Maple 17 Questions and Posts

These are Posts and Questions associated with the product, Maple 17

I am getting errors while applying the HPM method.
I have attached the maple file.

HPM.mw

Please help me to get the solution.

Thanks in advance.

Dear all

I would like if we can solve a problem of a  field homomorphism between two fields. 

Please, if possible a code that help me to define the homomorphism between finite field. 

homomorphism_finite_field.mw

Thank you 

Dear all

I have a linear  system with four equations,  I used solve to get the result but unfortunately nothing returned

linear_system.mw

Thank you 

Dear all

I have a code that compute the elements of the sigma algebra generated by C in the domain X 
If X is a discrete set and C is also a discrete set 

I get a good results 

But in change X to be an interval and C will be set of three elements

No result obtained 

sigma_algebra.mw

Thank you

Dear all 

I have a simple equation that can be solved by hand. But, can Maple solve this equation 

cos(x)> a,   with a :  real number.

Can we get all possible solution with different values of a, 

Equation.mw

thank you for your help  

Dear all

I have a non continuous function at 0,  how can I use the deifnition of Borel measurable funciton, to show that f is Borel measurable function

borel_M_fct.mw

thank you for your help 

Dear all

I have an equation, I would like to introduce a variable R[0], how can I use subs in my equaiton 

subs_equation.mw

Thank you

Dear all

Can I compute using maple intersection between discrete sets

intersection_sets.mw

thank you for your help 

Dear all

How can I determine a positive constant M such that the following inequality hold for any positive values of a, b,c. 

More precisley, I determine M such that  f(a,b,c) greater or equal M a^2 

The constant M is a positive constant depend only on alpha 

find_positive_constant_M.mw

thank you for your help 

Dear all

I would like to compute Hardy−Littlewood maximal function : we use polar coordinate for a radial function  and then evalaute integral with respect the radius r 

Hardy_maximal_function.mw

Thank you for your help 


u := c1*BesselK(0, alpha1*r) + c2*BesselI(0, alpha1*r) + c3*BesselK(0, alpha2*r) + c4*BesselI(0, alpha2*r) - A1*k^2*(k^2 - (-alpha^2*j*s + 4*c*s)/c)*BesselK(0, k*r)/((-alpha1^2 + k^2)*(-alpha2^2 + k^2)) - B1*k^2*(k^2 - (-alpha^2*j*s + 4*c*s)/c)*BesselI(0, k*r)/((-alpha1^2 + k^2)*(-alpha2^2 + k^2)) + ur*(-alpha^2*j*s + 4*c*s)/(c*(1 + c));

w := (-1 - c)/(2*s*(4.*c - alpha^2*j))*collect(diff(diff(r*diff(u, r), r)/r, r) + (alpha^2 - 4*c*s)*diff(u, r)/(1 + c) - A1*k^3*BesselK(1, k*r) + B1*k^3*BesselI(1, k*r), [c1, c2, c3, c4], factor);

om := (-1)/2*diff(u, r)/r;

fn1 := collect(simplify(subs(subs(r = 1, u))), [c1, c2, c3, c4], factor);
fn2 := collect(simplify(subs(subs(r = sigma, u))), [c1, c2, c3, c4], factor);
fn3 := collect(simplify(subs(r = 1, w)), [c1, c2, c3, c4], factor);
fn4 := collect(simplify(subs(r = sigma, w)), [c1, c2, c3, c4], factor);
soln := simplify(solve({fn1 = 0, fn2 = 0, fn3 = 0, fn4 = 0}, {c1, c2, c3, c4}));

What is the result of the following?

solve((4*t1+4*sqrt(t1^2-4*t2))>0,{t2});
 

Dear all

I  have a PDE, I would like to substitute the funciton T by another funciton 

How transform the old PDE to a new PDE

transfirm_equation_using_change_variable.mw

thank you

Dear all

I have an equation obtained from partial derivable of some functions, I would like to compute the limit when my variable named Pe goes to infinity. 

I hope to get a more appreciate presentation of my code to obtain the limit (  Pe -> + infty)

limit_infinity.mw

All derivative are well compute, but How can I add the limit as Pe goes to infinity

Thank you 

I am trying to obtain the solution of the differential equation f'''+ff''-f'^2-Mf'=0, with f(0)=0, f'(0)=1, and f'(5)=0 with M=0.5 using finite element method

But got this error. I attached the file also.

restart

with(LinearAlgebra):

with(plots):

M := .5;

.5

(1)

a := 0;

0

(2)

b := 5;

5

(3)

N := 50;

50

(4)

h := (b-a)/N;

1/10

(5)

nodes := [seq(h*i+a, i = 0 .. N)];

[0, 1/10, 1/5, 3/10, 2/5, 1/2, 3/5, 7/10, 4/5, 9/10, 1, 11/10, 6/5, 13/10, 7/5, 3/2, 8/5, 17/10, 9/5, 19/10, 2, 21/10, 11/5, 23/10, 12/5, 5/2, 13/5, 27/10, 14/5, 29/10, 3, 31/10, 16/5, 33/10, 17/5, 7/2, 18/5, 37/10, 19/5, 39/10, 4, 41/10, 21/5, 43/10, 22/5, 9/2, 23/5, 47/10, 24/5, 49/10, 5]

(6)

elements := [seq([i, i+1], i = 0 .. N-1)];

[[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [21, 22], [22, 23], [23, 24], [24, 25], [25, 26], [26, 27], [27, 28], [28, 29], [29, 30], [30, 31], [31, 32], [32, 33], [33, 34], [34, 35], [35, 36], [36, 37], [37, 38], [38, 39], [39, 40], [40, 41], [41, 42], [42, 43], [43, 44], [44, 45], [45, 46], [46, 47], [47, 48], [48, 49], [49, 50]]

(7)

bilinear := proc (u, v, w) options operator, arrow; int(diff(u(x), `$`(x, 3))+u(x)*(diff(u(x), `$`(x, 2)))-(diff(u(x), x))^2-M*u(x)*(diff(u(x), x)), x = w[1] .. w[2])+int((diff(u(x), x))*(diff(v(x), x)), x = w[1] .. w[2]) end proc;

proc (u, v, w) options operator, arrow; int(diff(u(x), `$`(x, 3))+u(x)*(diff(u(x), `$`(x, 2)))-(diff(u(x), x))^2-M*u(x)*(diff(u(x), x)), x = w[1] .. w[2])+int((diff(u(x), x))*(diff(v(x), x)), x = w[1] .. w[2]) end proc

(8)

Llinear := proc (v, w) options operator, arrow; v(a)*(diff(w(x), x)) end proc, x = a;

proc (v, w) options operator, arrow; v(a)*(diff(w(x), x)) end proc, x = 0

(9)

K := CreateMatrix(N+1, N+1, 0);

CreateMatrix(51, 51, 0)

(10)

F := CreateVector(N+1, 0);

CreateVector(51, 0)

(11)

for e in elements do x1 := nodes[e[1]]; x2 := nodes[e[2]]; h := x2-x1; Ke := bilinear(proc (x) options operator, arrow; piecewise(x < x1+(1/2)*h, 1-(x-x1)/h, (x2-x)/h) end proc, proc (x) options operator, arrow; piecewise(x < x1+(1/2)*h, (x-x1)/h, (x2-x)/h) end proc, [x1, x2]); Fe := Llinear(proc (v) options operator, arrow; v(x)*piecewise(x = x1, 1, x <> x1) end proc, [x1, x2]); for i in [e[1], e[2]] do for j in [e[1], e[2]] do K[i, j] := K[i, j]+Ke[i-e[1]+1, j-e[1]+1] end do; F[i] := F[i]+Fe[i-e[1]+1] end do end do

Error, invalid subscript selector

 

K[1, 1] := 1;

1

 

0

 

0

(12)

K[N+1, N+1] := 1;

1

 

0

(13)

u := LinearSolve(K, F)

Error, (in LinearAlgebra:-LinearSolve) invalid input: LinearAlgebra:-LinearSolve expects its 1st argument, A, to be of type {Matrix, list({Matrix, Vector})} but received K

 

f := unapply(u(x), x);

proc (x) options operator, arrow; u(x) end proc

 

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

 

 

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Download FEM.mw

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