Hello! 

For the last couple of days I've been trying really hard to solve the linear PDE 

 . Where R is a function R(t,q(t),p(t)) and H is the hamiltonian H=   .

(dH/dp= p and dH/dq= -2q-2), q and p depends on the time t, and I'm supposed to solve the PDE and then plot the gaussian distribution (2D). 

I tried doing this:

pde := diff(R(t, q1(t), p1(t)), t) = -(diff(R(t, q(t), p(t)), q(t)))*p(t)+(diff(R(t, q(t), p(t)), p(t)))*(-2*q(t)-2)

But pdsolve(pde) gives me:  "Error, (in pdsolve/info) the name of the indeterminate function must be given". 

When I change q(t) to q and p(t) to p I get:

R(t, q, p) = _F1(p^2-2*q^2-4*q, -(1/2)*ln(sqrt(2)*q+p+sqrt(2))*sqrt(2)+t)

And then I'm lost. How do I solve this PDE in maple? 

Thankful for any help 

Hi,

I'm attempting to plot the distribution of the fractional part of a sequence of real numbers in the interval (0,1], where the fractional part of a real number x is given by <x>=x-[x], where [x] is the floor function.

In particular, I'm attempting to plot <log(n)> and <n^a> where n is a natural number and 0<a<1.

I know that I can use frac() to obtain the fractional part of the expressions.

However, I'm not sure how to plot a two-dimensional plot where the x-axis consists of a range for n and the y-axis in the inteval [0,1). I found an example of what I'm trying to do here on page 1.

Does anyone have any tips on how to do this?

dsolve(f(x,y),y(x),parametric) in Maple 9.5 outputs an expression for y(_T) and for x(_T).

(from the book "Computer Algebra Recipes for Mathematical Physics by Richard H. Enns, section 7.1.1, finding the parametric equation of the brachistochrone)

but the same command in Maple 2016 outputs an expression for y(x) only.

Why do Maple 9.5 and Maple 2016 produce different output?

Where can I find a help page explaining or giving examples of dsolve, parametric?

I have made an algorithm for producing random walks (only possible to walk one step to either direction except downwards(EDIT: It is possible to go downwards, but it has to be when making a turn to the right or left). The walks are determined by the rand function:

R3:=rand(1..3): (1: go straight on; 2: turn right; 3: turn left)
M:=15; N:=1500;

Randwalk3:=proc(R3)
  local i,j,r,X,Y,L;
  for j from 1 to M do
    X[0,j]:=0;                                # Initialization
    Y[0,j]:=0;
    X[1,j]:=1;                                # The first step should still be taken to the point (1,0)
    Y[1,j]:=0;
    for i from 2 to N do
      r:=R3();
      if r=1 then X[i,j]:=2*X[i-1,j]-X[i-2,j]; Y[i,j]:=2*Y[i-1,j]-Y[i-2,j];                   # go straight on
      elif r=2 then X[i,j]:=X[i-1,j]+Y[i-1,j]-Y[i-2,j]; Y[i,j]:=Y[i-1,j]-X[i-1,j]+X[i-2,j];    # turn right
      else X[i,j]:=X[i-1,j]-Y[i-1,j]+Y[i-2,j]; Y[i,j]:=Y[i-1,j]+X[i-1,j]-X[i-2,j];             # turn left
      end if;
      if (X[i,j]=X[j,j] and Y[i,j]=Y[j,j]) then L[j]:=i; break; end if; (This is wrong)
    end do;
  end do:
  return [X,Y,L];
end proc:
 

The question from is like this:
Modify the algorithm such that it stops at r[i] if r[i] = r[j] for any 0 <= j <= i-2. r=(xi,yi). M is the number of random walks and N is the number of steps. The length of the paths should be stored in L[m] (m=1..M). How do I implement the if-test correctly?

Alle_opgaver.mw
 

Dear all

My son is studying at the Danish University, DTU, where he studies engineering. He is experiencing a problem with maple as the system writes :"There were problems during the loading process. Your worksheet may be incomplete". I can see that other people have had  their file corrected by a script by Joe Riel 6845.I just want to make sure that the right way to use this script is to open .mw file in an texteditor like notepad++ and then copy the script in top of the file and then save the file again and open it in maple ? I would appreciate your help very much. As it looks now,  my son has lost his entire work, if this error cant be corrected.

Best regards
Lars Wagenblast

I meet a interesting nonlinear system in the analysis of an mechanics problem. This system can be shown as following:

wherein, the X and Y is the solutions. A, B, S, and T is the symbolic parameters.

I want to express X and Y with A, B, S, T. Who can give me a help, thanks a lot!

PS:the mw file is given here.

A_symbolic_nonlinear_system.mw

Dear all,

I am trying to run a maple worksheet as an input file, in another maple worksheet. Therefore, I have exported my input worksheet to an inputfile (.mpl).

In the input file I have a variable H, which I vary in the second worksheet.

restart;
with(ExcelTools);
with(ListTools);
B := Import("C:\\Users\\s110950\\Dropbox\\Afstuderen\\New formula\\Importdata\\161005 - Staalprofielen.xlsx", "Blad1", "A7:AA344");

V := ["IPE 330", "IPE 360"];
currentdir("C:\\Users\\s110950\\Dropbox\\Afstuderen\\New formula\\Afrondingstraal")

for i  from 1 to 2 do
H := V[i];
cmaple.exe<"C:\\Users\\s110950\\Dropbox\\Afstuderen\\New formula\\Afrondingstraal\\Model38loop.mpl">;
 end do; 

However, it does not run the file. Does anyone know how to make it run?

Kind regards,
Bastiaan Overdorp

I've been tasked with generating "phase plots" which are visualizations of complex functions. 

A 2D phase plot is easy to create: Given a complex function F : C -> C colour points (x, y) in R^2 by [ arg(F(x+I*y)), 1, 1, colortype=HSV].   Something like the following seems to do the trick
    
    p := plot3d( 
        1,
        x=-5..5,
        y=-5..5,
        scaling=constrained,
        color=[ argument(f(x+I*y))/2/Pi, 1, 1, colortype=HSV],
        axes=none,
        style=patchnogrid,
    ):
    
    g := plottools[transform]((x,y,z)->[x,y],p);
    plots[display]( g(p) ):

Now, "colouring each point of R^2" is only possible using some type of bijection onto the Riemann sphere or Pseudosphere.

The pseudosphere is:

    x := (u,v) -> sech(u)*cos(v);
    y := sech(u)*sin(v);
    z := u - tanh(u);
    
    return  plot3d(
        [x(u,v),y(u,v),z(u,v)],
        u=0..3,
        v=0..2*Pi,
        numpoints=2^10,
        lightmodel=none,
        color=ColorFunc(u,v) );

In this case I need  ColorFunc to be:

ColorFunc := proc(u,v)
    x, y := v, exp(u);
    ans  := Re( f(x+I*y) );
    if ans > 2*Pi then
       return [0,0,0,colortype=HSV];
    end if;
    return [ans/2/Pi,1,1,colortype=HSV];
end proc;

But it seems that "ColorFunc" cannot be very sophisticated.  Namely, it cannot contain "frems" or even "if" statements because (as far as I can tell) of the order of evaluations.  

It seems possible that I can generate a psuedosphere then change colours AFTER by swapping out the COLOR information in a more sophisticated way.  How can I do this?  I really just need to know how to identify and swap out points from a MESH.

h1_y_h2.mw
 

im trying to build a matrix starting from a function, so i can later use this matrix to get a more simple function using linearfit from the statistics package, like a kind of regression.

i want to get a matrix starting from h__1(T1,T__1s) so it has to be a 3 columns matrix (T__1,T__1s,h__1). so as you can see, i have got the functions h__1 and h__2, but i need to evaluate it at differents values for T__1 and T__1s and building a kind of value-table in matrix form.

for h__1, T__1 must be higher than T__1s, or you could get imaginary values, don't know if that important for building the matrix.

thank you very much for your help.

Download h1_y_h2.mw

I want to plot some color points in CIE 1976 color space with SpatterPlot command exactly as showed on the help page. When I try:

restart:with(ColorTools):with(ImageTools):
barvy:=Color("Lab",[80.38,13.50,7.96]); 	
SpatterPlot(barvy,symbol="box");

I got the error:

Error, invalid input: ColorTools:-SpatterPlot expects its 1st argument, colors, to be of type list({ColorTools:-Color, name, string, list({float, nonnegint}), specfunc({COLOR, COLOUR})}), but received _m2194815429568

Where is the problem?
 

with(IterativeMaps);
with(ImageTools);
Logistic := Bifurcation([x], [r*x*(1-x)], [.5], 2.5, 4);
ArrayTools:-Dimensions(Logistic);
ColouringProcedures:-HueToRGB(Logistic);
Embed(Logistic);

This is the code for Bifurcation program of the Logistic map. How can I change the black background color of this figure, and How can I save this figure.

Download Sum_Sum.mw
 

Download Sum_Sum.mw

Please anyone, I have been battling with this problem for a while yet the error message keeps coming. Would be happy if responded to.

Thanks 
 

Download kuikennnnnn.mw
 

Let us consider the improper integral

int((abs(sin(2*x))-abs(sin(x)))/x, x = 0 .. infinity);

Si(Pi)-Si((1/2)*Pi)+sum(-(-1)^_k*Si(Pi*_k)+signum(sin((1/2)*Pi*_k))*Si((1/2)*Pi*_k)+Si(Pi*_k+Pi)*(-1)^_k-signum(cos((1/2)*Pi*_k))*Si((1/2)*Pi*_k+(1/2)*Pi), _k = 1 .. infinity)
                    

Mathematica 11 produces a similar expression and a warning

Integrate::isub: Warning: infinite subdivision of the integration domain has been used in computation of the definite integral \!\(\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Infinity]\)]\(\*FractionBox[\(\(-Abs[Sin[x]]\) + Abs[Sin[2\ x]]\), \(x\)] \[DifferentialD]x\)\). If the integral is not absolutely convergent, the result may be incorrect.

Up to Pedro Tamaroff http://math.stackexchange.com/questions/61828/proof-of-frullanis-theorem , the answer is 2/Pi*ln(2) because of 

J := int(abs(sin(2*x))-abs(sin(x)), x = 0 .. T) assuming T>2;
-1/2-signum(sin(T))*signum(cos(T))*cos(T)^2+(1/2)*signum(sin(T))*signum(cos(T))+cos(T)*signum(sin(T))+floor(2*T/Pi)

B := limit(J/T, T = infinity);
                               2 /Pi

K := x*(int((abs(sin(2*t))-abs(sin(t)))/t^2, t = x .. 1)) assuming x>0,x<1;

     2*sin(x)*cos(x)-2*Ci(2*x)*x+Ci(x)*x+sin(1)*x-sin(2)*x+2*Ci(2)*x-Ci(1)*x-sin(x)

                         
A := limit(K, x = 0, right);
                               0

Its numeric calculation results 

evalf(Int((abs(sin(2*x))-abs(sin(x)))/x, x = 0 .. infinity));
                        Float(undefined)

which seems not to be true.

The question is: how to obtain the reliable results for it with Maple, both symbolic and numeric? 

Hello. Two teams A and B (consisting of 2, 3 or even 4 players) compete and the outcome of each game is either a win or a loss. I have a to process the new (gaussian) laws of players given whom beats whom.

Given the initial means and standard deviations of the players, I have a algorithm (RC) which computes the new laws of the players. [the actual algorithm i use is different to the one i am showing here]. 

By way of example consider two teams with 2 players per side. Each person plays 2 games.

The initial laws of A1,A2,B1,B2 are given.

(A1,B1) --->(A1',B1').......[iteration 1. A1 beats B1, resulting in new laws A1' and B1'(computed by RC)]

(B2, A1') --->(B2', A1").......[ iteration 2. B2 beats A1. using A1' from iteration 1. A1 has played twice and is denoted by A1"]

(B2',A2) --->(B2",A2').......[ iteration 3. B2 beats A2. using B2' from iteration 2.  B2 has finished and is denoted by B2"]

(A2',B1') --->( A2",B1")......[ iteration 4. A2 beats B1. using B1' from iteration 1 and A2' from iteration 3. now all players have played their matches]

new laws A1" ,A2", B1" & B2" should be outputted.

my first code gets the result, but it is tedious to enter the iterations in the right place .especially for teams of 3 or more.

my second with parameters gets errors.

So what i want is to enter who beat who:

eg  [[B1, A1], [B2,A1], [B2, A2], [A2, B1]];
and the final laws are computed automatically.

bb_processing_edit.mw