MaplePrimes Questions

I can't understand why Maple interprets 1 .05  as 1 * 5 = 5 , and 2 .05  as 2 * 5 = 10 . Note the space between 1 and .05
In a different calculation I accidentally inserted a space between 1 and .05, and received a strange answer, and finally narrowed it down to a space.
But now I wonder why it is it is interpreting this way. Also I see that 2  0.05 produces an error. But  2 .05 is treated as 10. There is an implied multiplication? But the multiplication should be 2 * .05 , which is 1 and not 10.

Good day, all.

I would like to explore the structure of the discrete modified form of the logistic equation.

In particular, I wish to plot the logistic-map to investigate the bifurcations of the system.

Is there a routine available in Maple that I can use?

I would like to consider the standard logistic equation with the inclusion of a shape parameter, m, introduced as a power law.

That is:

f(x) = a*x*(1-x^m)

where a > 0 denotes the growth rate, and m > 0  is a shape parameter. I wish to fix the value of a and take m to be the bifurcation parameter (so the logistic map would show m versus x for any given a).

Please note: The standard logistic equation (in discrete form) is given by f(x) = a*x*(1-x)

I would be grateful for any advice and support you can provide and I thank you for taking the time to read this.

i found thus condition which if we substitute in equation must be equal to zero, i don't know  how i can get zero

test_pde1.mw

RandC := proc(k := getSystemTimeMS())
    local r,b,g,kk;
    kk := k+ parse(convert(Time(), string)[6..18]);
    kk := (randomize(round(k*time[real]() + getSystemTimeMS() + time[real]())));    
    (randomize(round(k*time[real]() + getSystemTimeMS() + time[real]())));    
    r := rand(0..1.0)();
    kk := k+ parse(convert(Time(), string)[6..18]);
    (randomize(round(k*time[real]() + getSystemTimeMS() + time[real]())));    
    kk := (randomize(round(kk*r + k + time[real]() + getSystemTimeMS())));    
    g := rand(0..1.0)();
    kk := k+ parse(convert(Time(), string)[6..18]);
    (randomize(round(k*time[real]() + getSystemTimeMS() + time[real]())));    
    kk := (randomize(round(kk*g + k*r*time[real]() + getSystemTimeMS())));
    b := rand(0..1.0)();
    [RGB(r,g,b)];
end proc:

Been trying to generate random colors but nothing works because obviously maple decides to cache the results if the arguments are the same. If I call RandC with an argument that changes it will give me different values. If not it will sometimes give me different values but usually there will be long strings of the same value.

Hence when I generate a sequence of random colors I will almost always get a sequence of the same color or a sequence that containst the same color many times. I'd like to be able to use RandC without having to provide arguments.

(all the junk in the function was trying to get it to randomize properly as I didnt' realize maple was caching. Also Value(Time()) does not return the ms and seems to do nothing which contradicts the help and hence the parse)

This seems like a dangerous thing for maple to do. Silently caching results that depend on random generation will result in non-random results. It could skew many results.

each time i use this i did not have any problem but this equation not seperate any one know what is problem?

restart

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

with(PDEtools)

P := U(xi)^3*mu*C[2]*h[9]+(2*I)*(diff(U(xi), xi))*a*k*mu+4*(diff(U(xi), xi))*k*mu^3*C[2]*h[7]-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*C[2]*h[7]-U(xi)^3*mu*C[2]*h[8]+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*C[2]*h[7]+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[9]-(6*I)*(diff(diff(U(xi), xi), xi))*k^2*mu^2*C[2]*h[7]+I*U(xi)*mu^4*C[2]*h[7]-I*(diff(U(xi), xi))*v-U(xi)*w+b*U(xi)^3-U(xi)*a*mu^2+(diff(diff(U(xi), xi), xi))*a*k^2+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[8]+C[1](-U(xi)^3*mu^2*h[2]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[4]-(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[5]+(diff(U(xi), xi))^2*U(xi)*k^2*h[2]-U(xi)^3*mu^2*h[5]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[5]-(4*(diff(U(xi), xi))*I)*k*mu^3*h[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*h[1]*I+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[2]+h[6]*U(xi)^5-U(xi)^3*mu^2*h[4]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[4]+U(xi)*mu^4*h[1]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*h[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*h[1]+h[3](k^2*(diff(U(xi), xi))^2+2*(0+I)*(diff(U(xi), xi))*k*mu*U(xi)-mu^2*U(xi)^2)*U(xi)) = 0

U(xi)^3*mu*C[2]*h[9]+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[8]+4*(diff(U(xi), xi))*k*mu^3*C[2]*h[7]-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*C[2]*h[7]-U(xi)^3*mu*C[2]*h[8]+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[9]-(6*I)*(diff(diff(U(xi), xi), xi))*k^2*mu^2*C[2]*h[7]+I*U(xi)*mu^4*C[2]*h[7]-I*(diff(U(xi), xi))*v+(2*I)*(diff(U(xi), xi))*a*k*mu-U(xi)*w+b*U(xi)^3-U(xi)*a*mu^2+(diff(diff(U(xi), xi), xi))*a*k^2+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*C[2]*h[7]+C[1](-U(xi)^3*mu^2*h[2]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[4]-(4*I)*(diff(U(xi), xi))*k*mu^3*h[1]+(diff(U(xi), xi))^2*U(xi)*k^2*h[2]-U(xi)^3*mu^2*h[5]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[5]+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*h[1]-(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[5]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[2]+h[6]*U(xi)^5-U(xi)^3*mu^2*h[4]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[4]+U(xi)*mu^4*h[1]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*h[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*h[1]+h[3](k^2*(diff(U(xi), xi))^2+(2*I)*(diff(U(xi), xi))*k*mu*U(xi)-mu^2*U(xi)^2)*U(xi)) = 0

(2)

Re(P)

Re(U(xi)^3*mu*C[2]*h[9]+4*(diff(U(xi), xi))*k*mu^3*C[2]*h[7]-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*C[2]*h[7]-U(xi)^3*mu*C[2]*h[8]-U(xi)*w+b*U(xi)^3-U(xi)*a*mu^2+(diff(diff(U(xi), xi), xi))*a*k^2+C[1](-U(xi)^3*mu^2*h[2]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[4]-(4*I)*(diff(U(xi), xi))*k*mu^3*h[1]+(diff(U(xi), xi))^2*U(xi)*k^2*h[2]-U(xi)^3*mu^2*h[5]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[5]+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*h[1]-(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[5]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[2]+h[6]*U(xi)^5-U(xi)^3*mu^2*h[4]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[4]+U(xi)*mu^4*h[1]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*h[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*h[1]+h[3](k^2*(diff(U(xi), xi))^2+(2*I)*(diff(U(xi), xi))*k*mu*U(xi)-mu^2*U(xi)^2)*U(xi)))-Im((diff(U(xi), xi))*U(xi)^2*k*C[2]*h[8]+(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[9]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*C[2]*h[7]+U(xi)*mu^4*C[2]*h[7]-(diff(U(xi), xi))*v+2*(diff(U(xi), xi))*a*k*mu+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*C[2]*h[7]) = 0

(3)
 

``

Download real_and_imaginary_.mw

Hi, I have plotted the bar graphs, and it's fine but I am interested in showing the value on each bar. How to implement this. As an example, I uploaded a picture for convenience.

Bar_graphs.mw

How to convert this mathematica code to Maple code? Is there any command? NN.pdf

I have encountered an issue: eq1 is not satisfied, though eq2 is satisfied for the parametric value (10). I need assistance in finding a way to ensure that both equations are satisfied simultaneously. Please provide guidance or suggest a potential approach for addressing this issue.verf_kk.mw

I have  a big problem in transformation How we can do suh transformation in  type of  procure  without use any hand work for example in physic abs|-| remove the exponential term how the maple remove that term automatically and collect all term and do my transformation this example is really hard one which is must do a lot by hand and mixed them which maybe a week take my time to get results and how i reach the results without spending that time i have a result of this equation and i am try to get but i don't know the results of this person is correct or not but i will share in here,  i did some try i will share in here too if in DEchange add U(xi) it will work and give me the other step but i need something more effective, when q^* is conjugate of q =exp(-ipsi(x,t))U(xi)

NULL

restart

with(PDEtools)

with(Physics)

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

 

 

tr := {t = tau, x = xi/k+v*tau^alpha/(k*alpha)+theta, u(x, t) = U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)), u[1](x, t) = U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))}

{t = tau, x = xi/k+v*tau^alpha/(k*alpha)+theta, u(x, t) = U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)), u[1](x, t) = U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))}

(2)

pde := I*(I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)-mu*tau+theta))*w-exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))*v)+a*(diff(u(x, t), `$`(x, 2)))+b*U(xi)^2*u(x, t)+C[1](h[1]*(diff(u(x, t), `$`(x, 4)))+h[2]*(diff(u(x, t), x))^2*u[1](x, t)+h[3]*abs(diff(u(x, t), x))^2*u(x, t)+h[4]*U(xi)^2*(diff(u(x, t), `$`(x, 2)))+h[5]*u(x, t)^2*(diff(u[1](x, t), `$`(x, 2)))+h[6]*U(xi)^4*u(x, t))+I*C[2]*(h[7]*(diff(u(x, t), `$`(x, 4)))+h[8]*U(xi)^2*(diff(u(x, t), x))+h[9]*u(x, t)^2*(diff(u[1](x, t), x))) = 0

I*(I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)-mu*tau+theta))*w-exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))*v)+a*(diff(diff(u(x, t), x), x))+b*U(xi)^2*u(x, t)+C[1](h[1]*(diff(diff(diff(diff(u(x, t), x), x), x), x))+h[2]*(diff(u(x, t), x))^2*u[1](x, t)+h[3]*abs(diff(u(x, t), x))^2*u(x, t)+h[4]*U(xi)^2*(diff(diff(u(x, t), x), x))+h[5]*u(x, t)^2*(diff(diff(u[1](x, t), x), x))+h[6]*U(xi)^4*u(x, t))+I*C[2]*(h[7]*(diff(diff(diff(diff(u(x, t), x), x), x), x))+h[8]*U(xi)^2*(diff(u(x, t), x))+h[9]*u(x, t)^2*(diff(u[1](x, t), x))) = 0

(3)

``

PDEtools:-dchange(tr, pde, [xi, tau, U, U(xi)])

I*(I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)-mu*tau+theta))*w-exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))*v)+a*((2*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))-U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^2)*k^2+b*U(xi)^3*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))+C[1](h[1]*(-(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k^3-6*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))/k^2+(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(U(xi), xi), xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^4)*k^4+h[2]*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))+I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)^2*k^2*U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))+h[3]*abs((exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))+I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)*k)^2*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))+h[4]*U(xi)^2*((2*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))-U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^2)*k^2+h[5]*U(xi)^2*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)))^2*((diff(diff(U(xi), xi), xi))*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))-(2*I)*(diff(U(xi), xi))*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k-U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^2)*k^2+h[6]*U(xi)^5*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)))+I*C[2]*(h[7]*(-(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k^3-6*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))/k^2+(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(U(xi), xi), xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^4)*k^4+h[8]*U(xi)^2*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))+I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)*k+h[9]*U(xi)^2*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)))^2*((diff(U(xi), xi))*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))-I*U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)*k) = 0

(4)
 

NULL


Download find_ODE.mw

I have a procedure that I am trying to run that would be an improvement/more sophisticated way of solving a problem that I have previously solved. When I try and run my procedure I am getting an error, and from what I gather with the error is that there are some values when inserted into my procedure that cannot be evaluated. Just for context it is a procedure that contains numerical solutions to a system of DEs and and contains inequalities. 

I would like to know is there an easy method to figure out what values are giving me this error? 

Or a follow up, is there something wrong with my procedure that is giving me this error? I have included some commentary in my workshet as well to hopefully make everything clear. 

Thanks. 

Proc_Error.mw

Hi,

I just got 2 questions regarding symbols and answers in MapleFlow (I might be doing something wrong here).

- In trying to input the integral int(F(x), x = -pi/5 .. pi/5) - this is just an example! - as a symbol,

int(F(x), x = -pi/5 .. pi/5)

MapleFlow doesn´t accept fractions or multiplications for bondaries values, unless I input "int(F(x), x = -pi/5 .. pi/5 =". Is there anyway to do it?

- is it possible to have the answer as 2*cos((3*Pi)/10), like in Maple, instead of 2.00*cos(300e-3*pi) ()symbolic expression) or 1.18 (numeric expression)?

Thanks in advance for your help.

I have some library program files written using Maple 11 (or before).

I can read and use the file programs and they have worked fine for many years.

But I would like to actually see the programming commands that are buried within with a view to modification, so, according to the Maple "Help" file, I tried the following command sequence:

***********************************************************

restart;
interface(echo=4,quiet=false);
interface(echo);
interface(quiet);
                            1, false

                               4

                             false

read "C:\\Program Files (x86)\\Maple 11\\test3.m";

**************************************************************************

But there is no echo.

So, how do I read (and modify) these files?

Thank you

How can I check if a name has been used/entered already but was not assigned to a value

The variable palette only lists assigned names.

I tried unames() but this lists all unassigned names. A 'user' option (which filters for user-assigned names) as in anames() does not seem to exist.

One of my failed attempts (in 1D-Math):

restart;
unames():
initial_unames := {%}:
new_name;
{unames()} minus initial_unames; # should ideally return a reduced set containing new_name;
has(%,new_name)

What else can be done? (I am probably overlooking something very simple.)

Я пытаюсь найти корни уравнения u = 0,6*sqrt(t)—1 + exp(-t). Команда fsolve не дает никаких результатов .

For a right triangle with two legs of the right triangle a and b, draw three circles with radius r and one ellipse as shown in the diagram (the major axis of the ellipse is parallel to the hypotenuse of the right triangle). Find a relationship between a, b, and r

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