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.

Download FEM.mw

Dear all

I have a third order equations, I would like to know the sign of its roots, not necessary to find the roots since the equations contains some parameters. All parameters used are positives. 

roots.mw

thank you

Dear all

have a nice time. 

I have a system of nonlinear differential equation with continuous delay.  I tried to find some books that define a strategy to compute the characteristic equation but unfortunattely the most of papers or books give directly the formula without any proof. 

I tried with maple, but unfortunattely no solution up to now. 

I hope find the strategy how find the characteristic equation of the attached system.

characteristic_equation.mw

thanks 

Dear all 
For n geater or equal 2, I would like to solve to find an integrer n that such satisfy an inequality. 

I would like to see how large does n have to be for  the following ineqlaity satisfied. 
But, unfortunattely Maple return 
Warning, solutions may have been lost

restart;
epsilon:=0.001;
solve(10^n /factorial(n) <= epsilon, n);

thank you