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Consider the distribution of distances l between a point picked at random in the interior of a unit cube and on a face of the cube. The probability function, illustrated ...

Let f(x) be a monic polynomial of degree d with discriminant Delta. Then an odd integer n with (n,f(0)Delta)=1 is called a Frobenius pseudoprime with respect to f(x) if it ...

Finch (2010) gives an overview of known results for random Gaussian triangles. Let the vertices of a triangle in n dimensions be normal (normal) variates. The probability ...

The mean triangle area of a triangle picked inside a regular hexagon with unit area is A^_=289/3888 (Woolhouse 1867, Pfiefer 1989). This is a special case of a general ...

Also known as metric entropy. Divide phase space into D-dimensional hypercubes of content epsilon^D. Let P_(i_0,...,i_n) be the probability that a trajectory is in hypercube ...

The logarithmic capacity of a compact set E in the complex plane is given by gamma(E)=e^(-V(E)), (1) where V(E)=inf_(nu)int_(E×E)ln1/(|u-v|)dnu(u)dnu(v), (2) and nu runs over ...

Pick two real numbers x and y at random in (0,1) with a uniform distribution. What is the probability P_(even) that [x/y], where [r] denotes the nearest integer function, is ...

The (not necessarily regular) tetrahedron of least volume circumscribed around a convex body B with volume V is not known. If B is a parallelepiped, then the smallest-volume ...

Let n points xi_1, ..., xi_n be randomly distributed on a domain S, and let H be some event that depends on the positions of the n points. Let S^' be a domain slightly ...

Given an m×n matrix B, the Moore-Penrose generalized matrix inverse is a unique n×m matrix pseudoinverse B^+. This matrix was independently defined by Moore in 1920 and ...