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A polynomial having random coefficients.

Let V be a real symmetric matrix of large order N having random elements v_(ij) that for i<=j are independently distributed with equal densities, equal second moments m^2, ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...

A Poisson process is a process satisfying the following properties: 1. The numbers of changes in nonoverlapping intervals are independent for all intervals. 2. The ...

How can n points be distributed on a unit sphere such that they maximize the minimum distance between any pair of points? This maximum distance is called the covering radius, ...

The Euler numbers, also called the secant numbers or zig numbers, are defined for |x|<pi/2 by sechx-1=-(E_1^*x^2)/(2!)+(E_2^*x^4)/(4!)-(E_3^*x^6)/(6!)+... (1) ...

A Haar graph H(n) is a bipartite regular indexed by a positive integer and obtained by a simple binary encoding of cyclically adjacent vertices. Haar graphs may be connected ...

A convex planar domain in which the minimal generalized diameter is >1 always contains a circle of radius 1/3.

The even impulse pair is the Fourier transform of cos(pik), AdjustmentBox[I, BoxMargins -> {{0.13913, -0.13913}, {-0.5, 0.5}}]I(x)=1/2delta(x+1/2)+1/2delta(x-1/2). (1) It ...