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Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[ Style[ " H(u) = \!\(\*FractionBox[\(1 + \[Gamma]\), \(1 + \ \[Alpha]\)]\) \!\(\*FractionBox[\(\(\\ \)\(1 + \\ \[Alpha]\\ \ tanh[\*SqrtBox[\(iu\)]]/\*SqrtBox[\(iu\)]\)\), \(1 + \[Beta]\\ iu\\ + \\ \ \[Gamma]\\ tanh[\*SqrtBox[\(iu\)]]/\*SqrtBox[\(iu\)] + \\ \[Delta]\\ iu\\ \ tanh[\*SqrtBox[\(iu\)]]/\*SqrtBox[\(iu\)]\)]\)", Bold, Medium]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`loga$$], 0, "log \[Alpha]"}, -3, 3}, {{ Hold[$CellContext`logb$$], -2, "log \[Beta]"}, -3, 3}, {{ Hold[$CellContext`logc$$], 1, "log \[Gamma]"}, -3, 3}, {{ Hold[$CellContext`logd$$], -1, "log \[Delta]"}, -3, 3}, {{ Hold[$CellContext`w1$$], False, "\!\(\*SubscriptBox[\(\[Omega]\), \(c1\)]\)= 2.54"}, {False, True}}, {{ Hold[$CellContext`w2$$], False, "\!\(\*SubscriptBox[\(\[Omega]\), \(c2\)]\) =1/\[Beta]"}, { False, True}}}, Typeset`size$$ = {568., {194.375, 199.625}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`loga$69$$ = 0, $CellContext`logb$74$$ = 0, $CellContext`logc$75$$ = 0, $CellContext`logd$76$$ = 0, $CellContext`w1$77$$ = False, $CellContext`w2$78$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`loga$$ = 0, $CellContext`logb$$ = -2, $CellContext`logc$$ = 1, $CellContext`logd$$ = -1, $CellContext`w1$$ = False, $CellContext`w2$$ = False}, "ControllerVariables" :> { Hold[$CellContext`loga$$, $CellContext`loga$69$$, 0], Hold[$CellContext`logb$$, $CellContext`logb$74$$, 0], Hold[$CellContext`logc$$, $CellContext`logc$75$$, 0], Hold[$CellContext`logd$$, $CellContext`logd$76$$, 0], Hold[$CellContext`w1$$, $CellContext`w1$77$$, False], Hold[$CellContext`w2$$, $CellContext`w2$78$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`xmin = -2; $CellContext`xmax = Plus[0.5]; $CellContext`r = 1.75; $CellContext`a = 10^$CellContext`loga$$; $CellContext`b = 10^$CellContext`logb$$; $CellContext`c = 10^$CellContext`logc$$; $CellContext`d = 10^$CellContext`logd$$; $CellContext`wc1 = 2.54; $CellContext`wc2 = 1/$CellContext`b; $CellContext`wmin = Min[$CellContext`wc1, $CellContext`wc2]; $CellContext`wmax = Max[$CellContext`wc1, $CellContext`wc2]; $CellContext`dlogw = 4; $CellContext`den = Denominator[ Together[ $CellContext`HPr[ 5, $CellContext`a, $CellContext`b, $CellContext`c, $CellContext`d, \ $CellContext`p]]]; $CellContext`poles = Solve[$CellContext`den == 0, $CellContext`p]; $CellContext`lCroix = Table[ $CellContext`Croix[ ReplaceAll[$CellContext`p, Part[$CellContext`poles, $CellContext`i]]], {$CellContext`i, Length[$CellContext`poles]}]; $CellContext`num = Numerator[ Together[ $CellContext`HPr[ 5, $CellContext`a, $CellContext`b, $CellContext`c, $CellContext`d, \ $CellContext`p]]]; $CellContext`zeros = Solve[$CellContext`num == 0, $CellContext`p]; $CellContext`lCircles = Table[ Circle[{ Chop[ ReplaceAll[$CellContext`p, Part[$CellContext`zeros, $CellContext`i]]], 0}, 3 $CellContext`r], {$CellContext`i, Length[$CellContext`zeros]}]; Grid[{{ Plot[ Null, {$CellContext`x, 0, 1}, PlotStyle -> AbsoluteThickness[1.2], PlotRange -> {{-200, 2}, {-100, 100}}, Frame -> True, Epilog -> { AbsoluteThickness[1.5], Red, $CellContext`lCroix, Black, $CellContext`lCircles}, AspectRatio -> Automatic, FrameLabel -> {"Re s", "Im s"}, ImageSize -> {300, 200}, BaseStyle -> $CellContext`mySt], Plot[ Log[10, Abs[ $CellContext`H[$CellContext`a, $CellContext`b, $CellContext`c, \ $CellContext`d, I 10^$CellContext`logu]]], {$CellContext`logu, Log[10, $CellContext`wmin] - $CellContext`dlogw, Log[10, $CellContext`wmax] + $CellContext`dlogw}, PlotStyle -> AbsoluteThickness[1.5], Frame -> True, ImageSize -> 250, Axes -> None, FrameLabel -> {"log u", "log |H|"}, Epilog -> { AbsoluteDashing[{2, 2}], If[$CellContext`w1$$, {Red, Line[{{ Log[10, $CellContext`wc1], Log[10, Abs[ $CellContext`H[$CellContext`a, $CellContext`b, \ $CellContext`c, $CellContext`d, I 10^(Log[10, $CellContext`wmax] + $CellContext`dlogw)]]]}, { Log[10, $CellContext`wc1], 3}}]}, {}], If[$CellContext`w2$$, {Black, Line[{{ Log[10, $CellContext`wc2], Log[10, Abs[ $CellContext`H[$CellContext`a, $CellContext`b, \ $CellContext`c, $CellContext`d, I 10^(Log[10, $CellContext`wmax] + $CellContext`dlogw)]]]}, { Log[10, $CellContext`wc2], 3}}]}, {}]}, BaseStyle -> $CellContext`mySt]}, { ParametricPlot[{{ Re[ $CellContext`H[$CellContext`a, $CellContext`b, $CellContext`c, \ $CellContext`d, I 10^$CellContext`logu]], -Im[ $CellContext`H[$CellContext`a, $CellContext`b, \ $CellContext`c, $CellContext`d, I 10^$CellContext`logu]]}}, {$CellContext`logu, Log[10, $CellContext`wmin] - $CellContext`dlogw, Log[10, $CellContext`wmax] + $CellContext`dlogw}, Frame -> True, PlotRange -> All, FrameLabel -> {"Re H", "- Im H"}, PlotStyle -> AbsoluteThickness[1.5], PlotRange -> All, Epilog -> { AbsolutePointSize[6], If[$CellContext`w1$$, {Red, Point[{ Re[ $CellContext`H[$CellContext`a, $CellContext`b, \ $CellContext`c, $CellContext`d, I $CellContext`wc1]], -Im[ $CellContext`H[$CellContext`a, $CellContext`b, \ $CellContext`c, $CellContext`d, I $CellContext`wc1]]}]}, {}], If[$CellContext`w2$$, {Black, Point[{ Re[ $CellContext`H[$CellContext`a, $CellContext`b, \ $CellContext`c, $CellContext`d, I $CellContext`wc2]], -Im[ $CellContext`H[$CellContext`a, $CellContext`b, \ $CellContext`c, $CellContext`d, I $CellContext`wc2]]}]}, {}]}, ImageSize -> 250, BaseStyle -> {FontFamily -> "Helvetica", FontSize -> 10}], Plot[Arg[ $CellContext`H[$CellContext`a, $CellContext`b, $CellContext`c, \ $CellContext`d, I 10^$CellContext`logu]]/ Degree, {$CellContext`logu, Log[10, $CellContext`wmin] - $CellContext`dlogw, Log[10, $CellContext`wmax] + $CellContext`dlogw}, PlotStyle -> AbsoluteThickness[1.5], Frame -> True, ImageSize -> 260, Axes -> None, FrameLabel -> { "log u", "\!\(\*SubscriptBox[\(\[Phi]\), \(\"H\"\)]\)/\[Degree]"}, Epilog -> { AbsoluteDashing[{2, 2}], If[$CellContext`w1$$, {Red, Line[{{ Log[10, $CellContext`wc1], -150}, { Log[10, $CellContext`wc1], 150}}]}, {}], If[$CellContext`w2$$, {Black, Line[{{ Log[10, $CellContext`wc2], -150}, { Log[10, $CellContext`wc2], 150}}]}, {}]}, BaseStyle -> $CellContext`mySt]}}]), "Specifications" :> { Style[ " H(u) = \!\(\*FractionBox[\(1 + \[Gamma]\), \(1 + \[Alpha]\)]\ \) \!\(\*FractionBox[\(\(\\ \)\(1 + \\ \[Alpha]\\ \ tanh[\*SqrtBox[\(iu\)]]/\*SqrtBox[\(iu\)]\)\), \(1 + \[Beta]\\ iu\\ + \\ \ \[Gamma]\\ tanh[\*SqrtBox[\(iu\)]]/\*SqrtBox[\(iu\)] + \\ \[Delta]\\ iu\\ \ tanh[\*SqrtBox[\(iu\)]]/\*SqrtBox[\(iu\)]\)]\)", Bold, Medium], Delimiter, {{$CellContext`loga$$, 0, "log \[Alpha]"}, -3, 3, Appearance -> "Labeled"}, {{$CellContext`logb$$, -2, "log \[Beta]"}, -3, 3, Appearance -> "Labeled"}, {{$CellContext`logc$$, 1, "log \[Gamma]"}, -3, 3, Appearance -> "Labeled"}, {{$CellContext`logd$$, -1, "log \[Delta]"}, -3, 3, Appearance -> "Labeled"}, Delimiter, {{$CellContext`w1$$, False, "\!\(\*SubscriptBox[\(\[Omega]\), \(c1\)]\)= 2.54"}, { False, True}}, {{$CellContext`w2$$, False, "\!\(\*SubscriptBox[\(\[Omega]\), \(c2\)]\) =1/\[Beta]"}, { False, True}}}, "Options" :> {FrameLabel -> { Style[ "ER@SE/LEPMI, 2009. 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Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]], Pattern[$CellContext`d, Blank[]], Pattern[$CellContext`p, Blank[]]] := (1/( 1 + $CellContext`a)) (( 1 + $CellContext`a $CellContext`M[$CellContext`n, $CellContext`p])/( 1 + $CellContext`b $CellContext`p + ($CellContext`c + $CellContext`d \ $CellContext`p) $CellContext`M[$CellContext`n, $CellContext`p])); \ $CellContext`Croix[ Pattern[$CellContext`poles, Blank[]]] := Block[{$CellContext`x = Re[$CellContext`poles], $CellContext`y = Im[$CellContext`poles]}, { AbsoluteThickness[1.5], Line[{{$CellContext`x - $CellContext`r ($CellContext`xmax - \ $CellContext`xmin), $CellContext`y - $CellContext`r ($CellContext`xmax - \ $CellContext`xmin)}, {$CellContext`x + $CellContext`r ($CellContext`xmax - \ $CellContext`xmin), $CellContext`y + $CellContext`r ($CellContext`xmax - \ $CellContext`xmin)}}], Line[{{$CellContext`x - $CellContext`r ($CellContext`xmax - \ 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