## How I can normalized mode shape for the comparison...

Hello,

I obtained a mode shape from a vibration problem.

I want to normalized mode shape for the comparison of responses corresponding to different modes.

How I can normalize the mode shape that provided in the maple file?

The figure corresponds to this mode shape is plotted that is attached.

Thanks

mode_shapes.mw

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 (2)
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Determine the polynomials P∈R₃ [X] such that P (-1) = - 18 and whose remainders in the Euclidean division by X-1, X-2 and X-3 are equal to 6.

## how do I integrate HeunB function with complex arg...

I am trying to calculate the following integra
r*rr*g1^2*h1^2*f1^2*fh1^2*exp(-2*t)/t

here g1 is a kummerM functin in s, and also h1 is another kummerM function  in ss, and f1 and fh1 are the HeunB functions with complex arguments in r and rr. and t=sqrt((r-rr)^2+(s-ss)^2).I would like to integte over dr drr ds dss

## How to delete user defined Tasks?...

Dear friends,on the left I created two Tasks named a and aa.However,I do not know how to delete these two Tasks.Then I refer to the help pages below.

The text I marked says I should enter full filename.I do not know the fullfile name of customized Tasks.So does anyone know how to delete them?

## custom scale the axis...

Using mode with axis we can choose linear or log.  But what if we want some other custom scaled axis?

Seems if we want a y^3 y-axis, we'll have to cube root the data then use plottools to form our own scale.  Unless there's some other way I don't know.

## StringTools Escape command form options...

In the help file the permitted declartions for the second argument of the Escape command from the StringTools package are html,regexp and xml, to not specify one, which as far as I can tell instructs maple to take all characters as plain text with no escape characters.

Is this the complete list of options for the form when using the escape command?

Or is it possible to custom build escape rules?

## 2d builtin world map in 3d...

I thought the easiest way to show the world map, a projected flat map into 3d was to use the builtin one and just transform it.  You can zoom into it and rotate it no problem but unforunately it's not as clean as I thought.  Is it possible to have cleaner shading manipulating the Builtin map to 3d?

with(plots):
with(plottools):
with(DataSets):
with(Builtin):
m := WorldMap():
m1 := Display(m)

to3d := transform((x, y) -> [x, y, 0]):
m2 := to3d(m1)

display(m2)

## How can I customly program operations that are not...

If a maple command or function are not available on the target language  of the code generation of maple, is it possible to set myself the expected output for such cases so that the Csharp(...)  recognizes the cases and generates the expect code?

for example

h := proc(x::Array(1 .. 3, 1 .. 3), y::Array(1 .. 3, 1 .. 3)) local z; z := evalm(x &* y); return z[1, 1] + z[2, 2]; end proc;
CSharp(h);

The function names {`&*`, evalm} can not be recognized in the target language

but for the &* it shoud be easy to add a template with the desired C# output.

Is it possible to add templates in existing languages but not new language definitions?

## Duplicate variables shown when assume involves sub...

I'm using variable names that have subscripts, not as a table index but literal i.e. R__1 as a unique variable name.  It seems whenever I make assumptions on variables that have subscripts, when I use them the variables that have subscripts are printed twice:

Can anyone explain why this happens and how to get around it?

## What is the difference between an italic red promp...

Is it italic when copied and pasted?  Is it bold when copied from maple 8?  I just ahve not been able to work it out.

## How do I sum over non-spacetime indices?...

The only way that I can think of doing it is by multiplying by a tetrad.  Even then it does not work well see my worksheet:  The Dirac Equation in Robertson-Walker spacetime.

## Coupled PDEs:Error, (in pdsolve/numeric/animate) u...

Analysis of the semiclassical (SC) momentum rate equations

Plotting the ICs and BCs and examining sensitivity to the Re and Im forces

MRB: 24/2/2020, 27/2/2020, 2/3/2020.

We examine solution of the SC version of the momentum rate equations, in which O terms for  are removed. A high level of sensitivity to ICs and BCs makes solution finding difficult.

 > restart;
 > with(PDETools): with(CodeTools):with(plots):

We set up the initial conditions:

 > ICu := {u(x, 0) = .1*sin(2*Pi*x)}; ICv := {v(x, 0) = .2*sin(Pi*x)};
 (1)
 > plot([0.1*sin(2*Pi*x),0.2*sin(Pi*x)],x = 0..2, title="ICs:\n u(x,0) (red), v(x,0) (blue)",color=[red,blue],gridlines=true);

The above initial conditions represent a positive velocity field  (blue) and a colliding momentum field (red).

Here are the BCs

 > BCu := {u(0,t) = 0.5*(1-cos(2*Pi*t))};
 (2)
 > BCv := {v(0,t) = 0.5*sin(2*Pi*t),v(2,t)=-0.5*sin(2*Pi*t)};
 (3)
 > plot([0.5*(1-cos(2*Pi*t)),0.5*sin(2*Pi*t),-0.5*sin(2*Pi*t)],t=0..1,color=[red,blue,blue],linestyle=[dash,dash,dot],title="BCs:\n u(0,t) (red-dash),\n v(0,t) (blue-dash), v(1,t) (blue-dot)",gridlines=true);
 >

We can now set up the PDEs for the semiclassical case.

 > hBar:= 1:m:= 1:Fu:= 0.2:Fv:= 0.1:#1.0,0.2
 > pdeu := diff(u(x,t),t)+u(x,t)/m*(diff(u(x,t),x)) = Fu;
 (4)
 > pdev := diff(v(x,t),t)+u(x,t)/m*(diff(v(x,t),x))-hBar*(diff(u(x,t),x\$2))/(2*m)+v(x,t)*(diff(u(x,t),x))/m = Fv;
 (5)
 > ICu:={u(x,0) = 0.1*sin(2*Pi*x)};
 (6)
 > ICv:={v(x,0) = 0.2*sin(Pi*x/2)};
 (7)
 > IC := ICu union ICv;
 (8)
 > BCu := {u(0,t) = 0.5*(1-cos(2*Pi*t)), D[1](u)(2,t) = 0.1*cos(2*Pi*t)};
 (9)
 > BCv := {v(0,t) = 0.2*(1-cos(2*Pi*t))};
 (10)
 > BC := BCu union BCv;
 (11)

We now set up the PDE solver:

 > pds := pdsolve({pdeu,pdev},{BC[],IC[]},time = t,range = 0..2,numeric);#'numeric' solution
 (12)
 > Cp:=pds:-animate({[u, color = red, linestyle = dash],[v,color = blue,linestyle = dash]},t = 30,frames = 400,numpoints = 400,title="Semiclassical momentum equations solution for Re and Im momenta u(x,t) (red) and v(x,t) (blue) \n under respective constant positive forces [0.2, 0.1] \n with sinusoidal boundary conditions at x = 0, 1 and sinusoidal initial conditions: \n time = %f ", gridlines = true,linestyle=solid):Cp;
 (13)

Observations on the quantum case:

The classical equation for  is independent of the equation for .   (red) is a solution of the classical Burgers equation subject to a force 0.2, but  is NOT influenced by .  On the otherhand,  (blue) is a solution of the quantum dynamics equation subject to force 0.1 and is influenced by .   This one way causality (u )  is a feature of the semiclassical case, and it emphasises the controlling influence of the classical , which modulates the quantum solution for .  Causally, we have u.

The initial conditions are of low momentum amplitude:0.1 for the classical  (red) field and.2 for  (blue)  but their influence is soon washed out by the boundary conditions  and  that drive the momentum dynamics.

The temporal frequency of the boundary condition on the -field is twice that of the classical -field. This is evident in the above blue transient plot. Moreover, the boundary condition on the classical -momentum (red), drives that field in the positive direction, initially overtaking the quantum  field, as consistent with the applied forces [0.2, 0.1]. Although initially of greater amplitude than the classical field, the  momentum field is asymptotically of the same amplitude as the  field, but has greater spatial and temporal frequency, owing to the boundary conditions.

Referring to the semiclassical momentum rate equations, we note that the classical field  (red) modulates the quantum momentum rate equation for .

 >

I am having difficulty getting solutions to a pair of PDEs.  Would anyone like to cast an eye over the attached file, incase I am missing something.

Thanks

Melvin

## Can someone help with the simplification of this c...

Please I found out that the MatrixInverse on the assignment statement P3 does not run for about three days now. Please kindly help to simplify the code. Thank you and kind regards.

restart; omega := v/h;
r := a[0]+a[1]*x+a[2]*sinh(omega*x)+a[3]*cosh(omega*x)+a[4]*cos(omega*x)+a[5]*sin(omega*x);
b := diff(r, x);

c := eval(b, x = q) = f[n];
d := eval(r, x = q+3*h) = y[n+3]; e := eval(b, x = q+3*h) = f[n+3];
g := eval(b, x = q+2*h) = f[n+2];
i := eval(b, x = q+h) = f[n+1];
j := eval(b, x = q+4*h) = f[n+4];
k := solve({c, d, e, g, i, j}, {a[0], a[1], a[2], a[3], a[4], a[5]});
Warning,  computation interrupted
assign(k);
cf := r;
s4 := y[n+4] = simplify(eval(cf, x = q+4*h));
s3 := y[n+2] = simplify(eval(cf, x = q+2*h));
s2 := y[n+1] = simplify(eval(cf, x = q+h));
s1 := y[n] = simplify(eval(cf, x = q));

with(LinearAlgebra);
with(plots);
h := 1;
YN_1 := seq(y[n+k], k = 1 .. 4);
A1, a0 := GenerateMatrix([s1, s2, s3, s4], [YN_1]);
eval(A1);
YN := seq(y[n-k], k = 3 .. 0, -1);
A0, b1 := GenerateMatrix([s1, s2, s3, s4], [YN]);
eval(A0);
FN_1 := seq(f[n+k], k = 1 .. 4);
B1, b2 := GenerateMatrix([s1, s2, s3, s4], [FN_1]);
eval(B1);
FN := seq(f[n-k], k = 3 .. 0, -1);
B0, b3 := GenerateMatrix([s1, s2, s3, s4], [FN]);
eval(B0);
ScalarMultiply(R, A1)-A0;
det := Determinant(ScalarMultiply(R, A1)-A0);
P1 := A1-ScalarMultiply(B1, z);
P2 := combine(simplify(P1, size), trig);
P3 := MatrixInverse(P2);
P4 := A0-ScalarMultiply(B0, z);
P5 := MatrixMatrixMultiply(P3, P4);
P6 := Eigenvalues(P5);
f := P6[4];
T := unapply(f, z);
implicitplot(f, z = -5 .. 5, v = -5 .. 5, filled = true, grid = [5, 5], gridrefine = 8, labels = [z, v], coloring = [blue, white]);

## Maple GUI issues...

Why the performance of Maple GUI is bad. It is really hard to type anything in thew gui.