In this paper it is described a method to compute the distance between sets, that implies the formation of distance functions different from Hausdorff metric. Two functions with metric properties, which describe quantitatively distances between sets, are formed. First function can be used for sets arbitrary situated from each other. Second distance is more suited for sets clustered by rank link...

We isolate conditions on the relative asymptotic size of sets of natural numbers A,B that guarantee a nonempty intersection of the corresponding sets of distances. Such conditions apply to a large class of zero density sets. We also show that a variant of Khintchine’s Recurrence Theorem holds for all infinite sets A = {a1 < a2 < . . .} where ann n3/2.

This paper is concerned with the simulation of the Partial Diierential Equation (PDE) driven evolution of a closed surface by means of an implicit representation. In most applications, the natural choice for the implicit representation is the signed distance function to the closed surface. Osher and Sethian propose to evolve the distance function with a Hamilton-Jacobi equation. Unfortunately t...

A two-distance set in E is a point set X in the d-dimensional Euclidean space such that the distances between distinct points in X assume only two different nonzero values. Based on results from classical distance geometry, we develop an algorithm to classify, for a given d, all maximal (largest possible) two-distance sets in E. Using this algorithm we have completed the full classification for...