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FontColor->RGBColor[1, 0, 0]], " the audience ", StyleBox["with prototype problems", FontColor->RGBColor[1, 0, 0]], " studied in our workgroup, to show how to ", StyleBox["use ", FontColor->RGBColor[1, 0, 0]], StyleBox["Mathematica", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontSlant->"Italic"], "in our problems, and finally we would like to ", StyleBox["suggest improvements", FontColor->RGBColor[1, 0, 0]], " in ", StyleBox["Mathematica", FontSlant->"Italic"], " which would make our work more effective. \n\nNumerous phenomena in \ physics, chemistry, biology, and economy can be modelled by boundary-value \ problems for differential equations. These boundary-value problems (BVPs for \ short) can often be written in an operator form\n\n", Cell[BoxData[ StyleBox[\(\(L \((u)\) + H \((u, \ p)\) = f\)\(\ \)\(,\)\), "DisplayFormula", FontSlant->"Italic"]], "NumberedEquation", FontFamily->"Verdana", FontColor->RGBColor[0, 0, 1]] }], "Text"], Cell[TextData[{ "here\n\n", StyleBox["L", "InlineFormula", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], " (linear or nonlinear) mapping between appropriate function spaces ", StyleBox["X", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], " and ", StyleBox["Y ", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[";", FontSlant->"Italic"], "\n\n", StyleBox["H: X \[Cross] ", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^n\)], FontColor->RGBColor[0, 0, 1]], StyleBox["\[RightArrow] ", FontColor->RGBColor[0, 0, 1]], StyleBox["Y", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], " being an nonlinear operator ;\n\n", StyleBox["f ", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Element] ", FontColor->RGBColor[0, 0, 1]], StyleBox["Y", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], " being fixed ;\n\n", StyleBox["p \[Element] ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^n\)], FontColor->RGBColor[0, 0, 1]], " being parameters . \n\n", StyleBox["Solvability, multiplicity and bifurcation of solutions", FontColor->RGBColor[1, 0, 0]], " are of particular interest for people from praxis. Note that the BVPs \ depending on parameters describe such important phenomena as resonance, in \ which the real systems usually undergo drastic changes leading to their \ collapse (suitable small perturbations in external forcings effect in big \ changes in their corresponding responses).", StyleBox["\n\n", FontSlant->"Italic"], StyleBox["Examples of problems:", FontWeight->"Bold"], StyleBox["\n\n", FontSlant->"Italic"], "Mathematical models of stationary processes from nonlinear heat trasfer,\n\ nonlinear reaction-diffusion theory, magnetohydrodynamics and glaceology :\n\n\ ", StyleBox["- div(", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(grad\ u\)\( | \^\(p - 2\)\)\(\ \)\(grad\)\(\ \)\)\)], FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[") - ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(u\)\( | \^\(p - 2\)\)\)\)], FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" + ", FontColor->RGBColor[0, 0, 1]], StyleBox["g", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["(", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[", ", FontColor->RGBColor[0, 0, 1]], StyleBox["x", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[", ", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[")= ", FontColor->RGBColor[0, 0, 1]], StyleBox["f", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" , in ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[CapitalOmega]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" ;\n \ ", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["=0, on \[PartialD]", FontColor->RGBColor[0, 0, 1]], StyleBox["\[CapitalOmega]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], "\nor its one-dimensional variant\n\n", StyleBox["- (", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", RowBox[{ StyleBox["u", FontSlant->"Italic"], "'"}], SuperscriptBox["|", RowBox[{ StyleBox["p", FontSlant->"Italic"], StyleBox["-", FontSlant->"Italic"], StyleBox[" ", FontSlant->"Italic"], StyleBox["2", FontSlant->"Plain"]}]]}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["')' - ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda] ", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(u\)\( | \^\(p - 2\)\)\)\)], FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" + ", FontColor->RGBColor[0, 0, 1]], StyleBox["g", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["(", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[", ", FontColor->RGBColor[0, 0, 1]], StyleBox["x", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[", ", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[")= ", FontColor->RGBColor[0, 0, 1]], StyleBox["f", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[", in (0,1);\n ", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["(", FontColor->RGBColor[0, 0, 1]], StyleBox["0", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[")=0, ", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["(1)=0 . 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For that reason, numerical experiments \ become an indispensable tool of nonlinear analyst nowadays in the following \ way. In order to get at least rough idea about the qualitative behavior, one \ performs a set of numerical experiments by discretizing over the domain of \ parameters. This approach leads to an enormous amount of BVPs usually. To \ solve such a number of BVPs would hardly be possible without parallelization. \ The parallelization with respect to the discretized set of parameters can be \ considered as a pure data-parallel approach (same code, different data). ", StyleBox["Parallel Computing Toolkit", FontSlant->"Italic"], " (PCT for short) brings data-parallel methods into ", StyleBox["Mathematica ", FontSlant->"Italic"], "efficiently.\n\n", StyleBox["Example of an numerical experiment:", FontWeight->"Bold"], "\n\nGiven ", StyleBox["1<", FontColor->RGBColor[0, 0, 1]], StyleBox["p", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], ", let us investigate the set of all ", StyleBox["(", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[", ", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[") \[Element] ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`"\[DoubleStruckCapitalR]"\)], "InlineFormula", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Cross]", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["W", RowBox[{"1", ",", StyleBox["p", FontSlant->"Plain"]}]], "(", \(0, 1\), ")"}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], " satisfying the following\n\n", StyleBox["- (", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", RowBox[{ StyleBox["u", FontSlant->"Italic"], "'"}], SuperscriptBox["|", RowBox[{ StyleBox["p", FontSlant->"Italic"], StyleBox["-", FontSlant->"Italic"], StyleBox[" ", FontSlant->"Italic"], StyleBox["2", FontSlant->"Plain"]}]]}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["')' - ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda] ", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(u\)\( | \^\(p - 2\)\)\)\)], FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" = ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{\(f\^T\), "+", " ", RowBox[{ StyleBox["a", FontSlant->"Italic"], " ", SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"]}]}], TraditionalForm]], "Text", FontColor->RGBColor[0, 0, 1]], " ", StyleBox[", in (0,1);\n ", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["(", FontColor->RGBColor[0, 0, 1]], StyleBox["0", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[")=0, ", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["(1)=0 . \n ", FontColor->RGBColor[0, 0, 1]], "\nboundary value problem with ", StyleBox["\[Lambda]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], " being close to ", Cell[BoxData[ FormBox[ SubscriptBox[ StyleBox["\[Lambda]", FontSlant->"Italic"], "1"], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], ".\n\nHere ", Cell[BoxData[ FormBox[ StyleBox[ SubscriptBox[ StyleBox["\[Lambda]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], "1"], FontColor->RGBColor[0, 0, 1]], TraditionalForm]]], StyleBox[" \[Element] ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`"\[DoubleStruckCapitalR]"\)], "InlineFormula", FontColor->RGBColor[0, 0, 1]], " and ", Cell[BoxData[ FormBox[ SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], " ", StyleBox["\[Element]", FontColor->RGBColor[0, 0, 1]], " ", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ SuperscriptBox["W", RowBox[{"1", ",", StyleBox["p", FontSlant->"Plain"]}]], "(", \(0, 1\), ")"}], FontColor->RGBColor[0, 0, 1]], TraditionalForm]]], " satisfy\n\n", StyleBox["- (", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", " ", RowBox[{ FormBox[ SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], "TraditionalForm"], "'"}], SuperscriptBox["|", RowBox[{ StyleBox["p", FontSlant->"Italic"], StyleBox["-", FontSlant->"Italic"], StyleBox[" ", FontSlant->"Italic"], StyleBox["2", FontSlant->"Plain"]}]]}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ RowBox[{" ", StyleBox[ FormBox[ SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], "TraditionalForm"], FontFamily->"Times New Roman CE", FontColor->RGBColor[0, 0, 1]]}]], TextAlignment->Left, TextJustification->1], StyleBox["')' - ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ SubscriptBox[ StyleBox["\[Lambda]", FontSlant->"Italic"], "1"], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", " ", FormBox[ SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], "TraditionalForm"], \( | \^\(p - 2\)\)}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{" ", FormBox[ SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], "TraditionalForm"]}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox[" = 0", FontColor->RGBColor[0, 0, 1]], " ", StyleBox[", in (0,1);\n ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ RowBox[{" ", FormBox[ StyleBox[ SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], FontSize->16], "TraditionalForm"]}]], TextAlignment->Left, TextJustification->1, FontColor->RGBColor[0, 0, 1]], StyleBox["(", FontColor->RGBColor[0, 0, 1]], StyleBox["0", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[")=0, ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ RowBox[{" ", FormBox[ SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], "TraditionalForm"]}]], TextAlignment->Left, TextJustification->1, FontSize->16, FontColor->RGBColor[0, 0, 1]], StyleBox["(1)=0 ;\n ", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontSize->9, FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ UnderoverscriptBox[ StyleBox["\[Integral]", FontSize->36], StyleBox["0", FontSize->10], StyleBox["1", FontSize->10]], TraditionalForm]], FontSize->9, FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", " ", FormBox[ SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], "TraditionalForm"], \( | \^p\)}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox["=1.\n", FontColor->RGBColor[0, 0, 1]], "Note that this problem is related with the so-called nonlinear Fredholm \ alternative.\nFredholm alternative is the necessary and sufficient condition \ for the solvability of \nabstract equations with compact linear operators. In \ 1960-ties atempts to extend \nthis theory to nonlinear but still homogeneous \ operators have been started. ", Cell[BoxData[ \(TraditionalForm\`\*"\"\<\>"\)], "InlineFormula", FontColor->RGBColor[0, 0, 1]], "It is easy \nto see that the differential operator ", StyleBox["u \[RightTeeArrow]", FontColor->RGBColor[0, 0, 1]], " ", StyleBox["-(", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", RowBox[{ StyleBox["u", FontSlant->"Italic"], "'"}], SuperscriptBox["|", RowBox[{ StyleBox["p", FontSlant->"Italic"], StyleBox["-", FontSlant->"Italic"], StyleBox[" ", FontSlant->"Italic"], StyleBox["2", FontSlant->"Plain"]}]]}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["')' - ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda] ", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(u\)\( | \^\(p - 2\)\)\)\)], FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`\*"\"\<\>"\)], "InlineFormula", FontColor->RGBColor[0, 0, 1]], "is ", StyleBox["(", FontColor->RGBColor[0, 0, 1]], StyleBox["p-", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["1)", FontColor->RGBColor[0, 0, 1]], "-homogeneous:", StyleBox[" \n \n", FontColor->RGBColor[0, 0, 1]], StyleBox["-(", "DisplayFormula", FontColor->RGBColor[0, 0, 1]], StyleBox[Cell[BoxData[ FormBox[ RowBox[{"|", RowBox[{ RowBox[{"(", RowBox[{"a", " ", StyleBox["u", FontSlant->"Italic"]}], StyleBox[")", FontSlant->"Italic"]}], "'"}], SuperscriptBox["|", RowBox[{ StyleBox["p", FontSlant->"Italic"], StyleBox["-", FontSlant->"Italic"], StyleBox[" ", FontSlant->"Italic"], StyleBox["2", FontSlant->"Plain"]}]], \((a\ u)\)}], TraditionalForm]], "DisplayFormula", FontColor->RGBColor[0, 0, 1]], "DisplayFormula"], StyleBox["')' - ", "DisplayFormula", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda] ", "DisplayFormula", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[Cell[BoxData[ FormBox[ RowBox[{\(\(|\)\((a\ u)\)\( | \^\(p - 2\)\)\((a\ u)\)\), " ", "=", StyleBox["-", FontColor->RGBColor[0, 0, 1]]}], TraditionalForm]], "DisplayFormula", FontColor->RGBColor[0, 0, 1]], "DisplayFormula"], StyleBox[Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(a\)\( | \^\(p - 2\)\)\(a\)\(\ \)\)\)], "DisplayFormula", FontColor->RGBColor[0, 0, 1]], "DisplayFormula"], StyleBox["{(", "DisplayFormula", FontColor->RGBColor[0, 0, 1]], StyleBox[Cell[BoxData[ FormBox[ RowBox[{"|", RowBox[{ StyleBox["u", FontSlant->"Italic"], "'"}], SuperscriptBox["|", RowBox[{ StyleBox["p", FontSlant->"Italic"], StyleBox["-", FontSlant->"Italic"], StyleBox[" ", FontSlant->"Italic"], StyleBox["2", FontSlant->"Plain"]}]]}], TraditionalForm]], "DisplayFormula", FontColor->RGBColor[0, 0, 1]], "DisplayFormula"], StyleBox["u", "DisplayFormula", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["')' - ", "DisplayFormula", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda] ", "DisplayFormula", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(u\)\( | \^\(p - 2\)\)\)\)], "DisplayFormula", FontColor->RGBColor[0, 0, 1]], "DisplayFormula"], StyleBox["u", "DisplayFormula", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["}", "DisplayFormula", FontColor->RGBColor[0, 0, 1]], StyleBox["\n\n\n\n\n", FontColor->RGBColor[0, 0, 1]], StyleBox["Parallelization with", "Section"], StyleBox[" ", "Section", FontColor->RGBColor[0, 0, 1]], StyleBox["NDSolve", "Section", FontColor->RGBColor[1, 0, 1]], StyleBox["\n\n", FontColor->RGBColor[0, 0, 1]], "For mathematically correct setting of the problem and thorough discussion \ of numerical experiments, we kindly invite the reader to see [3], [4]. ", StyleBox["\n\n", FontColor->RGBColor[0, 0, 1]], "It is well known fact that the shooting method is very robust approach of \ solving BVPs for ODE's.", StyleBox[" ", FontColor->RGBColor[0, 0, 1]], "Corresponding initial-value problem for the first-order system of ODE's:\n\ \n", StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["' = ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", StyleBox["v", FontSlant->"Italic"], SuperscriptBox["|", RowBox[{ RowBox[{ StyleBox["p", FontSlant->"Italic"], "'"}], "-", "2"}]], "v"}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], " ;\n", StyleBox["v", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["' = -", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", StyleBox["u", FontSlant-> "Italic"], \( | \^\(p - 2\)\), \(\(u\)\(\ \ \)\(+\)\)}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{\(f\^T\), "+", " ", RowBox[{"a", " ", SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"]}]}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], " ;\n", Cell[BoxData[ FormBox[ SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox["'= ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", StyleBox["w", FontSlant->"Italic"], SuperscriptBox["|", RowBox[{ RowBox[{ StyleBox["p", FontSlant->"Italic"], "'"}], "-", "2"}]], "w"}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox[" ;\nw' = ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], SuperscriptBox[ StyleBox["|", FontSlant->"Italic"], \(p - 2\)], SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], " "}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox[" \n\n", FontColor->RGBColor[0, 0, 1]], "subject to", StyleBox["\n\n", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["(0) = 0\n", FontColor->RGBColor[0, 0, 1]], StyleBox["v", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["(0) = ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", StyleBox[\(u(0)\), FontSlant->"Italic"], \( | \^\(p - 2\)\), \(u(0)\), " "}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox["= ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", StyleBox["\[Alpha]", FontSlant->"Italic"], \( | \^\(p - 2\)\), StyleBox["\[Alpha]", FontSlant->"Italic"], " "}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox[" \n", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox["(0) = 0\nw(0) = ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox[ FormBox[ RowBox[{ SubscriptBox[ StyleBox["\[Pi]", FontSlant->"Italic"], "p"], " "}], "TraditionalForm"], \(p - 1\)], FontColor->RGBColor[0, 0, 1]], TraditionalForm]]], StyleBox["\n", FontColor->RGBColor[0, 0, 1]], "\nResulting system contains nonlinearities which are ", StyleBox["not", FontColor->RGBColor[1, 0, 0]], " all ", StyleBox["Lipschitz", FontColor->RGBColor[1, 0, 0]], " continuous. For that reason, ", StyleBox["uniqueness", FontColor->RGBColor[1, 0, 0]], " of solutions is ", StyleBox["not", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->True}], StyleBox[" guarranteed", FontColor->RGBColor[1, 0, 0]], ". We speak of ", StyleBox["numerical experiment", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->True}], " rather than of numerical computation of solutions.\n\nWe are ready to \ apply numerical methods now.\n\n", StyleBox["General philosophy of problem solving in ", FontWeight->"Bold"], StyleBox["Mathematica\n\n", FontWeight->"Bold", FontSlant->"Italic"], "Use build-in ", StyleBox["Mathematica", FontSlant->"Italic"], " functions as much as possible. \n\n", StyleBox["General philosophy of data-parallel approach:", FontWeight->"Bold"], "\n\nDivide the problem into independent parts where different data are \ processed by the same code. \n\n", StyleBox["Solution:\n\n", FontWeight->"Bold"], "Let ", StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["(", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[", ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Alpha]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[", ", FontColor->RGBColor[0, 0, 1]], StyleBox["a", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[", 1)", FontColor->RGBColor[0, 0, 1]], " denote the value of the solution ", StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], " to the initial boudary value problem.\n\nIt is not difficult to define \ corresponding numerical function in ", StyleBox["Mathematica ", FontSlant->"Italic"], "using \n", StyleBox["NDSolve", FontColor->RGBColor[1, 0, 1]], " . \n\n", StyleBox["\n", FontWeight->"Bold"], "We parallelize with respect to the parameter ", StyleBox["a", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" \[Element] ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`"\[DoubleStruckCapitalR]"\)], "InlineFormula", FontColor->RGBColor[0, 0, 1]], ", ", StyleBox["i.e.", FontSlant->"Italic"], ", we consider set of discrete values\n ", Cell[BoxData[ \(TraditionalForm\`a\_i\)], FontColor->RGBColor[0, 0, 1]], " ", StyleBox["\[Element] ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`"\[DoubleStruckCapitalR]"\)], "InlineFormula", FontColor->RGBColor[0, 0, 1]], " , ", StyleBox["i ", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Element] {1, 2, 3, ..., n}", FontColor->RGBColor[0, 0, 1]], ", where ", StyleBox["n ", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Element] \[DoubleStruckCapitalN]", FontColor->RGBColor[0, 0, 1]], " is an multiple of the number of processors available, typically. \n\n\n\ Value of ", Cell[BoxData[ \(TraditionalForm\`a\_i\)], FontColor->RGBColor[0, 0, 1]], " given, we use ", StyleBox["ContourPlot", FontColor->RGBColor[1, 0, 1]], " to function ", StyleBox["u(#1, #2, ", FontColor->RGBColor[1, 0, 1]], Cell[BoxData[ \(TraditionalForm\`a\_i\)], FontColor->RGBColor[0, 0, 1]], StyleBox[", 1)&", FontColor->RGBColor[1, 0, 1]], " with an option ", StyleBox["Contours \[Rule] {0}", FontColor->RGBColor[1, 0, 1]], ".\nComplexity of this step is ", StyleBox["O(", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ SuperscriptBox["PlotPoints", StyleBox["2", FontColor->RGBColor[0, 0, 1]]], TraditionalForm]], FontColor->RGBColor[1, 0, 1]], StyleBox[")", FontColor->RGBColor[0, 0, 1]], " passed to ContourPlot. \n\n\nNodes of contour lines are then refined \ using ", StyleBox["FindRoot", FontColor->RGBColor[1, 0, 1]], " ; complexity being ", StyleBox["O(", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`PlotPoints\)], FontColor->RGBColor[1, 0, 1]], StyleBox[")", FontColor->RGBColor[0, 0, 1]], ".\n\nSee figures attached in postscript files ", StyleBox["Fredholm.ps", FontColor->RGBColor[0, 1, 0]], ", ", StyleBox["LandesmanLazer.ps", FontColor->RGBColor[0, 1, 0]], ", ", StyleBox["Oscilatory.ps", FontColor->RGBColor[0, 1, 0]], ".\n\n\n\n\n", StyleBox["Parallelization for symbolic code\n", "Section"], "\nGiven ", StyleBox["1<", FontColor->RGBColor[0, 0, 1]], StyleBox["p", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], ", let us find ", StyleBox["(", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[", ", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[") \[Element] ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`"\[DoubleStruckCapitalR]"\)], "InlineFormula", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Cross]", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["W", RowBox[{"1", ",", StyleBox["p", FontSlant->"Plain"]}]], "(", \(0, 1\), ")"}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], " satisfying the following\n\n", StyleBox["- (", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", RowBox[{ StyleBox["u", FontSlant->"Italic"], "'"}], SuperscriptBox["|", RowBox[{ StyleBox["p", FontSlant->"Italic"], StyleBox["-", FontSlant->"Italic"], StyleBox[" ", FontSlant->"Italic"], StyleBox["2", FontSlant->"Plain"]}]]}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["')' - ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda] ", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(u\)\( | \^\(p - 2\)\)\)\)], FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" = ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{\(f\^T\), "+", " ", RowBox[{ StyleBox["a", FontSlant->"Italic"], " ", SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"]}]}], TraditionalForm]], "Text", FontColor->RGBColor[0, 0, 1]], " ", StyleBox[", in (0,1);\n ", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["(", FontColor->RGBColor[0, 0, 1]], StyleBox["0", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[")=0, ", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["(1)=0 . \n ", FontColor->RGBColor[0, 0, 1]], "\nboundary value problem with ", StyleBox["\[Lambda]", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], " being close to ", Cell[BoxData[ FormBox[ SubscriptBox[ StyleBox["\[Lambda]", FontSlant->"Italic"], "1"], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], ". Let us use spectral Ritz-Galerkin method now. \n\nCorresponding \ potential:\n\n", Cell[BoxData[ FormBox[ UnderoverscriptBox[ StyleBox["\[Integral]", FontSize->36], StyleBox["0", FontSize->10], StyleBox["1", FontSize->10]], TraditionalForm]], FontSize->24, FontColor->RGBColor[0, 0, 1]], StyleBox["(", FontSize->24, FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`-\+p\%1\)], FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{"|", RowBox[{ StyleBox["u", FontSlant->"Italic"], "'"}], SuperscriptBox["|", StyleBox["p", FontSlant->"Italic"]]}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox[" - ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Lambda] ", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`-\+p\%1\)], FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(u\)\)\)], FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ SuperscriptBox["|", StyleBox["p", FontSlant->"Italic"]], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox[" + (", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{\(f\^T\), "+", " ", RowBox[{ StyleBox["a", FontSlant->"Italic"], " ", SubscriptBox[ StyleBox["\[CurlyPhi]", FontSlant->"Italic"], "1"], StyleBox[" ", FontColor->RGBColor[0, 0, 1]]}]}], TraditionalForm]], "Text", FontColor->RGBColor[0, 0, 1]], StyleBox[")", FontColor->RGBColor[0, 0, 1]], " ", StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[")", FontSize->24, FontColor->RGBColor[0, 0, 1]], StyleBox[" \[DifferentialD]x ,", FontColor->RGBColor[0, 0, 1]], "\n\nFor ", StyleBox["p", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["=2 ", FontColor->RGBColor[0, 0, 1]], StyleBox["k", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[", ", FontColor->RGBColor[0, 0, 1]], StyleBox["k ", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Element] \[DoubleStruckCapitalN] ", FontColor->RGBColor[0, 0, 1]], "we can handle this problem symbolically (at least partially).\n\nWe take\n\ \n", Cell[BoxData[ FormBox[ StyleBox[\(u(x) = b1\ \(sin(x)\) + b2\ \(sin(2\ x)\) + b3\ \(sin(3\ x)\) + b4\ \(sin(4\ x)\)\), FontColor->RGBColor[0, 0, 1]], TraditionalForm]]], "\n\nas the finite dimensional approximation of u.\n\n\n\n\nFor ", StyleBox["p", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["=4", FontColor->RGBColor[0, 0, 1]], " and ", StyleBox["f", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["(", FontColor->RGBColor[0, 0, 1]], StyleBox["x", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[")=sin(2 ", FontColor->RGBColor[0, 0, 1]], StyleBox["x", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[")", FontColor->RGBColor[0, 0, 1]], ", the ", Cell[BoxData[ StyleBox[\(integrand\ in\ the\ potential\ is\ computed\ \(\(by\)\(:\)\)\ \), FontWeight->"Plain"]], "Input", FontFamily->"Verdana"], "\n\n\n", Cell[BoxData[ \(int = \[IndentingNewLine]ReleaseHold[\[IndentingNewLine]Hold[\((1/ p\ D[u[x], x]^p - \[Lambda]/p\ \((u[x])\)^p + f[x]\ u[x])\)] /. {u[x] \[Rule] b1\ Sin[x] + b2\ Sin[2\ x] + b3\ Sin[3\ x] + b4\ Sin[4\ x], \[IndentingNewLine]f[x] -> Sin[2\ x]}\ \[IndentingNewLine]]\)], "Input"], "\n\n\n", Cell[BoxData[ \(1\/4\ \((b1\ Cos[x] + 2\ b2\ Cos[2\ x] + 3\ b3\ Cos[3\ x] + 4\ b4\ \ Cos[4\ x])\)\^4 + Sin[2\ x]\ \((b1\ Sin[x] + b2\ Sin[2\ x] + b3\ Sin[3\ x] + b4\ Sin[4\ x])\) - 1\/4\ \[Lambda]\ \((b1\ Sin[x] + b2\ Sin[2\ x] + b3\ Sin[3\ x] + b4\ \ Sin[4\ x])\)\^4\)]], "\n\n\n\n\n", Cell[BoxData[ RowBox[{ StyleBox["Calculating", FontFamily->"Arial"], StyleBox[" ", FontFamily->"Arial"], StyleBox["the", FontFamily->"Arial"], StyleBox[" ", FontFamily->"Arial"], StyleBox["potential", FontFamily->"Arial"], StyleBox[" ", FontFamily->"Arial"], StyleBox["by", FontFamily->"Arial"], StyleBox[" ", FontFamily->"Arial"], StyleBox["direct", FontFamily->"Arial"], StyleBox[" ", FontFamily->"Arial"], RowBox[{ StyleBox["integration", FontFamily->"Arial"], StyleBox[":", FontFamily->"Arial"], StyleBox["\[IndentingNewLine]", FontWeight->"Plain"]}]}]], "Input", FontFamily->"Verdana", FontWeight->"Plain"], "\n", Cell[BoxData[ \(Integrate[int, \ {x, \ 0, \ Pi}]\ // \ Timing\)], "Input"], "\n\n\n", Cell[BoxData[ RowBox[{"{", RowBox[{ StyleBox[\(27.139`\ Second\), FontColor->RGBColor[1, 0, 0]], ",", \(\(3\ b1\^4\ \[Pi]\)\/32 + \(b2\ \[Pi]\)\/2 + 3\/2\ b1\^2\ b2\^2\ \[Pi] + \(3\ b2\^4\ \[Pi]\)\/2 + 3\/8\ b1\^3\ b3\ \[Pi] + 9\/2\ b1\ b2\^2\ b3\ \[Pi] + 27\/8\ b1\^2\ b3\^2\ \[Pi] + 27\/2\ b2\^2\ b3\^2\ \[Pi] + \(243\ b3\^4\ \[Pi]\)\/32 + 3\ b1\^2\ b2\ b4\ \[Pi] + 18\ b1\ b2\ b3\ b4\ \[Pi] + 27\ b2\ b3\^2\ b4\ \[Pi] + 6\ b1\^2\ b4\^2\ \[Pi] + 24\ b2\^2\ b4\^2\ \[Pi] + 54\ b3\^2\ b4\^2\ \[Pi] + 24\ b4\^4\ \[Pi] - 3\/32\ b1\^4\ \[Pi]\ \[Lambda] - 3\/8\ b1\^2\ b2\^2\ \[Pi]\ \[Lambda] - 3\/32\ b2\^4\ \[Pi]\ \[Lambda] + 1\/8\ b1\^3\ b3\ \[Pi]\ \[Lambda] - 3\/8\ b1\ b2\^2\ b3\ \[Pi]\ \[Lambda] - 3\/8\ b1\^2\ b3\^2\ \[Pi]\ \[Lambda] - 3\/8\ b2\^2\ b3\^2\ \[Pi]\ \[Lambda] - 3\/32\ b3\^4\ \[Pi]\ \[Lambda] + 3\/8\ b1\^2\ b2\ b4\ \[Pi]\ \[Lambda] - 3\/4\ b1\ b2\ b3\ b4\ \[Pi]\ \[Lambda] - 3\/8\ b2\ b3\^2\ b4\ \[Pi]\ \[Lambda] - 3\/8\ b1\^2\ b4\^2\ \[Pi]\ \[Lambda] - 3\/8\ b2\^2\ b4\^2\ \[Pi]\ \[Lambda] - 3\/8\ b3\^2\ b4\^2\ \[Pi]\ \[Lambda] - 3\/32\ b4\^4\ \[Pi]\ \[Lambda]\)}], "}"}]]], "\n\n\n\n", Cell[BoxData[ StyleBox[\(Tricky\ way\ of\ integration\ by\ using\ linearity\ of\ the\ \ \(\(integral\)\(:\)\)\), FontWeight->"Plain"]], "Input", FontFamily->"Verdana"], "\n\n\n", Cell[BoxData[ \(Map[\[IndentingNewLine]Integrate[#, \ {x, \ 0, \ Pi}] &, Expand[int]\[IndentingNewLine]]\ // \ Timing\)], "Input"], "\n\n\n", Cell[BoxData[ RowBox[{"{", RowBox[{ StyleBox[\(5.167`\ Second\), FontColor->RGBColor[1, 0, 0]], ",", \(\(3\ b1\^4\ \[Pi]\)\/32 + \(b2\ \[Pi]\)\/2 + 3\/2\ b1\^2\ b2\^2\ \[Pi] + \(3\ b2\^4\ \[Pi]\)\/2 + 3\/8\ b1\^3\ b3\ \[Pi] + 9\/2\ b1\ b2\^2\ b3\ \[Pi] + 27\/8\ b1\^2\ b3\^2\ \[Pi] + 27\/2\ b2\^2\ b3\^2\ \[Pi] + \(243\ b3\^4\ \[Pi]\)\/32 + 3\ b1\^2\ b2\ b4\ \[Pi] + 18\ b1\ b2\ b3\ b4\ \[Pi] + 27\ b2\ b3\^2\ b4\ \[Pi] + 6\ b1\^2\ b4\^2\ \[Pi] + 24\ b2\^2\ b4\^2\ \[Pi] + 54\ b3\^2\ b4\^2\ \[Pi] + 24\ b4\^4\ \[Pi] - 3\/32\ b1\^4\ \[Pi]\ \[Lambda] - 3\/8\ b1\^2\ b2\^2\ \[Pi]\ \[Lambda] - 3\/32\ b2\^4\ \[Pi]\ \[Lambda] + 1\/8\ b1\^3\ b3\ \[Pi]\ \[Lambda] - 3\/8\ b1\ b2\^2\ b3\ \[Pi]\ \[Lambda] - 3\/8\ b1\^2\ b3\^2\ \[Pi]\ \[Lambda] - 3\/8\ b2\^2\ b3\^2\ \[Pi]\ \[Lambda] - 3\/32\ b3\^4\ \[Pi]\ \[Lambda] + 3\/8\ b1\^2\ b2\ b4\ \[Pi]\ \[Lambda] - 3\/4\ b1\ b2\ b3\ b4\ \[Pi]\ \[Lambda] - 3\/8\ b2\ b3\^2\ b4\ \[Pi]\ \[Lambda] - 3\/8\ b1\^2\ b4\^2\ \[Pi]\ \[Lambda] - 3\/8\ b2\^2\ b4\^2\ \[Pi]\ \[Lambda] - 3\/8\ b3\^2\ b4\^2\ \[Pi]\ \[Lambda] - 3\/32\ b4\^4\ \[Pi]\ \[Lambda]\)}], "}"}]]], "\n\n\n", Cell[BoxData[ \(Speed\ \(\(up\)\(:\)\)\)], "Input"], "\n\n", Cell[BoxData[ \(27.139`\ /5.167`\)], "Input"], "\n", Cell[BoxData[ \(5.252370814786143`\)], "Output", FontColor->RGBColor[1, 0, 0]], "\n\nHere, ", Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{ StyleBox["w", "Text", FontWeight->"Plain"], StyleBox["e", FontFamily->"Verdana", FontWeight->"Plain"]}]], StyleBox[" ", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox["use", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox[" ", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox["the", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox[" ", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox["fact", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox[" ", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox["that", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox[" ", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox["expanded", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox[" ", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox["integrand", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox[" ", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox["has", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox[" ", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox["the", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox[" ", FontFamily->"Verdana", FontWeight->"Plain"], StyleBox["head", FontFamily->"Verdana", FontWeight->"Plain"], " ", RowBox[{ StyleBox["Plus", FontColor->RGBColor[1, 0, 1]], " ", ":"}]}]], "Input"], "\n\n", Cell[BoxData[ \(Expand[int]\)], "Input"], "\n\n", Cell[BoxData[ \(1\/4\ b1\^4\ Cos[x]\^4 + 2\ b1\^3\ b2\ Cos[x]\^3\ Cos[2\ x] + 6\ b1\^2\ b2\^2\ Cos[x]\^2\ Cos[2\ x]\^2 + 8\ b1\ b2\^3\ Cos[x]\ Cos[2\ x]\^3 + 4\ b2\^4\ Cos[2\ x]\^4 + 3\ b1\^3\ b3\ Cos[x]\^3\ Cos[3\ x] + 18\ b1\^2\ b2\ b3\ Cos[x]\^2\ Cos[2\ x]\ Cos[3\ x] + 36\ b1\ b2\^2\ b3\ Cos[x]\ Cos[2\ x]\^2\ Cos[3\ x] + 24\ b2\^3\ b3\ Cos[2\ x]\^3\ Cos[3\ x] + 27\/2\ b1\^2\ b3\^2\ Cos[x]\^2\ Cos[3\ x]\^2 + 54\ b1\ b2\ b3\^2\ Cos[x]\ Cos[2\ x]\ Cos[3\ x]\^2 + 54\ b2\^2\ b3\^2\ Cos[2\ x]\^2\ Cos[3\ x]\^2 + 27\ b1\ b3\^3\ Cos[x]\ Cos[3\ x]\^3 + 54\ b2\ b3\^3\ Cos[2\ x]\ Cos[3\ x]\^3 + 81\/4\ b3\^4\ Cos[3\ x]\^4 + 4\ b1\^3\ b4\ Cos[x]\^3\ Cos[4\ x] + 24\ b1\^2\ b2\ b4\ Cos[x]\^2\ Cos[2\ x]\ Cos[4\ x] + 48\ b1\ b2\^2\ b4\ Cos[x]\ Cos[2\ x]\^2\ Cos[4\ x] + 32\ b2\^3\ b4\ Cos[2\ x]\^3\ Cos[4\ x] + 36\ b1\^2\ b3\ b4\ Cos[x]\^2\ Cos[3\ x]\ Cos[4\ x] + 144\ b1\ b2\ b3\ b4\ Cos[x]\ Cos[2\ x]\ Cos[3\ x]\ Cos[4\ x] + 144\ b2\^2\ b3\ b4\ Cos[2\ x]\^2\ Cos[3\ x]\ Cos[4\ x] + 108\ b1\ b3\^2\ b4\ Cos[x]\ Cos[3\ x]\^2\ Cos[4\ x] + 216\ b2\ b3\^2\ b4\ Cos[2\ x]\ Cos[3\ x]\^2\ Cos[4\ x] + 108\ b3\^3\ b4\ Cos[3\ x]\^3\ Cos[4\ x] + 24\ b1\^2\ b4\^2\ Cos[x]\^2\ Cos[4\ x]\^2 + 96\ b1\ b2\ b4\^2\ Cos[x]\ Cos[2\ x]\ Cos[4\ x]\^2 + 96\ b2\^2\ b4\^2\ Cos[2\ x]\^2\ Cos[4\ x]\^2 + 144\ b1\ b3\ b4\^2\ Cos[x]\ Cos[3\ x]\ Cos[4\ x]\^2 + 288\ b2\ b3\ b4\^2\ Cos[2\ x]\ Cos[3\ x]\ Cos[4\ x]\^2 + 216\ b3\^2\ b4\^2\ Cos[3\ x]\^2\ Cos[4\ x]\^2 + 64\ b1\ b4\^3\ Cos[x]\ Cos[4\ x]\^3 + 128\ b2\ b4\^3\ Cos[2\ x]\ Cos[4\ x]\^3 + 192\ b3\ b4\^3\ Cos[3\ x]\ Cos[4\ x]\^3 + 64\ b4\^4\ Cos[4\ x]\^4 - 1\/4\ b1\^4\ \[Lambda]\ Sin[x]\^4 + b1\ Sin[x]\ Sin[2\ x] - b1\^3\ b2\ \[Lambda]\ Sin[x]\^3\ Sin[2\ x] + b2\ Sin[2\ x]\^2 - 3\/2\ b1\^2\ b2\^2\ \[Lambda]\ Sin[x]\^2\ Sin[2\ x]\^2 - b1\ b2\^3\ \[Lambda]\ Sin[x]\ Sin[2\ x]\^3 - 1\/4\ b2\^4\ \[Lambda]\ Sin[2\ x]\^4 - b1\^3\ b3\ \[Lambda]\ Sin[x]\^3\ Sin[3\ x] + b3\ Sin[2\ x]\ Sin[3\ x] - 3\ b1\^2\ b2\ b3\ \[Lambda]\ Sin[x]\^2\ Sin[2\ x]\ Sin[3\ x] - 3\ b1\ b2\^2\ b3\ \[Lambda]\ Sin[x]\ Sin[2\ x]\^2\ Sin[3\ x] - b2\^3\ b3\ \[Lambda]\ Sin[2\ x]\^3\ Sin[3\ x] - 3\/2\ b1\^2\ b3\^2\ \[Lambda]\ Sin[x]\^2\ Sin[3\ x]\^2 - 3\ b1\ b2\ b3\^2\ \[Lambda]\ Sin[x]\ Sin[2\ x]\ Sin[3\ x]\^2 - 3\/2\ b2\^2\ b3\^2\ \[Lambda]\ Sin[2\ x]\^2\ Sin[3\ x]\^2 - b1\ b3\^3\ \[Lambda]\ Sin[x]\ Sin[3\ x]\^3 - b2\ b3\^3\ \[Lambda]\ Sin[2\ x]\ Sin[3\ x]\^3 - 1\/4\ b3\^4\ \[Lambda]\ Sin[3\ x]\^4 - b1\^3\ b4\ \[Lambda]\ Sin[x]\^3\ Sin[4\ x] + b4\ Sin[2\ x]\ Sin[4\ x] - 3\ b1\^2\ b2\ b4\ \[Lambda]\ Sin[x]\^2\ Sin[2\ x]\ Sin[4\ x] - 3\ b1\ b2\^2\ b4\ \[Lambda]\ Sin[x]\ Sin[2\ x]\^2\ Sin[4\ x] - b2\^3\ b4\ \[Lambda]\ Sin[2\ x]\^3\ Sin[4\ x] - 3\ b1\^2\ b3\ b4\ \[Lambda]\ Sin[x]\^2\ Sin[3\ x]\ Sin[4\ x] - 6\ b1\ b2\ b3\ b4\ \[Lambda]\ Sin[x]\ Sin[2\ x]\ Sin[3\ x]\ Sin[ 4\ x] - 3\ b2\^2\ b3\ b4\ \[Lambda]\ Sin[2\ x]\^2\ Sin[3\ x]\ Sin[ 4\ x] - 3\ b1\ b3\^2\ b4\ \[Lambda]\ Sin[x]\ Sin[3\ x]\^2\ Sin[ 4\ x] - 3\ b2\ b3\^2\ b4\ \[Lambda]\ Sin[2\ x]\ Sin[3\ x]\^2\ Sin[ 4\ x] - b3\^3\ b4\ \[Lambda]\ Sin[3\ x]\^3\ Sin[4\ x] - 3\/2\ b1\^2\ b4\^2\ \[Lambda]\ Sin[x]\^2\ Sin[4\ x]\^2 - 3\ b1\ b2\ b4\^2\ \[Lambda]\ Sin[x]\ Sin[2\ x]\ Sin[4\ x]\^2 - 3\/2\ b2\^2\ b4\^2\ \[Lambda]\ Sin[2\ x]\^2\ Sin[4\ x]\^2 - 3\ b1\ b3\ b4\^2\ \[Lambda]\ Sin[x]\ Sin[3\ x]\ Sin[4\ x]\^2 - 3\ b2\ b3\ b4\^2\ \[Lambda]\ Sin[2\ x]\ Sin[3\ x]\ Sin[4\ x]\^2 - 3\/2\ b3\^2\ b4\^2\ \[Lambda]\ Sin[3\ x]\^2\ Sin[4\ x]\^2 - b1\ b4\^3\ \[Lambda]\ Sin[x]\ Sin[4\ x]\^3 - b2\ b4\^3\ \[Lambda]\ Sin[2\ x]\ Sin[4\ x]\^3 - b3\ b4\^3\ \[Lambda]\ Sin[3\ x]\ Sin[4\ x]\^3 - 1\/4\ b4\^4\ \[Lambda]\ Sin[4\ x]\^4\)]], "\n\n\nWe can define:\n\n", Cell[BoxData[ RowBox[{\(pot[\[Lambda]_, \ p_, \ f_, b1_, b2_, b3_, b4_, \ b5_]\), ":=", RowBox[{ StyleBox["Map", FontColor->RGBColor[1, 0, 0]], StyleBox["[", FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]", RowBox[{ StyleBox[\(Integrate[#, \ {x, 0, Pi}] &\), FontColor->RGBColor[0, 1, 0]], ",", "\[IndentingNewLine]", StyleBox[\(Expand[\[IndentingNewLine]ReleaseHold[\ \[IndentingNewLine]Hold[\((1/p\ D[u[x], x]^p - \[Lambda]/p\ \((u[x])\)^p + f[x]\ u[x])\)] /. u[x] \[Rule] b1\ Sin[x] + b2\ Sin[2\ x] + b3\ Sin[3\ x] + b4\ Sin[ 4\ x]\[IndentingNewLine]]\[IndentingNewLine]]\), FontColor->RGBColor[0, 0, 1]]}], "\[IndentingNewLine]", StyleBox["]", FontColor->RGBColor[1, 0, 0]]}]}]], "Input"], "\n\n\nUsage:\n\n", Cell[BoxData[ \(pot[\[Lambda], \ 3, \ Sin[2 #] &, \ b1, b2, b3, b4]\)], "Input"], "\n\n\n\n", Cell[BoxData[ \(Parallelization\ is\ usefull\ here\)], "Input", FontFamily->"Verdana"], " !\n\n\nuse ", StyleBox["ParallelMap", FontColor->RGBColor[1, 0, 1]], " instead of ", StyleBox["Map", FontColor->RGBColor[1, 0, 1]], "\n\n\nTo avoid a lot of communication, use partitioning.\n\n", StyleBox["Example of partitioning:", FontWeight->"Bold"], "\n\nOn a 5-node homogeneous cluster, do the following\n\n", Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["ParallelMap", FontColor->RGBColor[0, 1, 0], Background->GrayLevel[1]], StyleBox["[", FontColor->RGBColor[0, 1, 0], Background->GrayLevel[1]], StyleBox["\[IndentingNewLine]", Background->GrayLevel[1]], RowBox[{ RowBox[{ RowBox[{ StyleBox["Map", FontColor->RGBColor[0, 0, 1], Background->None], StyleBox["[", FontColor->RGBColor[0, 0, 1], Background->None], StyleBox["\[IndentingNewLine]", Background->RGBColor[0.976471, 0.886275, 0.823529]], RowBox[{ StyleBox[\((Integrate[#, \ {x, 0, Pi}] &)\), FontColor->RGBColor[1, 0, 0], Background->None], StyleBox[",", Background->None], StyleBox[" ", Background->None], StyleBox["#", FontColor->RGBColor[0, 0, 1], Background->None]}], StyleBox["\[IndentingNewLine]", Background->RGBColor[0.976471, 0.886275, 0.823529]], StyleBox["]", FontColor->RGBColor[0, 0, 1], Background->None]}], StyleBox["&", FontColor->RGBColor[0, 0, 1], Background->None]}], StyleBox[",", Background->None], StyleBox[" ", Background->None], StyleBox["\[IndentingNewLine]", Background->RGBColor[0.976471, 0.886275, 0.823529]], RowBox[{ StyleBox["With", Background->None], StyleBox["[", Background->None], StyleBox[ RowBox[{\({numberOfNodes = 5}\), ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"Partition", "[", RowBox[{ RowBox[{"List", "@@", StyleBox[\(Expand[\[IndentingNewLine]ReleaseHold[\ \[IndentingNewLine]Hold[\((1/p\ D[u[x], x]^p - \[Lambda]/p\ \((u[x])\)^p + f[x]\ u[x])\)] /. {u[x] \[Rule] b1\ Sin[x] + b2\ Sin[2\ x] + b3\ Sin[3\ x] + b4\ Sin[4\ x], \[IndentingNewLine]f[ x] -> Sin[ 2\ x]}\ \[IndentingNewLine]]\ \[IndentingNewLine]]\), FontColor->RGBColor[0, 0, 1]]}], ",", " ", "numberOfNodes", ",", "numberOfNodes", ",", " ", \({1, 1}\), ",", " ", "0"}], "]"}], " ", "//", " ", "Transpose"}]}], Background->None], StyleBox["\[IndentingNewLine]", Background->RGBColor[0.976471, 0.886275, 0.823529]], StyleBox["]", Background->None]}]}], StyleBox["\[IndentingNewLine]", Background->RGBColor[0.976471, 0.886275, 0.823529]], StyleBox["]", FontColor->RGBColor[0, 1, 0], Background->GrayLevel[1]]}], StyleBox["\[IndentingNewLine]", Background->GrayLevel[1]]}]], "Input"], "\n\n\n", StyleBox["More clear explanation to partitioning:", FontWeight->"Bold"], "\n\n", Cell[BoxData[{ \(With[{numberOfNodes = 5}, \[IndentingNewLine]Partition[\[IndentingNewLine]{int01, int02, int03, int04, int05, \[IndentingNewLine]int06, int07, int08, int09, int10, \[IndentingNewLine]int11}, \[IndentingNewLine]\ \ \ numberOfNodes, numberOfNodes, \ {1, 1}, \ 0]\ \[IndentingNewLine] // \ Transpose\[IndentingNewLine]]\ \), "\[IndentingNewLine]", \(\ \(\(//\)\(\ \)\(TableForm\)\)\)}], "Input"], "\n\n\n", Cell[BoxData[ TagBox[GridBox[{ { StyleBox[ RowBox[{ StyleBox[\(processor\ 1\), FontColor->RGBColor[1, 0, 0]], " ", ":", " ", "int01"}], FontColor->RGBColor[1, 0, 0]], StyleBox["int06", FontColor->RGBColor[1, 0, 0]], StyleBox["int11", FontColor->RGBColor[1, 0, 0]]}, { RowBox[{\(processor\ 2\), StyleBox[" ", FontColor->GrayLevel[0]], ":", " ", "int02"}], "int07", "0"}, { StyleBox[ RowBox[{ StyleBox[\(processor\ 3\), FontColor->RGBColor[1, 0, 0]], " ", ":", " ", "int03"}], FontColor->RGBColor[1, 0, 0]], StyleBox["int08", FontColor->RGBColor[1, 0, 0]], StyleBox["0", FontColor->RGBColor[1, 0, 0]]}, {\(processor\ 4\ : \ \ \ \ \ \ int04\), "int09", "0"}, { StyleBox[\(processor\ 5\ : \ \ \ \ \ \ int05\), FontColor->RGBColor[1, 0, 0]], StyleBox["int10", FontColor->RGBColor[1, 0, 0]], StyleBox["0", FontColor->RGBColor[1, 0, 0]]} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$]]]], "Output", GeneratedCell->False, CellAutoOverwrite->False], "\n\n", Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(\n\)\)\)], "Input"], "\nEquations to solve:\n\nD[", Cell[BoxData[ StyleBox[\(pot[\[Lambda], \ 3, \ Sin[2 #] &, \ b1, b2, b3, b4]\), FontColor->RGBColor[1, 0, 0]]], "Input"], ", b1] == 0\nD[", Cell[BoxData[ StyleBox[\(pot[\[Lambda], \ 3, \ Sin[2 #] &, \ b1, b2, b3, b4]\), FontColor->RGBColor[1, 0, 0]]], "Input"], ", b2] == 0\nD[", Cell[BoxData[ StyleBox[\(pot[\[Lambda], \ 3, \ Sin[2 #] &, \ b1, b2, b3, b4]\), FontColor->RGBColor[1, 0, 0]]], "Input"], ", b3] == 0\nD[", Cell[BoxData[ StyleBox[\(pot[\[Lambda], \ 3, \ Sin[2 #] &, \ b1, b2, b3, b4]\), FontColor->RGBColor[1, 0, 0]]], "Input"], ", b4] == 0\n\n\nUsing ", StyleBox["FindRoot ", FontColor->RGBColor[1, 0, 1]], "(or ", StyleBox["Reduce", FontColor->RGBColor[1, 0, 1]], " if the number of variables is not very big) we can obtain bifurcation \ diagram in 3-D ", StyleBox[" \[DoubleStruckCapitalR]\[Cross]W", FontColor->RGBColor[0, 0, 1]], " where ", StyleBox["W", FontColor->RGBColor[0, 0, 1]], " is spanned by 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Since the resulting \ amplitudes of tube oscillations may become large causing damage of the heat \ exchanger,this phenomena of self-excitation has to be avoided whenever \ possible. Lacking satisfactory theoretical models in aeroelasticity we are \ limited to semi-empirical models. On purpose, we employ a nonlinear model:\n\n\ ", StyleBox["m u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["'' + ", FontColor->RGBColor[0, 0, 1]], StyleBox["b u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["' + ", FontColor->RGBColor[0, 0, 1]], StyleBox["k u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" - ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ SuperscriptBox[ StyleBox["V", FontSlant->"Italic"], "2"], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox[" \[Gamma] (", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["-", FontColor->RGBColor[0, 0, 1]], StyleBox["y", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["-", FontColor->RGBColor[0, 0, 1]], StyleBox["c", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[")(", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["-", FontColor->RGBColor[0, 0, 1]], StyleBox["y", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[")(", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["-", FontColor->RGBColor[0, 0, 1]], StyleBox["y", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["+", FontColor->RGBColor[0, 0, 1]], StyleBox["c", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[")=0\n ", FontColor->RGBColor[0, 0, 1]], StyleBox["y", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["'+\[Beta] ", FontColor->RGBColor[0, 0, 1]], StyleBox["y", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" = ", FontColor->RGBColor[0, 0, 1]], StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["\n ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`u(0) = u\_0\)], FontColor->RGBColor[0, 0, 1]], StyleBox[", ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ FormBox[\(\(u' \((0)\) = v\_0\)\(,\)\(\ \)\), "TraditionalForm"], \(y(0)\)}], "=", "0"}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], "\n\nintroduced by Tondl [Tondl, Quenching of Self-Excited Vibrations, \ Academia, Prague, 1991] in a slightly different context (here m, b, k are \ structural mass, damping, and stiffness, respectively, ", StyleBox["u", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], " is the deflection of the tube,", StyleBox[" y", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], " is an auxiliary variable, ", Cell[BoxData[ \(TraditionalForm\`V\^2\)], FontColor->RGBColor[0, 0, 1]], " the free-stream velocity, ", StyleBox["c", FontColor->RGBColor[0, 0, 1]], ", ", StyleBox["\[Beta]", FontColor->RGBColor[0, 0, 1]], " and ", StyleBox["\[Gamma]", FontColor->RGBColor[0, 0, 1]], " are parameters, ). \n\nRealistic values of parameters ", StyleBox["c", FontColor->RGBColor[0, 0, 1]], ", ", StyleBox["\[Beta]", FontColor->RGBColor[0, 0, 1]], " and ", StyleBox["\[Gamma]", FontColor->RGBColor[0, 0, 1]], " are difficult to estimate theoretically. For that reason we have decided \ to estimate them using parameter identification from measured data. There \ were several problems we encountered in doing so.We mention the most \ significant ones:\n\n(i) Ratio of the time needed to achieve either stable \ equilibrium or the limit cycle and the period of oscillations of the system \ is very high (about ", StyleBox["30000", FontFamily->"Courier", FontColor->RGBColor[0, 0, 1]], "). This forces to use very small integration step when solving the system \ numerically (small in comparison with the time domain) and to use enormous \ amount of data to which the solution of the nonlinear problem has to be \ fitted.This leads to possible accumulation of rounding errors.\n\n(ii) The \ objective function has many local critical points.To find the global minimum \ is very difficult.\n\n(iii) Fluctuations of the velocity of the free stream \ during the measurement.\n\nWe have partially solved problem (i) by using \ higher precision arithmetic supported by Mathematica (if it would not have \ been enough we can use multishooting methods). This approach is extremely \ both memory and time consuming, however.To partially overcome problem (ii),we \ use global optimization algorithms based on differential evolution (genetic \ algorithm) to get near to the prospective global minimum. Then we proceed by \ using standard local methods such as the Newton method to find the critical \ point. Finally,the problem (iii) was solved by considering the velocity of \ the free stream as a function of ", StyleBox["t", FontColor->RGBColor[0, 0, 1]], "." }], "Text", TextAlignment->Left, TextJustification->1], Cell[BoxData[ StyleBox[\(Conclusion\ - \ improvements\ suggestions\), "Section"]], "Input"], Cell[TextData[{ "\nIn processing of our problems we often use shooting method, which is \ implemented using ", StyleBox["NDSolve", FontFamily->"Courier", FontColor->RGBColor[1, 0, 1]], " accompanied with ", StyleBox["FindRoot", FontFamily->"Courier", FontColor->RGBColor[1, 0, 1]], ", ", StyleBox["ContourPlot", FontFamily->"Courier", FontColor->RGBColor[1, 0, 1]], " or ", StyleBox["NMinimize", FontFamily->"Courier", FontColor->RGBColor[1, 0, 1]], " in ", StyleBox["Mathematica", FontSlant->"Italic"], ". Since ", StyleBox["NDSolve", FontFamily->"Courier", FontColor->RGBColor[1, 0, 1]], " is called with the same equation and different initial conditions many \ times within the shooting, we found ", StyleBox["NDSolve", FontFamily->"Courier", FontColor->RGBColor[1, 0, 1]], " methods very useful (significant speed-up). In many of our problems \ parameters are present. However, ", StyleBox["NDSolve", FontFamily->"Courier", FontColor->RGBColor[1, 0, 1]], " methods are unable to process new choices of parameters. For that reason \ we would like to ask developers to include this possibility in NDSolve \ methods together with initial conditions in one command if possible (one \ would reduce number of high-level calls resulting in increase of speed). \ Finaly, I would like to present an example where also options of ", StyleBox["NDSolve", FontFamily->"Courier", FontColor->RGBColor[1, 0, 1]], " have to be changed in each step of computation of the bifurcation \ diagram. 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.09925 .58796 L .09927 .59379 L .09929 .59791 L .0993 .59952 L .09931 .60095 L .09932 .60159 L .09932 .6021 L .09933 .60252 L .09933 .60284 L .09934 .6032 L .09935 .60332 L .09936 .60314 L .09937 .60263 L .09938 .60224 L .09938 .60178 L .09939 .60072 L .09941 .59732 L .09943 .59328 L .09945 .58777 L .0995 .57095 L .09954 .55048 L .09962 .50139 L .0997 .43662 L .10001 .16224 L .10009 .10244 L .10016 .05814 L .1002 .03985 L .10023 .03212 L .10025 .02542 L .10027 .02104 L Mistroke .10028 .01917 L .10029 .01752 L .1003 .01634 L .10031 .01554 L .10032 .01503 L .10033 .01475 L .10034 .01475 L .10034 .01488 L .10035 .01508 L .10036 .01566 L .10037 .01656 L .10038 .01762 L .10039 .01883 L .10041 .02234 L .10043 .02732 L .10044 .03294 L .10049 .04916 L .10056 .08959 L .10063 .13974 L .10094 .41379 L .10102 .4808 L .1011 .53344 L .10114 .55705 L .10119 .57746 L .10121 .58469 L .10123 .59107 L .10125 .59549 L .10127 .5992 L .10128 .60069 L .10129 .60178 L .1013 .60255 L .10131 .60308 L .10131 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.10356 .50302 L .10364 .43963 L .10378 .30657 L .10394 .16386 L .10403 .10141 L Mistroke .10407 .07325 L .10412 .05145 L .10415 .03607 L .10417 .02972 L .1042 .02405 L .10421 .02142 L .10422 .01937 L .10423 .01764 L .10424 .01641 L .10425 .01553 L .10426 .01499 L .10427 .01473 L .10428 .01472 L .10428 .01481 L .10429 .01513 L .1043 .01575 L .10431 .01657 L .10432 .01753 L .10434 .02072 L .10436 .02482 L .1044 .03604 L .10444 .05269 L .10451 .09442 L .10459 .15456 L .10476 .30396 L .10493 .45472 L .105 .51007 L .10504 .53505 L .10509 .55789 L .10513 .57624 L .10516 .58895 L .10518 .59368 L .1052 .59776 L .10521 .59926 L .10522 .6006 L .10523 .60159 L .10524 .60232 L .10525 .60294 L .10526 .60325 L .10526 .60331 L .10528 .60306 L .10528 .60257 L .10529 .60177 L .1053 .60087 L .10531 .59963 L .10533 .59596 L .10535 .59061 L .1054 .57737 L .10543 .56007 L .10547 .54038 L Mistroke .10556 .48437 L .10572 .33889 L .10587 .20139 L .10595 .13679 L .10604 .08018 L .10608 .05747 L .10613 .03771 L .10615 .0309 L .10617 .02488 L .10619 .02045 L .10621 .0175 L .10622 .01637 L .10623 .01549 L .10624 .01496 L .10625 .01474 L .10625 .01472 L .10626 .01479 L .10626 .01495 L .10627 .01522 L .10628 .01591 L .10628 .01644 L .10629 .01701 L .10631 .0199 L .10633 .02354 L .10637 .03512 L .10641 .05031 L .10645 .07067 L .10652 .11704 L .10669 .25554 L .10685 .40111 L .10699 .51542 L .10707 .55934 L .1071 .57613 L .10714 .59004 L .10717 .59544 L .10719 .59914 L .1072 .6007 L .1072 .60137 L .10721 .60197 L .10721 .60241 L .10722 .60279 L .10723 .60321 L .10724 .60331 L .10725 .60312 L .10726 .6029 L .10726 .60256 L .10727 .60169 L .10728 .60059 L .10729 .59912 L .10731 .59567 L Mistroke .10733 .5906 L .10735 .58391 L .10739 .56858 L .10748 .5195 L .10756 .4634 L .10765 .39153 L .10781 .23499 L .10797 .10967 L .10805 .06328 L .10809 .04338 L .10811 .03565 L .10813 .02947 L .10815 .0246 L .10816 .02099 L .10818 .01793 L .10819 .01667 L .1082 .01577 L .10821 .01516 L .10822 .01479 L .10823 .01472 L .10824 .01488 L .10825 .01535 L .10826 .01575 L .10826 .01619 L .10827 .01723 L .10828 .01861 L .1083 .0223 L .10832 .0269 L .10836 .03834 L .1084 .05462 L .10844 .07673 L .10858 .18247 L .10874 .3229 L .10882 .39833 L .10891 .47273 L .109 .53163 L .10903 .55263 L .10907 .57176 L .10911 .5859 L .10913 .59124 L .10915 .5954 L .10917 .59908 L .10918 .60035 L .10919 .60144 L .1092 .60235 L .1092 .60293 L .10921 .60326 L .10922 .60332 L .10923 .60329 L .10924 .603 L Mistroke .10924 .60271 L .10925 .60237 L .10926 .60149 L .10927 .6004 L .10929 .59703 L .10931 .59198 L .10935 .57904 L .10939 .5631 L .10946 .52282 L .10954 .46831 L .10984 .19669 L .10992 .13184 L .11 .08092 L .11004 .05827 L .11008 .0387 L .1101 .03184 L .11013 .02579 L .11014 .02165 L .11015 .01971 L .11016 .01819 L .11017 .01692 L .11018 .01602 L .11019 .01529 L .1102 .01502 L .1102 .01484 L .11021 .01472 L .11022 .01489 L .11023 .01538 L .11024 .01575 L .11025 .01626 L .11026 .01852 L .11027 .02022 L .11028 .02205 L .11032 .03128 L .11036 .04623 L .1104 .06753 L .11049 .11827 L .11064 .24624 L .11081 .40343 L .11089 .46853 L .11097 .52787 L .11101 .55021 L .11105 .56986 L .11109 .58324 L .11113 .59408 L .11115 .59817 L .11116 .59996 L .11117 .60128 L .11118 .60216 L .11119 .60285 L Mistroke .11119 .60308 L .1112 .60324 L .11121 .60331 L .11122 .6031 L .11123 .60257 L .11124 .60177 L .11125 .60078 L .11126 .59824 L .11128 .59458 L .1113 .58901 L .11133 .5815 L .11137 .56409 L .11145 .51944 L .11161 .39372 L .11178 .23877 L .11186 .16814 L .11194 .10979 L .11201 .06742 L .11204 .04995 L .11208 .03454 L .1121 .02868 L .11212 .02349 L .11213 .02114 L .11214 .0193 L .11215 .01774 L .11216 .01658 L .11217 .0158 L .11218 .0152 L .11219 .01481 L .1122 .01472 L .11221 .01487 L .11222 .01534 L .11223 .01607 L .11224 .01699 L .11226 .01988 L .11228 .02363 L .1123 .02889 L .11232 .03585 L .11237 .05411 L .11241 .0753 L .11256 .18458 L .11272 .33477 L .11281 .41431 L .1129 .48182 L .11298 .53627 L .11301 .55569 L .11305 .57343 L .11309 .58699 L .11311 .59208 L .11312 .59604 L Mistroke .11313 .59784 L .11314 .59951 L .11315 .60067 L .11316 .6017 L .11317 .60253 L .11318 .60286 L .11318 .60309 L .11319 .6033 L .1132 .60325 L .11321 .60311 L .11321 .60287 L .11322 .6022 L .11323 .60165 L .11323 .60103 L .11324 .59961 L .11326 .59611 L .11329 .59105 L .11333 .57802 L .11336 .56214 L .11344 .51803 L .11351 .46545 L .11368 .32044 L .11383 .186 L .11391 .12414 L .11399 .07087 L .11403 .05015 L .11406 .04097 L .11408 .03254 L .1141 .02623 L .11412 .02162 L .11414 .0183 L .11415 .01704 L .11416 .01597 L .11417 .01556 L .11417 .01521 L .11418 .01481 L .11419 .01472 L .1142 .01489 L .11421 .01536 L .11422 .01575 L .11422 .0162 L .11423 .01737 L .11424 .01898 L .11426 .02288 L .11428 .02772 L .11432 .03972 L .11436 .05694 L .1144 .07606 L .11448 .12966 L .11463 .25305 L Mistroke .11479 .40593 L .11487 .46698 L .11495 .52417 L .11499 .54635 L .11503 .56643 L .11506 .58047 L .1151 .59204 L .11512 .59698 L .11513 .59871 L .11514 .6003 L .11515 .60149 L .11516 .60234 L .11517 .60295 L .11518 .60316 L .11518 .60328 L .11519 .6033 L .1152 .60309 L .11521 .60263 L .11522 .60186 L .11523 .60074 L .11524 .59939 L .11526 .59611 L .11528 .59168 L .11529 .5866 L .11534 .57178 L .11538 .55317 L .11542 .52895 L .11557 .41786 L .11572 .27397 L .11581 .19924 L .1159 .12814 L .11594 .09735 L .11598 .07221 L .11602 .05172 L .11606 .03666 L .1161 .02584 L .11612 .02175 L .11613 .01833 L .11615 .01698 L .11615 .01602 L .11616 .01561 L .11617 .01524 L .11618 .01483 L .11619 .01472 L .1162 .0149 L .1162 .0153 L .11621 .01599 L .11622 .01704 L .11623 .01828 L .11626 .02208 L Mistroke .11628 .02653 L .1163 .03241 L .11633 .04675 L .11637 .06316 L .11646 .11537 L .11654 .17752 L .11685 .45193 L .11693 .51316 L .117 .55805 L .11704 .57527 L .11709 .58934 L .11711 .59524 L .11712 .59755 L .11713 .59935 L .11714 .60067 L .11715 .60182 L .11716 .60226 L .11716 .60265 L .11717 .60296 L .11717 .60317 L .11718 .60332 L .11719 .6032 L .1172 .60277 L .11721 .60206 L .11722 .60115 L .11723 .60009 L .11725 .59694 L .11727 .59269 L .11729 .58681 L .11733 .57114 L .11738 .55122 L .11742 .52513 L .1175 .46738 L .11766 .33007 L .11783 .17583 L .11791 .11478 L .11796 .08625 L .118 .06326 L .11804 .04548 L .11806 .03766 L .11808 .03062 L .1181 .02565 L .11812 .02125 L .11813 .01968 L .11813 .01823 L .11814 .0171 L .11815 .01624 L .11816 .01546 L .11817 .01516 L .11817 .01492 L Mistroke .11818 .01477 L .11818 .01472 L .11819 .01486 L .1182 .01528 L .11821 .01591 L .11822 .01688 L .11823 .01822 L .11826 .02244 L .11828 .0279 L .11832 .04186 L .11836 .05957 L .1184 .0794 L .11848 .13513 L .11865 .27386 L .1188 .41239 L .11894 .52389 L .11899 .54855 L .11903 .56806 L .11906 .58212 L .11908 .58811 L .1191 .59348 L .11912 .59769 L .11913 .59916 L .11914 .60053 L .11915 .60151 L .11916 .60232 L .11917 .60292 L .11918 .60324 L .11918 .60331 L .11919 .6033 L .11919 .60321 L .1192 .603 L .11921 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.13747 .59649 L .13749 .59207 L .13751 .58599 L .13756 .56989 L .13764 .52807 L .13771 .47792 L .13788 .33783 L .13805 .19196 L .13812 .13511 L .1382 .08242 L .13824 .06272 L .13828 .04497 L .13831 .0318 L .13835 .02293 L .13837 .0194 L .13838 .01699 L .1384 .01599 L .1384 .01533 L Mistroke .13841 .01507 L .13841 .01487 L .13843 .01472 L .13843 .01484 L .13844 .01502 L .13845 .01527 L .13846 .016 L .13846 .01654 L .13847 .01712 L .13849 .01996 L .13851 .02366 L .13855 .03469 L .13858 .04829 L .13866 .09031 L .13874 .1415 L .13881 .19799 L .13912 .46494 L .1392 .5224 L .13928 .56387 L .13932 .57952 L .13936 .59205 L .13938 .59715 L .1394 .59911 L .13941 .60059 L .13942 .60165 L .13943 .6025 L .13944 .60305 L .13944 .60323 L .13945 .60331 L .13946 .60325 L .13947 .60292 L .13948 .60235 L .13949 .60162 L .1395 .6005 L .13951 .59896 L .13953 .59534 L .13955 .5904 L .13957 .5839 L .13961 .56911 L .13968 .53358 L .13976 .48255 L .13993 .34261 L .14008 .20612 L .14016 .14517 L .14024 .08894 L .14028 .06775 L .14032 .04879 L .14036 .03454 L .14039 .02486 L .14041 .02095 L Mistroke .14043 .01775 L .14044 .01656 L .14045 .01603 L .14045 .01562 L .14046 .01503 L .14047 .01476 L .14048 .01473 L .14049 .01494 L .1405 .01531 L .14051 .01593 L .14052 .01684 L .14053 .01809 L .14055 .02109 L .14057 .02542 L .14059 .03139 L .14063 .04725 L .14071 .08741 L .1408 .14269 L .14087 .20205 L .14104 .35027 L .14112 .42045 L .1412 .48717 L .14128 .53821 L .14132 .55843 L .14136 .57382 L .14139 .58643 L .14143 .59522 L .14145 .5987 L .14147 .60106 L .14147 .60196 L .14148 .60269 L .1415 .60316 L .14151 .60332 L .14151 .60322 L .14152 .60284 L .14153 .60253 L .14154 .60213 L .14155 .60118 L .14156 .59996 L .14156 .59856 L .14158 .5953 L .14162 .5848 L .14167 .56874 L .14174 .53018 L .14183 .47427 L .14199 .33328 L .14216 .18592 L .14224 .12503 L .14232 .0782 L .14236 .05773 L Mistroke .14239 .04238 L .14243 .02914 L .14245 .02366 L .14248 .01967 L .14249 .01711 L .1425 .01617 L .14251 .0154 L .14252 .01497 L .14253 .01474 L .14254 .01474 L .14255 .01493 L .14256 .0154 L .14257 .01609 L .14258 .01712 L .14259 .01851 L .14261 .02157 L .14263 .02596 L .14267 .03766 L .14271 .05418 L .14278 .09362 L .14295 .21859 L .14311 .36025 L .14325 .47938 L .14333 .52953 L .14337 .55142 L .14341 .57073 L .14343 .57893 L .14346 .58664 L .14348 .59246 L .1435 .59671 L .14352 .59999 L .14353 .60132 L .14353 .60182 L .14354 .60228 L .14355 .60288 L .14356 .60321 L .14356 .6033 L .14357 .60331 L .14358 .60313 L .14359 .60272 L .1436 .602 L .14361 .60108 L .14362 .60004 L .14364 .59663 L .14366 .59231 L .1437 .58065 L .14374 .56352 L .14382 .52229 L .14389 .47382 L .14405 .33833 L Mistroke .1442 .20436 L .14435 .09645 L .14439 .07226 L .14443 .05283 L .14447 .03763 L .14451 .02672 L .14452 .02233 L .14453 .02041 L .14455 .01868 L .14455 .01747 L .14456 .01639 L .14457 .01564 L .14458 .01514 L .14459 .01493 L .14459 .01478 L .1446 .01473 L .14461 .01494 L .14462 .01536 L .14463 .01607 L .14464 .01715 L .14465 .01862 L .14466 .0203 L .1447 .0285 L .14473 .03914 L .14477 .0541 L .14481 .07336 L .14497 .18139 L .14512 .30842 L .14527 .43789 L .14534 .49703 L .14543 .54786 L .14547 .56792 L .14549 .57684 L .14552 .58505 L .14554 .59127 L .14556 .59585 L .14557 .59767 L .14558 .59937 L .14559 .60061 L .1456 .60168 L .1456 .60218 L .14561 .60255 L .14562 .60307 L .14563 .6033 L .14564 .60327 L .14564 .60316 L .14565 .60295 L .14566 .60238 L .14567 .60189 L .14567 .60135 L Mistroke .14568 .60008 L .1457 .59703 L .14572 .59332 L .14576 .58188 L .1458 .56773 L .14584 .54882 L .14591 .50587 L .14607 .37672 L .14623 .23746 L .14632 .16841 L .1464 .10466 L .14645 .07809 L .14649 .05685 L .14653 .04007 L .14655 .03399 L .14657 .02824 L .14659 .02403 L .1466 .02036 L .14661 .01873 L .14662 .01748 L .14663 .0165 L .14664 .0157 L .14665 .0151 L .14666 .01479 L .14667 .01472 L .14668 .01481 L .14668 .01497 L .14669 .01546 L .1467 .01614 L .14671 .01712 L .14672 .01844 L .14674 .0219 L .14676 .02619 L .1468 .03684 L .14684 .05198 L .14688 .07247 L .14703 .17092 L .14718 .30409 L .14735 .45076 L .14743 .50743 L .14747 .53409 L .14752 .55587 L .14755 .57265 L .1476 .58697 L .14761 .59189 L .14763 .59619 L .14765 .59932 L .14767 .60139 L .14768 .60225 L .14769 .60282 L Mistroke .1477 .6032 L .14771 .60332 L .14771 .60326 L .14772 .60312 L .14773 .60262 L .14774 .60185 L .14775 .6009 L .14777 .59857 L .14778 .59511 L .14782 .58529 L .14786 .57046 L .14791 .54991 L .14799 .5019 L .14832 .22727 L .1484 .16233 L .14848 .10238 L .14852 .07794 L .14856 .05815 L .1486 .04344 L .14864 .03062 L .14865 .02588 L .14867 .02171 L .14868 .01982 L .14869 .01835 L .1487 .01711 L .14871 .01619 L .14872 .01554 L .14873 .01505 L .14874 .01476 L .14875 .01473 L .14876 .01489 L .14877 .01528 L .14877 .01586 L .14878 .01657 L .1488 .01895 L .14882 .02204 L .14884 .02638 L .14886 .03211 L .1489 .04721 L .14894 .06474 L .14902 .11086 L .14909 .16365 L .14926 .30479 L .14942 .44394 L .1495 .50225 L .14957 .54598 L .14961 .56338 L .14965 .57901 L .14969 .59033 L .1497 .59427 L Mistroke .14972 .59775 L .14973 .59943 L .14974 .60072 L .14975 .60169 L .14976 .6025 L .14977 .60299 L .14978 .60325 L .14979 .60331 L .1498 .60315 L .14981 .60269 L .14981 .6023 L .14982 .60186 L .14983 .60084 L .14984 .59947 L .14986 .5964 L .14988 .59198 L .14992 .58042 L .14996 .56413 L .15003 .52531 L .1502 .40222 L .15036 .26235 L .1505 .14361 L .15058 .09312 L .15066 .05092 L .15071 .03422 L .15072 .02846 L .15075 .02326 L .15077 .01947 L .15079 .01691 L .1508 .01592 L .15081 .01527 L .15081 .01502 L .15082 .01483 L .15083 .01472 L .15083 .01477 L .15084 .01491 L .15085 .01535 L .15086 .01611 L .15087 .01728 L .15089 .02028 L .15091 .02409 L .15095 .03379 L .15099 .0478 L .15107 .09236 L .15115 .14619 L .15132 .28346 L .15147 .4167 L .15162 .52476 L .1517 .56416 L .15174 .58088 L Mistroke .15176 .5874 L .15178 .59248 L .1518 .59667 L .15182 .59961 L .15183 .6009 L .15184 .60187 L .15185 .60263 L .15185 .60293 L .15186 .60314 L .15187 .60331 L .15188 .60324 L .15189 .6029 L .15189 .60259 L .1519 .60223 L .15191 .60129 L .15192 .59993 L .15194 .59659 L .15196 .59241 L .15198 .58779 L .15202 .57459 L .15209 .54154 L .15217 .49147 L .15224 .43604 L .15241 .29278 L .15257 .1557 L .15265 .10031 L .15273 .06027 L .15276 .04464 L .1528 .03123 L .15282 .02637 L .15284 .02213 L .15286 .01925 L .15287 .01689 L .15288 .01591 L .15289 .01525 L .1529 .01488 L .15291 .01472 L .15292 .01483 L .15293 .01502 L .15294 .01527 L .15295 .01598 L .15296 .01691 L .15297 .01945 L .15299 .02261 L .15303 .03266 L .15307 .04582 L .15311 .06365 L .15318 .10469 L .15335 .23025 L .15351 .3689 L Mistroke .15359 .43858 L .15368 .50361 L .15376 .54987 L .1538 .57037 L .15384 .58533 L .15386 .59058 L .15388 .59516 L .1539 .59827 L .15392 .60082 L .15393 .60188 L .15394 .60259 L .15394 .60288 L .15395 .60311 L .15396 .60331 L .15397 .60325 L .15398 .60291 L .15399 .60239 L .154 .6016 L .15401 .60047 L .15402 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.5836 L .19281 .58872 L .19283 .59349 L .19285 .59706 L .19286 .59964 L .19287 .60078 L .19288 .6018 L .1929 .60256 L .1929 .60286 L .19291 .60307 L .19292 .60329 L .19293 .6033 L .19294 .60306 L .19295 .60261 L .19295 .60204 L .19296 .60121 L .19298 .59893 L .193 .59609 L .19302 .5928 L .19305 .58319 L .19309 .56961 L .19318 .53208 L .19326 .47825 L .19342 .35666 L .19358 .23039 L .19366 .16779 L .19375 .10869 L .19384 .06387 L .19387 .04839 L .19391 .03463 L Mistroke .19393 .02949 L .19395 .02483 L .19397 .0215 L .19399 .01862 L .194 .0173 L .19401 .01632 L .19402 .0156 L .19403 .01507 L .19404 .0148 L .19405 .01472 L .19405 .01482 L .19406 .01516 L .19407 .01544 L .19408 .01576 L .19409 .01654 L .1941 .01761 L .19411 .01905 L .19413 .02237 L .19415 .02623 L .19419 .03801 L .19423 .05466 L .19431 .0919 L .19439 .14407 L .19472 .39814 L .19487 .50389 L .19495 .54988 L .19499 .56728 L .19503 .58067 L .19507 .5914 L .19509 .59573 L .1951 .59758 L .19511 .59932 L .19512 .60064 L .19513 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.1974 .60242 L .19741 .60293 L .19742 .60322 L .19743 .60332 L Mistroke .19744 .6032 L .19745 .6029 L .19746 .60239 L .19747 .60172 L .19748 .60096 L .1975 .59846 L .19752 .59531 L .19755 .58767 L .19759 .57666 L .19766 .54506 L .19775 .49843 L .19792 .3767 L .19809 .23988 L .19824 .12756 L .19832 .08281 L .19836 .0632 L .1984 .04575 L .19844 .03356 L .19846 .02828 L .19848 .02354 L .1985 .02008 L .19852 .01766 L .19852 .01673 L .19853 .01602 L .19854 .01544 L .19855 .015 L .19856 .01475 L .19857 .01472 L .19857 .01474 L .19858 .01497 L .19859 .01539 L .1986 .01574 L .1986 .01614 L .19861 .01706 L .19864 .01996 L .19866 .02342 L .19867 .02738 L .19872 .039 L .19879 .06753 L .19886 .10834 L .19917 .3335 L .19933 .46183 L .19941 .50933 L .19949 .55187 L .19952 .56781 L .19956 .58176 L .1996 .59184 L .19962 .5953 L .19964 .59831 L .19965 .59965 L Mistroke .19966 .60088 L .19967 .6018 L .19968 .60245 L .19969 .60298 L .19969 .60317 L .1997 .60328 L .19971 .6033 L .19971 .60322 L .19972 .60308 L .19973 .60264 L .19974 .60201 L .19975 .60128 L .19976 .60031 L .19978 .59743 L .1998 .59396 L .19983 .5848 L .19987 .5717 L .19995 .53998 L .20003 .49036 L .20011 .43609 L .20028 .30606 L .20043 .18574 L .20058 .0895 L .20065 .05392 L .2007 .03845 L .20072 .03227 L .20074 .02733 L .20076 .02313 L .20078 .02004 L .2008 .01742 L .20081 .01636 L .20082 .01559 L .20083 .01508 L .20083 .0149 L .20084 .01478 L .20085 .01472 L .20086 .01487 L .20086 .01505 L .20087 .01528 L .20088 .01589 L .20089 .01678 L .2009 .01805 L .20092 .02084 L .20094 .02409 L .20098 .0338 L .20101 .04572 L .20105 .05938 L .20113 .09848 L .20121 .15025 L .20136 .26123 L Mistroke .20152 .38885 L .20166 .49251 L .20174 .53569 L .20182 .57169 L .20186 .58597 L .20188 .59094 L .2019 .59546 L .20192 .59879 L .20194 .60109 L .20195 .60202 L .20196 .60265 L .20197 .60289 L .20197 .6031 L .20198 .60324 L .20198 .60331 L .202 .60326 L .202 .60315 L .20201 .60295 L .20202 .60244 L .20203 .60175 L .20204 .60069 L .20205 .59949 L .20207 .59598 L .20209 .59206 L .20211 .58687 L .20215 .575 L .20223 .54253 L .2023 .5031 L .20261 .26767 L .20277 .1496 L .20284 .10597 L .20291 .06655 L .20295 .05115 L .20299 .03752 L .20301 .0313 L .20303 .02648 L .20305 .02266 L .20307 .01942 L .20308 .01807 L .20309 .01684 L .2031 .01597 L .20311 .01536 L .20312 .01509 L .20312 .0149 L .20313 .01472 L .20314 .01473 L .20314 .01479 L .20315 .01494 L .20315 .01518 L .20316 .01577 L Mistroke .20317 .01622 L .20318 .01669 L .2032 .01908 L .20322 .02205 L .20324 .026 L .20327 .03644 L .20331 .04876 L .20339 .08553 L .20354 .17815 L .2037 .30684 L .20386 .42679 L .20401 .52392 L .20408 .56041 L .20412 .57654 L .20417 .58835 L .2042 .59639 L .20421 .59806 L .20422 .59959 L .20423 .60079 L .20424 .60169 L .20425 .60247 L .20426 .60278 L .20427 .60303 L .20428 .60328 L .20428 .60332 L .20429 .60329 L .2043 .60308 L .20431 .60269 L .20432 .60202 L .20433 .60116 L .20434 .59908 L .20436 .59611 L .2044 .58885 L .20444 .57707 L .20447 .56358 L .20456 .52525 L .20463 .48084 L .2048 .35834 L .20496 .22807 L .20511 .12054 L .20519 .07827 L .20526 .04727 L .2053 .03433 L .20532 .02878 L .20534 .02389 L .20536 .02057 L .20537 .0191 L .20538 .01776 L .20539 .01675 L .2054 .016 L Mistroke .20541 .01542 L .20542 .01503 L .20543 .01477 L .20543 .01472 L .20544 .01473 L .20545 .01491 L .20546 .01531 L .20547 .01585 L .20547 .01652 L .20549 .01861 L .20551 .02175 L .20553 .0254 L .20558 .03632 L .20561 .04853 L .20565 .06468 L .20572 .10108 L .20588 .20699 L .20605 .33938 L .20621 .45827 L .20628 .50296 L .20635 .544 L .20643 .57514 L .20647 .5875 L .20651 .59587 L .20653 .59926 L .20654 .60055 L .20655 .60152 L .20656 .60223 L .20657 .60278 L .20658 .60314 L .20659 .60331 L .20659 .60331 L .2066 .60323 L .20661 .60292 L .20661 .60264 L .20662 .60233 L .20663 .60138 L .20664 .60029 L .20665 .59909 L .20667 .5957 L .20671 .58703 L .20675 .57448 L .20683 .54383 L .20691 .50036 L .20699 .4426 L .20716 .31229 L .20732 .19234 L .20739 .13901 L .20748 .08947 L .20752 .07038 L Mistroke .20756 .05292 L .20759 .04018 L .20763 .02946 L .20765 .02515 L .20767 .02128 L .20769 .01853 L .2077 .01663 L .20772 .01579 L .20772 .01522 L .20773 .01489 L .20774 .01472 L .20775 .01478 L .20776 .0149 L .20777 .0151 L .20778 .01563 L .20779 .01634 L .2078 .01831 L .20782 .02088 L .20786 .02755 L .20789 .03734 L .20793 .05098 L .20801 .08487 L .20809 .13297 L .20826 .2545 L .20843 .38672 L .20858 .49482 L .20866 .53848 L .20873 .57002 L .20877 .58218 L .20881 .59222 L .20883 .59653 L .20885 .59965 L .20886 .60071 L .20887 .60164 L .20887 .60204 L .20888 .60242 L .20889 .60293 L .2089 .60324 L .20891 .60332 L .20892 .60318 L .20892 .603 L .20893 .60277 L .20894 .60219 L .20895 .60133 L .20897 .59917 L .20899 .5963 L .20901 .59246 L .20904 .58355 L .20909 .57007 L .20912 .55457 L Mistroke .20921 .5098 L .20937 .39903 L .20952 .28254 L .20969 .15842 L .20976 .11194 L .20984 .06953 L .20988 .05371 L .20992 .03949 L .20996 .02892 L .20999 .02175 L .21001 .01884 L .21003 .01683 L .21004 .01597 L .21005 .01538 L .21005 .01514 L .21006 .01494 L .21007 .01473 L .21008 .01475 L .21008 .01485 L .21009 .015 L .2101 .01548 L .2101 .01585 L .21011 .01625 L .21013 .01829 L .21015 .02099 L .21017 .02484 L .21019 .02927 L .21023 .03962 L .21031 .07209 L .21038 .10947 L .21045 .15793 L .21078 .4087 L .21086 .46496 L .21095 .51731 L .21103 .55687 L .21106 .5708 L .2111 .58299 L .21112 .58801 L .21114 .59273 L .21116 .59632 L .21117 .59896 L .21119 .60128 L .21121 .60219 L .21121 .60251 L .21122 .6028 L .21123 .60316 L .21124 .60331 L .21124 .60331 L .21125 .60326 L .21126 .603 L Mistroke .21126 .6026 L .21127 .60199 L .21128 .60115 L .21129 .60018 L .21131 .59801 L .21133 .59505 L .21137 .5859 L .2114 .57474 L .21148 .54201 L .21156 .5023 L .21172 .38765 L .21188 .26089 L .21204 .14959 L .21211 .10578 L .21218 .06757 L .21222 .05131 L .21226 .03676 L .2123 .02662 L .21232 .02304 L .21234 .01993 L .21235 .01856 L .21236 .01728 L .21237 .01634 L .21238 .01566 L .21238 .01536 L .21239 .0151 L .2124 .0149 L .2124 .01477 L .21241 .01472 L .21241 .01473 L .21242 .01492 L .21243 .01533 L .21244 .01566 L .21244 .01603 L .21245 .01685 L .21246 .01796 L .21248 .02046 L .2125 .02386 L .21254 .03251 L .21258 .04481 L .21265 .07445 L .21273 .11855 L .21282 .17664 L .21298 .29865 L .21314 .4183 L .21322 .47546 L .21331 .52792 L .21335 .54826 L .21339 .56651 L .21343 .58031 L Mistroke .21347 .59034 L .21351 .59721 L .21353 .59995 L .21354 .60174 L .21355 .60246 L .21356 .60293 L .21357 .60324 L .21358 .60331 L .21358 .60331 L .21359 .60317 L .2136 .60281 L .21361 .60225 L .21362 .60158 L .21364 .59943 L .21366 .59677 L .2137 .58835 L .21374 .57759 L .21378 .56497 L .21386 .52842 L .21394 .47788 L .21427 .23144 L .21435 .17361 L .21443 .11848 L .21451 .07857 L .21459 .04521 L .21463 .03212 L .21465 .02749 L .21467 .0232 L .21469 .02014 L .21471 .01761 L .21472 .01655 L .21473 .01579 L .21474 .01523 L .21475 .01489 L .21476 .01473 L .21476 .01474 L .21477 .01493 L .21478 .01528 L .21479 .01575 L .2148 .01632 L .21482 .01805 L .21483 .02044 L .21485 .02379 L .21489 .03282 L .21493 .04588 L .21497 .06127 L .21505 .09744 L .21522 .20631 L .21552 .43965 L .21568 .53601 L Mistroke .21576 .57041 L .21581 .58482 L .21583 .59038 L .21585 .59468 L .21587 .59799 L .21589 .60032 L .2159 .60135 L .21591 .60212 L .21592 .60273 L .21592 .60298 L .21593 .60315 L .21594 .60331 L .21595 .60328 L .21596 .60303 L .21596 .6028 L .21597 .60253 L .21598 .60182 L .21599 .60079 L .21601 .59822 L .21603 .595 L .21605 .59142 L .21609 .58115 L .21616 .5552 L .21624 .51541 L .21631 .47054 L .21648 .34959 L .21664 .22309 L .2168 .11913 L .21687 .07819 L .21694 .04794 L .21698 .03518 L .217 .02965 L .21702 .02471 L .21704 .02132 L .21706 .01839 L .21707 .01737 L .21708 .01646 L .21709 .01578 L .2171 .01529 L .21711 .0149 L .21712 .01473 L .21713 .01475 L .21713 .01484 L .21714 .01499 L .21715 .01535 L .21716 .01592 L .21717 .01671 L .21718 .01763 L .2172 .0204 L .21722 .02373 L Mistroke .21726 .03391 L .2173 .04705 L .21735 .06495 L .21743 .10625 L .21776 .33934 L .21792 .45818 L .218 .50774 L .21807 .54559 L .21814 .574 L .21818 .58485 L .21821 .59394 L .21824 .59752 L .21825 .60003 L .21826 .60112 L .21828 .60206 L .21828 .6024 L .21829 .6027 L .2183 .6031 L .2183 .60329 L .21831 .6033 L .21832 .60315 L .21833 .60285 L .21834 .60233 L .21835 .60155 L .21837 .59952 L .21839 .59655 L .21841 .5924 L .21845 .58242 L .21849 .56976 L .21853 .55567 L .2187 .46297 L .21901 .22658 L .21917 .11865 L .21924 .08096 L .21932 .04868 L .21936 .03519 L .21938 .0303 L .2194 .02566 L .21941 .02226 L .21943 .01929 L .21944 .01796 L .21945 .01695 L .21946 .0161 L .21947 .01551 L .21948 .01505 L .21949 .01477 L .2195 .01472 L .21951 .01484 L .21952 .01499 L .21952 .0152 L Mistroke .21953 .01573 L .21954 .01653 L .21955 .01766 L .21958 .02046 L .2196 .02449 L .21964 .03439 L .21968 .04779 L .21972 .06307 L .21981 .107 L .21997 .21282 L .22028 .44813 L .22037 .50075 L .22046 .54737 L .2205 .56455 L .22054 .57946 L .22058 .58943 L .2206 .59393 L .22062 .59732 L .22064 .60005 L .22065 .60116 L .22066 .60209 L .22067 .60268 L .22068 .60306 L .22069 .60328 L .22069 .60332 L .2207 .60329 L .22071 .60311 L .22072 .60277 L .22073 .60222 L .22074 .60142 L .22076 .59939 L .22077 .59691 L .22082 .58858 L .22086 .57584 L .22094 .54349 L .22102 .50358 L .2211 .45094 L .22127 .32695 L .22144 .19914 L .22159 .10058 L .22167 .06336 L .22171 .04762 L .22175 .0341 L .22179 .02514 L .22181 .02126 L .22183 .01842 L .22184 .01742 L .22185 .01653 L .22186 .0159 L .22187 .01538 L Mistroke .22188 .01498 L .22188 .01477 L .2219 .01472 L .2219 .01486 L .22191 .01519 L .22192 .01566 L .22193 .01636 L .22194 .01733 L .22196 .01998 L .22198 .02321 L .22202 .03153 L .22206 .04195 L .22214 .07331 L .22222 .11906 L .22255 .35302 L .2227 .46132 L .22278 .50982 L .22286 .55168 L .22291 .56869 L .22295 .58363 L .22297 .58891 L .223 .59367 L .22302 .59728 L .22304 .59987 L .22304 .60093 L .22306 .60188 L .22307 .60259 L .22307 .60288 L .22308 .60309 L .22309 .60329 L .2231 .6033 L .22311 .6031 L .22311 .60291 L .22312 .60265 L .22313 .60202 L .22314 .60128 L .22316 .59899 L .22318 .59613 L .2232 .59278 L .22323 .58389 L .22327 .57115 L .22336 .53654 L .2235 .44966 L .22383 .20968 L .22398 .11227 L .22406 .06937 L .22414 .03984 L .22418 .02915 L .2242 .0243 L .22422 .02071 L Mistroke .22424 .01783 L .22425 .01669 L .22427 .01577 L .22428 .0152 L .22429 .01487 L .22429 .01476 L .2243 .01472 L .2243 .01473 L .22431 .01481 L .22432 .01508 L .22433 .01557 L .22433 .0159 L .22434 .01631 L .22435 .0172 L .22437 .01949 L .22439 .02223 L .22443 .03139 L .22447 .04331 L .22455 .07368 L .22463 .11631 L .22478 .21331 L .22494 .33383 L .22511 .45874 L .22519 .50849 L .22528 .55138 L .22535 .57857 L .22539 .58973 L .22541 .59371 L .22543 .5972 L .22545 .6 L .22546 .60098 L .22547 .60184 L .22547 .60224 L .22548 .60254 L .22549 .603 L .22549 .60316 L .2255 .60327 L .22551 .60332 L .22551 .60329 L .22552 .60309 L .22553 .6027 L .22554 .60219 L .22555 .60147 L .22557 .5992 L .22559 .59633 L .22563 .58951 L .22566 .57944 L .22574 .5513 L .22582 .51095 L .2259 .46621 L Mistroke .22606 .34719 L .22623 .22267 L .22638 .12072 L .22646 .07994 L .22653 .04972 L .22657 .03677 L .22659 .03112 L .22661 .02604 L .22663 .02247 L .22665 .01932 L .22666 .0182 L .22667 .01716 L .22668 .01637 L .22669 .01576 L .2267 .01523 L .2267 .01502 L .22671 .01486 L .22671 .01475 L .22672 .01472 L .22673 .01481 L .22674 .01509 L .22675 .01552 L .22676 .01617 L .22677 .01708 L .22679 .01995 L .22682 .02366 L .22686 .0332 L .2269 .04537 L .22694 .05911 L .22702 .09834 L .22717 .192 L .22733 .31434 L .2275 .43825 L .22766 .53065 L .22773 .56432 L .22778 .57903 L .22782 .58965 L .22785 .59648 L .22787 .59933 L .22789 .60132 L .2279 .60207 L .22791 .60268 L .22792 .60303 L .22793 .60326 L .22794 .60331 L .22794 .60325 L .22795 .60315 L .22796 .60279 L .22797 .60227 L .22798 .60159 L Mistroke .22799 .60069 L .22801 .59857 L .22803 .59524 L .22805 .59145 L .22809 .5808 L .22813 .5677 L .2282 .53804 L .22828 .4971 L .2286 .26652 L .22875 .15962 L .22883 .11141 L .22892 .06942 L .22896 .05217 L .229 .03679 L .22903 .03127 L .22905 .02622 L .22907 .0223 L .22909 .0194 L .22911 .01702 L .22912 .0161 L .22912 .01572 L .22913 .01538 L .22914 .01496 L .22915 .01476 L .22916 .01472 L .22916 .01474 L .22917 .01493 L .22918 .01529 L .22919 .01584 L .2292 .01654 L .22921 .01732 L .22923 .01981 L .22925 .0229 L .22929 .03077 L .22933 .04232 L .22941 .07443 L .22949 .11355 L .22956 .15693 L .22987 .38322 L .23003 .48961 L .23011 .53486 L .23015 .55541 L .2302 .57164 L .23024 .58431 L .23026 .58972 L .23028 .59446 L .2303 .59769 L .23031 .59911 L .23033 .6004 L .23034 .60138 L Mistroke .23035 .6021 L .23035 .60265 L .23036 .60302 L .23037 .60325 L .23038 .60332 L .23039 .6032 L .2304 .6029 L .23041 .60247 L .23042 .60195 L .23044 .6003 L .23046 .59783 L .23048 .59431 L .23052 .58573 L .23056 .5732 L .2306 .55854 L .23067 .52424 L .23084 .4211 L .23115 .19488 L .23131 .09666 L .23139 .05958 L .23144 .04311 L .23148 .03098 L .23152 .02258 L .23154 .01916 L .23155 .01786 L .23156 .01685 L .23157 .01608 L .23158 .01552 L .23159 .01507 L .2316 .01479 L .23161 .01472 L .23162 .01483 L .23163 .01497 L .23163 .01518 L .23164 .0157 L .23165 .01641 L .23166 .01723 L .23168 .01968 L .2317 .02252 L .23172 .02621 L .23175 .03425 L .23179 .04542 L .23187 .07804 L .23195 .11654 L .23211 .22587 L .23228 .34846 L .23243 .4564 L .23258 .53993 L .23262 .55835 L .23266 .57301 L Mistroke .2327 .58455 L .23274 .5929 L .23276 .59641 L .23277 .59899 L .23279 .60115 L .2328 .60203 L .23281 .60265 L .23282 .60306 L .23283 .60319 L .23284 .60329 L .23285 .6033 L .23285 .60316 L .23286 .603 L .23287 .60278 L .23288 .60223 L .23289 .60144 L .2329 .60032 L .23292 .5979 L .23293 .59508 L .23297 .58668 L .23301 .57639 L .23305 .56455 L .23312 .53077 L .23321 .48563 L .23335 .38696 L .23366 .16711 L .23374 .118 L .23381 .07867 L .23385 .06054 L .2339 .04399 L .23394 .03202 L .23396 .02733 L .23398 .02367 L .234 .02073 L .23402 .01817 L .23404 .01631 L .23405 .01559 L .23406 .01512 L .23407 .01483 L .23408 .01472 L .23408 .01475 L .23409 .01491 L .2341 .01525 L .23411 .01579 L .23412 .01641 L .23413 .01724 L .23415 .01976 L .23417 .02281 L .23421 .03224 L .23426 .04407 L Mistroke .23429 .05795 L .23445 .13802 L .2346 .23702 L .23491 .46182 L .235 .51056 L .23508 .55338 L .23513 .56901 L .23517 .5825 L .23521 .59143 L .23523 .59543 L .23525 .59841 L .23527 .60076 L .23528 .60169 L .23529 .60245 L .2353 .60292 L .23531 .6032 L .23532 .60332 L .23532 .6033 L .23533 .60324 L .23534 .603 L .23535 .60265 L .23535 .60211 L .23536 .60136 L .23538 .59927 L .2354 .59673 L .23544 .5887 L .23549 .57657 L .23557 .54595 L .23565 .5084 L .23573 .45878 L .2359 .34094 L .23607 .21723 L .23622 .11808 L .2363 .07878 L .23634 .06138 L .23638 .04568 L .23642 .03347 L .23646 .02498 L .23648 .02177 L .2365 .01898 L .2365 .01792 L .23651 .01698 L .23652 .01624 L .23653 .01569 L .23654 .01519 L .23655 .015 L .23655 .01485 L .23656 .01472 L .23657 .01477 L .23658 .01497 L Mistroke .23659 .01536 L .2366 .01588 L .23661 .0165 L .23663 .0185 L .23665 .02152 L .23669 .02923 L .23673 .03889 L .23676 .05175 L .23684 .08113 L .23701 .17975 L .23717 .29466 L .23732 .4018 L .2374 .45792 L .23748 .50448 L .23756 .54596 L .23764 .5748 L .23768 .58657 L .23772 .59491 L .23774 .59829 L .23776 .60065 L .23777 .60159 L .23778 .60239 L .23779 .6027 L .23779 .60296 L .2378 .60315 L .2378 .60326 L .23781 .60332 L .23782 .60319 L .23783 .60294 L .23784 .6025 L .23785 .60185 L .23786 .60094 L .23788 .59877 L .2379 .59616 L .23792 .59318 L .23796 .58454 L .238 .57223 L .23804 .55846 L .23812 .51935 L .23827 .42759 L .23844 .30867 L .23861 .18657 L .23876 .09453 L .23884 .05966 L .23888 .04503 L .23893 .03257 L .23896 .02428 L .23899 .0207 L .23901 .01811 L .23902 .01714 L Mistroke .23902 .01637 L .23903 .01579 L .23904 .01532 L .23905 .01496 L .23906 .01477 L .23907 .01472 L .23908 .01485 L .23909 .01515 L .2391 .01559 L .23911 .01625 L .23912 .01715 L .23914 .01963 L .23916 .02263 L .2392 .03039 L .23923 .04003 L .23931 .06918 L .2394 .11153 L .23973 .33342 L .23989 .44757 L .23997 .49615 L .24004 .53408 L .24012 .56546 L .24015 .57693 L .24019 .58695 L .24021 .59112 L .24023 .59504 L .24025 .59798 L .24027 .60012 L .24027 .60108 L .24029 .60193 L .2403 .60259 L .2403 .60286 L .24031 .60305 L .24032 .60327 L .24033 .60331 L .24034 .60317 L .24035 .60285 L .24036 .60239 L .24037 .60173 L .24038 .60008 L .24041 .59737 L .24042 .59418 L .24047 .58497 L .24051 .5734 L .24058 .54672 L .24065 .50928 L .24098 .291 L .24113 .18488 L .24129 .08987 L .24134 .07 L Mistroke .24138 .05203 L .24142 .03835 L .24146 .0283 L .2415 .02135 L .24152 .01852 L .24154 .01662 L .24155 .01583 L .24156 .01528 L .24157 .01507 L .24157 .0149 L .24158 .01477 L .24158 .01472 L .2416 .01477 L .2416 .01499 L .24161 .01541 L .24162 .0157 L .24163 .01607 L .24165 .01786 L .24166 .0192 L .24167 .02064 L .24171 .02787 L .24174 .03684 L .24178 .04873 L .24186 .08087 L .24195 .12645 L .24227 .34757 L .24242 .45005 L .2425 .4973 L .24258 .53976 L .24263 .55909 L .24267 .57377 L .24271 .5858 L .24275 .59416 L .24277 .59733 L .24279 .59995 L .2428 .60095 L .24281 .60183 L .24282 .60224 L .24283 .60256 L .24283 .60281 L .24284 .60302 L .24285 .60326 L .24286 .60332 L .24287 .60321 L .24287 .60307 L .24288 .60289 L .24289 .60243 L .24289 .60187 L .24291 .6001 L .24293 .59761 L Mistroke .24295 .59473 L .24299 .58622 L .24303 .57583 L .24307 .56393 L .24315 .53025 L .24323 .48421 L .24356 .25852 L .24372 .14886 L .2438 .10367 L .24388 .06933 L .24391 .05512 L .24395 .04194 L .24398 .03256 L .24402 .02444 L .24404 .02103 L .24406 .01848 L .24408 .0165 L .24409 .01571 L .2441 .01519 L .24411 .01489 L .24412 .01474 L .24413 .01473 L .24414 .01489 L .24415 .01524 L .24416 .01576 L .24417 .01637 L .24418 .01719 L .2442 .01927 L .24422 .0222 L .24425 .02929 L .2443 .04068 L .24434 .05379 L .24442 .09047 L .24451 .13445 L .24481 .3436 L .24498 .45975 L .24514 .54282 L .24522 .57244 L .24526 .58498 L .24528 .58984 L .2453 .59371 L .24532 .5968 L .24533 .5991 L .24535 .60107 L .24536 .60189 L .24537 .6025 L .24538 .60293 L .24539 .60321 L .2454 .60331 L .24541 .60328 L Mistroke .24542 .60306 L .24543 .60286 L .24543 .60263 L .24544 .60207 L .24545 .60131 L .24547 .59919 L .24549 .59652 L .24553 .58976 L .24557 .57998 L .24561 .56656 L .24569 .53544 L .24576 .4997 L .24607 .28877 L .24623 .17904 L .24637 .09543 L .24645 .06013 L .24653 .03542 L .24657 .02583 L .24659 .02227 L .24661 .01955 L .24662 .01826 L .24663 .01709 L .24664 .0163 L .24665 .01561 L .24666 .01533 L .24666 .01509 L .24667 .01489 L .24668 .01478 L .24668 .01472 L .24669 .01472 L .2467 .01487 L .24671 .01515 L .24672 .01562 L .24673 .01622 L .24673 .01691 L .24676 .01912 L .24678 .02191 L .24681 .02945 L .24686 .04062 L .24693 .06776 L .24701 .10051 L .24732 .3024 L .24748 .41479 L .24756 .46852 L .24765 .51798 L .24773 .55402 L .24777 .56946 L .24782 .58296 L .24786 .59243 L .24788 .59591 L Mistroke .2479 .59854 L .24792 .6006 L .24792 .60144 L .24794 .60219 L .24794 .60269 L .24795 .60302 L .24796 .60324 L .24797 .60332 L .24798 .60323 L .24799 .60299 L .248 .60254 L .24801 .60194 L .24803 .60043 L .24805 .59819 L .24807 .59499 L .24809 .59077 L .24813 .58111 L .24821 .55409 L .2483 .5136 L .24862 .30408 L .24877 .20037 L .24893 .10373 L .24902 .0637 L .24906 .04816 L .2491 .03651 L .24914 .02699 L .24918 .02047 L .2492 .01792 L .24922 .01622 L .24923 .01559 L .24924 .0153 L .24924 .01509 L .24925 .01492 L .24925 .01479 L .24926 .01473 L .24926 .01472 L .24927 .01481 L .24928 .01507 L .24929 .01548 L .2493 .01598 L .24932 .01762 L .24934 .02008 L .24936 .02319 L .24938 .02671 L .24942 .03688 L .2495 .06025 L .24957 .09336 L .24974 .19237 L .2499 .30416 L .25005 .40693 L Mistroke .25013 .46061 L .25021 .50524 L .2503 .54518 L .25037 .57332 L .25041 .58502 L .25045 .59352 L .25047 .59707 L .25049 .59966 L .25051 .60082 L .25052 .60171 L .25053 .60243 L .25053 .60273 L .25054 .60298 L .25055 .60324 L .25056 .60332 L .25057 .60324 L .25058 .60298 L .25059 .6026 L .2506 .60211 L .25062 .60056 L .25064 .59837 L .25066 .59522 L .2507 .58654 L .25074 .5752 L .25079 .55994 L .25087 .52494 L .25104 .4277 L .2512 .31695 L .25136 .20535 L .2515 .11706 L .25158 .07978 L .25166 .04806 L .25171 .03486 L .25173 .03008 L .25175 .02556 L .25177 .02222 L .25179 .01931 L .2518 .01801 L .25181 .01701 L .25182 .01618 L .25183 .01557 L .25184 .01516 L .25185 .01487 L .25186 .01472 L .25187 .01476 L .25188 .01494 L .25189 .01533 L .25189 .01559 L .2519 .01592 L .25191 .01666 L Mistroke .25193 .0186 L .25195 .02103 L .25198 .02715 L .25202 .037 L .25206 .04847 L .25215 .08235 L .2523 .16336 L .25246 .27363 L .25263 .39177 L .25279 .48837 L .25286 .52788 L .25295 .56255 L .25298 .57512 L .25302 .58606 L .25306 .59399 L .25308 .59688 L .2531 .5991 L .25312 .60104 L .25313 .60182 L .25314 .60248 L .25314 .60274 L .25315 .60297 L .25316 .60324 L .25317 .60332 L .25318 .60324 L .25319 .60303 L .2532 .60271 L .2532 .60223 L .25321 .60155 L .25323 .59969 L .25325 .5974 L .25329 .59028 L .25334 .57942 L .25342 .55181 L .2535 .51442 L .25358 .47355 L .25374 .365 L .25391 .24823 L .25406 .14883 L .25421 .0724 L .25429 .04482 L .25433 .03294 L .25435 .02822 L .25437 .02446 L .25439 .02134 L .25441 .01859 L .25443 .01656 L .25445 .01576 L .25445 .01548 L .25446 .01522 L Mistroke .25447 .0149 L .25448 .01473 L .25449 .01473 L .25449 .01487 L .2545 .0152 L .25451 .01566 L .25453 .01637 L .25454 .01723 L .25455 .01914 L .25457 .02176 L .25461 .02793 L .25464 .03666 L .25468 .04868 L .25477 .08001 L .25484 .11619 L .25501 .21764 L .25517 .33184 L .25532 .435 L .25547 .51914 L .25556 .55543 L .25563 .58009 L .25567 .58956 L .25569 .59371 L .25571 .59693 L .25573 .59932 L .25575 .60102 L .25575 .60174 L .25576 .60236 L .25577 .60285 L .25578 .60316 L .25579 .60331 L .2558 .60329 L .25581 .60321 L .25582 .60309 L .25582 .60291 L .25583 .60266 L .25584 .60204 L .25585 .60129 L .25587 .59893 L .25589 .59615 L .25591 .59304 L .25595 .5841 L .25599 .57327 L .25603 .55937 L .2561 .52857 L .25627 .43608 L .25657 .22938 L .25674 .12519 L .25682 .08513 L .2569 .05517 L Mistroke .25694 .04218 L .25697 .0325 L .25701 .02415 L .25704 .02067 L .25706 .01812 L .25708 .01645 L .25709 .01582 L .2571 .01529 L .2571 .01497 L .25711 .01477 L .25712 .01472 L .25713 .01477 L .25714 .015 L .25715 .01536 L .25716 .01591 L .25717 .01669 L .25719 .01842 L .25721 .02095 L .25725 .02827 L .25729 .03775 L .25736 .06188 L .25744 .09632 L .25753 .1425 L .25786 .35814 L .25801 .45604 L .25817 .54089 L .25821 .55821 L .25826 .57366 L .2583 .58521 L .25834 .5935 L .25836 .5966 L .25838 .59901 L .25839 .60011 L .2584 .60112 L .25841 .60187 L .25842 .60244 L .25843 .6029 L .25843 .60307 L .25844 .60321 L .25844 .60329 L .25845 .60332 L .25846 .6033 L .25846 .60322 L .25847 .60295 L .25848 .60273 L .25848 .60248 L .25849 .60186 L .2585 .60114 L .25852 .59931 L .25854 .59665 L Mistroke .25858 .58928 L .25862 .58079 L .25866 .56955 L .25874 .53624 L .25882 .49745 L .25914 .29301 L .2593 .18571 L .25945 .10322 L .25953 .06701 L .2596 .04097 L .25965 .03029 L .25968 .02287 L .25971 .01992 L .25973 .01744 L .25974 .01649 L .25975 .0157 L .25976 .0154 L .25976 .01516 L .25977 .01486 L .25978 .01473 L .25979 .01474 L .2598 .0149 L .25981 .01517 L .25982 .0156 L .25983 .01624 L .25985 .01806 L .25987 .02054 L .25989 .02393 L .25993 .03193 L .25997 .0424 L .26001 .05439 L .26008 .08203 L .26024 .16679 L .26039 .26273 L .26055 .37455 L .2607 .47074 L .26085 .54399 L .26089 .56031 L .26093 .57353 L .26097 .5841 L .26101 .59199 L .26104 .59787 L .26106 .60014 L .26107 .60107 L .26108 .60191 L .26109 .60254 L .2611 .60296 L .26111 .60312 L .26112 .60323 L .26112 .6033 L Mistroke .26113 .60332 L .26114 .60323 L .26115 .60301 L .26116 .60262 L .26117 .60203 L .26118 .60066 L .2612 .59865 L .26124 .5936 L .26128 .58528 L .26131 .57552 L .26139 .54813 L .26147 .51546 L .26163 .42093 L .26194 .21061 L .2621 .11632 L .26219 .07668 L .26223 .0587 L .26228 .04451 L .26232 .03325 L .26236 .02524 L .26238 .02189 L .2624 .01896 L .26241 .01767 L .26242 .01669 L .26243 .01594 L .26244 .01562 L .26244 .01533 L .26245 .01498 L .26246 .01479 L .26247 .01472 L .26248 .01479 L .26249 .015 L .2625 .01535 L .26251 .01582 L .26252 .01635 L .26254 .0181 L .26256 .02069 L .2626 .02726 L .26264 .03617 L .26267 .04655 L .26276 .07712 L .26293 .16385 L .26324 .36932 L .26339 .4687 L .26348 .5133 L .26357 .55234 L .26361 .56816 L .26365 .58051 L .26369 .5894 L .26371 .59314 L Mistroke .26373 .59659 L .26375 .59904 L .26377 .60105 L .26378 .60189 L .26379 .60249 L .2638 .60293 L .26381 .60319 L .26382 .60331 L .26383 .60329 L .26384 .60317 L .26385 .60292 L .26386 .60251 L .26387 .60191 L .26389 .60042 L .26391 .59816 L .26393 .59505 L .26397 .58765 L .26401 .57592 L .26405 .56262 L .26422 .49096 L .26437 .39887 L .26454 .28696 L .26469 .18462 L .26477 .13615 L .26486 .09124 L .26495 .05667 L .26503 .03365 L .26506 .0257 L .26508 .02236 L .26511 .01946 L .26512 .0175 L .26513 .01666 L .26514 .01593 L .26515 .01541 L .26516 .01506 L .26517 .01484 L .26518 .01473 L .26519 .01474 L .26519 .01482 L .2652 .01494 L .26521 .01526 L .26522 .01574 L .26523 .01631 L .26524 .01696 L .26526 .01883 L .26528 .02148 L .2653 .02447 L .26534 .03313 L .26541 .055 L .26548 .08286 L Mistroke .26564 .16517 L .26579 .25875 L .2661 .46275 L .26619 .5073 L .26628 .5474 L .26632 .56256 L .26636 .57612 L .2664 .58644 L .26644 .59376 L .26646 .59669 L .26648 .59928 L .2665 .60114 L .2665 .60178 L .26651 .60235 L .26652 .60281 L .26653 .60311 L .26654 .60322 L .26654 .60329 L .26655 .60331 L .26656 .60315 L .26657 .60286 L .26658 .60238 L .26659 .60167 L .26661 .60003 L .26663 .59764 L .26667 .59165 L .26671 .58383 L .26674 .57493 L .26682 .54834 L .26689 .5166 L .26706 .4247 L .26737 .21963 L .26753 .12604 L .26761 .08558 L .2677 .05152 L .26774 .04018 L .26778 .0302 L .2678 .02557 L .26782 .02204 L .26784 .01915 L .26786 .0171 L .26788 .01586 L .26789 .01536 L .2679 .01503 L .26791 .0148 L .26792 .01472 L .26793 .01479 L .26794 .01499 L .26795 .01533 L .26796 .01577 L Mistroke .26797 .01639 L .26798 .01721 L .268 .01939 L .26802 .02198 L .26805 .02873 L .2681 .03826 L .26817 .06122 L .26826 .09742 L .26833 .13746 L .26866 .3411 L .2688 .43558 L .26889 .48354 L .26896 .52265 L .26905 .55705 L .26912 .58065 L .26917 .59018 L .2692 .59686 L .26923 .59954 L .26925 .60138 L .26926 .6021 L .26927 .6027 L .26927 .60293 L .26928 .60311 L .26929 .60324 L .26929 .6033 L .2693 .6033 L .26931 .60315 L .26932 .6029 L .26933 .60249 L .26934 .6019 L .26935 .6011 L .26937 .59922 L .26941 .59445 L .26944 .58715 L .26948 .57691 L .26953 .56329 L .26961 .53227 L .26978 .44391 L .26994 .34158 L .27025 .14685 L .27033 .10459 L .2704 .07114 L .27045 .05562 L .27049 .04149 L .27053 .0312 L .27057 .0238 L .27059 .02095 L .27061 .01874 L .27062 .01773 L .27063 .01679 L Mistroke .27064 .0161 L .27065 .01557 L .27066 .01514 L .27066 .01497 L .27067 .01484 L .27067 .01475 L .27068 .01472 L .27069 .01473 L .27069 .01479 L .2707 .01501 L .27071 .0152 L .27071 .01542 L .27072 .01595 L .27073 .01659 L .27075 .01845 L .27077 .02109 L .27081 .02754 L .27085 .03691 L .2709 .05 L .27098 .08003 L .27106 .11422 L .27122 .20945 L .27154 .41668 L .27169 .49933 L .27177 .53776 L .27185 .56661 L .27189 .57759 L .27192 .58712 L .27194 .59126 L .27197 .5951 L .27199 .59794 L .27201 .60008 L .27202 .60104 L .27203 .60188 L .27204 .60248 L .27205 .6029 L .27206 .60318 L .27206 .60328 L .27207 .60332 L .27208 .60331 L .27208 .60326 L .27209 .60314 L .27209 .60298 L .2721 .60261 L .27211 .60205 L .27213 .60064 L .27215 .5983 L .27217 .59556 L .27221 .58855 L .27225 .57881 L Mistroke .27233 .55563 L .27241 .52311 L .2725 .47965 L .27282 .27691 L .27297 .18242 L .27313 .09605 L .27322 .0602 L .27326 .04746 L .2733 .03571 L .27334 .02697 L .27338 .02087 L .2734 .01838 L .27342 .01667 L .27343 .01598 L .27344 .0154 L .27345 .01517 L .27345 .01498 L .27346 .01485 L .27346 .01477 L .27347 .01472 L .27348 .01479 L .27349 .01501 L .2735 .0154 L .27351 .01566 L .27351 .01599 L .27352 .01671 L .27354 .0185 L .27356 .0207 L .27358 .02359 L .27362 .03018 L .27366 .04108 L .2737 .05382 L .27378 .08365 L .27394 .16496 L .27409 .25621 L .27425 .36348 L .27441 .45715 L .27455 .53129 L .27464 .56283 L .27471 .5841 L .27475 .59209 L .27477 .59558 L .27479 .59826 L .27481 .60023 L .27483 .60162 L .27484 .60222 L .27485 .60267 L .27485 .60302 L .27487 .60325 L .27487 .60331 L Mistroke .27488 .60332 L .27488 .60328 L .27489 .60321 L .2749 .60297 L .27491 .60257 L .27492 .60197 L .27493 .60124 L .27495 .59904 L .27497 .59649 L .27499 .59366 L .27503 .58555 L .27511 .56353 L .27518 .53608 L .27535 .453 L .27566 .25402 L .27582 .15813 L .27597 .08609 L .27604 .05718 L .27612 .03437 L .27616 .02584 L .2762 .02004 L .27622 .01766 L .27624 .0161 L .27625 .01549 L .27626 .01522 L .27627 .01502 L .27627 .01489 L .27628 .01479 L .27628 .01473 L .27629 .01472 L .2763 .01481 L .2763 .01492 L .27631 .01507 L .27632 .01545 L .27633 .01594 L .27635 .0175 L .27637 .01988 L .27639 .02261 L .27641 .0261 L .27645 .0339 L .27652 .05361 L .2766 .0824 L .27676 .15966 L .27692 .26173 L .27708 .36464 L .27725 .46829 L .27733 .50958 L .27742 .54644 L .27749 .57127 L .27753 .58165 L Mistroke .27757 .59074 L .27761 .59708 L .27763 .59962 L .27764 .6006 L .27765 .60139 L .27766 .602 L .27767 .60253 L .27768 .6029 L .27769 .60313 L .2777 .60328 L .27771 .60331 L .27772 .6032 L .27773 .60296 L .27774 .60256 L .27775 .60194 L .27777 .60036 L .27779 .59824 L .27781 .59578 L .27785 .58844 L .2779 .57803 L .27797 .55475 L .27805 .52218 L .2782 .44693 L .27853 .24 L .27869 .14341 L .27877 .10338 L .27884 .07247 L .27892 .04674 L .27895 .03732 L .27899 .02907 L .27901 .02558 L .27903 .02229 L .27905 .01978 L .27907 .01792 L .27909 .01627 L .2791 .01562 L .2791 .01537 L .27911 .01516 L .27912 .01488 L .27913 .01474 L .27913 .01472 L .27914 .01473 L .27915 .01487 L .27916 .01512 L .27917 .01553 L .27918 .01605 L .27918 .01663 L .27921 .01848 L .27923 .02081 L .27927 .02707 L Mistroke .27931 .03627 L .27939 .05869 L .27946 .08575 L .27961 .15935 L .27977 .25862 L .27994 .36625 L .28009 .45847 L .28024 .53258 L .28032 .56112 L .28036 .57417 L .2804 .58437 L .28044 .5923 L .28046 .59563 L .28048 .59851 L .2805 .60042 L .28051 .60124 L .28052 .60196 L .28053 .6025 L .28054 .60287 L .28055 .60313 L .28056 .60327 L .28056 .60331 L .28057 .60331 L .28058 .60322 L .28059 .60297 L .2806 .60276 L .2806 .60253 L .28062 .6014 L .28063 .60064 L .28064 .59967 L .28066 .59714 L .28068 .5937 L .28073 .58562 L .28081 .56341 L .2809 .5302 L .28106 .44983 L .28139 .24668 L .28155 .1509 L .28163 .11053 L .2817 .07875 L .28177 .05372 L .28185 .03309 L .28189 .02496 L .28191 .02184 L .28193 .0195 L .28194 .01756 L .28196 .01619 L .28197 .01562 L .28198 .01523 L .28199 .01492 L Mistroke .282 .01475 L .28201 .01472 L .28202 .01477 L .28202 .01485 L .28203 .01509 L .28204 .01547 L .28205 .01593 L .28206 .01646 L .28208 .01803 L .2821 .02027 L .28212 .02282 L .28216 .03029 L .28223 .04823 L .28231 .07388 L .28246 .14698 L .28261 .23211 L .28292 .42693 L .28308 .51111 L .28317 .54863 L .28322 .5634 L .28326 .57525 L .28329 .58479 L .28333 .59182 L .28337 .5977 L .28339 .60006 L .2834 .601 L .28341 .60171 L .28342 .60228 L .28343 .60276 L .28344 .60296 L .28344 .6031 L .28345 .60328 L .28346 .60332 L .28347 .60324 L .28348 .60302 L .28349 .60269 L .2835 .60214 L .28351 .60146 L .28353 .59979 L .28355 .5974 L .28357 .5941 L .28361 .58697 L .28365 .5785 L .28373 .55307 L .28381 .52076 L .2839 .47878 L .28423 .28095 L .2844 .18108 L .28455 .10228 L .28462 .07095 L Mistroke .2847 .04721 L .28474 .03671 L .28478 .02758 L .2848 .0243 L .28482 .02135 L .28483 .01925 L .28485 .01741 L .28486 .01659 L .28487 .01596 L .28488 .01547 L .28489 .01509 L .2849 .01484 L .28491 .01473 L .28492 .01472 L .28493 .01482 L .28494 .01506 L .28494 .01525 L .28495 .01546 L .28496 .01601 L .28497 .01676 L .28499 .01856 L .28501 .02067 L .28505 .02611 L .28509 .03393 L .28516 .05309 L .28523 .0799 L .28532 .11635 L .28548 .20734 L .28581 .40665 L .28595 .48847 L .28603 .52489 L .28612 .55701 L .28616 .57138 L .2862 .58221 L .28625 .59091 L .28629 .59704 L .28631 .59932 L .28633 .60117 L .28634 .6023 L .28635 .60276 L .28636 .60306 L .28637 .60318 L .28637 .60327 L .28638 .60332 L .28639 .60323 L .2864 .60303 L .28641 .60269 L .28642 .60215 L .28644 .60142 L .28645 .60058 L Mistroke .28648 .59642 L .28651 .59325 L .28653 .58976 L .28661 .56985 L .28668 .54606 L .28676 .51456 L .28709 .32815 L .28725 .22499 L .28741 .1389 L .28756 .07232 L .28763 .04743 L .28768 .03632 L .28772 .02784 L .28776 .02162 L .28778 .01897 L .2878 .01708 L .28781 .01637 L .28782 .01582 L .28782 .01542 L .28783 .01509 L .28784 .01485 L .28785 .01473 L .28786 .01473 L .28787 .01486 L .28788 .01498 L .28788 .01516 L .28789 .0156 L .2879 .01617 L .28791 .01682 L .28794 .01875 L .28796 .02148 L .288 .02754 L .28804 .03638 L .28812 .05935 L .28819 .08685 L .28836 .1676 L .28868 .35927 L .28884 .45282 L .28898 .52377 L .28907 .55491 L .28914 .57769 L .28918 .58727 L .28922 .59416 L .28924 .59723 L .28926 .59953 L .28929 .60136 L .2893 .60209 L .28931 .60268 L .28932 .60302 L .28932 .60315 L Mistroke .28933 .60324 L .28934 .60332 L .28935 .6033 L .28935 .60324 L .28936 .60305 L .28937 .60273 L .28938 .60225 L .28939 .60167 L .28941 .59988 L .28943 .59768 L .28948 .59081 L .28952 .58271 L .28956 .57176 L .28964 .54642 L .2898 .47603 L .28997 .38145 L .29027 .19734 L .29044 .10978 L .29052 .07636 L .29059 .0512 L .29067 .03188 L .29071 .02451 L .29073 .02152 L .29075 .0189 L .29077 .01698 L .29078 .01632 L .29079 .01573 L .2908 .01529 L .29081 .015 L .29082 .0148 L .29083 .01472 L .29084 .01476 L .29085 .01493 L .29086 .01522 L .29087 .01558 L .29089 .01655 L .2909 .01797 L .29092 .01995 L .29094 .02253 L .29098 .02842 L .29102 .03653 L .29106 .04744 L .29121 .1004 L .29136 .1787 L .29153 .27745 L .29169 .37506 L .29186 .4722 L .29194 .51112 L .29203 .54598 L .2921 .56978 L Mistroke .29214 .57989 L .29218 .58892 L .2922 .59275 L .29222 .59578 L .29224 .59838 L .29226 .60027 L .29227 .601 L .29228 .60169 L .29229 .60218 L .2923 .60262 L .29231 .60297 L .29232 .60321 L .29233 .60331 L .29234 .6033 L .29235 .60316 L .29235 .60302 L .29236 .60285 L .29237 .60244 L .29238 .60187 L .2924 .60054 L .29242 .59858 L .29246 .59244 L .29251 .58446 L .29259 .56249 L .29267 .53457 L .29282 .46643 L .29312 .28794 L .29329 .18732 L .29345 .1089 L .29352 .07693 L .29361 .04911 L .29365 .03893 L .29369 .03004 L .29372 .02402 L .29376 .01911 L .29378 .01725 L .29379 .01648 L .2938 .01581 L .29381 .01535 L .29382 .01516 L .29382 .01499 L .29383 .01479 L .29384 .01472 L .29385 .01475 L .29386 .0149 L .29387 .01519 L .29388 .01558 L .2939 .01657 L .29392 .01805 L .29394 .02032 L Mistroke .29396 .02344 L .294 .03082 L .29408 .05039 L .29416 .07551 L .29424 .10972 L .29441 .19567 L .29473 .38811 L .29488 .47007 L .29504 .54202 L .29513 .57062 L .29517 .58149 L .29521 .5895 L .29523 .59282 L .29525 .5959 L .29527 .59814 L .29529 .60014 L .29531 .60174 L .29532 .60238 L .29533 .60263 L .29533 .60283 L .29534 .60311 L .29535 .60327 L .29536 .60332 L .29537 .60329 L .29537 .60323 L .29538 .60304 L .29539 .60272 L .2954 .60234 L .29541 .60183 L .29543 .6003 L .29545 .5984 L .29549 .59379 L .29552 .58723 L .29561 .56582 L .29569 .53934 L .29584 .4709 L .29601 .37896 L .29634 .1854 L .2965 .1045 L .29658 .07277 L .29665 .0493 L .29669 .03981 L .29673 .03114 L .29676 .02509 L .2968 .01999 L .29682 .01793 L .29684 .01645 L .29685 .01583 L .29686 .01538 L .29687 .01502 L Mistroke .29687 .01489 L .29688 .01479 L .29689 .01472 L .2969 .01475 L .29691 .01492 L .29692 .0152 L .29693 .01557 L .29694 .016 L .29696 .01729 L .29697 .01906 L .29699 .0211 L .29703 .02707 L .29707 .0343 L .29711 .04264 L .29718 .06623 L .29727 .09914 L .2976 .27115 L .29791 .45274 L .29799 .49365 L .29808 .53199 L .29816 .55926 L .2982 .57125 L .29824 .58209 L .29828 .59067 L .29832 .5966 L .29834 .5988 L .29836 .6007 L .29837 .6014 L .29838 .60202 L .29839 .60247 L .2984 .60284 L .29841 .60313 L .29842 .60328 L .29843 .60332 L .29844 .60328 L .29844 .60321 L .29845 .60299 L .29846 .60269 L .29847 .60223 L .29848 .60167 L .2985 .59998 L .29852 .5979 L .29857 .59138 L .29861 .58425 L .29865 .57482 L .29872 .55336 L .29889 .48568 L .29922 .30113 L .29938 .20488 L .29953 .12581 L Mistroke .29968 .06588 L .29977 .04162 L .2998 .03342 L .29984 .02611 L .29988 .02058 L .2999 .01832 L .29992 .01671 L .29993 .0161 L .29994 .01562 L .29995 .01528 L .29996 .015 L .29997 .0148 L .29998 .01472 L .29998 .01474 L .29999 .01488 L .3 .015 L .30001 .01517 L .30002 .01558 L .30003 .01612 L .30004 .01672 L .30006 .0185 L .30008 .021 L .30012 .02722 L .30016 .03464 L .30024 .05538 L .30031 .08034 L .30048 .15425 L .3008 .33342 L .3011 .49737 L .30118 .53121 L .30126 .55797 L .3013 .5703 L .30134 .5816 L .30139 .58984 L .30142 .59582 L .30144 .59798 L .30146 .59986 L .30148 .60145 L .30149 .60205 L .3015 .60249 L .30151 .60287 L .30151 .60303 L .30152 .60315 L .30153 .60328 L .30154 .60332 L .30154 .60329 L .30155 .60322 L .30156 .6031 L .30156 .60296 L .30157 .6026 L Mistroke .30158 .60209 L .3016 .60065 L .30163 .59847 L .30167 .59284 L .30171 .58535 L .30175 .57667 L .30184 .55213 L .30191 .52262 L .30206 .45361 L .30237 .27826 L .30253 .18956 L .3027 .10598 L .30278 .07502 L .30286 .04833 L .30291 .03803 L .30294 .02995 L .30298 .02412 L .30302 .01936 L .30304 .01762 L .30305 .01687 L .30306 .0162 L .30307 .01571 L .30308 .01529 L .30308 .015 L .30309 .01483 L .3031 .01476 L .3031 .01472 L .30311 .01475 L .30312 .01489 L .30313 .01512 L .30314 .01549 L .30315 .01602 L .30318 .01752 L .3032 .01957 L .30322 .02192 L .30326 .02887 L .3033 .03733 L .30334 .04708 L .3035 .1019 L .30365 .17119 L .30396 .34911 L .30412 .43841 L .30421 .48062 L .3043 .5199 L .30438 .54967 L .30442 .56303 L .30446 .57533 L .30451 .58476 L .30454 .59171 L .30456 .59449 L Mistroke .30458 .59708 L .3046 .59913 L .30462 .60065 L .30464 .60192 L .30465 .60245 L .30466 .60283 L .30467 .60309 L .30467 .60324 L .30468 .60332 L .30469 .60329 L .3047 .60322 L .3047 .60313 L .30471 .60299 L .30472 .6028 L .30473 .60239 L .30474 .60181 L .30476 .60036 L .30478 .59858 L .30482 .59314 L .30486 .58643 L .30495 .56546 L .30502 .53975 L .3051 .51089 L .30526 .43103 L .30558 .25256 L .30574 .16692 L .30588 .10022 L .30595 .07233 L .30604 .04758 L .30607 .03791 L .30612 .02938 L .30614 .02548 L .30616 .02245 L .30618 .02007 L .3062 .01795 L .30622 .01646 L .30623 .01591 L .30624 .01548 L .30625 .01511 L .30626 .01488 L .30627 .01474 L .30628 .01472 L .30628 .01473 L .30629 .01483 L .3063 .01502 L .30631 .01527 L .30632 .01563 L .30634 .01675 L .30636 .01817 L .30639 .02243 L Mistroke .30644 .02899 L .30648 .0379 L .30652 .04806 L .30669 .10423 L .30683 .17366 L .30715 .35247 L .3073 .43287 L .30746 .50955 L .30754 .53937 L .30762 .56572 L .30766 .57745 L .30771 .58635 L .30775 .59314 L .30777 .59611 L .30779 .59845 L .30781 .60025 L .30782 .60103 L .30783 .60174 L .30784 .60223 L .30785 .60266 L .30786 .60296 L .30786 .60316 L .30787 .6033 L .30788 .60331 L .30789 .60322 L .3079 .60303 L .30791 .60289 L .30791 .60269 L .30792 .6022 L .30795 .60095 L .30796 .59936 L .30798 .59756 L .30802 .59226 L .30806 .5862 L .30809 .57844 L .30817 .55792 L .30825 .52991 L .3084 .46598 L .30873 .28444 L .3089 .19253 L .30905 .11826 L .3092 .06214 L .30927 .04143 L .30932 .03224 L .30936 .02526 L .30939 .02019 L .30942 .01804 L .30944 .01653 L .30945 .01596 L .30946 .01553 L Mistroke .30946 .01522 L .30947 .01497 L .30948 .01479 L .30949 .01472 L .3095 .01475 L .30951 .01488 L .30952 .01499 L .30952 .01516 L .30953 .01555 L .30954 .01605 L .30955 .01662 L .30957 .01829 L .3096 .02062 L .30964 .02577 L .30968 .03326 L .30976 .05267 L .30983 .07597 L .31 .1451 L .31032 .31565 L .31062 .47798 L .31078 .54216 L .31087 .5691 L .31095 .58713 L .31099 .59354 L .31101 .59638 L .31103 .5986 L .31105 .60027 L .31106 .60148 L .31108 .60247 L .31109 .60285 L .3111 .60311 L .31111 .60328 L .31112 .60332 L .31113 .6033 L .31113 .60325 L .31114 .60306 L .31115 .60277 L .31116 .60236 L .31118 .60135 L .3112 .59969 L .31122 .59771 L .31127 .59162 L .31131 .58443 L .31135 .57475 L .31143 .55244 L .31158 .49599 L .31191 .32695 L .31207 .23605 L .31222 .15713 L .31238 .09001 L Mistroke .31245 .06368 L .31252 .04393 L .3126 .02797 L .31264 .02201 L .31266 .01944 L .31269 .01758 L .3127 .01628 L .31272 .01543 L .31273 .01512 L .31274 .01487 L .31275 .01474 L .31276 .01472 L .31277 .0148 L .31278 .01496 L .31279 .01517 L .3128 .01548 L .31282 .01647 L .31283 .01773 L .31287 .02143 L .31291 .02703 L .31298 .0413 L .31307 .06485 L .31315 .09223 L .31346 .24362 L .31377 .41157 L .31394 .49383 L .31409 .55217 L .31417 .57374 L .31421 .58285 L .31425 .59072 L .31429 .59607 L .31431 .59832 L .31433 .60027 L .31435 .60165 L .31437 .60254 L .31438 .60285 L .31439 .6031 L .3144 .60325 L .31441 .60331 L .31442 .60329 L .31442 .60324 L .31443 .60315 L .31444 .6029 L .31445 .60257 L .31446 .60207 L .31447 .60149 L .31449 .59981 L .31451 .59792 L .31453 .59542 L .31457 .58968 L Mistroke .31465 .57373 L .31472 .55393 L .31487 .49861 L .31503 .4204 L .31536 .24478 L .3155 .16808 L .31567 .09699 L .31574 .0695 L .31583 .04582 L .31587 .03543 L .31591 .02778 L .31596 .02182 L .31598 .01957 L .316 .01784 L .31601 .01657 L .31602 .01604 L .31603 .01557 L .31604 .01534 L .31604 .01517 L .31605 .01491 L .31606 .01476 L .31607 .01472 L .31608 .01477 L .31609 .01493 L .3161 .0152 L .31611 .01553 L .31612 .01599 L .31613 .01662 L .31616 .01828 L .31619 .02215 L .31623 .02781 L .3163 .04192 L .31639 .06397 L .31647 .0944 L .31664 .16413 L .31696 .33789 L .31713 .42435 L .31728 .49582 L .31742 .55017 L .31751 .57307 L .31758 .58863 L .31762 .59445 L .31764 .59704 L .31766 .59907 L .31768 .60061 L .31769 .60128 L .3177 .60189 L .31771 .60232 L .31772 .6027 L .31772 .60297 L Mistroke .31773 .60315 L .31774 .60329 L .31775 .60332 L .31775 .60331 L .31776 .60323 L .31777 .60303 L .31778 .60276 L .31779 .60242 L .31781 .60135 L .31783 .59975 L .31785 .59787 L .3179 .59221 L .31794 .58584 L .31798 .57751 L .31805 .55869 L .31822 .49958 L .31855 .33446 L .31887 .16593 L .31901 .10211 L .3191 .07237 L .31918 .04965 L .31925 .03257 L .3193 .02541 L .31933 .02044 L .31936 .01837 L .31938 .01687 L .31939 .01619 L .3194 .01567 L .3194 .01543 L .31941 .01521 L .31942 .01505 L .31942 .01492 L .31943 .01477 L .31944 .01473 L .31944 .01472 L .31945 .01474 L .31945 .01479 L .31946 .01497 L .31947 .01524 L .31948 .01557 L .3195 .01663 L .31952 .01802 L .31954 .01963 L .31958 .02438 L .31962 .02987 L .31965 .03692 L .31973 .05609 L .31982 .08313 L .31997 .14661 L .32014 .22909 L Mistroke .32048 .40653 L .32064 .48589 L .32072 .51586 L .3208 .54444 L .32087 .56577 L .32095 .58359 L .32099 .59107 L .32103 .59637 L .32105 .59839 L .32107 .6002 L .32109 .60153 L .3211 .60244 L .32111 .60279 L .32112 .60306 L .32113 .60322 L .32114 .60331 L .32115 .60331 L .32116 .60326 L .32116 .6032 L .32117 .603 L .32118 .60272 L .32119 .60238 L .3212 .60194 L .32122 .60093 L .32123 .59955 L .32125 .59766 L .32129 .59252 L .32134 .58522 L .32142 .56748 L .3215 .54384 L .32159 .51221 L .32175 .4417 L .32207 .27165 L .32239 .11959 L .32247 .08801 L .32256 .05949 L .32264 .0386 L .32268 .03078 L .32272 .02497 L .32276 .02036 L .32278 .0184 L .3228 .01693 L .32281 .01639 L .32282 .0159 L .32282 .01554 L .32283 .01523 L .32284 .01498 L .32285 .01482 L .32286 .01472 L .32287 .01473 L Mistroke .32288 .01482 L .32289 .01503 L .3229 .01531 L .32291 .01565 L .32293 .0168 L .32295 .0183 L .32299 .02249 L .32304 .02879 L .32311 .04381 L .32319 .0661 L .32336 .1274 L .32369 .28572 L .324 .44588 L .32416 .51384 L .32424 .54328 L .32433 .56874 L .32437 .57906 L .32441 .58715 L .32446 .5935 L .32449 .59795 L .32451 .59966 L .32453 .60096 L .32455 .60202 L .32456 .60245 L .32457 .60282 L .32458 .60308 L .32458 .60319 L .32459 .60326 L .3246 .60332 L .32461 .60328 L .32462 .60315 L .32463 .60296 L .32464 .60267 L .32465 .60226 L .32467 .60115 L .32469 .59953 L .32473 .59552 L .32477 .58892 L .32482 .58124 L .3249 .56161 L .32498 .53798 L .32528 .40622 L .32561 .23545 L .32578 .15627 L .32593 .09401 L .326 .06895 L .32608 .04922 L .32611 .04012 L .32616 .03175 L .32619 .02596 L Mistroke .32623 .02104 L .32625 .01904 L .32627 .01753 L .32629 .01639 L .32631 .0155 L .32632 .01517 L .32632 .01502 L .32633 .01491 L .32634 .01477 L .32635 .01472 L .32635 .01472 L .32636 .01476 L .32637 .01489 L .32637 .01501 L .32638 .01514 L .32639 .01555 L .3264 .01601 L .32641 .01662 L .32643 .01806 L .32647 .0218 L .32652 .02792 L .32656 .03522 L .32664 .05462 L .32672 .07818 L .32687 .13423 L .32718 .28385 L .32751 .44977 L .32767 .51796 L .32775 .54516 L .32783 .56581 L .3279 .58271 L .32794 .58884 L .32797 .59418 L .32799 .59643 L .32801 .59855 L .32803 .60015 L .32805 .60134 L .32807 .60238 L .32808 .60277 L .32808 .60293 L .32809 .60307 L .3281 .60324 L .32811 .60331 L .32811 .60332 L .32812 .6033 L .32813 .6032 L .32814 .60302 L .32815 .60273 L .32816 .60239 L .32817 .602 L Mistroke .32819 .60076 L .32821 .59922 L .32825 .59509 L .32829 .58901 L .32837 .57417 L .32844 .55607 L .32859 .50585 L .32875 .43478 L .32907 .27217 L .32938 .12619 L .32954 .06928 L .32962 .04759 L .32967 .03765 L .32971 .02985 L .32975 .02408 L .32977 .02159 L .32979 .01936 L .32981 .01783 L .32983 .01649 L .32984 .01602 L .32985 .01559 L .32986 .01529 L .32987 .01504 L .32987 .01491 L .32988 .01483 L .32989 .01473 L .3299 .01472 L .3299 .01474 L .32991 .01479 L .32991 .01486 L .32992 .01507 L .32993 .01523 L .32993 .0154 L .32995 .01585 L .32996 .01639 L .32998 .01768 L .32999 .01918 L .33004 .02366 L .33007 .02889 L .33011 .036 L .3302 .05459 L .33034 .10081 L .33066 .24398 L .33097 .40107 L .33113 .47338 L .33121 .50694 L .3313 .53816 L .33139 .56318 L .33147 .58097 L .33151 .58777 L Mistroke .33155 .59378 L .33159 .59813 L .3316 .59973 L .33162 .60098 L .33163 .60154 L .33164 .60207 L .33165 .60247 L .33166 .60277 L .33167 .60304 L .33167 .60315 L .33168 .60323 L .33169 .60331 L .3317 .60331 L .33171 .60323 L .33172 .60307 L .33173 .60282 L .33174 .6025 L .33175 .60174 L .33177 .60064 L .33179 .59898 L .33182 .59672 L .33186 .59143 L .33194 .57751 L .33201 .55946 L .33209 .53463 L .33226 .47073 L .33259 .31597 L .3329 .16469 L .33305 .10106 L .33314 .07337 L .33322 .04922 L .33327 .0394 L .33331 .03159 L .33335 .02538 L .33339 .02089 L .33343 .01775 L .33344 .01658 L .33346 .01563 L .33347 .01526 L .33348 .01501 L .33349 .0149 L .33349 .01481 L .3335 .01472 L .33351 .01473 L .33352 .01482 L .33353 .01497 L .33354 .01521 L .33355 .01554 L .33356 .01592 L .33358 .01704 L Mistroke .3336 .01848 L .33362 .02041 L .33366 .02489 L .3337 .03006 L .33378 .04688 L .33386 .06801 L .33402 .1229 L .33417 .186 L .33449 .34104 L .33479 .48184 L .33495 .53835 L .33503 .56321 L .33511 .58101 L .33515 .58775 L .33519 .59364 L .33523 .59793 L .33526 .60074 L .33528 .60139 L .33529 .60197 L .3353 .60239 L .33531 .60275 L .33531 .60291 L .33532 .60304 L .33533 .60322 L .33533 .60328 L .33534 .60331 L .33534 .60332 L .33535 .60329 L .33536 .60319 L .33537 .60302 L .33538 .60276 L .33539 .60238 L .33541 .60132 L .33543 .59999 L .33547 .59653 L .33551 .5915 L .33558 .57908 L .33567 .5589 L .33575 .53585 L .33607 .406 L .33638 .25433 L .33653 .18063 L .3367 .11015 L .33678 .08313 L .33687 .05858 L .33695 .04009 L .33702 .02746 L .33706 .0225 L .33708 .0203 L .3371 .01855 L Mistroke .33712 .01722 L .33714 .01609 L .33715 .0157 L .33716 .01536 L .33716 .01512 L .33717 .01493 L .33718 .01484 L .33718 .01477 L .33719 .01472 L .3372 .01475 L .33721 .01487 L .33722 .01507 L .33723 .01523 L .33723 .0154 L .33726 .0164 L .33728 .01764 L .3373 .01906 L .33734 .0233 L .33738 .02842 L .33742 .03516 L .33749 .05049 L .33766 .09927 L .33783 .16661 L .33799 .24085 L .3383 .39151 L .33845 .46193 L .33863 .52698 L .3387 .55111 L .33879 .57229 L .33883 .58068 L .33887 .58745 L .33891 .59288 L .33894 .59696 L .33898 .60015 L .339 .6014 L .33901 .60192 L .33902 .6024 L .33903 .60277 L .33904 .60303 L .33904 .60314 L .33905 .60321 L .33906 .60328 L .33906 .60331 L .33907 .60331 L .33908 .60324 L .33909 .60308 L .3391 .60283 L .33911 .60253 L .33912 .6022 L .33914 .60126 L Mistroke .33915 .60013 L .33917 .59882 L .33921 .59511 L .33925 .58983 L .33933 .57504 L .33941 .55728 L .33957 .50397 L .33989 .36458 L .3402 .21557 L .34036 .14698 L .34053 .0845 L .34061 .06157 L .3407 .04175 L .34074 .034 L .34078 .02784 L .34081 .02299 L .34085 .01944 L .34087 .01792 L .34089 .01678 L .3409 .01581 L .34091 .01542 L .34093 .0151 L .34094 .0149 L .34095 .01476 L .34096 .01472 L .34097 .01474 L .34097 .01479 L .34098 .01486 L .34098 .01495 L .34099 .01508 L .341 .01536 L .34101 .01576 L .34103 .0167 L .34104 .01781 L .34108 .0212 L .34112 .02543 L .34116 .0304 L .34123 .04468 L .34131 .06454 L .34146 .11111 L .34176 .23887 L .34209 .39248 L .34239 .51908 L .34255 .56536 L .34264 .58214 L .34268 .58956 L .34272 .59507 L .34276 .59901 L .34279 .60067 L .34281 .60185 L Mistroke .34283 .6026 L .34284 .60291 L .34285 .60312 L .34286 .60326 L .34287 .60332 L .34287 .60332 L .34288 .60329 L .34289 .60319 L .3429 .603 L .34291 .60275 L .34292 .6021 L .34294 .60113 L .34296 .59975 L .343 .59643 L .34304 .59244 L .34311 .58008 L .34319 .56459 L .34335 .51647 L .34366 .38896 L .34399 .23248 L .34416 .15972 L .34431 .10193 L .34446 .05799 L .34454 .0412 L .34458 .0338 L .34462 .02729 L .34466 .02253 L .34468 .02046 L .3447 .0186 L .34472 .0172 L .34474 .0162 L .34475 .01581 L .34476 .01545 L .34477 .0152 L .34478 .01499 L .34479 .01482 L .3448 .01473 L .3448 .01472 L .34481 .01473 L .34482 .01481 L .34482 .01489 L .34483 .01499 L .34484 .01524 L .34485 .01565 L .34486 .01611 L .34488 .01718 L .3449 .01867 L .34494 .02225 L .34498 .02705 L .34502 .03256 L Mistroke .3451 .04866 L .34518 .06888 L .34527 .09509 L .3456 .22769 L .34592 .37705 L .34623 .50443 L .34639 .55348 L .34647 .57241 L .34651 .58121 L .34656 .58826 L .34659 .59348 L .34664 .59793 L .34666 .59947 L .34668 .60083 L .34669 .60184 L .34671 .60253 L .34672 .60285 L .34673 .60299 L .34673 .6031 L .34674 .60324 L .34675 .60331 L .34676 .60332 L .34676 .6033 L .34677 .60321 L .34678 .60312 L .34679 .60302 L .3468 .60271 L .34681 .60239 L .34682 .60202 L .34684 .60095 L .34686 .5996 L .34688 .59782 L .34692 .59366 L .34696 .58877 L .34704 .5741 L .34712 .55527 L .34721 .53058 L .34754 .40272 L .34786 .25516 L .34817 .12583 L .34833 .07424 L .34841 .05368 L .34849 .03581 L .34854 .0292 L .34858 .02405 L .34861 .02037 L .34865 .0174 L .34867 .0162 L .34869 .01541 L .3487 .0151 L Mistroke .34871 .01497 L .34872 .01487 L .34873 .01475 L .34873 .01472 L .34874 .01472 L .34875 .01476 L .34876 .01488 L .34876 .01497 L .34877 .0151 L .34878 .01538 L .3488 .01616 L .34882 .01715 L .34885 .01986 L .34889 .0239 L .34897 .03406 L .34905 .05078 L .34913 .07026 L .34945 .1818 L .34975 .31854 L .35008 .46071 L .35023 .51526 L .35039 .56143 L .35048 .57998 L .35052 .58648 L .35056 .59243 L .3506 .59688 L .35064 .59999 L .35066 .60128 L .35068 .60218 L .35069 .60256 L .3507 .60289 L .35071 .60301 L .35071 .60312 L .35072 .60325 L .35073 .60331 L .35074 .60331 L .35075 .60323 L .35076 .60309 L .35077 .60289 L .35078 .60267 L .3508 .60198 L .35082 .60097 L .35084 .59955 L .35088 .59614 L .35092 .59196 L .35096 .5865 L .35103 .57416 L .35118 .53558 L .35133 .48734 L .35164 .35859 L Mistroke .35197 .21036 L .35213 .14362 L .35229 .09121 L .35244 .05205 L .35252 .03588 L .35259 .02506 L .35263 .02092 L .35265 .0191 L .35267 .01769 L .35269 .01662 L .35271 .01586 L .35272 .01553 L .35273 .01523 L .35274 .01499 L .35275 .01484 L .35276 .01474 L .35277 .01472 L .35277 .01473 L .35278 .01477 L .35278 .01482 L .35279 .01491 L .3528 .01513 L .35281 .01541 L .35282 .01581 L .35283 .01633 L .35285 .01751 L .35288 .01892 L .35291 .02233 L .35295 .02658 L .35299 .03232 L .35307 .04719 L .35322 .08413 L .35338 .13544 L .35354 .20138 L .35387 .34754 L .35419 .4794 L .35435 .53253 L .3545 .56915 L .35458 .58415 L .35466 .59442 L .3547 .59843 L .35474 .60107 L .35476 .60205 L .35477 .60248 L .35478 .6028 L .35479 .60295 L .35479 .60306 L .3548 .60322 L .35481 .60327 L .35481 .60331 L Mistroke .35482 .60332 L .35482 .60331 L .35483 .60324 L .35484 .60311 L .35485 .60289 L .35486 .60263 L .35488 .60199 L .3549 .60109 L .35494 .59815 L .35498 .59444 L .35506 .58439 L .35513 .57162 L .35529 .53186 L .35544 .48362 L .35575 .35517 L .35605 .22179 L .35622 .15376 L .35638 .10038 L .35645 .07793 L .35654 .05698 L .35662 .04092 L .35669 .0292 L .35673 .02432 L .35676 .02071 L .3568 .01769 L .35683 .01652 L .35684 .016 L .35685 .0156 L .35686 .0153 L .35687 .01505 L .35687 .01494 L .35688 .01486 L .35689 .01475 L .3569 .01472 L .35691 .01474 L .35692 .01483 L .35693 .01498 L .35693 .01509 L .35694 .01524 L .35695 .01556 L .35697 .01637 L .35699 .01766 L .35702 .01918 L .35706 .02283 L .3571 .02796 L .35718 .04036 L .35726 .0561 L .35733 .07358 L .35765 .17973 L .35795 .30862 L Mistroke .35827 .44502 L .35842 .49911 L .35858 .54722 L .35867 .56777 L .35875 .58282 L .35883 .59345 L .35887 .59738 L .35889 .59905 L .35892 .60057 L .35894 .60165 L .35896 .60241 L .35897 .60274 L .35898 .60297 L .35898 .60307 L .35899 .60316 L .359 .60328 L .35901 .60332 L .35902 .6033 L .35903 .60322 L .35904 .60309 L .35904 .6029 L .35905 .60269 L .35907 .60206 L .35909 .60106 L .35911 .59988 L .35916 .59628 L .3592 .59208 L .35924 .58655 L .35932 .57257 L .35941 .55309 L .35957 .50738 L .3599 .38342 L .36022 .24778 L .36052 .12949 L .36068 .0812 L .36076 .05937 L .36085 .04281 L .36093 .02976 L .36097 .02447 L .36102 .0201 L .36103 .01865 L .36106 .01734 L .36107 .01642 L .36109 .01565 L .3611 .01529 L .36111 .01503 L .36113 .01486 L .36113 .01479 L .36114 .01475 L .36115 .01472 L Mistroke .36115 .01472 L .36116 .01475 L .36117 .01484 L .36118 .015 L .36119 .01521 L .3612 .01551 L .36122 .01623 L .36124 .01716 L .36125 .01821 L .36129 .02128 L .36133 .02559 L .3614 .03508 L .36148 .04883 L .36164 .0861 L .3618 .13877 L .36213 .26813 L .36245 .40147 L .36275 .51176 L .36291 .55445 L .363 .57299 L .36308 .58617 L .36312 .59126 L .36316 .59569 L .36319 .59869 L .36323 .60112 L .36325 .6021 L .36327 .60274 L .36328 .603 L .36329 .60311 L .3633 .60319 L .36331 .60329 L .36331 .60331 L .36332 .60332 L .36333 .60328 L .36334 .60319 L .36335 .60302 L .36336 .60277 L .36338 .60219 L .3634 .60131 L .36342 .60019 L .36344 .5987 L .36348 .59526 L .36355 .58632 L .36364 .57188 L .36372 .5549 L .36387 .51487 L .36404 .45996 L .36436 .33205 L .36467 .20436 L .36483 .14583 L Mistroke .365 .09136 L .36508 .0704 L .36516 .05141 L .36524 .03701 L .36532 .02682 L .36536 .02254 L .3654 .01902 L .36542 .01769 L .36544 .01654 L .36545 .016 L .36546 .01559 L .36547 .01528 L .36549 .01502 L .3655 .01486 L .3655 .0148 L .36551 .01475 L .36552 .01472 L .36553 .01473 L .36553 .01476 L .36554 .01482 L .36554 .01489 L .36555 .01498 L .36556 .01519 L .36557 .01548 L .36559 .01624 L .36561 .0172 L .36565 .01963 L .36568 .02282 L .36573 .02724 L .36581 .039 L .36588 .05315 L .36596 .06907 L .36627 .16391 L .3666 .29392 L .36691 .42223 L .36722 .52481 L .36738 .56332 L .36746 .57957 L .36754 .59078 L .36758 .59499 L .36762 .59851 L .36766 .60076 L .36768 .60173 L .3677 .60242 L .36771 .60272 L .36772 .60298 L .36773 .60308 L .36773 .60316 L .36774 .60326 L .36775 .60331 L Mistroke .36776 .60331 L .36777 .60326 L .36778 .60315 L .36779 .60297 L .3678 .6027 L .36781 .60235 L .36782 .60194 L .36785 .60096 L .36787 .59983 L .36791 .59682 L .36795 .59254 L .36803 .58209 L .3681 .56969 L .36818 .55372 L .36848 .46553 L .3688 .34234 L .36912 .21756 L .36927 .15919 L .36945 .10381 L .36961 .06154 L .36968 .04671 L .36976 .03373 L .36981 .02792 L .36985 .02349 L .36989 .0201 L .36991 .01868 L .36993 .01741 L .36995 .01646 L .36997 .01577 L .36997 .0155 L .36998 .01526 L .36999 .01507 L .37 .01493 L .37001 .01481 L .37002 .01473 L .37003 .01472 L .37003 .01473 L .37004 .01476 L .37005 .01485 L .37006 .015 L .37007 .01519 L .37008 .01542 L .3701 .01613 L .37012 .017 L .37016 .01973 L .3702 .023 L .37024 .02734 L .37031 .03693 L .37039 .05041 L .37055 .08601 L Mistroke .37071 .1353 L .37104 .25618 L .37136 .38264 L .37167 .49149 L .37183 .53639 L .37191 .55544 L .372 .57266 L .37208 .5854 L .37211 .58994 L .37215 .59416 L .37219 .59724 L .37222 .59984 L .37224 .60097 L .37226 .6018 L .37228 .60246 L .3723 .60291 L .37231 .60308 L .37232 .60321 L .37233 .60329 L .37234 .60332 L .37235 .6033 L .37235 .60327 L .37236 .60322 L .37237 .6031 L .37238 .60292 L .37239 .60267 L .3724 .60233 L .37242 .60153 L .37246 .59942 L .3725 .59665 L .37254 .59293 L .37261 .58427 L .37268 .57221 L .37276 .55625 L .37291 .52018 L .37324 .41158 L .37356 .28814 L .37387 .17291 L .37402 .1222 L .37419 .07564 L .37427 .0583 L .37436 .04267 L .37444 .03097 L .37451 .02296 L .37455 .01984 L .37457 .01844 L .37459 .01732 L .37461 .01645 L .37463 .01571 L .37463 .01545 L Mistroke .37464 .01522 L .37465 .01504 L .37466 .01491 L .37467 .01479 L .37468 .01473 L .37469 .01472 L .3747 .01473 L .3747 .01476 L .37471 .01484 L .37472 .01498 L .37473 .01517 L .37474 .0154 L .37476 .0161 L .37478 .01696 L .37483 .01964 L .37486 .02269 L .3749 .02674 L .37498 .03606 L .37506 .05043 L .37514 .06645 L .37546 .15585 L .37577 .26712 L .3761 .39217 L .37641 .49834 L .37657 .54055 L .37671 .57054 L .37679 .58313 L .37687 .59235 L .37691 .59623 L .37695 .59909 L .37697 .60038 L .37699 .60138 L .37702 .60228 L .37703 .60258 L .37704 .60285 L .37705 .60304 L .37706 .60318 L .37707 .60326 L .37707 .60331 L .37708 .60331 L .37709 .60327 L .3771 .60318 L .37711 .60311 L .37711 .60302 L .37714 .60256 L .37715 .6022 L .37716 .60183 L .3772 .59989 L .37723 .5976 L .37727 .59443 L Mistroke .37735 .58599 L .37743 .57382 L .3775 .56015 L .37767 .52116 L .37799 .4212 L .3783 .30719 L .37863 .18693 L .37879 .13394 L .37894 .0913 L .37909 .05823 L .37917 .04355 L .37924 .03252 L .37932 .02357 L .37937 .02008 L .37939 .01863 L .37941 .01731 L .37944 .01631 L .37946 .0156 L .37948 .01511 L .37949 .01494 L .37949 .01487 L .3795 .01481 L .37951 .01474 L .37952 .01472 L .37953 .01474 L .37953 .01477 L .37954 .01481 L .37955 .01491 L .37955 .01506 L .37956 .01526 L .37957 .01549 L .37959 .01611 L .37961 .01685 L .37965 .01911 L .37969 .02209 L .37974 .02608 L .37981 .03547 L .37988 .04631 L .38004 .07713 L .3802 .12036 L .38053 .22769 L .38085 .34408 L .38115 .45077 L .38132 .50207 L .38147 .54127 L .38155 .55754 L .38163 .57263 L .38171 .58417 L .38179 .5926 L .38183 .59612 L Mistroke .38186 .59874 L .3819 .60096 L .38192 .60184 L .38193 .60224 L .38194 .60254 L .38195 .60278 L .38196 .60299 L .38197 .60308 L .38198 .60315 L .38199 .60326 L .38199 .60331 L .382 .60332 L .38201 .60328 L .38202 .60321 L .38203 .60314 L .38204 .60306 L .38205 .60287 L .38207 .60236 L .38209 .60153 L .38211 .60053 L .38215 .5981 L .3822 .59464 L .38228 .58617 L .38235 .57529 L .38243 .56309 L .38274 .48662 L .38305 .38751 L .38337 .2705 L .38368 .16369 L .38384 .11668 L .38401 .07401 L .38409 .05765 L .38418 .04299 L .38426 .03192 L .38433 .02413 L .38437 .0211 L .38441 .01854 L .38444 .01662 L .38447 .01583 L .38448 .01555 L .38449 .01528 L .3845 .01508 L .38451 .01494 L .38451 .01483 L .38452 .01476 L .38453 .01472 L .38454 .01472 L .38455 .01474 L .38456 .0148 L .38457 .01491 L Mistroke .38458 .01508 L .38459 .01528 L .3846 .0155 L .38463 .01674 L .38465 .01773 L .38467 .01882 L .38472 .02189 L .3848 .02955 L .38487 .03883 L .38495 .05091 L .3851 .08272 L .38525 .11986 L .38556 .21693 L .3859 .33381 L .38621 .44261 L .38652 .52862 L .38668 .56186 L .38676 .57534 L .38685 .58699 L .38689 .5915 L .38693 .59512 L .38697 .59802 L .387 .60015 L .38704 .60166 L .38706 .6023 L .38707 .60274 L .38708 .60294 L .38709 .60308 L .3871 .6032 L .38711 .60328 L .38712 .60332 L .38713 .60331 L .38714 .60328 L .38715 .6032 L .38716 .60308 L .38717 .6029 L .38719 .60239 L .38721 .60173 L .38723 .60097 L .38728 .59869 L .38732 .59539 L .38741 .58713 L .38748 .57709 L .38763 .55085 L .3878 .51318 L .38812 .41817 L .38844 .3116 L .38877 .19858 L .38893 .14738 L .38909 .1057 L Mistroke .38925 .0696 L .3894 .04343 L .38947 .03361 L .38955 .02529 L .38959 .02161 L .38963 .01883 L .38967 .01695 L .38969 .01613 L .38971 .01554 L .38972 .01529 L .38973 .01508 L .38974 .01494 L .38975 .01482 L .38976 .01478 L .38976 .01474 L .38977 .01472 L .38977 .01472 L .38978 .01473 L .38979 .01476 L .3898 .0148 L .38981 .0149 L .38981 .01503 L .38983 .01543 L .38985 .01599 L .38988 .01676 L .38991 .01859 L .38995 .02113 L .39002 .02722 L .3901 .03594 L .39018 .04765 L .39033 .07463 L .39066 .15927 L .39098 .26169 L .39129 .36626 L .39162 .46899 L .39178 .51238 L .39193 .54643 L .39208 .57223 L .39216 .58346 L .39224 .59159 L .39228 .59493 L .39232 .59788 L .39235 .5999 L .39239 .60159 L .39241 .60229 L .39243 .60277 L .39244 .60296 L .39245 .60312 L .39246 .60319 L .39246 .60324 L Mistroke .39247 .60328 L .39248 .6033 L .39249 .60332 L .3925 .6033 L .39251 .60323 L .39251 .60318 L .39252 .60312 L .39253 .60298 L .39254 .60279 L .39256 .60233 L .39258 .6017 L .3926 .60084 L .39264 .59885 L .39268 .59574 L .39273 .59223 L .39281 .5834 L .39289 .57285 L .39305 .54466 L .39319 .51177 L .39351 .42383 L .39381 .32556 L .39414 .21938 L .39445 .12846 L .39461 .09009 L .39478 .05633 L .39486 .04378 L .39495 .03281 L .39502 .02545 L .3951 .01952 L .39514 .01747 L .39516 .01659 L .39518 .01592 L .3952 .01547 L .39522 .0151 L .39523 .01494 L .39524 .01483 L .39525 .01477 L .39525 .01472 L .39527 .01472 L .39527 .01475 L .39528 .01478 L .39529 .01482 L .3953 .01494 L .39531 .01511 L .39532 .01534 L .39534 .01589 L .39536 .01655 L .39538 .01742 L .39542 .0194 L .39546 .02224 L Mistroke .3955 .02543 L .39559 .03463 L .39575 .05808 L .39591 .08729 L .39607 .12636 L .3964 .219 L .39671 .31885 L .39704 .42315 L .39736 .50934 L .3975 .54113 L .39767 .56924 L .39774 .57979 L .39782 .58903 L .39787 .59317 L .39791 .59634 L .39795 .59881 L .39797 .59994 L .39799 .60086 L .39801 .60161 L .39803 .60227 L .39805 .60273 L .39806 .6029 L .39807 .60304 L .39808 .60315 L .39809 .60322 L .3981 .60328 L .39811 .60332 L .39812 .60332 L .39813 .60328 L .39814 .60322 L .39814 .60313 L .39815 .60301 L .39816 .60284 L .39818 .60244 L .3982 .60181 L .39822 .60109 L .39827 .59916 L .39831 .59648 L .39839 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L .41008 .59147 L .41012 .59455 L .41016 .5973 L .4102 .59922 L .41024 .60091 L .41026 .60151 L .41028 .60206 L .4103 .60245 L .41031 .6028 L .41032 .60295 L .41033 .60309 L .41034 .60315 L .41035 .6032 L .41036 .60327 L .41036 .6033 L .41037 .60332 L .41039 .60331 L .41039 .60327 L .4104 .60323 L .41041 .60319 L .41042 .60308 L .41043 .60294 L .41044 .60279 L .41046 .60235 L .41048 .60173 L .41052 .60037 L .41056 .5987 L .41064 .59357 L .41073 .58669 L .41081 .57853 L .41095 .55912 L .41126 .50399 L .41159 .42766 L .4119 .34376 L .41223 .25177 L .41255 .16862 L Mistroke .41286 .1007 L .41302 .07263 L .41319 .04769 L .41327 .03846 L .41335 .03019 L .41343 .02401 L .41351 .01968 L .41355 .0179 L .41359 .01644 L .41361 .01586 L .41363 .01542 L .41365 .01506 L .41366 .01491 L .41367 .01486 L .41368 .01482 L .41369 .01476 L .4137 .01472 L .4137 .01472 L .41371 .01473 L .41372 .01476 L .41373 .01482 L .41374 .01491 L .41375 .01503 L .41377 .01534 L .41379 .01573 L .41384 .01694 L .41388 .01847 L .41392 .02058 L .414 .02562 L .41408 .03197 L .41415 .0391 L .41446 .08365 L .41463 .11616 L .41479 .15103 L .4151 .22645 L .41543 .31335 L .41575 .39648 L .41605 .4695 L .41638 .53366 L .41653 .55709 L .41669 .57742 L .41678 .58614 L .41686 .59264 L .41694 .59743 L .41698 .59931 L .41702 .60097 L .41704 .60158 L .41706 .60214 L .41708 .60255 L .4171 .60289 L Mistroke .41711 .60302 L .41712 .60313 L .41713 .6032 L .41714 .60326 L .41715 .6033 L .41716 .60332 L .41717 .60332 L .41718 .6033 L .41718 .60328 L .41719 .60325 L .4172 .60318 L .41721 .60308 L .41722 .60297 L .41724 .60263 L .41726 .60216 L .4173 .6011 L .41734 .59954 L .41742 .59543 L .4175 .59037 L .41766 .57459 L .41782 .55529 L .41798 .5292 L .41831 .46529 L .41862 .39204 L .41895 .30788 L .41927 .2271 L .41958 .15552 L .41991 .0916 L .42007 .06603 L .42022 .04644 L .42037 .03189 L .42045 .02562 L .42052 .02112 L .42056 .01928 L .4206 .01766 L .42064 .01645 L .42068 .01563 L .4207 .01526 L .42072 .015 L .42073 .0149 L .42074 .01481 L .42074 .01478 L .42075 .01475 L .42076 .01473 L .42076 .01472 L .42077 .01472 L .42078 .01473 L .42079 .01477 L .4208 .0148 L .4208 .01484 L Mistroke .42081 .01492 L .42082 .01503 L .42084 .01529 L .42086 .01563 L .42088 .01608 L .42092 .01711 L .42096 .01872 L .421 .02052 L .42109 .0256 L .42117 .0318 L .42133 .04774 L .42148 .06666 L .42179 .11911 L .4221 .18194 L .42242 .25744 L .42273 .33342 L .42306 .41197 L .42338 .48017 L .42369 .5345 L .42384 .55665 L .42401 .57644 L .42409 .58371 L .42418 .59031 L .42425 .59528 L .42433 .59885 L .42436 .60026 L .4244 .60147 L .42443 .60202 L .42445 .60246 L .42447 .60277 L .42448 .60292 L .42449 .60303 L .4245 .60313 L .42451 .60321 L .42452 .60327 L .42452 .60329 L .42453 .6033 L .42454 .60332 L .42455 .60331 L .42456 .60329 L .42457 .60325 L .42457 .60322 L .42458 .60318 L .42459 .60307 L .42461 .60281 L .42464 .60248 L .42466 .60205 L .4247 .60102 L .42473 .59981 L .42481 .5962 L Mistroke .42489 .59175 L .42496 .58656 L .42512 .57171 L .42527 .55413 L .42558 .50568 L .42588 .44755 L .42621 .37718 L .42652 .3055 L .42684 .22993 L .42716 .16239 L .42747 .10617 L .42764 .07972 L .42779 .05922 L .42795 .04159 L .4281 .02914 L .42818 .02435 L .42826 .02032 L .42834 .01736 L .42838 .01617 L .4284 .01572 L .42842 .01537 L .42844 .01511 L .42846 .01491 L .42848 .01482 L .42848 .01479 L .42849 .01477 L .4285 .01473 L .4285 .01472 L .42851 .01472 L .42852 .01472 L .42853 .01474 L .42854 .01477 L .42854 .01482 L .42855 .01489 L .42857 .01498 L .42859 .01521 L .4286 .01548 L .42862 .01583 L .42866 .01675 L .42873 .01907 L .42882 .02277 L .42889 .02712 L .42906 .04021 L .42921 .05588 L .42937 .07682 L .4297 .12807 L .43001 .18755 L .43034 .25777 L .43066 .32818 L .43097 .39464 L Mistroke .4313 .46003 L .43162 .51438 L .43192 .556 L .43208 .57266 L .43224 .58666 L .43233 .59197 L .43241 .5966 L .43245 .59832 L .4325 .59988 L .43254 .60107 L .43257 .60194 L .43261 .60259 L .43263 .60284 L .43265 .60306 L .43266 .60314 L .43267 .60321 L .43268 .60324 L .43268 .60326 L .43269 .6033 L .4327 .60332 L .43271 .60332 L .43272 .60331 L .43273 .60328 L .43274 .60324 L .43275 .60319 L .43277 .60305 L .43279 .60285 L .43281 .60257 L .43284 .60191 L .43288 .60112 L .43296 .59837 L .43304 .59479 L .43319 .58559 L .43335 .57211 L .4335 .55664 L .43381 .5146 L .43412 .4645 L .43444 .40354 L .43475 .34043 L .43509 .2721 L .4354 .20841 L .43571 .15207 L .43604 .10024 L .43635 .06052 L .43651 .04493 L .43665 .03339 L .43681 .02403 L .43689 .02039 L .43694 .01877 L .43698 .01753 L Mistroke .43701 .01661 L .43705 .01581 L .43707 .01547 L .43709 .01521 L .43711 .01501 L .43712 .01492 L .43713 .01486 L .43714 .01481 L .43715 .01477 L .43716 .01474 L .43717 .01472 L .43718 .01472 L .43719 .01472 L .4372 .01473 L .4372 .01476 L .43721 .0148 L .43722 .01484 L .43724 .01499 L .43726 .01517 L .43728 .01541 L .43732 .01607 L .43736 .01685 L .43744 .01924 L .43751 .02224 L .43759 .02575 L .43775 .03596 L .43789 .04817 L .43821 .08246 L .43851 .12467 L .43883 .1775 L .43914 .23372 L .43947 .29655 L .43979 .35734 L .4401 .41361 L .44042 .46867 L .44073 .51484 L .44107 .55459 L .44123 .57041 L .44139 .58233 L .44154 .59144 L .44161 .59511 L .4417 .5983 L .44174 .59964 L .44178 .60071 L .44182 .60158 L .44185 .60223 L .44189 .6027 L .44191 .60289 L .44192 .60306 L .44193 .60313 L Mistroke .44194 .60319 L .44195 .60323 L .44196 .60327 L .44197 .60329 L .44198 .60331 L .44199 .60332 L .442 .60332 L .442 .60331 L .44201 .6033 L .44202 .60327 L .44203 .60324 L .44204 .60318 L .44206 .60304 L .44208 .60286 L .44212 .60238 L .44215 .60178 L .44223 .59993 L .44232 .59709 L .44248 .58979 L .44265 .57907 L .44298 .54943 L .4433 .51146 L .44361 .46773 L .44394 .41538 L .44425 .36125 L .44456 .30767 L .44488 .25104 L .44519 .19884 L .44552 .14782 L .44584 .10471 L .44615 .07018 L .44631 .05562 L .44648 .04202 L .44664 .03148 L .44679 .02404 L .44687 .02117 L .44695 .01863 L .44703 .01671 L .44707 .01593 L .44711 .01538 L .44713 .01518 L .44716 .015 L .44717 .01493 L .44718 .01486 L .44719 .01481 L .4472 .01477 L .44721 .01474 L .44722 .01472 L .44723 .01472 L .44723 .01472 L Mistroke .44724 .01472 L .44725 .01473 L .44726 .01475 L .44727 .01478 L .44728 .01482 L .4473 .01491 L .44732 .01505 L .44735 .01538 L .44739 .01586 L .44743 .01653 L .44751 .01837 L .44758 .02059 L .44775 .02744 L .4479 .0359 L .44807 .04735 L .4484 .0763 L .44871 .11133 L .44902 .1505 L .44934 .19678 L .44965 .24436 L .44998 .29662 L .4503 .34704 L .4506 .39421 L .45093 .44157 L .45124 .48317 L .45157 .52186 L .45189 .55281 L .4522 .576 L .45236 .5853 L .45253 .59306 L .45261 .59585 L .45269 .59835 L .45277 .60023 L .45284 .60157 L .45288 .60216 L .45292 .60265 L .45294 .60284 L .45296 .60301 L .45297 .60309 L .45298 .60315 L .45299 .6032 L .45301 .60325 L .45302 .60328 L .45303 .6033 L .45303 .60331 L .45304 .60332 L .45305 .60332 L .45306 .60331 L .45307 .6033 L .45308 .60329 L Mistroke .45308 .60327 L .4531 .6032 L .45312 .60315 L .45313 .60309 L .45317 .6028 L .45321 .6024 L .45325 .60186 L .45332 .60057 L .45341 .59852 L .45349 .59618 L .45364 .59031 L .45381 .5821 L .45413 .56053 L .45445 .53358 L .45476 .50267 L .45508 .4653 L .45539 .42591 L .45572 .38146 L .45604 .33721 L .45635 .29431 L .45668 .24935 L .45699 .20769 L .45729 .16996 L .45762 .13307 L .45793 .10144 L .45826 .07262 L .45857 .05001 L .45888 .03338 L .45904 .02683 L .4592 .0214 L .45929 .01932 L .45938 .01751 L .45942 .01683 L .45946 .01621 L .4595 .01573 L .45954 .01537 L .45958 .01508 L .45959 .01498 L .45961 .01488 L .45963 .01481 L .45964 .01478 L .45965 .01476 L .45966 .01474 L .45967 .01472 L .45968 .01472 L .45968 .01472 L .45969 .01472 L .45969 .01472 L .4597 .01472 L .45971 .01473 L Mistroke .45972 .01474 L .45973 .01476 L .45975 .01482 L .45977 .0149 L .4598 .01508 L .45984 .01535 L .45992 .01615 L .46 .01735 L .46014 .02043 L .46031 .02541 L .46047 .03152 L .46078 .04666 L .46111 .06749 L .46142 .09168 L .46175 .12123 L .46207 .15285 L .46238 .18559 L .46271 .22225 L .46303 .2587 L .46333 .29423 L .46365 .33196 L .46397 .36762 L .4643 .40423 L .46462 .43771 L .46492 .46783 L .46525 .49722 L .46556 .52257 L .46587 .54396 L .46619 .56331 L .4665 .57842 L .46666 .58475 L .46683 .59061 L .46699 .59521 L .46714 .5985 L .4673 .60101 L .46739 .602 L .46743 .60235 L .46747 .60268 L .46751 .60291 L .46755 .6031 L .46757 .60318 L .46759 .60324 L .4676 .60326 L .46761 .60328 L .46762 .60329 L .46763 .60331 L .46764 .60331 L .46765 .60332 L .46766 .60332 L .46767 .60332 L Mistroke .46768 .60331 L .46769 .6033 L .4677 .60329 L .46771 .60327 L .46772 .60324 L .46774 .60319 L .46778 .60305 L .46782 .60286 L .46786 .60259 L .46793 .60197 L .46801 .60108 L .4681 .59985 L .46825 .59701 L .46842 .59306 L .46875 .5826 L .46907 .56941 L .46937 .55407 L .4697 .53514 L .47001 .51467 L .47034 .49082 L .47066 .46613 L .47097 .44107 L .4713 .41336 L .47162 .38594 L .47192 .35916 L .47224 .33051 L .47256 .30305 L .47289 .27426 L .47321 .24715 L .47351 .22188 L .47384 .19605 L .47415 .1724 L .47446 .15092 L .47478 .12954 L .47509 .11052 L .47542 .09208 L .47573 .07613 L .47604 .0625 L .47636 .04989 L .47668 .0396 L .47701 .03065 L .47733 .02395 L .47764 .01925 L .47779 .01748 L .47788 .01675 L .47796 .01609 L .47804 .01559 L .47812 .01523 L .47816 .01509 L .47819 .01497 L Mistroke .47823 .01488 L .47827 .0148 L .47829 .01477 L .47831 .01475 L .47833 .01473 L .47834 .01472 L .47834 .01472 L .47835 .01472 L .47836 .01472 L .47837 .01472 L .47838 .01472 L .47839 .01472 L .4784 .01472 L .47841 .01473 L .47841 .01473 L .47842 .01474 L .47845 .01476 L .47847 .01479 L .47851 .01487 L .47855 .01498 L .47859 .01511 L .47867 .01543 L .47875 .01587 L .4789 .01691 L .47907 .01854 L .47923 .02047 L .47954 .02515 L .47987 .03151 L .48018 .03888 L .48048 .04703 L .48081 .05675 L .48112 .06703 L .48145 .07884 L .48177 .09098 L .48207 .10328 L .4824 .11694 L .48271 .13055 L .48302 .14399 L .48334 .1586 L .48365 .17287 L .48398 .1882 L .48429 .20304 L .4846 .21733 L .48492 .23249 L .48523 .24698 L .48557 .26222 L .48589 .27669 L .48619 .29039 L .48652 .30466 L .48684 .3181 L Mistroke .48714 .3307 L .48746 .34375 L .48777 .35594 L .4881 .36848 L .48842 .38013 L .48873 .39093 L .48905 .40198 L .48936 .41219 L .4897 .42256 L .49002 .4321 L .49033 .44085 L .49066 .44971 L .49097 .45781 L .49128 .4652 L .4916 .47265 L .49191 .47942 L .49224 .4862 L .49256 .49234 L .49287 .49788 L .49319 .50341 L .49351 .50839 L .49381 .51286 L .49413 .51729 L .49444 .52126 L .49477 .52516 L .49509 .52862 L .49539 .53169 L .49572 .53468 L .49603 .53731 L .49636 .53984 L .49668 .54204 L .49699 .54393 L .49732 .54571 L .49763 .54722 L .49794 .54848 L .49826 .54961 L .49857 .55052 L .4989 .55128 L .49907 .55158 L .49922 .55182 L .49938 .55202 L .49953 .55217 L .49961 .55223 L .49969 .55228 L .49977 .55232 L .49984 .55235 L .49988 .55236 L .4999 .55236 L .49992 .55236 L .49994 .55237 L Mistroke .49995 .55237 L .49996 .55237 L .49997 .55237 L .49998 .55237 L .49998 .55237 L .49999 .55237 L .5 .55237 L .50001 .55237 L .50001 .55237 L .50002 .55237 L .50003 .55237 L .50004 .55237 L .50005 .55237 L .50007 .55236 L .50009 .55236 L .50011 .55236 L .50016 .55235 L .50019 .55234 L .50024 .55232 L .50031 .55228 L .50039 .55223 L .50047 .55217 L .50063 .55202 L .50079 .5518 L .50112 .55124 L .50143 .55051 L .50173 .54963 L .50206 .5485 L .50237 .54722 L .50269 .54564 L .50301 .54391 L .50332 .54204 L .50364 .53981 L .50395 .53743 L .50429 .53465 L .50461 .5317 L .50491 .5286 L .50524 .52502 L .50556 .52129 L .50586 .51741 L .50618 .51297 L .50649 .50838 L .50682 .50315 L .50714 .49775 L .50745 .49221 L .50777 .48594 L .50809 .47951 L .50842 .47227 L .50874 .46486 L .50905 .45733 L Mistroke .50938 .44888 L .50969 .44031 L .51 .43166 L .51032 .42201 L .51063 .41229 L .51096 .40149 L .51128 .39063 L .51159 .37977 L .51192 .36778 L .51223 .35582 L .51253 .34395 L .51286 .33092 L .51317 .31803 L .5135 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.07747 L .52461 .09349 L .52491 .11055 L .52524 .13041 L .52555 .15111 L .52588 .17467 L .5262 .19877 L .5265 .22308 L .52683 .24999 L .52714 .27672 L .52747 .30575 L .5278 .3341 L .5281 .36147 L .52843 .39038 L .52875 .41775 L .52905 .44335 L .52938 .46952 L .52969 .49336 L .53002 .51691 L .53034 .53754 L .53065 .5552 L .53097 .57133 L .53129 .58402 L .53159 .59337 L Mistroke .53175 .59701 L .53191 .60003 L .53199 .60114 L .53208 .6021 L .53212 .60245 L .53217 .60276 L .53221 .60298 L .53224 .60314 L .53226 .6032 L .53228 .60325 L .53229 .60327 L .5323 .60329 L .53231 .6033 L .53232 .60331 L .53233 .60332 L .53234 .60332 L .53235 .60332 L .53236 .60331 L .53237 .60331 L .53238 .6033 L .53239 .60328 L .5324 .60326 L .53242 .60322 L .53244 .60315 L .53248 .60295 L .53253 .60271 L .53256 .60242 L .53265 .60161 L .53273 .6006 L .53288 .59808 L .53304 .59445 L .53318 .59024 L .5335 .57853 L .5338 .56382 L .53412 .54454 L .53444 .52261 L .53477 .49593 L .53508 .46723 L .53539 .43718 L .53571 .40297 L .53603 .36832 L .53636 .33021 L .53668 .2928 L .53699 .25675 L .53732 .21896 L .53764 .18377 L .53794 .15161 L .53826 .11984 L .53857 .09223 L .53891 .0667 L Mistroke .53923 .04639 L .53953 .03128 L .53969 .0253 L .53986 .02037 L .53993 .01866 L .54001 .01715 L .54009 .01606 L .54016 .01534 L .5402 .01506 L .54022 .01494 L .54024 .01486 L .54026 .01479 L .54027 .01477 L .54028 .01475 L .54029 .01473 L .54029 .01472 L .5403 .01472 L .54031 .01472 L .54032 .01472 L .54033 .01472 L .54033 .01473 L .54034 .01475 L .54035 .01477 L .54037 .01483 L .54039 .01491 L .54041 .01502 L .54044 .01517 L .54048 .01551 L .54055 .0164 L .54064 .01776 L .54073 .01961 L .54081 .02172 L .54097 .02709 L .54112 .0333 L .54144 .05079 L .54175 .07278 L .54207 .10138 L .54239 .13351 L .54269 .1681 L .54301 .20825 L .54332 .24932 L .54365 .29469 L .54397 .33906 L .54428 .38139 L .5446 .42502 L .54491 .46462 L .54525 .50301 L .54557 .53538 L .54588 .56138 L .54603 .5724 L Mistroke .5462 .58269 L 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.01472 L .55279 .01473 L .5528 .01475 L .5528 .01478 L .55281 .01482 L .55282 .01487 L .55285 .01501 L .55287 .0152 L .55289 .01544 L .55293 .01603 L .55297 .01673 L .55306 .01887 L .55314 .02138 L .55322 .02468 L .55338 .03268 L .55353 .04224 L .55384 .06886 L .55417 .10592 L .55448 .14904 L .55479 .19606 L .55511 .25043 L .55543 .30517 L .55576 .36378 L .55608 .41852 L .55639 .46759 L .55672 .51386 L .55703 .55084 L .55734 .57793 L .55749 .58825 L .55766 .59641 L .55774 .59926 L .55779 .60046 L .55783 .60151 L .55787 .60223 L .55789 .60254 L .55792 .60281 L .55794 .60301 L Mistroke .55796 .60315 L .55797 .60321 L .55797 .60325 L .55798 .60328 L .55799 .6033 L .558 .60332 L .55801 .60332 L .55801 .60332 L .55802 .60331 L .55803 .60328 L .55804 .60327 L .55804 .60325 L .55805 .6032 L .55808 .60305 L .5581 .60287 L .55812 .60266 L .55816 .60205 L .55819 .60132 L .55823 .60051 L .55831 .59821 L .55839 .59507 L .55846 .59153 L .55863 .58127 L .55878 .56932 L .55894 .55344 L .55927 .51451 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.56725 .60318 L .56726 .60323 L .56727 .60328 L .56727 .60329 L .56728 .60331 L .56729 .60332 L .5673 .60332 L .56731 .6033 L .56731 .60328 L .56732 .60326 L .56733 .60321 L Mistroke .56734 .60315 L .56736 .60297 L .56738 .60276 L .56739 .6025 L .56744 .60171 L .56747 .60073 L .56756 .59768 L .56764 .59401 L .56771 .58974 L .56788 .57708 L .56804 .56088 L .56818 .54287 L .5685 .49518 L .56881 .43947 L .56913 .37268 L .56944 .30455 L .56977 .23216 L .57009 .16657 L .5704 .11098 L .57056 .08667 L .57073 .06346 L .57089 .04508 L .57104 .03187 L .57112 .02669 L .5712 .02207 L .57124 .02 L .57128 .01839 L .57133 .01703 L .57137 .01606 L .57138 .01567 L .57141 .01532 L .57143 .01505 L .57144 .01494 L .57145 .01485 L .57146 .01479 L .57147 .01475 L .57148 .01473 L .57149 .01472 L .5715 .01472 L .5715 .01473 L .57151 .01475 L .57152 .0148 L .57153 .01486 L .57155 .01501 L .57157 .01524 L .5716 .01581 L .57164 .01665 L .57168 .01784 L .57176 .02115 L .57184 .02517 L Mistroke .572 .03763 L .57216 .05311 L .57232 .07404 L .57265 .12654 L .57297 .18864 L .57327 .25562 L .57359 .33048 L .5739 .40156 L .57423 .47115 L .57455 .52787 L .57486 .56924 L .57502 .58459 L .5751 .59124 L .57518 .59604 L .57522 .59796 L .57526 .59967 L .5753 .60088 L .57534 .60191 L .57536 .60237 L .57538 .60271 L .5754 .60298 L .57542 .60316 L .57543 .60323 L .57543 .60326 L .57544 .60328 L .57545 .60331 L .57546 .60332 L .57546 .60331 L .57547 .6033 L .57548 .60327 L .57549 .60324 L .57549 .60321 L .5755 .60311 L .57553 .60288 L .57554 .60259 L .57559 .60166 L .57563 .60053 L .57567 .59902 L .57574 .59563 L .57582 .59081 L .57597 .57774 L .57614 .55882 L .57647 .5079 L .57679 .44469 L .5771 .37476 L .57742 .2955 L .57774 .21977 L .57804 .15241 L .57836 .09151 L .57851 .06855 L Mistroke .57867 .04767 L .57883 .03176 L .57892 .02521 L .579 .02051 L .57904 .01869 L .57908 .01709 L .5791 .0165 L .57912 .01596 L .57914 .01557 L .57916 .01524 L .57917 .0151 L .57918 .01499 L .57919 .0149 L .5792 .01483 L .57921 .01478 L .57921 .01475 L .57922 .01472 L .57923 .01472 L .57924 .01473 L .57925 .01476 L .57926 .01481 L .57927 .01489 L .57929 .01509 L .57931 .01538 L .57933 .01576 L .57935 .01627 L .57939 .01747 L .57947 .02062 L .57955 .02577 L .57963 .03194 L .57978 .04689 L .57995 .06841 L .58027 .12401 L .58058 .19121 L .58091 .27208 L .58123 .3532 L .58153 .4284 L .58186 .49926 L .58217 .55319 L .58234 .57514 L .58242 .58322 L .5825 .59033 L .58258 .59553 L .58262 .59776 L .58266 .59975 L .5827 .60118 L .58274 .60218 L .58276 .60254 L .58277 .60286 L .58278 .60298 L Mistroke .58279 .60309 L .5828 .60317 L .58281 .60323 L .58282 .60328 L .58282 .6033 L .58283 .60331 L .58284 .60332 L .58284 .60332 L .58285 .60329 L .58286 .60324 L .58287 .60318 L .58288 .60309 L .58289 .60297 L .58291 .60263 L .58293 .60221 L .58298 .6009 L .58302 .59934 L .58306 .59758 L .58314 .59245 L .58322 .58618 L .58329 .57911 L .58346 .55884 L .58377 .50585 L .58411 .4324 L .58443 .3508 L .58474 .26861 L .58506 .1845 L .58538 .11364 L .58568 .06058 L .58584 .04055 L .58593 .03176 L .58601 .0252 L .58609 .02016 L .58613 .01815 L .58615 .0173 L .58618 .01652 L .5862 .01595 L .58622 .01552 L .58623 .0152 L .58625 .01495 L .58626 .01485 L .58627 .01481 L .58627 .01478 L .58628 .01473 L .58629 .01472 L .5863 .01472 L .5863 .01472 L .58631 .01476 L .58632 .01479 L .58633 .01482 L Mistroke .58634 .01493 L .58635 .01505 L .58636 .0152 L .58638 .01555 L .5864 .01608 L .58642 .01668 L .58646 .01817 L .5865 .01995 L .58657 .02424 L .58665 .03029 L .58681 .04737 L .58698 .0717 L .58728 .13009 L .5876 .2082 L .58792 .29251 L .58825 .38382 L .58857 .46528 L .58887 .5305 L .58903 .55717 L .58911 .56865 L .5892 .57929 L .58928 .58754 L .58936 .59362 L .58943 .59808 L .58946 .59981 L .5895 .60131 L .58952 .60192 L .58955 .60246 L .58957 .60285 L .58958 .603 L .58959 .60311 L .58959 .60319 L .5896 .60325 L .58961 .6033 L .58962 .60332 L .58963 .60331 L .58964 .60328 L .58965 .60322 L .58966 .60315 L .58967 .60304 L .58968 .6029 L .5897 .60258 L .58972 .60206 L .58974 .60147 L .58978 .5999 L .58983 .59772 L .5899 .59275 L .58999 .58574 L .59013 .56879 L .5903 .54255 L Mistroke .59046 .51184 L .59077 .44011 L .5911 .3509 L .59141 .2606 L .59172 .17772 L .59204 .10205 L .59219 .07373 L .59235 .04856 L .59244 .03765 L .59252 .02935 L .5926 .02312 L .59264 .02039 L .59268 .01835 L .59272 .01674 L .59274 .01611 L .59276 .01555 L .59278 .01513 L .5928 .01496 L .5928 .0149 L .59281 .01484 L .59282 .01477 L .59282 .01474 L .59283 .01472 L .59284 .01472 L .59285 .01472 L .59285 .01474 L .59286 .01479 L .59287 .01487 L .59288 .01499 L .59289 .01514 L .59291 .01546 L .59293 .01592 L .59297 .01736 L .59301 .01915 L .59309 .02412 L .59317 .0303 L .59333 .04979 L .59348 .07357 L .59365 .10588 L .59397 .18434 L .59428 .27255 L .59461 .37032 L .59493 .45849 L .59524 .52901 L .59539 .5575 L .59556 .58078 L .59564 .58934 L .59569 .59305 L .59573 .59635 L .59577 .59872 L Mistroke .59582 .60077 L .59584 .60148 L .59586 .60211 L .59588 .60254 L .5959 .60291 L .59591 .60306 L .59592 .60317 L .59593 .60326 L .59593 .60329 L .59594 .60331 L .59595 .60332 L .59596 .6033 L .59597 .60325 L .59598 .60317 L .59599 .60304 L .596 .60288 L .59602 .60248 L .59604 .60191 L .59607 .60111 L .59611 .59935 L .59615 .59693 L .59623 .59118 L .5963 .5838 L .59638 .57401 L .59653 .55168 L .59686 .48173 L .59718 .39499 L .59749 .30235 L .59781 .20444 L .59813 .12116 L .59843 .05987 L .59858 .03776 L .59867 .02844 L .59871 .02506 L .59875 .02196 L .59879 .01942 L .59883 .01758 L .59885 .01685 L .59887 .01618 L .59888 .01567 L .5989 .01529 L .59891 .01511 L .59892 .01497 L .59893 .01485 L .59894 .0148 L .59894 .01476 L .59895 .01474 L .59895 .01472 L .59896 .01472 L .59897 .01473 L Mistroke .59898 .01476 L .59898 .01479 L .59899 .01484 L .599 .01494 L .59901 .01508 L .59903 .01549 L .59905 .01599 L .59907 .01658 L .59911 .01825 L .59915 .02067 L .59923 .02663 L .59931 .03435 L .59938 .04314 L .59953 .06647 L .59969 .09931 L .60002 .18112 L .60033 .27438 L .60065 .37775 L .60097 .46967 L .60128 .54084 L .60143 .56818 L .60152 .5802 L .6016 .58913 L .60168 .59605 L .60173 .59878 L .60175 .59993 L .60177 .60098 L .60179 .60174 L .60181 .60231 L .60183 .60275 L .60185 .60305 L .60186 .60317 L .60187 .60322 L .60187 .60326 L .60188 .60331 L .60189 .60332 L .6019 .60331 L .6019 .60329 L .60191 .60323 L .60192 .60318 L .60192 .60312 L .60193 .60296 L .60196 .60255 L .60197 .60204 L .60202 .60041 L .60206 .59842 L .6021 .59575 L .60217 .58979 L .60225 .58128 L .6024 .55851 L Mistroke .60257 .52598 L .6029 .44156 L .60322 .34357 L .60352 .24495 L .60385 .1479 L .60416 .07367 L .60424 .05851 L .60433 .04446 L .60441 .0344 L .60449 .02567 L .60453 .02242 L .60458 .01956 L .60462 .01746 L .60465 .01606 L .60467 .01547 L .60469 .01508 L .6047 .01493 L .60471 .01486 L .60472 .01481 L .60472 .01477 L .60473 .01474 L .60473 .01472 L .60474 .01472 L .60475 .01474 L .60476 .0148 L .60477 .01489 L .60478 .01501 L .60479 .01518 L .6048 .01542 L .60482 .01597 L .60486 .01744 L .6049 .01933 L .60494 .02195 L .60498 .02542 L .60507 .03453 L .60515 .0452 L .6053 .07121 L .60547 .10748 L .60579 .1978 L .60611 .29919 L .60644 .40828 L .60676 .50058 L .60691 .5352 L .60707 .56586 L .60715 .57751 L .60723 .58767 L .60727 .59224 L .60732 .59572 L .60736 .59843 L .6074 .60065 L Mistroke .60742 .60142 L .60744 .60209 L .60745 .60241 L .60746 .60266 L .60747 .60288 L .60748 .60304 L .60749 .60315 L .60749 .60323 L .6075 .60329 L .60751 .60332 L .60752 .60331 L .60753 .60326 L .60754 .60318 L .60755 .60308 L .60756 .60293 L .60757 .60273 L .60759 .60226 L .60761 .60154 L .60763 .60071 L .60768 .59838 L .60772 .59549 L .60779 .5884 L .60788 .57846 L .60802 .55464 L .60818 .52182 L .60833 .48469 L .60863 .39099 L .60896 .27997 L .60928 .17652 L .60959 .09345 L .60974 .06059 L .60983 .04583 L .60991 .03463 L .60999 .02571 L .61003 .02205 L .61008 .01897 L .6101 .01792 L .61012 .01697 L .61014 .01627 L .61016 .01566 L .61017 .01537 L .61018 .01514 L .61019 .01497 L .6102 .0149 L .6102 .01483 L .61021 .01479 L .61021 .01475 L .61022 .01472 L .61023 .01472 L .61024 .01477 L Mistroke .61025 .01485 L .61026 .01491 L .61026 .01498 L .61028 .01534 L .6103 .0158 L .61032 .01643 L .61036 .01817 L .6104 .02078 L .61047 .02721 L .61055 .03527 L .61071 .06065 L .61085 .09185 L .61117 .17962 L .61148 .28142 L .6118 .39366 L .61211 .49037 L .61227 .53093 L .61236 .54917 L .61245 .56584 L .61253 .57831 L .61261 .58921 L .61265 .59304 L .61269 .59649 L .61273 .59894 L .61277 .60095 L .61279 .60184 L .61281 .60246 L .61282 .6027 L .61283 .60292 L .61284 .60308 L .61285 .60319 L .61285 .60324 L .61286 .60328 L .61287 .60332 L .61287 .60332 L .61288 .60331 L .61289 .60328 L .61289 .60325 L .6129 .6032 L .6129 .60313 L .61291 .60295 L .61293 .60272 L .61294 .60246 L .61296 .60181 L .61298 .60102 L .61301 .5991 L .61305 .59638 L .6131 .59267 L .61318 .5835 L .61325 .57284 L Mistroke .61342 .54128 L .61374 .4559 L .61405 .35279 L .61438 .23655 L .6147 .13487 L .61485 .09246 L .615 .06077 L .61507 .04739 L .61516 .03531 L .6152 .02981 L .61524 .02547 L .61528 .02202 L .61532 .01903 L .61534 .01791 L .61536 .01691 L .61538 .01615 L .6154 .01559 L .61542 .01519 L .61543 .01502 L .61543 .01489 L .61544 .0148 L .61545 .01473 L .61546 .01472 L .61547 .01473 L .61548 .01479 L .61549 .0149 L .6155 .01505 L .61551 .01521 L .61553 .01577 L .61555 .01648 L .61559 .01845 L .61564 .02141 L .61572 .02923 L .61579 .03881 L .61596 .06848 L .61612 .10484 L .61628 .15243 L .61661 .26357 L .61693 .37811 L .61723 .4788 L .6174 .52537 L .61756 .55953 L .61763 .57315 L .61772 .58521 L .61775 .58974 L .61779 .59386 L .61783 .59686 L .61787 .59941 L .61789 .60045 L .61791 .6014 L Mistroke .61793 .60211 L .61794 .60261 L .61795 .60284 L .61796 .60304 L .61797 .60312 L .61797 .60319 L .61798 .60328 L .61799 .60331 L .618 .60331 L .61801 .60326 L .61802 .60317 L .61803 .60304 L .61804 .60286 L .61806 .60242 L .61808 .60185 L .61809 .60119 L .61813 .59925 L .61817 .59652 L .61824 .58937 L .61833 .57888 L .61847 .5529 L .61863 .51505 L .6188 .4661 L .61911 .36136 L .61943 .24158 L .61974 .13639 L .6199 .09207 L .61998 .07215 L .62007 .05396 L .62015 .0405 L .62024 .02881 L .62028 .02477 L .62032 .02117 L .62036 .01849 L .62039 .01666 L .62041 .0159 L .62043 .01536 L .62044 .01514 L .62045 .01495 L .62046 .01482 L .62047 .01475 L .62048 .01472 L .62049 .01472 L .6205 .01477 L .62051 .01486 L .62052 .015 L .62053 .01518 L .62054 .01563 L .62056 .01632 L .62059 .01726 L Mistroke .62062 .01949 L .62067 .02266 L .62071 .02708 L .62079 .03729 L .62087 .04921 L .62103 .08448 L .62135 .17818 L .62165 .28897 L .62198 .41012 L .62229 .51066 L .62246 .55281 L .62254 .56828 L .62262 .58174 L .6227 .59134 L .62274 .59557 L .62278 .59871 L .6228 .59991 L .62282 .60088 L .62284 .60162 L .62286 .60226 L .62286 .60256 L .62287 .60279 L .62288 .60298 L .62289 .60312 L .6229 .60323 L .62291 .60327 L .62291 .6033 L .62292 .60332 L .62293 .60329 L .62294 .6032 L .62295 .60307 L .62296 .60288 L .62297 .60261 L .62299 .60201 L .62301 .60115 L .62305 .599 L .62309 .59632 L .62317 .58804 L .62326 .57567 L .62342 .54389 L .62359 .49935 L .62389 .39693 L .62422 .27283 L .62453 .15898 L .62469 .10939 L .62486 .06566 L .62494 .04936 L .62503 .03536 L .6251 .02617 L .62514 .02213 L Mistroke .62518 .01914 L .62522 .01685 L .62524 .01592 L .62525 .01557 L .62527 .0153 L .62527 .01509 L .62528 .01494 L .62529 .01481 L .6253 .01474 L .62531 .01472 L .62532 .01474 L .62533 .01478 L .62533 .01484 L .62534 .01497 L .62535 .01516 L .62536 .01538 L .62538 .01604 L .6254 .0168 L .62542 .0178 L .62546 .01999 L .62549 .02307 L .62557 .03221 L .62565 .0434 L .62582 .07785 L .62597 .11919 L .62613 .17311 L .62646 .29561 L .62677 .41646 L .62693 .4723 L .62711 .52425 L .62719 .54485 L .62727 .56355 L .62735 .57801 L .62743 .58846 L .6275 .59642 L .62754 .59953 L .62756 .60065 L .62758 .60163 L .6276 .60228 L 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.65512 .01686 L .65514 .01587 L .65516 .01523 L .65517 .01501 L .65518 .01484 L .65519 .01475 L .6552 .01472 L .65521 .01474 L .65522 .01486 L .65523 .01504 L .65524 .01526 L .65525 .01561 L .65526 .01608 L .65528 .01719 L .6553 .01869 L .65532 .02068 L .65536 .02526 L .65545 .03817 L .65554 .05753 L .6557 .10563 L .65603 .24188 L .65634 .39147 L .65665 .51584 L Mistroke .6568 .56195 L .65689 .58081 L .65693 .5874 L .65697 .59317 L .65701 .59736 L .65703 .59914 L .65705 .6007 L .65707 .60181 L .65708 .6022 L .65709 .60257 L .6571 .60283 L .6571 .60304 L .65711 .60321 L .65712 .60329 L .65713 .60332 L .65713 .60332 L .65714 .60325 L .65715 .60318 L .65716 .60309 L .65717 .60279 L .65718 .60244 L .65719 .60204 L .65721 .60088 L .65723 .59953 L .65725 .59772 L .65729 .59356 L .65736 .58221 L .65745 .56488 L .65762 .51573 L .65794 .38227 L .65825 .23432 L .6584 .16408 L .65857 .0983 L .65865 .07333 L .65874 .05108 L .65882 .03467 L .65889 .02389 L .65893 .01981 L .65895 .01821 L .65897 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J., \"", StyleBox["Numerical Experiments for Nonlinear Problems", FontSlant->"Italic"], "'', Ph.D. Thesis, University of West Bohemia, Pilsen, 2001, pp. 97. \n", StyleBox["[3]", FontColor->RGBColor[0, 0, 1]], " \[CapitalCHacek]epi\[CHacek]ka, J., Dr\[AAcute]bek, P., Girg, P., \ Quasilinear Boundary Value Problems: Existence and Multiplicity Results, in \ \n\"", StyleBox["Variational Methods: Open Problems, Recent Progress, and \ Numerical Algorithms\", John M. Neuberger", FontVariations->{"CompatibilityType"->0}], ", ", StyleBox["Northern Arizona University", FontVariations->{"CompatibilityType"->0}], ", Editor, ", StyleBox["Contemporary Mathematics Series", FontSlant->"Italic"], ", AMS, 2004, 285 pp., Softcover, ISBN 0-8218-3339-1", StyleBox[".", FontSize->12], "\n", StyleBox["[4]", FontColor->RGBColor[0, 0, 1]], " \[CapitalCHacek]epi\[CHacek]ka, J., Dr\[AAcute]bek, P., Girg, P., Open \ problems related to the ", StyleBox["p", "InlineFormula"], "-Laplacian operator, \n", StyleBox["Bol. Soc. Esp. Mat. Apl. ", FontSlant->"Italic"], StyleBox["29", FontWeight->"Bold"], "(2004), pp. 13-34", StyleBox[".", FontVariations->{"CompatibilityType"->0}], StyleBox[" \n", FontSlant->"Italic"], StyleBox["[5]", FontColor->RGBColor[0, 0, 1]], " Del Toro, P., Girg, P., Roca, F., Dirichlet Problem with Nonlinearity \ Depending only on the Derivative, ", StyleBox[" ", FontSize->12], StyleBox["Appl. Math. Lett.", FontSlant->"Italic"], " ", StyleBox["16", FontWeight->"Bold"], "(2003), pp. 7-12.", StyleBox[" ", FontSize->12], "\n", StyleBox["[6]", FontColor->RGBColor[0, 0, 1]], " Dr\[AAcute]bek, P., Girg, P., Roca, F., On the Range Properties of \ Certain Landesman-Lazer-type Problem, ", StyleBox["J. Math. Anal. Appl.", FontSlant->"Italic"], " ", StyleBox["257", FontWeight->"Bold"], "(2001), pp. 131-140. \n", StyleBox["[7]", FontColor->RGBColor[0, 0, 1]], " Dr\[AAcute]bek, P., Girg, P., Tak\[AAcute]\[CHacek], P., Ulm, M., The \ Fredholm alternative for the ", StyleBox["p", "InlineFormula"], "-Laplacian: bifurcation\nfrom infinity, existence and multiplicity of \ solutions, ", StyleBox["Indiana Univ. Math. J.", FontSlant->"Italic"], ", ", StyleBox["53 ", FontWeight->"Bold"], "(2) (2004), pp. 433-482.\n", StyleBox["[8]", FontColor->RGBColor[0, 0, 1]], " Dr\[AAcute]bek, P., Girg, P., Tak\[AAcute]\[CHacek], P., Bounded \ perturbations of homogeneous quasilinear operators using bifurcations from \ infinity, to appear in ", StyleBox["J. Differential Equations", FontSlant->"Italic"], ", accepted 2003, electronic version available on-line via ", ButtonBox["www.elsevier.com", ButtonData:>{"www.elsevier.com", None}, ButtonStyle->"Hyperlink"], " (2004).\n", StyleBox["[9] ", FontColor->RGBColor[0, 0, 1]], "Frisch J., Personal Communication (permanent).\n", StyleBox["[10] ", FontColor->RGBColor[0, 0, 1]], "Girg, P., Some Notes on Aeroelastics of Tube Arrays, Technical Report, \ University of West Bohemia, Pilsen 2004. \n", StyleBox["[11]", FontColor->RGBColor[0, 0, 1]], " Girg, P., Roca, F., Villegas, S., Semilinear Sturm Liouville Problem with \ Periodic Nonlinearity, to appear in ", StyleBox["Nonlinear Analysis", FontSlant->"Italic"], " ", StyleBox["T.M.A., ", FontSlant->"Italic"], StyleBox["accepted 2000.", FontVariations->{"CompatibilityType"->0}], "\n", StyleBox["[12] ", FontColor->RGBColor[0, 0, 1]], "Girg, P., Tak\[AAcute]\[CHacek], P., ", StyleBox["Bifurcations of Positive and Negative Continua in Quasilinear \ Elliptic Eigenvalue Problems", FontSlant->"Italic"], ",\nin Preparation.\n", StyleBox["[13] ", FontColor->RGBColor[0, 0, 1]], "Girg, P., ", "Mathematical Model of Heat-Exchanger Tube and Parameter Identification", ", in \"Interaction of Dynamic Systems with Surroundings and Systems with \ Feedbacsk\", I. 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Since numerical experiments are important tool in my theoretical \ research in various topics in nonlinear analysis, research presented in this \ contribution has been supported from several sources depending on subject\n\ (in chronological ordering):\nby the Grant number 201/03/0671 (quasilinear \ differential equations; nonlinear stationary diffusion); \nby the Grant \ number 101/02/1225 (nonlinear models of heat exchanger tubes);\nby ", StyleBox["the Humboldt Foundation", FontColor->RGBColor[0.419608, 0.670588, 0.545098]], " during my 12-month fellowship 2003/04 (quasilinear differential equations \ with periodic nonlinearity).\n\n Finally, I would like to thank to Wolfram \ Research staff for organizing very nice conference and especially for \ possibility of consulting and solving our problems. My special thanks go to \ Joy Costa, Rob Knapp , Roman Maeder, and Michael Trott . 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CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, AutoStyleOptions->{"UnmatchedBracketStyle"->None}, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->None, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0.6, 0.100008, 0.100008]], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->14], Cell[StyleData["Message", "SlideShow"], CellMargins->{{100, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->14], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->7, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{66, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->None, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->14], Cell[StyleData["Print", "SlideShow"], CellMargins->{{100, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->14], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, LanguageCategory->None, FormatType->InputForm, CounterIncrements->"Graphics", ImageMargins->{{43, Inherited}, {Inherited, 0}}, StyleMenuListing->None, FontFamily->"Courier", FontSize->10], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "SlideShow"], ImageMargins->{{100, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Printout"], ImageMargins->{{30, Inherited}, {Inherited, 0}}, Magnification->0.8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], LanguageCategory->None, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0.392157, 0.396078, 0.717647]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12], Cell[StyleData["CellLabel", "SlideShow"], FontSize->12], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["FrameLabel"], LanguageCategory->None, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9], Cell[StyleData["FrameLabel", "Presentation"], FontSize->12], Cell[StyleData["FrameLabel", "SlideShow"], FontSize->12], Cell[StyleData["FrameLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Presentation Specific", "Section"], Cell[CellGroupData[{ Cell[StyleData["Author"], CellMargins->{{100, 27}, {2, 20}}, FontFamily->"Times", FontSize->24, FontSlant->"Italic"], Cell[StyleData["Author", "Presentation"], CellMargins->{{200, 27}, {2, 50}}, FontSize->28], Cell[StyleData["Author", "SlideShow"], CellMargins->{{200, 27}, {2, 50}}, FontSize->28], Cell[StyleData["Author", "Printout"], CellMargins->{{100, 27}, {2, 20}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Affiliation"], CellMargins->{{100, 27}, {30, 12}}, FontFamily->"Times", FontSize->24, FontSlant->"Italic"], Cell[StyleData["Affiliation", "Presentation"], CellMargins->{{200, 27}, {2, 10}}, FontSize->28], Cell[StyleData["Affiliation", "SlideShow"], CellMargins->{{200, 27}, {2, 10}}, FontSize->28], Cell[StyleData["Affiliation", "Printout"], CellMargins->{{100, 27}, {2, 12}}, FontSize->14] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Header Graphic", "Section"], Cell[CellGroupData[{ Cell[StyleData["ConferenceGraphicCell"], ShowCellBracket->False, CellMargins->{{0, 0}, {0, 0}}, Evaluatable->False, PageBreakBelow->False, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1], Magnification->1], Cell[StyleData["ConferenceGraphicCell", "Presentation"]], Cell[StyleData["ConferenceGraphicCell", "SlideShow"]], Cell[StyleData["ConferenceGraphicCell", "Printout"], FontSize->8] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Inline Formatting", "Section"], Cell["\<\ These styles are for modifying individual words or letters in a \ cell exclusive of the cell tag.\ \>", "Text"], Cell[StyleData["RM"], StyleMenuListing->None, FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["BF"], StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["IT"], StyleMenuListing->None, FontSlant->"Italic"], Cell[StyleData["TR"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["TI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["TB"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["TBI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["MR"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["MO"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["MB"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["MBO"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["SR"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["SO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SB"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["SBO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Italic"], Cell[CellGroupData[{ Cell[StyleData["SO10"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SO10", "Printout"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->7, FontWeight->"Plain", FontSlant->"Italic"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["InlineFormula", "SlideShow"], LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{60, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["DisplayFormula", "SlideShow"], CellMargins->{{100, 50}, {Inherited, Inherited}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["DisplayFormula", "Printout"], FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Program"], CellFrame->{{0, 0}, {0.5, 0.5}}, CellMargins->{{60, 4}, {0, 8}}, CellHorizontalScrolling->True, Hyphenation->False, LanguageCategory->"Formula", ScriptLevel->1, FontFamily->"Courier"], Cell[StyleData["Program", "Presentation"], CellMargins->{{24, 50}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["Program", "SlideShow"], CellMargins->{{100, 50}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["Program", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->9] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Outline Styles", "Section"], Cell[CellGroupData[{ Cell[StyleData["Outline1"], CellMargins->{{60, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 50}, ParagraphIndent->-38, CounterIncrements->"Outline1", CounterAssignments->{{"Outline2", 0}, {"Outline3", 0}, {"Outline4", 0}}, FontSize->18, FontWeight->"Bold", CounterBoxOptions->{CounterFunction:>CapitalRomanNumeral}], Cell[StyleData["Outline1", "SlideShow"]], Cell[StyleData["Outline1", "Printout"], CounterBoxOptions->{CounterFunction:>CapitalRomanNumeral}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline2"], CellMargins->{{90, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 60}, ParagraphIndent->-27, CounterIncrements->"Outline2", CounterAssignments->{{"Outline3", 0}, {"Outline4", 0}}, FontSize->15, FontWeight->"Bold", CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "A", "Z"], #]&)}], Cell[StyleData["Outline2", "SlideShow"]], Cell[StyleData["Outline2", "Printout"], CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "A", "Z"], #]&)}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline3"], CellMargins->{{120, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 70}, ParagraphIndent->-21, CounterIncrements->"Outline3", CounterAssignments->{{"Outline4", 0}}, FontSize->12, CounterBoxOptions->{CounterFunction:>Identity}], Cell[StyleData["Outline3", "SlideShow"]], Cell[StyleData["Outline3", "Printout"], CounterBoxOptions->{CounterFunction:>Identity}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline4"], CellMargins->{{150, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 80}, ParagraphIndent->-18, CounterIncrements->"Outline4", FontSize->10, CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "a", "z"], #]&)}], Cell[StyleData["Outline4", "SlideShow"]], Cell[StyleData["Outline4", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext \ ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonFrame->"None", ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"], FontSize->16], Cell[StyleData["Hyperlink", "SlideShow"]], Cell[StyleData["Hyperlink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"], FontSize->16], Cell[StyleData["MainBookLink", "SlideShow"]], Cell[StyleData["MainBookLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"], FontSize->16], Cell[StyleData["AddOnsLink", "SlideShow"]], Cell[StyleData["AddOnsLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLink", "SlideShow"]], Cell[StyleData["RefGuideLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLinkText"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLinkText", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLinkText", "SlideShow"]], Cell[StyleData["RefGuideLinkText", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"], FontSize->16], Cell[StyleData["GettingStartedLink", "SlideShow"]], Cell[StyleData["GettingStartedLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DemosLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Demos", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["DemosLink", "SlideShow"]], Cell[StyleData["DemosLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["TourLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Tour", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["TourLink", "SlideShow"]], Cell[StyleData["TourLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"], FontSize->16], Cell[StyleData["OtherInformationLink", "SlideShow"]], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["MasterIndexLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MasterIndex", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MasterIndexLink", "SlideShow"]], Cell[StyleData["MasterIndexLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard \ ButtonFunctions, for use in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, Placeholder]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder \ objects in palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Placeholder->True, StyleMenuListing->None, FontSlant->"Italic", FontColor->RGBColor[0.890623, 0.864698, 0.384756], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "SlideShow"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["PrimaryPlaceholder"], StyleMenuListing->None, DrawHighlighted->True, FontSlant->"Italic", Background->RGBColor[0.912505, 0.891798, 0.507774], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["PrimaryPlaceholder", "Presentation"]], Cell[StyleData["PrimaryPlaceholder", "SlideShow"]], Cell[StyleData["PrimaryPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles \ of most cells. If a cell's FormatType matches the name of one of the styles \ defined below, then that style is applied between the cell's style and its \ own options. This is particularly true of Input and Output.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, Hyphenation->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[1]], Cell[StyleData["InputForm"], InputAutoReplacements->{}, AllowInlineCells->False, Hyphenation->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{0.6, 1}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, "TwoByteSyntaxCharacterAutoReplacement"->True, LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, "TwoByteSyntaxCharacterAutoReplacement"->True, LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an \ inline cell within another.\ \>", "Text"], Cell[StyleData["InlineCell"], LanguageCategory->"Formula", ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216]] }, Closed]], Cell[CellGroupData[{ Cell["Automatic Styles", "Section"], Cell["\<\ The cells below define styles that are used to affect the display \ of certain types of objects in typeset expressions. For example, \ \"UnmatchedBracket\" style defines how unmatched bracket, curly bracket, and \ parenthesis characters are displayed (typically by coloring them to make them \ stand out).\ \>", "Text"], Cell[StyleData["UnmatchedBracket"], StyleMenuListing->None, FontColor->RGBColor[0.760006, 0.330007, 0.8]], Cell[StyleData["Completions"], StyleMenuListing->None, FontFamily->"Courier"] }, Closed]], Cell[CellGroupData[{ Cell["Styles from HelpBrowser", "Section"], Cell[CellGroupData[{ Cell[StyleData["MathCaption"], CellFrame->{{0, 0}, {0, 0.5}}, CellMargins->{{66, 12}, {2, 24}}, PageBreakBelow->False, CellFrameMargins->{{8, 8}, {8, 2}}, CellFrameColor->GrayLevel[0.700008], CellFrameLabelMargins->4, LineSpacing->{1, 1}, ParagraphSpacing->{0, 8}, StyleMenuListing->None, FontColor->GrayLevel[0.2]], Cell[StyleData["MathCaption", "Presentation"], FontSize->18], Cell[StyleData["MathCaption", "SlideShow"], CellMargins->{{100, 50}, {Inherited, Inherited}}], Cell[StyleData["MathCaption", 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