Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

restart;
M := -6*alpha*eta^2*mu*(lambda^2*mu+1)/`ϑ`+12*alpha*eta^2*lambda*mu^(3/2)*(sqrt(mu)*cot(A+sqrt(mu)*eta*(-t*(-alpha*eta^2*mu+f)+x))*lambda+1)/(`ϑ`*cot(A+sqrt(mu)*eta*(-t*(-alpha*eta^2*mu+f)+x)))-6*alpha*eta^2*mu*(sqrt(mu)*cot(A+sqrt(mu)*eta*(-t*(-alpha*eta^2*mu+f)+x))*lambda+1)^2/(`ϑ`*cot(A+sqrt(mu)*eta*(-t*(-alpha*eta^2*mu+f)+x))^2)+6*mu*eta^2*alpha*sqrt(sigma*(1+cot(A+sqrt(mu)*eta*(-t*(-alpha*eta^2*mu+f)+x))^2))/(sqrt(sigma)*theta*cot(A+sqrt(mu)*eta*(-t*(-alpha*eta^2*mu+f)+x))^2);
             2    /      2       \   
  6 alpha eta  mu \lambda  mu + 1/   
- -------------------------------- + 
             ϑ              

                                1                               
  ------------------------------------------------------------- 
                /      (1/2)     /   /          2       \    \\ 
  ϑ cot\A + mu      eta \-t \-alpha eta  mu + f/ + x// 

  /            2          (3/2) /  (1/2)    / 
  \12 alpha eta  lambda mu      \mu      cot\A

       (1/2)     /   /          2       \    \\           \\   
   + mu      eta \-t \-alpha eta  mu + f/ + x// lambda + 1// - 

                                1                                
  -------------------------------------------------------------- 
                                                               2 
                /      (1/2)     /   /          2       \    \\  
  ϑ cot\A + mu      eta \-t \-alpha eta  mu + f/ + x//  

  /           2    /  (1/2)    / 
  \6 alpha eta  mu \mu      cot\A

       (1/2)     /   /          2       \    \\           \  \   
   + mu      eta \-t \-alpha eta  mu + f/ + x// lambda + 1/^2/ + 

  /                /      / 
  |        2       |      | 
  \6 mu eta  alpha \sigma \1

                                                       2\\      \/
        /      (1/2)     /   /          2       \    \\ ||      | 
   + cot\A + mu      eta \-t \-alpha eta  mu + f/ + x// //^(1/2)/ 

  /                 
  |     (1/2)       
  \sigma      theta 

                                                    2\
     /      (1/2)     /   /          2       \    \\ |
  cot\A + mu      eta \-t \-alpha eta  mu + f/ + x// /
alpha := 2;
                               2
eta := 3;
                               3
mu := 1.5;
                              1.5
lambda := 2;
                               2
theta := 3;
                               3
sigma := .5;
                              0.5
b := .5;
                              0.5
f := 5;
                               5
y := 0;
                               0
plot3d([abs(M)], x = -3 .. 3, t = -3 .. 3);
 

general_solution.mwI want to calculate the diff equations numerical solutions at z=500 with calling the integrals with limits -500..Z and i want the datefile of resualts

 

i am currently using Maple 18, i have a problem on inserting 12 row by 12 column matrix and above is seem to be impossible. please can help or direct me on how to insert 12 row by 12 column matrix in maple. because my maple 18 seem to stop in 10 row by 10 column matrix.  thanks

restart;
Digits := 15;

b := -I;

a := sqrt(2);

epsilon := 1;

f := proc (t) options operator, arrow; evalf(Int(exp(I*k*t)/((1+a^2*sin(k)^2)*(k-b)^epsilon), k = -infinity .. infinity)) end proc;

f(1.3)

 

I tried different methods like _d01amc, but either I have this error:

Error, (in evalf/int) NE_QUAD_NO_CONV:
  The integral is probably divergent or slowly convergent.


or it takes forever.

I also tried to map the interval to some finite length (k=tan(u)), but then I get

Error, (in evalf/int) NE_QUAD_BAD_SUBDIV:
  Extremely bad integrand behaviour occurs around the
  sub-interval (-1,5707963e+000, -1,5707963e+000 ).


disgusting integrand?

Hi

I would like to solve the integrodifferential equation and then look to the  stability of the origin.

Is it  stable, uniformly stable, asymptotically stable and uniformly asumptotically stable.

Please see the following code.

Code.mw

Thanks

 

 

restart;

Digits := 32;

t0 := 1;

eq := 1-w*v^2-2*v*exp(-t/v);

equ := eval(eq, v = -t/ln(u));

us := solve(eval(equ, t = t0), u);

vs := -t0/ln(us);

plot(Re(vs), w = 0 .. 10, view = 0 .. 1)

 

 

I want to plot the solution of this equation, but it doesn't quite work. I tried to transform it, because I thought the singularity in the denominator of the exponential causes the issues.

any suggestions?

Hello,

I'm wondering which connection formulas maple has access to?

For instance consider the following exmple

restart;

hypergeom([a, b], [c], 1);

`assuming`([convert(%, GAMMA)], [c-a-b > 0])

 

it should be simplified to GAMMA functions, but I do not get maple to do it. Are there packages for this?

 

Same for higher functions pFq for example

hypergeom([1, 1, 2*q-2+L], [2, L+1], 1)

under appropriate assumptions.

This is a follow up question to https://mapleprimes.com/questions/225877-Partial-Integration-Hint:

restart;

with(Physics, KroneckerDelta);

Digits := 15;

t4 := 1/3;

n := 4;

q := 4/7;

i1 := evalf(Int(t^n*exp(-t)*GAMMA(2*q-2, t*(1-t4)*(1/t4)), t = 0 .. infinity, method = _d01amc));

i2 := expand(simplify(GAMMA(2*q-2)*add(binomial(n, m)*(KroneckerDelta[m, 0]-GAMMA(3-2*q)*(1/GAMMA(3-2*q-m))*t4^m*(1-t4)^(2*q-2))*(-1)^m*factorial(n-m), m = 0 .. n)));

`~`[evalf]([op(i2)]);

add(%);

i3 := expand(simplify(eval((-1)^n*GAMMA(2*q-2)*(diff((1-(1+t4*x*(1/(1-t4)))^(2-2*q))*(1/x), x$n)), x = 1)));

`~`[evalf]([op(i3)]);

add(%)

 

Interestingly this works up to n=3. It seems that the second term is wrongly manipulated and it should be 168/6 instead of 175/6?

 

I doubt the derivatives are wrong since I checked individually. I also hardly doubt this is a numerical round off, as the discrepancy is too large.

Is this a bug, or is there actually an error?

How do I remove infinity from a list

s:=[f(x) , exp(a), GAMMA(2x)-1 , infinity , 1, -infinity]

remove(has,%,infinity)

does not work.

It should yield

s:=[f(x) , exp(a), GAMMA(2x)-1 , 1]

Hello, I am getting the following output from maple: (-ln(lambda)-gamma-ln(k+b))/(k+b) . I have all variables (lambda, k, b) but not gamma and I am not sure what actually it is. I believe it is some kind of Gamma function but I cannot find any expressions for that. Ussually for gamma function I get something like GAMMA(x). Does someone know what this lower case gamma is?

Dear all;

I need a help to get a simple code about the null hypothesis test.

A drug is administrad to a population X of size 50 while a  placebo is given to a population Y of size 25.

Observed results of good bad and no effects are given in the following vectors for both population.

X=[ 20,11,19];

Y=[4,4,17];

test the null hypothesis H0: population independent of treatment versus the one tailed alternative that they are dependent by computing the theoretical contingency table with entries T[i,j] where i=1,2

for the two rows and j=1,2,3 for the three columns. At what p-value can we reject H0.

Many thanks

With this application, you visualize the DNA chain using the position vector as a fundamental tool to describe its curvature and radius of curvature. I also show the native maple syntax for the graphics. You can download the maple center app to show different DNA trajectories based on the position vector. Developed for students of health sciences.
 

k_adn.zip  (In spanish)

https://www.maplesoft.com/applications/download.aspx?SF=154486/Plot_of_curvature_and_radius_of_curvature.mw

Lenin Araujo Castillo

Ambassador of Maple

in this problem i used slip coundary condition.

the plot want to starts in 0.2, but the plot starts in 0

bc := f(0) = 0, (D(f))(0) = ak*((D^2)(f))(0), (D(f))(N) = 1, g(0) = -de*((D^2)(f))(0), g(N) = 0, T(0) = 1+be*(D(T))(0), T(N) = 0:

How to type double drivative in BC.

ψ =-0.09,-0.07,-0.04,-0.01,0,0.01,0.04,0.07,0.09

these are the ψ values.

then X=

here we can take eta =0..2 and X=-15..15
using this relation how to plot streamlines for eta against X.

Code:
restart; with(plots); fcns := {T(eta), f(eta)}; ep := .1; M := 1; kp := .5; n := 1; ec := .1; pr := 1; s := .1; N := 5; sys := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))*(diff(f(eta), eta))+ep*ep+(M+1/kp)*(ep-(diff(f(eta), eta))) = 0, diff(T(eta), eta, eta)+pr*(f(eta)*(diff(T(eta), eta))-n*(diff(f(eta), eta))*T(eta))+pr*(ec*(diff(f(eta), eta, eta))*(diff(f(eta), eta, eta))+ec*(M+1/kp)*(diff(f(eta), eta))^2+s*T(eta)) = 0; bc := f(0) = 0, (D(f))(0) = 1, (D(f))(N) = ep, T(0) = 1, T(N) = 0; R := dsolve(eval({bc, sys}), numeric, method = bvp[midrich], abserr = 0.1e-9, output = operator); psi = [-0.9e-1, -0.7e-1, -0.4e-1, -0.1e-1, 0, 0.1e-1, 0.4e-1, 0.7e-1, 0.9e-1]; for i to 9 do X[i] = psi[i]/f(eta); print(plots:-contourplot(X[i](X, eta), eta = 0 .. N, X = 0 .. 6)) end do

 


 

make a program that generates 20 numbers between 1 and 100, calculate the sum and the average of even numbers

please help, I do not know how to do it and the teacher wants this with "for, do and an external accountant

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