(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 23628, 614] NotebookOptionsPosition[ 22760, 583] NotebookOutlinePosition[ 23093, 598] CellTagsIndexPosition[ 23050, 595] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearAll", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"S", "[", RowBox[{ RowBox[{"{", RowBox[{"ast_", ",", "bst_"}], "}"}], ",", RowBox[{"{", RowBox[{"as_", ",", "bs_"}], "}"}], ",", RowBox[{"{", RowBox[{"at_", ",", "bt_"}], "}"}], ",", RowBox[{"{", RowBox[{"zs_", ",", "zt_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Gamma", " ", "Product", " ", "terms", " ", "with", " ", RowBox[{"only", " ", "'"}], RowBox[{"s", "'"}], " ", "as", " ", "argument", " ", "with", " ", "other", " ", "paameters"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Pas", "=", RowBox[{"Function", "[", RowBox[{"u", ",", RowBox[{"Product", "[", RowBox[{ RowBox[{"Gamma", "[", RowBox[{"1", "-", RowBox[{"as", "[", RowBox[{"[", RowBox[{"1", ",", "n"}], "]"}], "]"}], "+", "u"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", RowBox[{"as", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Qas", "=", RowBox[{"Function", "[", RowBox[{"u", ",", RowBox[{"Product", "[", RowBox[{ RowBox[{"Gamma", "[", RowBox[{ RowBox[{"as", "[", RowBox[{"[", RowBox[{"2", ",", "n"}], "]"}], "]"}], "-", "u"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", RowBox[{"as", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Pbs", "=", RowBox[{"Function", "[", RowBox[{"u", ",", RowBox[{"Product", "[", RowBox[{ RowBox[{"Gamma", "[", RowBox[{ RowBox[{"bs", "[", RowBox[{"[", RowBox[{"1", ",", "n"}], "]"}], "]"}], "-", "u"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", RowBox[{"bs", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Qbs", "=", RowBox[{"Function", "[", RowBox[{"u", ",", RowBox[{"Product", "[", RowBox[{ RowBox[{"Gamma", "[", RowBox[{"1", "-", RowBox[{"bs", "[", RowBox[{"[", RowBox[{"2", ",", "n"}], "]"}], "]"}], "+", "u"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", RowBox[{"bs", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Ms", "=", RowBox[{"Function", "[", RowBox[{"u", ",", RowBox[{ RowBox[{"Pas", "[", "u", "]"}], " ", RowBox[{ RowBox[{"Pbs", "[", "u", "]"}], "/", RowBox[{"(", RowBox[{ RowBox[{"Qas", "[", "u", "]"}], " ", RowBox[{"Qbs", "[", "u", "]"}]}], ")"}]}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Gamma", " ", "Product", " ", "terms", " ", "with", " ", RowBox[{"only", " ", "'"}], RowBox[{"t", "'"}], " ", "as", " ", "argument", " ", "with", " ", "other", " ", "paameters"}], "*)"}], "\[IndentingNewLine]", RowBox[{"Pat", "=", RowBox[{"Function", "[", RowBox[{"u", ",", RowBox[{"Product", "[", RowBox[{ RowBox[{"Gamma", "[", RowBox[{"1", "-", RowBox[{"at", "[", RowBox[{"[", RowBox[{"1", ",", "n"}], "]"}], "]"}], "+", "u"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", RowBox[{"at", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Qat", "=", RowBox[{"Function", "[", RowBox[{"u", ",", RowBox[{"Product", "[", RowBox[{ RowBox[{"Gamma", "[", RowBox[{ RowBox[{"at", "[", RowBox[{"[", RowBox[{"2", ",", "n"}], "]"}], "]"}], "-", "u"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", RowBox[{"at", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Pbt", "=", RowBox[{"Function", "[", RowBox[{"u", ",", RowBox[{"Product", "[", RowBox[{ RowBox[{"Gamma", "[", RowBox[{ RowBox[{"bt", "[", RowBox[{"[", RowBox[{"1", ",", "n"}], "]"}], "]"}], "-", "u"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", RowBox[{"bt", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Qbt", "=", RowBox[{"Function", "[", RowBox[{"u", ",", RowBox[{"Product", "[", RowBox[{ RowBox[{"Gamma", "[", RowBox[{"1", "-", RowBox[{"bt", "[", RowBox[{"[", RowBox[{"2", ",", "n"}], "]"}], "]"}], "+", "u"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", RowBox[{"bt", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Mt", "=", RowBox[{"Function", "[", RowBox[{"u", ",", RowBox[{ RowBox[{"Pat", "[", "u", "]"}], " ", RowBox[{ RowBox[{"Pbt", "[", "u", "]"}], "/", RowBox[{"(", RowBox[{ RowBox[{"Qat", "[", "u", "]"}], " ", RowBox[{"Qbt", "[", "u", "]"}]}], ")"}]}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"Gamma", " ", "Product", " ", "terms", " ", "with", " ", RowBox[{"only", " ", "'"}], "s"}], "+", RowBox[{ RowBox[{"t", "'"}], " ", "as", " ", "argument", " ", "with", " ", "other", " ", "paameters"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"Past", "=", RowBox[{"Function", "[", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v"}], "}"}], ",", RowBox[{"Product", "[", RowBox[{ RowBox[{"Gamma", "[", RowBox[{ RowBox[{"ast", "[", RowBox[{"[", RowBox[{"1", ",", "n"}], "]"}], "]"}], "+", "u", "+", "v"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", RowBox[{"ast", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Qast", "=", RowBox[{"Function", "[", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v"}], "}"}], ",", RowBox[{"Product", "[", RowBox[{ RowBox[{"Gamma", "[", RowBox[{"1", "-", RowBox[{"ast", "[", RowBox[{"[", RowBox[{"2", ",", "n"}], "]"}], "]"}], "-", "u", "-", "v"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", RowBox[{"ast", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Qbst", "=", RowBox[{"Function", "[", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v"}], "}"}], ",", RowBox[{"Product", "[", RowBox[{ RowBox[{"Gamma", "[", RowBox[{ RowBox[{"bst", "[", RowBox[{"[", RowBox[{"2", ",", "n"}], "]"}], "]"}], "+", "u", "+", "v"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", RowBox[{"bst", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Mst", "=", RowBox[{"Function", "[", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v"}], "}"}], ",", RowBox[{ RowBox[{"Past", "[", RowBox[{"u", ",", "v"}], "]"}], " ", "/", RowBox[{"(", RowBox[{ RowBox[{"Qast", "[", RowBox[{"u", ",", "v"}], "]"}], " ", RowBox[{"Qbst", "[", RowBox[{"u", ",", "v"}], "]"}]}], ")"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Rs", "=", RowBox[{"1", "/", "4"}]}], ";", "\[IndentingNewLine]", RowBox[{"Rt", "=", RowBox[{ RowBox[{"-", "1"}], "/", "4"}]}], ";", "\[IndentingNewLine]", RowBox[{"Zs", "=", "zs"}], ";", "\[IndentingNewLine]", RowBox[{"Zt", "=", "zt"}], ";", "\[IndentingNewLine]", RowBox[{"W", "=", "50"}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", "\"\\"", "]"}], ";", "\[IndentingNewLine]", RowBox[{"value", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"1", "/", "2"}], "/", "2"}], "/", "Pi"}], "/", "Pi"}], "/", "I"}], "/", "I"}], " ", RowBox[{"NIntegrate", "[", RowBox[{ RowBox[{ RowBox[{"Ms", "[", "s", "]"}], " ", RowBox[{"Mt", "[", "t", "]"}], RowBox[{"Mst", "[", RowBox[{"s", ",", "t"}], "]"}], " ", RowBox[{"Zs", "^", "s"}], " ", RowBox[{"Zt", "^", "t"}]}], ",", " ", RowBox[{"{", RowBox[{"s", ",", " ", RowBox[{"Rs", "-", RowBox[{"I", " ", "W"}]}], ",", " ", RowBox[{"Rs", "+", RowBox[{"I", " ", "W"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", RowBox[{"Rt", "-", RowBox[{"I", " ", "W"}]}], ",", " ", RowBox[{"Rt", "+", RowBox[{"I", " ", "W"}]}]}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "value", "]"}], ";"}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "the", " ", "Rs", " ", "and", " ", "Rt", " ", "should", " ", "be", " ", "carefully", " ", "designed"}], "*)"}]}], "\[IndentingNewLine]", RowBox[{"S", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1.5"}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "1", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "0", "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "0.5", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"26.95", ",", "8"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.616949586228819*^9, 3.616949590183234*^9}, { 3.616950675774328*^9, 3.6169507870596933`*^9}, {3.6169508272424717`*^9, 3.616951023098634*^9}, {3.6169510562904377`*^9, 3.6169511373127413`*^9}, { 3.6169511693259697`*^9, 3.616951245046405*^9}, {3.6169514024681797`*^9, 3.6169514101521177`*^9}, 3.617034126910762*^9, 3.6170374232931957`*^9, { 3.617037461918535*^9, 3.617037462741332*^9}, 3.6170375765938253`*^9, { 3.617037624346439*^9, 3.617037630154531*^9}, 3.617037662127263*^9, 3.6170460545829163`*^9, {3.6170460864381332`*^9, 3.617046088165038*^9}, { 3.6170461756634083`*^9, 3.617046205214099*^9}, {3.617099325597043*^9, 3.617099330629182*^9}, {3.6170997410916557`*^9, 3.6170997423363028`*^9}, 3.617099956931986*^9, {3.61710020403601*^9, 3.617100205992488*^9}, 3.617100367135396*^9, {3.6171004395726337`*^9, 3.617100441356423*^9}, { 3.617101082200294*^9, 3.6171010866152983`*^9}, {3.617101500754704*^9, 3.6171015144658937`*^9}, {3.617364678193541*^9, 3.617364684929327*^9}}], Cell[BoxData["\<\"Numerical Integration:\"\>"], "Print", CellChangeTimes->{3.6170460990287533`*^9, 3.617046195162456*^9, 3.617099396570243*^9, 3.6170997445956*^9, 3.6171000124514923`*^9, 3.617100208521146*^9, 3.617100369275988*^9, 3.617100443834948*^9, 3.6171010892179213`*^9, 3.6173646898655243`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Numerical integration converging too slowly; suspect one \ of the following: singularity, value of the integration is 0, highly \ oscillatory integrand, or WorkingPrecision too small. \\!\\(\\*ButtonBox[\\\"\ \[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/NIntegrate/slwcon\\\", ButtonNote -> \ \\\"NIntegrate::slwcon\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.617046099096487*^9, 3.617046206739867*^9, 3.617099421084609*^9, 3.617099766119774*^9, 3.617100038934971*^9, 3.617100223678257*^9, 3.6171003840066833`*^9, 3.617100459513476*^9, 3.6171011092886257`*^9, 3.61736470525543*^9}], Cell[BoxData[ RowBox[{"0.6052697856074759`", "\[VeryThinSpace]", "-", RowBox[{"9.491268737418512`*^-18", " ", "\[ImaginaryI]"}]}]], "Output", CellChangeTimes->{3.617046111246526*^9, 3.617046222139749*^9, 3.617099491881619*^9, 3.617099801228232*^9, 3.617100085678123*^9, 3.617100274462709*^9, 3.617100404523614*^9, 3.617100549239435*^9, 3.6171011235192204`*^9, 3.6173647158428917`*^9}] }, Open ]], Cell[BoxData[""], "Input"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.617037596120826*^9, 3.617037596146923*^9}}], Cell[BoxData[""], "Input", CellChangeTimes->{{3.616951048891755*^9, 3.6169510496982527`*^9}, { 3.6169512760293818`*^9, 3.616951392178103*^9}, {3.6170367615094547`*^9, 3.617036884267662*^9}, {3.617037635855012*^9, 3.617037639009962*^9}}], Cell[CellGroupData[{ Cell[BoxData[""], "Input", CellChangeTimes->{{3.6169510397838697`*^9, 3.6169510405600348`*^9}, { 3.61695142978362*^9, 3.616951538547695*^9}, {3.6169515957940207`*^9, 3.6169517050935793`*^9}, {3.616952361762246*^9, 3.616952376649561*^9}, { 3.616956278861335*^9, 3.616956290261325*^9}, {3.6169563892147627`*^9, 3.616956529267399*^9}, {3.616957472632782*^9, 3.616957474639587*^9}, 3.616957614664485*^9, {3.616957666106017*^9, 3.6169577196345863`*^9}, { 3.616958372476008*^9, 3.616958475700729*^9}, {3.616958585431674*^9, 3.616958640689905*^9}, {3.616958743985106*^9, 3.616958750732491*^9}, { 3.6169587861572237`*^9, 3.616958802620613*^9}, {3.6169589861077213`*^9, 3.616958989137423*^9}, {3.617018294471961*^9, 3.617018302464053*^9}, { 3.617036567132985*^9, 3.617036589127294*^9}, {3.617036903439218*^9, 3.617036917412418*^9}, {3.6170369703365507`*^9, 3.6170370166332693`*^9}, { 3.617045967030375*^9, 3.617045968373321*^9}, 3.6170460618960342`*^9, 3.61704609231565*^9}], Cell[BoxData[ RowBox[{"S", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1.5`"}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "1", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "0", "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "0.5`", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0.3`", ",", "0.3`"}], "}"}]}], "]"}]], "Output", CellChangeTimes->{3.617046068605693*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"NIntegrate", "::", "nlim"}], "MessageName"], RowBox[{ ":", " "}], "\<\"\[NoBreak]\\!\\(s\\)\[NoBreak] = \ \[NoBreak]\\!\\(\\(\\(0.25` \[VeryThinSpace]\\)\\) - \\(\\(1.`\\\\ \ IW\\)\\)\\)\[NoBreak] is not a valid limit of integration. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/NIntegrate/nlim\\\", \ ButtonNote -> \\\"NIntegrate::nlim\\\"]\\)\"\>"}]], "Message", "MSG", GeneratedCell->False, CellAutoOverwrite->False, CellChangeTimes->{ 3.6169574852376623`*^9, 3.61695761809383*^9, 3.616957725396164*^9, { 3.61695864850679*^9, 3.616958669083952*^9}, {3.616958754345278*^9, 3.616958760248107*^9}, {3.616958833108034*^9, 3.616958836614422*^9}, { 3.617010954468068*^9, 3.6170109567326727`*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"NIntegrate", "::", "nlim"}], "MessageName"], RowBox[{ ":", " "}], "\<\"\[NoBreak]\\!\\(s\\)\[NoBreak] = \ \[NoBreak]\\!\\(\\(\\(0.25` \[VeryThinSpace]\\)\\) - \\(\\(1.`\\\\ \ IW\\)\\)\\)\[NoBreak] is not a valid limit of integration. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/NIntegrate/nlim\\\", \ ButtonNote -> \\\"NIntegrate::nlim\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{ 3.6169574852376623`*^9, 3.61695761809383*^9, 3.616957725396164*^9, { 3.61695864850679*^9, 3.616958669083952*^9}, {3.616958754345278*^9, 3.616958760248107*^9}, {3.616958833108034*^9, 3.616958836662711*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"NIntegrate", "::", "nlim"}], "MessageName"], RowBox[{ ":", " "}], "\<\"\[NoBreak]\\!\\(s\\)\[NoBreak] = \ \[NoBreak]\\!\\(\\(\\(0.25` \[VeryThinSpace]\\)\\) - \\(\\(1.`\\\\ \ IW\\)\\)\\)\[NoBreak] is not a valid limit of integration. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/NIntegrate/nlim\\\", \ ButtonNote -> \\\"NIntegrate::nlim\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{ 3.6169574852376623`*^9, 3.61695761809383*^9, 3.616957725396164*^9, { 3.61695864850679*^9, 3.616958669083952*^9}, {3.616958754345278*^9, 3.616958760248107*^9}, {3.616958833108034*^9, 3.616958836726451*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"NIntegrate", "::", "nlim"}], "MessageName"], RowBox[{ ":", " "}], "\<\"\[NoBreak]\\!\\(s\\)\[NoBreak] = \ \[NoBreak]\\!\\(\\(\\(0.25` \[VeryThinSpace]\\)\\) - \\(\\(1.`\\\\ \ IW\\)\\)\\)\[NoBreak] is not a valid limit of integration. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/NIntegrate/nlim\\\", \ ButtonNote -> \\\"NIntegrate::nlim\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{ 3.6169574852376623`*^9, 3.61695761809383*^9, 3.616957725396164*^9, { 3.61695864850679*^9, 3.616958669083952*^9}, {3.616958754345278*^9, 3.616958760248107*^9}, {3.616958833108034*^9, 3.616958836802257*^9}}], Cell[BoxData[ RowBox[{"Return", "[", RowBox[{"-", FractionBox[ RowBox[{"NIntegrate", "[", RowBox[{ RowBox[{ RowBox[{"MT", "[", RowBox[{"s", ",", "t"}], "]"}], " ", SuperscriptBox["Zs", "s"], " ", SuperscriptBox["Zt", "t"]}], ",", RowBox[{"{", RowBox[{"s", ",", RowBox[{"Rs", "-", "IW"}], ",", RowBox[{"Rs", "+", "IW"}]}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", RowBox[{"Rt", "-", "IW"}], ",", RowBox[{"Rt", "+", "IW"}]}], "}"}]}], "]"}], RowBox[{"4", " ", SuperscriptBox["\[Pi]", "2"]}]]}], "]"}]], "Output", CellChangeTimes->{ 3.616957618235601*^9, 3.616957725518355*^9, {3.616958648648117*^9, 3.616958669216748*^9}, {3.616958754456738*^9, 3.616958760362095*^9}, { 3.616958833236751*^9, 3.6169588368035393`*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"Syntax", "::", "sntxi"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Incomplete expression; more input is needed \ \[NoBreak]\\!\\(\\\"\\\"\\)\[NoBreak].\"\>"}]], "Message", "MSG", CellChangeTimes->{ 3.6169574852376623`*^9, 3.61695761809383*^9, 3.616957725396164*^9, { 3.61695864850679*^9, 3.616958669083952*^9}, {3.616958754345278*^9, 3.616958760248107*^9}, {3.616958833108034*^9, 3.616958836943424*^9}}] }, Open ]] }, WindowSize->{1680, 998}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"10.0 for Linux x86 (64-bit) (June 27, 2014)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 13818, 356, 737, "Input"], Cell[14401, 380, 311, 4, 23, "Print"], Cell[14715, 386, 788, 14, 23, "Message"], Cell[15506, 402, 398, 6, 64, "Output"] }, Open ]], Cell[15919, 411, 26, 0, 32, "Input"], Cell[15948, 413, 92, 1, 32, "Input"], Cell[16043, 416, 242, 3, 32, "Input"], Cell[CellGroupData[{ Cell[16310, 423, 1012, 14, 32, "Input"], Cell[17325, 439, 996, 36, 31, "Output"], Cell[18324, 477, 846, 17, 23, "Message"], Cell[19173, 496, 744, 14, 23, "Message"], Cell[19920, 512, 744, 14, 23, "Message"], Cell[20667, 528, 744, 14, 23, "Message"], Cell[21414, 544, 860, 24, 50, "Output"], Cell[22277, 570, 467, 10, 23, "Message"] }, Open ]] } ] *) (* End of internal cache information *)