Is there any Maple code that allows to view a complex function using the "domain coloring" technique?

This technique is described for example in Wikypedia: https://en.wikipedia.org/wiki/Domain_coloring

How I can determine a function that satisfy these boundary and initial conditions.

Thank you

S2

Maple Worksheet - Error

Failed to load the worksheet //convert/S2
 

Download S2

How I can do ?

Thank you.

Substitution of . 5,6,7) into Eqs. 1–(4), gives the new equation as functions of the generalized coordinates,
u_m,n(t);  v_m,n ( t), and w_m,n ( t). These expressions are then inserted in the Lagrange equations (see Eq. 8)) a set of N second-order coupled ordinary differential equations with both quadratic   and cubic nonlinearities.

In Eq (8) q are generalized coordinate such as uvw  and .

\where the elements of the vector, are the time-dependent generalized coordinates.

L_Maple
 

Download L_Maple

How come maple doesn't support symbolic matrix calculus?

For example, I'd like to differentiate or simplify expressions with relation to general vectors and matrices. Besides simpifying the expressions, in runtime (e.g. optimizing a function in matlab) my vector and matrix size change according to the data, so deriving specific expressions element-wise would only be valid for a specific case.

A simple example (A is a matrix, x is a vector):

f(x) = ||Ax||^2

df/dx = 2A'Ax

Recently, I stumbled into this

http://www.matrixcalculus.org/

where you can try my example above: norm2(A*x)^2

I was wondering how come that mature symbolic softwares on the market (maple and mathematica) can't do it?

While googling around for Season 8 spoilers, I found data sets that can be used to create a character interaction network for the books in the A Song of Ice and Fire series, and the TV show they inspired, Game of Thrones.

The data sets are the work of Dr Andrew Beveridge, an associate professor at Macalaster College (check out his Network of Thrones blog).

You can create an undirected, weighted graph using this data and Maple's GraphTheory package.

Then, you can ask yourself really pressing questions like

• Who is the most influential person in Westeros? How has their influence changed over each season (or indeed, book)?
• How are Eddard Stark and Randyll Tarly connected?
• What do eigenvectors have to do with the battle for the Iron Throne, anyway?

These two applications (one for the TV show, and another for the novels) have the answers, and more.

• Game of Thrones and Graph Theory
• A Song of Ice and Fire and Graph Theory

The graphs for the books tend to be more interesting than those for the TV show, simply because of the far broader range of characters and the intricacy of the interweaving plot lines.

Let’s look at some of the results.

This a small section of the character interaction network for the first book in the A Song of Ice and Fire series (this is the entire visualization - it's big, simply because of the shear number of characters)

The graph was generated by GraphTheory:-DrawGraph (with method = spring, which models the graph as a system of protons repelling each other, connected by springs).

The highlighted vertices are the most influential characters, as determined by their Eigenvector centrality (more on this later).

The importance of a vertex can be described by its centrality, of which there are several variants.

Eigenvector centrality, for example, is the dominant eigenvector of the adjacency matrix, and uses the number and importance of neighboring vertices to quantify influence.

This plot shows the 15 most influential characters in Season 7 of the TV show Game of Thrones. Jon Snow is the clear leader.

Here’s how the Eigenvector centrality of several characters change over the books in the A Song of Ice and Fire series.

A clique is a group of vertices that are all connected to every other vertex in the group. Here’s the largest clique in Season 7 of the TV show.

Game of Thrones has certainly motivated me to learn more about graph theory (yes, seriously, it has). It's such a wide, open field with many interesting real-world applications.

Enjoy tinkering!

I define the spherical Bessel function with j([n, z]) := sqrt(2)*sqrt(Pi/z)*BesselJ(n + 1/2, z)/2.  Then I attempt to plot with

Digits := 20;
plot(j([1, z]), z = 0 .. 25);

I get an empty plot and an error message: 

Warning, expecting only range variable z in expression j([1, z]) to be plotted but found name j

which makes no sense to me.

(I am using Maple 2019.)

Hi

I would like to solve the non-linear system to obtain rho1 and rho2 .

But when i use solve i get the following error
Error, (in solve) cannot solve for an unknown function with other operations in its arguments

system.mw

many thanks

>SIRvector := [op(SIRvector), op(evalf(solve(eval({Yeqnx(1), Yeqny(1), Yeqnz(1)}, SIRvector), {JJ(1), RR(1), SS(1)})))];

I have a picture. I tried to find the formula of the curve
My code

t := proc (x) options operator, arrow; b*x^10+c*x^9+d*x^8+e*x^7+f*x^6+g*x^5+h*x^4+i*x^3+j*x^2+k*x+l end proc

And solve
solve([t(-2) = 2, t(0) = -2, t(1) = 0, t(2.5) = -3, t(3.5) = 0, t(-1) = 0, eval(diff(t(x), x), x = -2) = 0, eval(diff(t(x), x), x = 0) = 0, eval(diff(t(x), x), x = 2.5) = 0, eval(diff(t(x), x), x = 1) = 0, t(2.8) = 0], [b, c, d, e, f, g, h, i, j, k, l])

[[b = -0.2688965311e-1, c = .1687428810, d = -0.3166922031e-1, e = -1.490599337, f = 1.885667707, g = 3.845330330, h = -6.939129440, i = -2.523473874, j = 7.112020606, k = 0., l = -2.]]

I ploted

plot(-.2688965311*x^10+.1687428810*x^9-.3166922031*x^8-1.490599337*x^7+1.885667707*x^6+3.845330330*x^5-6.939129440*x^4-2.523473874*x^3+7.112020606*x^2-2, x = -3.5 .. 4.5)

The result too far with picture. How can I repair?

I want to made a comparison via plots of RK-4, NSFD and LWM.

Restart

eqn1 := diff(x(t), t) = x(t)*(2-(1/20)*x(t))-x(t-tau)*y(t)/(x(t)+10)-10;

eqn2 := diff(y(t), t) = y(t)*(x(t)/(x(t)+10)-2/3);

bc := x(0) = 40, y(0) = 16,tau=0;

sol := dsolve({bc, eqn1, eqn2}, numeric);

plots[odeplot](sol, 0 .. 10);

I got the plot Vertically x and horizontally t but i need vertically y and horizontally x, Please help me, how can i write the code for ploting, thanks in advance.

I am trying to calculate the contour integral of exp(-z/A)/z^{2+n}, for constant A and integer n. Here is the Maple code (forgive me, very beginner Maple user here!):

restart;

f := exp(-z/A)/z^(2 + n);
                                 /  z\
                              exp|- -|
                                 \  A/
                         f := --------
                               (2 + n)
                              z       


op~([singular(f, z)]);
                            [z = 0]
poles := [0];
                          poles := [0]
C := z -> is(abs(z) < 1);
assume(2 <= n);
(2*Pi)*I*add(residue(f, z = a), a = select(C, poles));
                              /   /  z\       \
                              |exp|- -|       |
                              |   \  A/       |
                2 I Pi residue|--------, z = 0|
                              | (2 + n)       |
                              \z              /

You can do this by hand by simply expanding the exponential, but how do I make Maple actually do the calculation? (instead of just answering with "residue...".

hi, i am trying to solve a PDE f(x,z,t) with mixed boundary conditions, while Maple just gives u(x,z,t)=0 which is incorrect, so i believe somewhere must be wrong, someone has an idea?  

Governing equation: ,    0<x<M, 0<z<L, t>0

IC: heat source is a point at (0, z0):  u(x,z,0)=c*dirac(x-0)*dirac(z-z0) , where c is a temperature at t=0.

boundarys of domain are cauchy boundaries: du(0,z,t)/dx=0;  du(M,z,t)/dx=0; du(x,0,t)/dz=0;  du(x,L,t)/dz=0

the code is: 

PDE := diff(u(x, z, t), t) = a*(diff(u(x, z, t), x, x))+b*(diff(u(x, z, t), z, z));
IBC := u(x, z, 0) = c*Dirac(x-0)*Dirac(z-z0), (D[1](u))(0, z, t) = 0, (D[1](u))(M, z, t) = 0, (D[2](u))(x, 0, t) = 0, (D[2](u))(x, L, t) = 0;

pdsolve([PDE, IBC], u(x, z, t)) assuming 0<x<M, 0<z<L

thanks in advance!! 

Hi, 

I was able to determine a cubic spline fit, F(v), to x1 and y1. Now I have vector x2 which I would like to use F(v) to calculate y2 as another Vector[row]. I am having trouble accomplishing this task. Any help is greatly appreciated. Thanks.
 

Download splfit.mw

I have a similar matrix.

Build through matrixplot, not exactly what I need to get. I need a way to plot without zero values on the graph.