Markiyan Hirnyk

Markiyan Hirnyk
8 years, 334 days

These are questions asked by Markiyan Hirnyk

Let a finite set of closed intervals in the plane be given.
How to find all the intersections of these, outputing the intersection points together with the intersecting intervals?
This is a problem of computational geometry
In other words, how to realize the sweep line algorithm in Maple?

PS. I'd like to note that computational geometry has serious applications, in particular, in robotics.

How to calculate the integral of (z-z0)*z/sqrt((x-x0)^2+(y-y0)^2+(z-z0)^2)
over the unit sphere {(x,y,z):x^2+y^2+z^2<=1}
under the assumtion x0^2+y0^2+z0^2<=1 (x0^2+y0^2+z0^2>1)?
Its physical interpretation suggests the integral can be expressed through  elementary functions of the parameters.

My tries are
VectorCalculus:-int((z-z0)*z/sqrt((x-x0)^2+(y-y0)^2+(z-z0)^2),[x,y,z]=Sphere(<0,0,0>,1)) assuming x0^2+y0^2+z0^2<=1;


[r,psi,theta]=Parallelepiped(0..1,0..Pi,0..2*Pi)) assuming x0^2+y0^2+z0^2<=1;

The both are spinning on my comp. Also


is spinning.
Edt. The omitted part of the code assuming x0^2+y0^2+z0^2<=1 is added.

How to calculate floor(10^(10^(10^(10^(10^(-10^10))))))? My simpleminded try is

Error, numeric exception: underflow
PS. I think that is about 10^(10^10).

Let us consider the expression

f := log[x](1+(x^a-1)*(x^b-1)/(x-1));
Does it define a convex function on the interval 0..1 and on the interval 1..infinity if the parameters a>0, a< 1, b >0, b <1?

My try is



At the same time I have got problems in the general case. For example,

Error, (in @) too many levels of recursion


That's all right if



Is it possible to numerically calculate  the integral

int((-12*y^2+1)*ln(abs(Zeta(x+I*y)))/(4*y^2+1)^3, [y = 0 .. infinity, x = 1/2 .. infinity])

in Maple?

The code

int((-12*y^2+1)*ln(abs(Zeta(x+I*y)))/(4*y^2+1)^3, [y = 0 .. infinity, x = 1/2 .. infinity],numeric,epsilon=0.1)

has been executed on my comp  without any output since this morning.




1 2 3 4 5 6 7 Last Page 1 of 24