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A radial function is a function phi:R^+->R satisfying phi(x,c)=phi(|x-c|) for points c in some subset Xi subset R^n. Here, |·| denotes the standard Euclidean norm in R^n and ...

Hoffman (1998, p. 90) calls the sum of the exponents in the prime factorization of a number its roundness. The first few values for n=1, 2, ... are 0, 1, 1, 2, 1, 2, 1, 3, 2, ...

In n dimensions for n>=5 the arrangement of hyperspheres whose convex hull has minimal content is always a "sausage" (a set of hyperspheres arranged with centers along a ...

Two complex measures mu and nu on a measure space X, are mutually singular if they are supported on different subsets. More precisely, X=A union B where A and B are two ...

A sparse matrix is a matrix that allows special techniques to take advantage of the large number of "background" (commonly zero) elements. The number of zeros a matrix needs ...

That part of a positive integer left after all square factors are divided out. For example, the squarefree part of 24=2^3·3 is 6, since 6·2^2=24. For n=1, 2, ..., the first ...

Stadium billiards refers to the investigation of the path of a billiard ball on a stadium-shaped billiard table, as first investigated by Bunimovich (1974).

The study of random geometric structures. Stochastic geometry leads to modelling and analysis tools such as Monte carlo methods.

A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the ...

The taxicab metric, also called the Manhattan distance, is the metric of the Euclidean plane defined by g((x_1,y_1),(x_2,y_2))=|x_1-x_2|+|y_1-y_2|, for all points ...