Markiyan Hirnyk

Markiyan Hirnyk
9 years, 157 days


These are questions asked by Markiyan Hirnyk

of the improper integral of exp((1-x)/((1-x)^2+y^2)) over the unit disk x^2+y^2 <= 1 with Maple? For purists the function is assumed to be undefined at (1,0). It is not so difficult to verify that statement  by hand. It is not easy to prove that with Maple.

My try was

f := evalc(exp(Re(1/(1-x-I*y))));


VectorCalculus:-int(f, [x, y] = Circle(`<,>`(0, 0), 1), numeric);

and

evalf(Int(f, [y = -sqrt(-x^2+1) .. sqrt(-x^2+1), x = -1 .. 1]));
.

Edit. The formula for f.                  

PS.

 

 

 

How to find all nonisomorphic undirected graphs with 5 vertexes? Of course, with Maple.

How to numerically solve the problem

with Maple? Such type problems arise in elasticity theory (for example, see https://zbmath.org/?q=an:01366371).

Edit. Typo in the code:sin(y(x)) instead of sin(x).

 

I solve the problem on computational geometry: "A cube of side one contains two cubes of sides a and b having non-overlapping interiors. How to prove the inequality a+b≤1?" To this end I use the DirectSearch package , namely,

Here are some comments to it. The cube of side a is centered at (x_1,y_1,z_1) and rotated by the angles phi_1, psi_1, theta_1 (see http://uk.wikipedia.org/wiki/%D0%95%D0%B9%D0%BB%D0%B5%D1%80%D0%BE%D0%B2%D1%96_%D0%BA%D1%83%D1%82%D0%B8 ) and the cube of side b is centered at (x_2,y_2,z_2) and rotated by the angles phi_2, psi_2, theta_2. The procedure

calculates the distance between these cubes, for example,

st := time(); dist(.2, .9, .2, .2, .2, .7, .7, .7, 0, 0, 0, 0, 0, 0); time()-st;

[HFloat(5.453016092898238e-11), [s1 = HFloat(0.2646161775314957),

  s2 = HFloat(0.2828503247068887),

  s3 = HFloat(0.29444713116943216),

  t1 = HFloat(0.2646161774916062),

  t2 = HFloat(0.28285032471998384),

  t3 = HFloat(0.2944471311346344)], 2527]
                            191.133
Unfortunately, my code (which is syntactically correct) is spinning on my wondercomp during 10 hours without any output. I don't understand it at all. Your advices are welcome.

twocubes.mw

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