Is there a way to take the laplacian of 1/r and get the "physics" answer of -4*pi*delta(\vec{r})?

with(plots):R := 5; alpha := (1/9)*Pi;
C1 := plot([R*cos(t), R*sin(t), t = 0 .. 2*Pi], color = blue);
A := [R*cos(alpha), R*sin(alpha)]; B := [R*cos(alpha+Pi), R*sin(alpha+Pi)]; AB := plot([A, B], scaling = constrained);
display({AB, C1}, scaling = constrained);# bad drawing

https://aws.amazon.com/getting-started/projects/deploy-elastic-hpc-cluster/

is it possible to use maple on high performance clusters?

i can only think to use c program to call cmaple with MPI in linux to use high performance clusters.

is there any other official method to do this?

if i upload my maple 2015 version to amazon for this computing, will it used up all license in this first chance of installation leading to that i can not install maple 2015 linux version to other machine?

https://docs.aws.amazon.com/AWSEC2/latest/WindowsGuide/ConfigWindowsHPC.html#ComputeNode

which virtual machine should i install the maple 12? on one virtual machine or all compute nodes?

how many compute nodes are need to compute dsolve 100,000 systems which may or may not have solution in maple 12?

Hi all

We denote the collecction of sets determined by the first k coin tosses

Suppose the imitial stock price is ,with up and down facter being and .

Up : S1(H)=u S0 and S1(T)=d S0

S_{N+1}= alpha S_N

where alpha =u or d

Let the probability of each and be and and   the sigma-lgebra generated by the coin tosses up to (and inchudling) time t:

After three coin tosses.

Can we propose a code computing the element of the filtration F1 and F3 and sigma(S3) (the sigma algebra generated by S3).

For example by hand we have F1={ emptyset, Omega, AH, AT}

Where AH={ w: w1=H}

AT={w: w1=T}

Can we compute

restart;
with(Finance);
S := [7.9, 7.5, 7.1, 6.5, 5., 3.7, 3.3, 2.95, 2.8];
         [7.9, 7.5, 7.1, 6.5, 5., 3.7, 3.3, 2.95, 2.8]
T := BinomialTree(3, S, .3);
TreePlot(T, thickness = 2, axes = BOXED, gridlines = true);

many thanks

Hello all,

I'm trying to do kinetic modeling of sequential dissociations with DE. I'm hitting a snag when modeling the third dissociation. The population should start at zero at t=0, but some of my model functions are non-zero at t=0. Is there anyway to fix this to force the funtions to go through zero?

Scheme:
PPPP -> intermediates -> PPP -> intermediates -> PP -> intermediates -> P  
(where P is a subunit and intermediates are confirmational changes before dissociation of a subunit)

a'..d' is the first dissociation
e' is the second dissociation
f'..l' is the third dissociation
Fits are evaluated by the residual sum of squares.

sol := dsolve([a' = -k1*a(x), b' = k1*a(x)-k1*b(x), c' = k1*b(x)-k1*c(x), d' = k1*c(x)-k1*d(x),
e' = k1*d(x)-k2*e(x), 
f' = k2*e(x)-k3*f(x), g' = k3*f(x)-k3*g(x), h' = k3*g(x)-k3*h(x), i' = k3*h(x)-k3*i(x), j' = k3*i(x)-k3*j(x), k' = k3*j(x)-k3*k(x), l' = k3*k(x)-k3*l(x), 
a(0) = 1, b(0) = 0, c(0) = 0, d(0) = 0, e(0) = 0, f(0) = 0, g(0) = 0, h(0) = 0, i(0) = 0, j(0) = 0, k(0) = 0, l(0) = 0],
{a(x), b(x), c(x), d(x), e(x), f(x), g(x), h(x), i(x), j(x), k(x), l(x)}, method = laplace);

f1 := sol[6];
f1 := rhs(f1);
g1 := sol[7];
g1 := rhs(g1);
h1 := sol[8];
h1 := rhs(h1);
i1 := sol[9];
i1 := rhs(i1);
j1 := sol[10];
j1 := rhs(j1);
kk := sol[11];
kk := rhs(kk);
l1 := sol[12];
l1 := rhs(l1);

xdata := Vector([0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180,200,210,220,230,240,250,260,270,280,290,300,310,320,330,340,350,360,370,380,390,400], datatype = float);
ydata := Vector([0.0034,0.00392,0.00184,0.00782,0.01873,0.03683,0.11016,0.09838,0.18402,0.24727,0.20901,0.2972,0.37635,0.49235,0.57845,0.4457,0.50285,0.5672,0.62783,0.57264,0.54918,0.44792,0.49795,0.55218,0.47512,0.46473,0.37989,0.32236,0.3323,0.20894,0.28473,0.21273,0.19855,0.13548,0.12725,0.13277,0.0784,0.07969,0.06162,0.03855], datatype = float);

k1 := 0.391491454107626e-1; 
k2 := 0.222503562261129e-1; 

z1:=f1;
z2:=f1+g1;
z3:=f1+g1+h1;
z4:=f1+g1+h1+i1;
z5:=f1+g1+h1+i1+j1;
z6:=f1+g1+h1+i1+j1+kk;
z7:=f1+g1+h1+i1+j1+kk+l1;

Statistics[NonlinearFit](z1,xdata, ydata, x, initialvalues = [k3=0.1], output = [parametervalues, residualsumofsquares]); 
A:=plot(xdata, ydata, style=point, symbol=solidcircle, color=blue, symbolsize=12,labels = ["time (minutes)", "Relative Abundance"], labeldirections = [horizontal, vertical]):
F:=Statistics[NonlinearFit](z1,xdata, ydata, x,initialvalues = [k3=0.1]):
B:=plot(F, x=xdata[1]..xdata[-1], color=red):
plots[display](A, B);

Statistics[NonlinearFit](z2,xdata, ydata, x, initialvalues = [k3=0.1], output = [parametervalues, residualsumofsquares]); 
A:=plot(xdata, ydata, style=point, symbol=solidcircle, color=blue, symbolsize=12,labels = ["time (minutes)", "Relative Abundance"], labeldirections = [horizontal, vertical]):
F:=Statistics[NonlinearFit](z2,xdata, ydata, x,initialvalues = [k3=0.1]):
B:=plot(F, x=xdata[1]..xdata[-1], color=red):
plots[display](A, B);

Statistics[NonlinearFit](z3,xdata, ydata, x, initialvalues = [k3=0.1], output = [parametervalues, residualsumofsquares]); 
A:=plot(xdata, ydata, style=point, symbol=solidcircle, color=blue, symbolsize=12,labels = ["time (minutes)", "Relative Abundance"], labeldirections = [horizontal, vertical]):
F:=Statistics[NonlinearFit](z3,xdata, ydata, x,initialvalues = [k3=0.1]):
B:=plot(F, x=xdata[1]..xdata[-1], color=red):
plots[display](A, B);

Statistics[NonlinearFit](z4,xdata, ydata, x, initialvalues = [k3=0.1], output = [parametervalues, residualsumofsquares]); 
A:=plot(xdata, ydata, style=point, symbol=solidcircle, color=blue, symbolsize=12,labels = ["time (minutes)", "Relative Abundance"], labeldirections = [horizontal, vertical]):
F:=Statistics[NonlinearFit](z4,xdata, ydata, x,initialvalues = [k3=0.1]):
B:=plot(F, x=xdata[1]..xdata[-1], color=red):
plots[display](A, B);

Statistics[NonlinearFit](z5,xdata, ydata, x, initialvalues = [k3=0.1], output = [parametervalues, residualsumofsquares]); 
A:=plot(xdata, ydata, style=point, symbol=solidcircle, color=blue, symbolsize=12,labels = ["time (minutes)", "Relative Abundance"], labeldirections = [horizontal, vertical]):
F:=Statistics[NonlinearFit](z5,xdata, ydata, x,initialvalues = [k3=0.1]):
B:=plot(F, x=xdata[1]..xdata[-1], color=red):
plots[display](A, B);

Statistics[NonlinearFit](z6,xdata, ydata, x, initialvalues = [k3=0.1], output = [parametervalues, residualsumofsquares]); 
A:=plot(xdata, ydata, style=point, symbol=solidcircle, color=blue, symbolsize=12,labels = ["time (minutes)", "Relative Abundance"], labeldirections = [horizontal, vertical]):
F:=Statistics[NonlinearFit](z6,xdata, ydata, x,initialvalues = [k3=0.1]):
B:=plot(F, x=xdata[1]..xdata[-1], color=red):
plots[display](A, B);

Statistics[NonlinearFit](z7,xdata, ydata, x, initialvalues = [k3=0.1], output = [parametervalues, residualsumofsquares]); 
A:=plot(xdata, ydata, style=point, symbol=solidcircle, color=blue, symbolsize=12,labels = ["time (minutes)", "Relative Abundance"], labeldirections = [horizontal, vertical]):
F:=Statistics[NonlinearFit](z7,xdata, ydata, x,initialvalues = [k3=0.1]):
B:=plot(F, x=xdata[1]..xdata[-1], color=red):
plots[display](A, B);

3rd_diss.mw

Example of Duffing equation with boundary conditions.
y'' + 0.2y' + y^3 - 0.3cos(s) = 0;
y(0) = y (2Pi);
y'(0) = y'(2Pi);
For convenience, we replace the original equation with a system of two first order equations:
--------------------------------------------------------------------------
x1'(t) = 2*Pi*x2(t);
x2'(t) = - 0.4*Pi*x2(t) - 2*Pi*x1(t)^3 +0.6*Pi*cos(2*Pi*t);
x1(0) = x1(1);
x2(0) = x2(1);
--------------------------------------------------------------------------
I have long wanted to apply an optimization package to solve a boundary value problem for ODE. The decision helped procedure for solving ODE, written by forum member vv.
It seems to me that two solutions have been found and that the solutions are weakly sensitive to the initial approximations. These are two closed trajectories. For example, these are points that belong to these solutions:
(0.5966963,  1.0482816) , ( - 0.3132584, 0.0664941).
I am wondering: are the solutions right, and how justified is the use of optimization methods for such tasks?
At the end of the program, the solution is checked on the original Duffing equation using standard Maple functions.   Duffing_equation_BC.mw

(In the figures, the trajectory bypass occurs three times.)

If worksheet execution was started and computer is locked before execution ends, Maple will stop responding and all work is lost. Execution of whole worksheet takes very long time, sometimes over 3 hours, so "do not lock computer during execution" is not solving the problem.

What are the most efficient way to write and evaluate a procedure in maple? Thank you.

I have made a document to give the results for a problem in table form and graph form.

The tables work out well. The graph results also come out well when I have that section alone in the document. But it does not give the updated curve here. Please correct me where I made mistake.
 

Startup Code Region contains all the codes.

Download Doubt_x_symbolic_required.mw

Thanks.

Hello,

I use MapleSim to model the dynamics of motorcycles.
I have been at MapleSim2018 for a few months and I have a problem of simplifying the equations generated by MapleSim from my model.
In MapleSim2018, he tells me:

Processing Equations...
SelectCompiler: Check for installed compiler successful
Simplifying system with 8919 equations
DSN/ix1lite: Warning, equation size increased past 100000 while performing equation simplification. Model will be simulated in partially unsimplified form
Simplification removed 8428 equations. Remaining equations: 491
Generating simulation code

the same model (exactly the same) in MapleSim2016, he tells me :

Processing Equations...
Simplifying system with 8942 equations
Simplification removed 8494 equations. Remaining equations: 448
Generating simulation code

When I generate code from two versions of Maple (2016 and 2018) and compile it into an executable, the MapleSim 2018 executable runs 20% slower than the MapleSim 2016 version of the executable (the results and the behavior of both models are equivalent)

It is very strange that a new version of MapleSim generates a slower code than the old version. it may be due to the limitation of DSN / ix1lite in MapleSim2018 ... while MapleSim2016 does not have this limitation (with more equations to simplify!).

I need help, if it is possible to activate the complete simplification in DSN / ix1lite?

it is a big problem for me, the use of MapleSim2018 is not possible because of that. My model does not pass in real time.

thanks.

Hello every one,

My slideshow now contains a lot of animation sequences and take
a very long time to load and a large amount of physical memory (>20GB).

To reduce this size I have decided to convert these animations to GIF format.
Unfortunatly Maple/MaplePayer do not play GIF animations.

I decide to put URLs (image icons pointing to GIF files) in the document.
Now the GIF are play by a WEB browser (program to operate in fullscreen 
mode to minimize any disturbance in the audience with IE11).

Now the issue:
Using F11 to start the Slideshow, cliking the URL start the browser with the requested
animated GIF, that is fine, but now Maple/MaplePayer both auto-exit fullscreen
mode just after that click. The speaker (me) now need to manage the return to
fullscreen (F11) at the current slide while thinking about what i have to
say next.

Is there any trick to prevent auto-exit from fulls-screen mode in this situation?

Thank you for your help

LL

Des suggestions de solutions? Merci.

A) a) Écrire une procédure qui produit une itération du calcul babylonien de la racine carrée d'un nombre positif k à partir     d'une première approximation x₀ .

    Entrée: k , x₀ .

    Sortie:  x₁ = (x₀+ k/x₀)/2 .

b) En utilisant la procédure trouvée en a), en écrire une autre, qui prend en entrée un entier positif n en plus des entiers k   et x₀ vus en a) et qui retourne en sortie n itérations du calcul babylonien de la racine carée de k.

 B)

Écrire une procédure récursive Maple qui prend en entrée deux nombres n et k et qui utilise l'identité (ⁿ _k) = (^{n -1}_k)+(^n-1 _k-1) pour retourner en sortie le coefficient binomial (n k) , cette procédure ne doit pas utiliser la commande Maple binomial.

TRADUCTION:

Suggestions for solutions? Thank you.

A) a) Write a procedure that produces an iteration of the Babylonian calculus of the square root of a positive number k from a     first approximation x₀.

    Input: k, x₀.

   Output: x₁ = (x₀ + k / x₀) / 2.

b) Using the procedure found in a), write another one, which takes as input a positive integer n in addition to the integers k and   x₀ seen in a) and which returns in exit n iterations of the Babylonian calculation of the square root of k.

B) Write a Maple recursive procedure that takes as input two numbers n and k and uses the identity (ⁿ _k) = (^n-1 _k)+ (^n-1 _k-1) to   return the binomial coefficient (ⁿ _k), this procedure should not use the binomial Maple command.

Hi , how we can read the fractional differential equations in maple with out solving . I means just read and determine which is the order of fractional differential equations.

thanks

Hello everyone!

In previous versions of Maple (e.g. Maple 2016) it used to be possible to use scaletorange and colorscheme options together as in:

densityplot(sin(x+y), x = -1 .. 1, y = -1 .. 1, colorscheme = [black, red, yellow, white], scaletorange = -.5 .. .5);

But Maple 2018 returns an error:

Error, (in plots/densityplot) the scaletorange option cannot be used with the colorscheme option

Why is that and can one work around this error in any simple way?

I need an example programme please help me i m beginner