, 433, 172, "Output",ExpressionUUID->"0f099d03-656a-4602-85f6-26b4b2405b3b"]
+Cell[399213, 7586, 1847, 47, 117, "Input",ExpressionUUID->"b03f723e-24d4-4097-8ca2-9b1145403bfb"],
+Cell[401063, 7635, 519, 11, 25, "Message",ExpressionUUID->"1ff6b3ff-f0d9-48ea-95df-10584520bc02"],
+Cell[401585, 7648, 519, 11, 25, "Message",ExpressionUUID->"82682d18-f80c-4d23-8675-d31ca1576f0e"],
+Cell[402107, 7661, 521, 11, 25, "Message",ExpressionUUID->"164319c1-a2e0-427a-9f70-94e763f48d8e"],
+Cell[402631, 7674, 486, 10, 25, "Message",ExpressionUUID->"5d8fc41c-1820-4591-bdb1-29d65ed68611"],
+Cell[403120, 7686, 25289, 433, 228, "Output",ExpressionUUID->"0f099d03-656a-4602-85f6-26b4b2405b3b"]
}, Open ]],
-Cell[87412, 1848, 1836, 43, 57, "Input",ExpressionUUID->"868d07c1-b3cf-44ff-a070-78c2a21c388b"],
+Cell[428424, 8122, 1836, 43, 96, "Input",ExpressionUUID->"868d07c1-b3cf-44ff-a070-78c2a21c388b"],
Cell[CellGroupData[{
-Cell[89273, 1895, 4656, 86, 73, "Input",ExpressionUUID->"7c02fde8-7f1a-472a-9e7d-0e95772516eb"],
-Cell[93932, 1983, 899, 22, 25, "Output",ExpressionUUID->"6b22737f-c85f-4c36-9b44-d9e694bee115"]
+Cell[430285, 8169, 4656, 86, 74, "Input",ExpressionUUID->"7c02fde8-7f1a-472a-9e7d-0e95772516eb"],
+Cell[434944, 8257, 899, 22, 55, "Output",ExpressionUUID->"6b22737f-c85f-4c36-9b44-d9e694bee115"]
}, Open ]],
Cell[CellGroupData[{
-Cell[94868, 2010, 1989, 49, 75, "Input",ExpressionUUID->"0e89b49c-ebf1-4e9a-800f-62ec63f935a1"],
-Cell[96860, 2061, 21952, 393, 154, "Output",ExpressionUUID->"7cf0a89e-6d18-442b-b56d-94b97702709f"]
+Cell[435880, 8284, 1989, 49, 96, "Input",ExpressionUUID->"0e89b49c-ebf1-4e9a-800f-62ec63f935a1"],
+Cell[437872, 8335, 21952, 393, 205, "Output",ExpressionUUID->"7cf0a89e-6d18-442b-b56d-94b97702709f"]
}, Open ]],
Cell[CellGroupData[{
-Cell[118849, 2459, 1382, 36, 24, "Input",ExpressionUUID->"6c30dc25-997d-4790-bfcd-6e15ebcf7cbc"],
-Cell[120234, 2497, 520, 12, 33, "Message",ExpressionUUID->"56028de4-0ddc-4ea7-bf21-a25534c5c68d"],
-Cell[120757, 2511, 521, 12, 40, "Message",ExpressionUUID->"3d57804e-381a-4ba2-8dce-4428206df060"],
-Cell[121281, 2525, 3161, 69, 259, "Output",ExpressionUUID->"56916602-5965-4962-8188-b6662a5aa173"]
+Cell[459861, 8733, 1382, 36, 75, "Input",ExpressionUUID->"6c30dc25-997d-4790-bfcd-6e15ebcf7cbc"],
+Cell[461246, 8771, 520, 12, 40, "Message",ExpressionUUID->"56028de4-0ddc-4ea7-bf21-a25534c5c68d"],
+Cell[461769, 8785, 521, 12, 40, "Message",ExpressionUUID->"3d57804e-381a-4ba2-8dce-4428206df060"],
+Cell[462293, 8799, 3161, 69, 245, "Output",ExpressionUUID->"56916602-5965-4962-8188-b6662a5aa173"]
}, Open ]],
-Cell[124457, 2597, 1713, 40, 64, "Input",ExpressionUUID->"b31259b6-cc89-48a8-920d-e9dbcee664fb"],
+Cell[465469, 8871, 1713, 40, 73, "Input",ExpressionUUID->"b31259b6-cc89-48a8-920d-e9dbcee664fb"],
Cell[CellGroupData[{
-Cell[126195, 2641, 3913, 66, 42, "Input",ExpressionUUID->"30d0f855-c86b-4121-855c-813e9ee04f96"],
-Cell[130111, 2709, 1064, 19, 28, "Message",ExpressionUUID->"f1cd282b-fb73-4166-8899-1f1b71289512"],
-Cell[131178, 2730, 3809, 57, 49, "Output",ExpressionUUID->"3b7bac7f-12db-4bb2-8d83-0f02d8f19997"]
+Cell[467207, 8915, 3913, 66, 53, "Input",ExpressionUUID->"30d0f855-c86b-4121-855c-813e9ee04f96"],
+Cell[471123, 8983, 1064, 19, 27, "Message",ExpressionUUID->"f1cd282b-fb73-4166-8899-1f1b71289512"],
+Cell[472190, 9004, 3809, 57, 48, "Output",ExpressionUUID->"3b7bac7f-12db-4bb2-8d83-0f02d8f19997"]
}, Open ]],
Cell[CellGroupData[{
-Cell[135024, 2792, 1587, 43, 105, "Input",ExpressionUUID->"e1346f99-b8a8-49f2-9bab-d7d94b52e5d3"],
-Cell[136614, 2837, 61160, 1040, 218, 39593, 685, "CachedBoxData", "BoxData", "Output",ExpressionUUID->"24eee5ea-c8f9-4063-9d36-9e38f4d71b1d"]
+Cell[476036, 9066, 1587, 43, 104, "Input",ExpressionUUID->"e1346f99-b8a8-49f2-9bab-d7d94b52e5d3"],
+Cell[477626, 9111, 61160, 1040, 217, 39593, 685, "CachedBoxData", "BoxData", "Output",ExpressionUUID->"24eee5ea-c8f9-4063-9d36-9e38f4d71b1d"]
}, Open ]],
Cell[CellGroupData[{
-Cell[197811, 3882, 1714, 46, 105, "Input",ExpressionUUID->"8b99e721-7bc5-4c63-b150-8946bb7d2007"],
-Cell[199528, 3930, 30207, 531, 218, "Output",ExpressionUUID->"d79294e8-cb2f-4112-ad68-da965b8a242a"]
+Cell[538823, 10156, 1714, 46, 104, "Input",ExpressionUUID->"8b99e721-7bc5-4c63-b150-8946bb7d2007"],
+Cell[540540, 10204, 30207, 531, 217, "Output",ExpressionUUID->"d79294e8-cb2f-4112-ad68-da965b8a242a"]
}, Open ]],
Cell[CellGroupData[{
-Cell[229772, 4466, 491, 13, 29, "Input",ExpressionUUID->"8dd8c18b-504b-469d-8072-a9fb0cc417df"],
-Cell[230266, 4481, 539, 12, 22, "Message",ExpressionUUID->"a55da929-28cd-4032-aea8-5daec85d020a"],
-Cell[230808, 4495, 539, 12, 22, "Message",ExpressionUUID->"d9f18df2-5058-4626-9d48-5486b1743e96"],
-Cell[231350, 4509, 2243, 56, 79, "Output",ExpressionUUID->"7ce119a6-a1c0-48cc-9d86-6e7b6a1eafe3"]
+Cell[570784, 10740, 491, 13, 28, "Input",ExpressionUUID->"8dd8c18b-504b-469d-8072-a9fb0cc417df"],
+Cell[571278, 10755, 539, 12, 21, "Message",ExpressionUUID->"a55da929-28cd-4032-aea8-5daec85d020a"],
+Cell[571820, 10769, 539, 12, 21, "Message",ExpressionUUID->"d9f18df2-5058-4626-9d48-5486b1743e96"],
+Cell[572362, 10783, 2243, 56, 78, "Output",ExpressionUUID->"7ce119a6-a1c0-48cc-9d86-6e7b6a1eafe3"]
}, Open ]],
Cell[CellGroupData[{
-Cell[233630, 4570, 561, 16, 29, "Input",ExpressionUUID->"b0a27cf9-de55-4cf4-9b19-ff7b3add442a"],
-Cell[234194, 4588, 913, 27, 75, "Output",ExpressionUUID->"d3fcf7af-82f3-49c4-81c0-3bf29938e0d1"]
+Cell[574642, 10844, 561, 16, 28, "Input",ExpressionUUID->"b0a27cf9-de55-4cf4-9b19-ff7b3add442a"],
+Cell[575206, 10862, 913, 27, 74, "Output",ExpressionUUID->"d3fcf7af-82f3-49c4-81c0-3bf29938e0d1"]
}, Open ]],
Cell[CellGroupData[{
-Cell[235144, 4620, 681, 19, 55, "Input",ExpressionUUID->"f49c10e4-6ea3-40fb-85e8-436bcc73196f"],
-Cell[235828, 4641, 4071, 86, 235, "Output",ExpressionUUID->"0ede64a7-b62f-453c-b5e6-06e4c6ab27af"]
+Cell[576156, 10894, 681, 19, 54, "Input",ExpressionUUID->"f49c10e4-6ea3-40fb-85e8-436bcc73196f"],
+Cell[576840, 10915, 4071, 86, 234, "Output",ExpressionUUID->"0ede64a7-b62f-453c-b5e6-06e4c6ab27af"]
}, Open ]],
Cell[CellGroupData[{
-Cell[239936, 4732, 486, 13, 29, "Input",ExpressionUUID->"67bd5207-9130-427b-afb3-21bda9c7e82e"],
-Cell[240425, 4747, 200, 4, 33, "Output",ExpressionUUID->"39e5dba9-9c25-42e4-8876-75a530e46ee5"]
+Cell[580948, 11006, 486, 13, 28, "Input",ExpressionUUID->"67bd5207-9130-427b-afb3-21bda9c7e82e"],
+Cell[581437, 11021, 200, 4, 32, "Output",ExpressionUUID->"39e5dba9-9c25-42e4-8876-75a530e46ee5"]
}, Open ]],
Cell[CellGroupData[{
-Cell[240662, 4756, 783, 22, 29, "Input",ExpressionUUID->"6db9bdd5-3bc4-4993-85d9-2bb9c2d0db38"],
-Cell[241448, 4780, 3496, 77, 249, "Output",ExpressionUUID->"028520eb-aee9-483d-9152-2416a8a91977"]
+Cell[581674, 11030, 783, 22, 28, "Input",ExpressionUUID->"6db9bdd5-3bc4-4993-85d9-2bb9c2d0db38"],
+Cell[582460, 11054, 3496, 77, 248, "Output",ExpressionUUID->"028520eb-aee9-483d-9152-2416a8a91977"]
}, Open ]],
Cell[CellGroupData[{
-Cell[244981, 4862, 1223, 33, 24, "Input",ExpressionUUID->"aab225ac-8e68-4d46-a4da-600fe6364133"],
-Cell[246207, 4897, 10880, 231, 176, "Output",ExpressionUUID->"6e880d59-ffe1-440b-af8b-754c17269f6e"]
+Cell[585993, 11136, 1223, 33, 23, "Input",ExpressionUUID->"aab225ac-8e68-4d46-a4da-600fe6364133"],
+Cell[587219, 11171, 10880, 231, 175, "Output",ExpressionUUID->"6e880d59-ffe1-440b-af8b-754c17269f6e"]
}, Open ]],
Cell[CellGroupData[{
-Cell[257124, 5133, 2115, 52, 66, "Input",ExpressionUUID->"f01a72f1-91c7-4454-9040-b54a61c9cd07"],
-Cell[259242, 5187, 615, 13, 19, "Message",ExpressionUUID->"46cbf58a-9f1b-42bc-8a11-616c84d0e1d7"],
-Cell[259860, 5202, 613, 13, 19, "Message",ExpressionUUID->"c25c6435-fc6d-4b46-b41c-a3d203aa09da"],
-Cell[260476, 5217, 613, 13, 19, "Message",ExpressionUUID->"3a09025b-666f-454b-9a32-9f324e354788"],
-Cell[261092, 5232, 580, 12, 19, "Message",ExpressionUUID->"5b1f7808-f0a6-4257-b7ed-4acdc8c4ac95"]
+Cell[598136, 11407, 2115, 52, 65, "Input",ExpressionUUID->"f01a72f1-91c7-4454-9040-b54a61c9cd07"],
+Cell[600254, 11461, 615, 13, 18, "Message",ExpressionUUID->"46cbf58a-9f1b-42bc-8a11-616c84d0e1d7"],
+Cell[600872, 11476, 613, 13, 18, "Message",ExpressionUUID->"c25c6435-fc6d-4b46-b41c-a3d203aa09da"],
+Cell[601488, 11491, 613, 13, 18, "Message",ExpressionUUID->"3a09025b-666f-454b-9a32-9f324e354788"],
+Cell[602104, 11506, 580, 12, 18, "Message",ExpressionUUID->"5b1f7808-f0a6-4257-b7ed-4acdc8c4ac95"]
}, Open ]],
Cell[CellGroupData[{
-Cell[261709, 5249, 536, 10, 24, "Input",ExpressionUUID->"1dfbee5f-7e33-4446-bc10-991ba8838497"],
-Cell[262248, 5261, 93071, 1628, 177, "Output",ExpressionUUID->"e57fa90a-27ff-4013-8fad-ca7e3c98d348"]
+Cell[602721, 11523, 536, 10, 23, "Input",ExpressionUUID->"1dfbee5f-7e33-4446-bc10-991ba8838497"],
+Cell[603260, 11535, 93071, 1628, 176, "Output",ExpressionUUID->"e57fa90a-27ff-4013-8fad-ca7e3c98d348"]
}, Open ]],
Cell[CellGroupData[{
-Cell[355356, 6894, 314, 8, 22, "Input",ExpressionUUID->"8499af31-a50c-4059-afac-b628095fc761"],
-Cell[355673, 6904, 368, 8, 25, "Output",ExpressionUUID->"9aaf347d-0fae-4cb5-8920-f15fee437a9e"]
+Cell[696368, 13168, 314, 8, 21, "Input",ExpressionUUID->"8499af31-a50c-4059-afac-b628095fc761"],
+Cell[696685, 13178, 368, 8, 24, "Output",ExpressionUUID->"9aaf347d-0fae-4cb5-8920-f15fee437a9e"]
}, Open ]],
Cell[CellGroupData[{
-Cell[356078, 6917, 577, 17, 24, "Input",ExpressionUUID->"fecf4a67-c7e8-40b5-8e36-582a0bab9fe6"],
-Cell[356658, 6936, 753, 23, 48, "Output",ExpressionUUID->"742a0341-4af8-4ba4-a799-e15a1e847a9c"]
+Cell[697090, 13191, 577, 17, 23, "Input",ExpressionUUID->"fecf4a67-c7e8-40b5-8e36-582a0bab9fe6"],
+Cell[697670, 13210, 753, 23, 47, "Output",ExpressionUUID->"742a0341-4af8-4ba4-a799-e15a1e847a9c"]
}, Open ]],
Cell[CellGroupData[{
-Cell[357448, 6964, 438, 11, 24, "Input",ExpressionUUID->"9884f3ff-ff57-4cf7-b122-2aebcb709801"],
-Cell[357889, 6977, 947, 26, 45, "Output",ExpressionUUID->"5f69419d-b0c1-4cd5-9616-460f429c823a"]
+Cell[698460, 13238, 438, 11, 23, "Input",ExpressionUUID->"9884f3ff-ff57-4cf7-b122-2aebcb709801"],
+Cell[698901, 13251, 947, 26, 44, "Output",ExpressionUUID->"5f69419d-b0c1-4cd5-9616-460f429c823a"]
}, Open ]],
Cell[CellGroupData[{
-Cell[358873, 7008, 549, 13, 24, "Input",ExpressionUUID->"c18d621f-7e5f-48db-8ae7-0fda0221c79c"],
-Cell[359425, 7023, 599, 17, 45, "Output",ExpressionUUID->"b45884b0-ccdc-4e99-ac15-83498ea86eff"]
+Cell[699885, 13282, 549, 13, 23, "Input",ExpressionUUID->"c18d621f-7e5f-48db-8ae7-0fda0221c79c"],
+Cell[700437, 13297, 599, 17, 44, "Output",ExpressionUUID->"b45884b0-ccdc-4e99-ac15-83498ea86eff"]
}, Open ]],
Cell[CellGroupData[{
-Cell[360061, 7045, 338, 7, 22, "Input",ExpressionUUID->"8e16b08d-33f5-4a51-9850-75f98a0e6a08"],
-Cell[360402, 7054, 2269, 65, 61, "Output",ExpressionUUID->"21b799e5-0965-4692-b4ba-6083041c0cdd"]
+Cell[701073, 13319, 338, 7, 21, "Input",ExpressionUUID->"8e16b08d-33f5-4a51-9850-75f98a0e6a08"],
+Cell[701414, 13328, 2269, 65, 60, "Output",ExpressionUUID->"21b799e5-0965-4692-b4ba-6083041c0cdd"]
}, Open ]],
Cell[CellGroupData[{
-Cell[362708, 7124, 237, 5, 22, "Input",ExpressionUUID->"4c8cb259-b56a-423e-957f-9a65ba700a16"],
-Cell[362948, 7131, 2063, 59, 109, "Output",ExpressionUUID->"312f09f3-55f8-4f9d-a42c-05ca1c4aea27"]
+Cell[703720, 13398, 237, 5, 21, "Input",ExpressionUUID->"4c8cb259-b56a-423e-957f-9a65ba700a16"],
+Cell[703960, 13405, 2063, 59, 108, "Output",ExpressionUUID->"312f09f3-55f8-4f9d-a42c-05ca1c4aea27"]
}, Open ]],
Cell[CellGroupData[{
-Cell[365048, 7195, 564, 14, 24, "Input",ExpressionUUID->"069edadd-116a-4ccf-831d-0fe6e07540fe"],
-Cell[365615, 7211, 1113, 29, 52, "Output",ExpressionUUID->"e6426e3c-3d4d-49f1-becd-dfef45704088"]
+Cell[706060, 13469, 564, 14, 23, "Input",ExpressionUUID->"069edadd-116a-4ccf-831d-0fe6e07540fe"],
+Cell[706627, 13485, 1113, 29, 51, "Output",ExpressionUUID->"e6426e3c-3d4d-49f1-becd-dfef45704088"]
}, Open ]],
Cell[CellGroupData[{
-Cell[366765, 7245, 522, 13, 24, "Input",ExpressionUUID->"3cd180b6-0e22-4832-af2b-e9ecec7e0a49"],
-Cell[367290, 7260, 5586, 138, 258, "Output",ExpressionUUID->"45f19748-f63a-49e1-8ced-a4f5c5dda272"]
+Cell[707777, 13519, 522, 13, 23, "Input",ExpressionUUID->"3cd180b6-0e22-4832-af2b-e9ecec7e0a49"],
+Cell[708302, 13534, 5586, 138, 257, "Output",ExpressionUUID->"45f19748-f63a-49e1-8ced-a4f5c5dda272"]
}, Open ]],
-Cell[372891, 7401, 366, 10, 22, "Input",ExpressionUUID->"3ffc56f5-fc40-4c69-bdce-f91a4aab1c67"],
+Cell[713903, 13675, 366, 10, 21, "Input",ExpressionUUID->"3ffc56f5-fc40-4c69-bdce-f91a4aab1c67"],
Cell[CellGroupData[{
-Cell[373282, 7415, 838, 23, 42, "Input",ExpressionUUID->"e131ab87-4ef6-4852-9ddd-e4499b39559a"],
-Cell[374123, 7440, 597, 16, 51, "Output",ExpressionUUID->"86a22957-07a1-48ab-90d1-d142a27afe22"]
+Cell[714294, 13689, 838, 23, 41, "Input",ExpressionUUID->"e131ab87-4ef6-4852-9ddd-e4499b39559a"],
+Cell[715135, 13714, 597, 16, 50, "Output",ExpressionUUID->"86a22957-07a1-48ab-90d1-d142a27afe22"]
}, Open ]],
Cell[CellGroupData[{
-Cell[374757, 7461, 921, 23, 42, "Input",ExpressionUUID->"22a30e99-2bd5-43a5-9353-3a3be14232a6"],
-Cell[375681, 7486, 2812, 74, 80, "Output",ExpressionUUID->"470e97c2-b944-4611-8c77-75e5a0915c04"]
+Cell[715769, 13735, 921, 23, 41, "Input",ExpressionUUID->"22a30e99-2bd5-43a5-9353-3a3be14232a6"],
+Cell[716693, 13760, 2812, 74, 80, "Output",ExpressionUUID->"470e97c2-b944-4611-8c77-75e5a0915c04"]
}, Open ]],
Cell[CellGroupData[{
-Cell[378530, 7565, 824, 23, 42, "Input",ExpressionUUID->"3752e4d8-bc7c-475c-b88c-a0d99559d99c"],
-Cell[379357, 7590, 2580, 68, 78, "Output",ExpressionUUID->"db6b4f65-90c7-4c37-9945-5690d8472368"]
+Cell[719542, 13839, 824, 23, 41, "Input",ExpressionUUID->"3752e4d8-bc7c-475c-b88c-a0d99559d99c"],
+Cell[720369, 13864, 2580, 68, 77, "Output",ExpressionUUID->"db6b4f65-90c7-4c37-9945-5690d8472368"]
}, Open ]],
Cell[CellGroupData[{
-Cell[381974, 7663, 463, 12, 40, "Input",ExpressionUUID->"6a34969c-5bbf-4acb-a54f-a9bfbf2c9f87"],
-Cell[382440, 7677, 8623, 160, 171, "Output",ExpressionUUID->"70cff46d-010d-4a9a-8cf5-3901b2a30edf"]
+Cell[722986, 13937, 463, 12, 40, "Input",ExpressionUUID->"6a34969c-5bbf-4acb-a54f-a9bfbf2c9f87"],
+Cell[723452, 13951, 8623, 160, 170, "Output",ExpressionUUID->"70cff46d-010d-4a9a-8cf5-3901b2a30edf"]
}, Open ]],
Cell[CellGroupData[{
-Cell[391100, 7842, 595, 17, 24, "Input",ExpressionUUID->"6afc45fb-65bc-47fe-b120-408f15ede40b"],
-Cell[391698, 7861, 470, 13, 50, "Output",ExpressionUUID->"4cdf78f8-6821-4e67-9385-8a091cc9cf9d"]
+Cell[732112, 14116, 595, 17, 23, "Input",ExpressionUUID->"6afc45fb-65bc-47fe-b120-408f15ede40b"],
+Cell[732710, 14135, 470, 13, 50, "Output",ExpressionUUID->"4cdf78f8-6821-4e67-9385-8a091cc9cf9d"]
}, Open ]],
Cell[CellGroupData[{
-Cell[392205, 7879, 236, 6, 22, "Input",ExpressionUUID->"b66a0012-a40b-4041-8ea9-a9cad40db85f"],
-Cell[392444, 7887, 301, 8, 39, "Output",ExpressionUUID->"9744135b-7d1f-4023-b02d-1bdf3b29d60f"]
+Cell[733217, 14153, 236, 6, 21, "Input",ExpressionUUID->"b66a0012-a40b-4041-8ea9-a9cad40db85f"],
+Cell[733456, 14161, 301, 8, 38, "Output",ExpressionUUID->"9744135b-7d1f-4023-b02d-1bdf3b29d60f"]
}, Open ]],
Cell[CellGroupData[{
-Cell[392782, 7900, 419, 12, 24, "Input",ExpressionUUID->"7ceb4bac-ce7b-4adc-aeb9-95a215777744"],
-Cell[393204, 7914, 720, 22, 40, "Output",ExpressionUUID->"9c7df971-6bfc-41f8-a68e-fb9921c0b017"]
+Cell[733794, 14174, 419, 12, 23, "Input",ExpressionUUID->"7ceb4bac-ce7b-4adc-aeb9-95a215777744"],
+Cell[734216, 14188, 720, 22, 40, "Output",ExpressionUUID->"9c7df971-6bfc-41f8-a68e-fb9921c0b017"]
}, Open ]],
Cell[CellGroupData[{
-Cell[393961, 7941, 492, 13, 24, "Input",ExpressionUUID->"07932986-b2e1-477a-9d99-1b9701e3af0c"],
-Cell[394456, 7956, 510, 11, 19, "Message",ExpressionUUID->"f0c4d2f9-9d6d-48c0-b78e-b8f84a7f6bb2"],
-Cell[394969, 7969, 5864, 115, 182, "Output",ExpressionUUID->"82bf5b22-f54c-4da8-bea6-61b7c42c3450"]
+Cell[734973, 14215, 492, 13, 23, "Input",ExpressionUUID->"07932986-b2e1-477a-9d99-1b9701e3af0c"],
+Cell[735468, 14230, 510, 11, 18, "Message",ExpressionUUID->"f0c4d2f9-9d6d-48c0-b78e-b8f84a7f6bb2"],
+Cell[735981, 14243, 5864, 115, 181, "Output",ExpressionUUID->"82bf5b22-f54c-4da8-bea6-61b7c42c3450"]
}, Open ]],
Cell[CellGroupData[{
-Cell[400870, 8089, 804, 22, 54, "Input",ExpressionUUID->"13e1541b-4ad9-4a40-89f2-be40a0e4d6fd"],
-Cell[401677, 8113, 479, 13, 51, "Output",ExpressionUUID->"dff49a57-ddf5-4e9d-aa0a-55006221f3c2"]
+Cell[741882, 14363, 804, 22, 53, "Input",ExpressionUUID->"13e1541b-4ad9-4a40-89f2-be40a0e4d6fd"],
+Cell[742689, 14387, 479, 13, 50, "Output",ExpressionUUID->"dff49a57-ddf5-4e9d-aa0a-55006221f3c2"]
}, Open ]],
Cell[CellGroupData[{
-Cell[402193, 8131, 650, 19, 24, "Input",ExpressionUUID->"6def2df0-3761-4f37-b66f-ba9071b93625"],
-Cell[402846, 8152, 534, 15, 42, "Output",ExpressionUUID->"175a2c7c-fa54-45c3-bf4f-c4ed89dad110"]
+Cell[743205, 14405, 650, 19, 23, "Input",ExpressionUUID->"6def2df0-3761-4f37-b66f-ba9071b93625"],
+Cell[743858, 14426, 534, 15, 41, "Output",ExpressionUUID->"175a2c7c-fa54-45c3-bf4f-c4ed89dad110"]
}, Open ]],
Cell[CellGroupData[{
-Cell[403417, 8172, 302, 7, 24, "Input",ExpressionUUID->"657e079b-66fb-4614-816e-af41b7fabf10"],
-Cell[403722, 8181, 454, 11, 19, "Message",ExpressionUUID->"f6532f4e-d02f-402b-985e-f8964b91f90e"],
-Cell[404179, 8194, 1129, 29, 32, "Output",ExpressionUUID->"5f2bc73c-3ef7-4874-86b3-dd3ac3e99858"]
+Cell[744429, 14446, 302, 7, 23, "Input",ExpressionUUID->"657e079b-66fb-4614-816e-af41b7fabf10"],
+Cell[744734, 14455, 454, 11, 18, "Message",ExpressionUUID->"f6532f4e-d02f-402b-985e-f8964b91f90e"],
+Cell[745191, 14468, 1129, 29, 31, "Output",ExpressionUUID->"5f2bc73c-3ef7-4874-86b3-dd3ac3e99858"]
}, Open ]],
Cell[CellGroupData[{
-Cell[405345, 8228, 325, 7, 24, "Input",ExpressionUUID->"49f74264-7484-4d5a-b52f-d0892384e631"],
-Cell[405673, 8237, 4933, 99, 175, "Output",ExpressionUUID->"26e2807e-1336-4751-8e74-d4414f081679"]
+Cell[746357, 14502, 325, 7, 23, "Input",ExpressionUUID->"49f74264-7484-4d5a-b52f-d0892384e631"],
+Cell[746685, 14511, 4933, 99, 174, "Output",ExpressionUUID->"26e2807e-1336-4751-8e74-d4414f081679"]
}, Open ]],
Cell[CellGroupData[{
-Cell[410643, 8341, 1059, 26, 48, "Input",ExpressionUUID->"3bd71288-3233-4171-a393-57251fb3dc52"],
-Cell[411705, 8369, 6890, 131, 180, "Output",ExpressionUUID->"203873a1-0dd1-4567-8d12-97eeeed127f7"]
+Cell[751655, 14615, 1059, 26, 47, "Input",ExpressionUUID->"3bd71288-3233-4171-a393-57251fb3dc52"],
+Cell[752717, 14643, 6890, 131, 180, "Output",ExpressionUUID->"203873a1-0dd1-4567-8d12-97eeeed127f7"]
}, Open ]],
Cell[CellGroupData[{
-Cell[418632, 8505, 1358, 35, 48, "Input",ExpressionUUID->"39644cf7-65fa-4952-a674-714ff8619dd6"],
-Cell[419993, 8542, 15118, 266, 179, "Output",ExpressionUUID->"16b2f1f1-4bda-4b9c-9a2d-c4721af32a8e"]
+Cell[759644, 14779, 1358, 35, 47, "Input",ExpressionUUID->"39644cf7-65fa-4952-a674-714ff8619dd6"],
+Cell[761005, 14816, 15118, 266, 178, "Output",ExpressionUUID->"16b2f1f1-4bda-4b9c-9a2d-c4721af32a8e"]
}, Open ]],
Cell[CellGroupData[{
-Cell[435148, 8813, 1607, 46, 65, "Input",ExpressionUUID->"72bac293-cf66-40a9-809d-4d0874dae037"],
-Cell[436758, 8861, 59065, 1048, 175, "Output",ExpressionUUID->"d758ff21-6281-4951-879d-9a8a224caf38"]
+Cell[776160, 15087, 1607, 46, 64, "Input",ExpressionUUID->"72bac293-cf66-40a9-809d-4d0874dae037"],
+Cell[777770, 15135, 59065, 1048, 174, "Output",ExpressionUUID->"d758ff21-6281-4951-879d-9a8a224caf38"]
}, Open ]],
Cell[CellGroupData[{
-Cell[495860, 9914, 1002, 31, 42, "Input",ExpressionUUID->"41ea287c-9ee3-4b18-b17d-5dfc6a4e056d"],
-Cell[496865, 9947, 3476, 103, 125, "Output",ExpressionUUID->"7b8e54ff-34ea-444e-8e78-ad376945c6d8"]
+Cell[836872, 16188, 1002, 31, 41, "Input",ExpressionUUID->"41ea287c-9ee3-4b18-b17d-5dfc6a4e056d"],
+Cell[837877, 16221, 3476, 103, 124, "Output",ExpressionUUID->"7b8e54ff-34ea-444e-8e78-ad376945c6d8"]
}, Open ]],
Cell[CellGroupData[{
-Cell[500378, 10055, 753, 23, 24, "Input",ExpressionUUID->"77ced036-93d3-4558-8eb2-1aeeb8345ed7"],
-Cell[501134, 10080, 840, 23, 40, "Output",ExpressionUUID->"49c3b3ed-cf01-4c58-acac-6b3b7b9cb822"]
+Cell[841390, 16329, 753, 23, 23, "Input",ExpressionUUID->"77ced036-93d3-4558-8eb2-1aeeb8345ed7"],
+Cell[842146, 16354, 840, 23, 40, "Output",ExpressionUUID->"49c3b3ed-cf01-4c58-acac-6b3b7b9cb822"]
}, Open ]],
Cell[CellGroupData[{
-Cell[502011, 10108, 1262, 35, 41, "Input",ExpressionUUID->"1dc20dd2-2639-4b38-8eb3-e39481c6a15e"],
-Cell[503276, 10145, 71734, 1205, 306, "Output",ExpressionUUID->"ae6c01c8-9abd-4358-a6f9-fb8f033a8ba4"]
+Cell[843023, 16382, 1262, 35, 40, "Input",ExpressionUUID->"1dc20dd2-2639-4b38-8eb3-e39481c6a15e"],
+Cell[844288, 16419, 71734, 1205, 305, "Output",ExpressionUUID->"ae6c01c8-9abd-4358-a6f9-fb8f033a8ba4"]
}, Open ]],
Cell[CellGroupData[{
-Cell[575047, 11355, 1045, 25, 40, "Input",ExpressionUUID->"25d7aa57-46b2-4829-8aad-b00b9ab2ecff"],
-Cell[576095, 11382, 1385, 34, 41, "Output",ExpressionUUID->"5f0c650e-d3ec-4a10-aad2-c391b45db45f"]
+Cell[916059, 17629, 1045, 25, 40, "Input",ExpressionUUID->"25d7aa57-46b2-4829-8aad-b00b9ab2ecff"],
+Cell[917107, 17656, 1385, 34, 40, "Output",ExpressionUUID->"5f0c650e-d3ec-4a10-aad2-c391b45db45f"]
}, Open ]]
}, Open ]]
}
diff --git a/schofield.wl b/schofield.wl
index 7597891..0d18848 100644
--- a/schofield.wl
+++ b/schofield.wl
@@ -31,31 +31,29 @@ $Assumptions = {θc > 0, θc > 1, gC[_] ∈ Reals, B > 0, γ > 0}
]
Δ[D_:2] := β[D] δ[D]
+t[θ_] := (θ)^2 - 1
+h[n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] θ^(2i+1), {i, 0, n}]
-f[θ_] := θ^2 - 1
-g[gC_:gC, θc_:θc][n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] θ^(2i+1), {i, 0, n}]
+RFf[y_] := π^-1 y Exp[1/y] ExpIntegralEi[-1/y]
+RF[n_][θ_] := A (RFf[B(θc-θ)] + RFf[B(θc+θ)]) + Sum[FC[i] θ^(2i) , {i, 0, n}]
-I\[ScriptCapitalM]f[y_] := (1 + 1 / x) Exp[-1/x]
-R\[ScriptCapitalM]f[y_] := (1 - y) Exp[1/y] ExpIntegralEi[-1/y] / (π y)
+ruleB[g_] := π / (2 1.3578383417066) (- g'[θc] / t[θc]^Δ[2])
-R\[ScriptCapitalM][2][B_, θc_, M0_][θ_] := - M0 (R\[ScriptCapitalM]f[B(θc - θ)] - R\[ScriptCapitalM]f[B(θc + θ)])
-
-ruleB[2][f_, g_] := π / (2 1.3578383417066) (Δ g[θc] f[θc]^(-Δ[2]-1) f'[θc] - g'[θc] / f[θc]^Δ[2])
-
-eqLow[D_:2][f_, g_][m_] := SeriesCoefficient[
- R\[ScriptCapitalM][D][B, θc, M0][θ] + f[θ]^β[D] Gl'[g[θ] / f[θ]^Δ[D]],
+eqLow[F_, h_][m_] := SeriesCoefficient[
+ F[θ] - t[θ]^2 (Gl[h[θ] t[θ]^-Δ[2]] + Log[t[θ]^2]/(8 π)),
{θ, θc, m},
Assumptions -> Join[$Assumptions, {θ < θc, θ > 1}]
]
-eqHigh[D_:2][f_, g_][m_] := SeriesCoefficient[
- R\[ScriptCapitalM][D][B, θc, M0][θ] + (-f[θ])^β[D] Gh'[g[θ] / (-f[θ])^Δ[D]],
+eqHigh[F_, h_][m_] := SeriesCoefficient[
+ F[θ] - (-t[θ])^2 (Gh[h[θ] (-t[θ])^-Δ[2]] + Log[(-t[θ])^2]/(8 π)),
{θ, 0, m},
Assumptions -> Join[$Assumptions, {θ > 0, θ < 1}]
]
-eqMid[D_:2][f_, g_][m_] := SeriesCoefficient[
- R\[ScriptCapitalM][D][B, θc, M0][θ] + g[θ]^(1/δ[D]) ((2 - α[D]) Φ'[η] - η Φ'[η]) / Δ[D] /. η -> f[θ] / g[θ]^(1 / Δ[D]),
+eqMid[F_, h_][m_] := SeriesCoefficient[
+ F[θ] - t[θ]^2 Log[h[θ]^2]/(8 Δ[2]π) - h[θ]^((2-α[2])/Δ[2]) Φ[η]
+ /. η -> t[θ] / h[θ]^(1 / Δ[2]),
{θ, 1, m},
Assumptions -> Join[$Assumptions, {θ > 0, θ < θc}]
]
@@ -103,9 +101,9 @@ dRule[sym_][f_, i_] := Derivative[i[[1]] - 1][sym][0] -> f (i[[1]] - 1)!
GlRules = MapIndexed[dRule[Gl], Gls];
GhRules = MapIndexed[dRule[Gh], Ghs];
-rules[f_, g_] := Join[{B -> ruleB[2][f, g]}, ΦRules, GlRules, GhRules]
+rules[g_] := Join[{B -> ruleB[g]}, ΦRules, GlRules, GhRules]
-eq[D_:2][f_, g_][m_] := Select[Flatten[{eqLow[D][f, g][#], eqMid[D][f, g][#], eqHigh[D][f, g][#]} & /@ Range[0, m]] /. rules[f, g], # != 0 &]
+eq[F_, g_][m_] := Select[Flatten[{eqLow[F, g][#], eqMid[F, g][#], eqHigh[F, g][#]} & /@ Range[0, m]] /. rules[g], !(# === 0) &]
EndPackage[]