We introduce a notion of curvature on finite, combinatorial graphs. It can be easily computed
by solving a linear system of equations. We show that graphs with curvature bounded below …

In this paper we elaborate on the interplay between energy optimization, positive
definiteness, and discrepancy. In particular, assuming the existence of a K-invariant …

Abstract Let G=(V, E) G=(V,E) be a finite, connected graph. We consider a greedy selection
of vertices: given a list of vertices x 1,⋯, xk x_1,\dots,x_k, take xk+ 1 x_k+1 to be any vertex …

We analyze relations between various forms of energies (reciprocal capacities), the
transfinite diameter, various Chebyshev constants and the so-called rendezvous or average …

One of our main results is the following: Let X be a compact connected subset of the
Euclidean space R n and r (X, d 2) the rendezvous number of X, where d 2 denotes the …

1. Introduction. A positive real number a is called a rendezvous number for the metric space
(M, d) if for any finite sequence p 1, p 2,•••, Pn of elements in M (with repetition allowed) …

Let (X, d) be a compact metric space and let ℳ (X) denote the space of all finite signed Borel
measures on X. Define I: ℳ (X)→ ℝ by and set M (X)= sup I (μ), where μ ranges over the …

Our main goals in writing Squigonometry: The Study of Imperfect Circles were to compile
results in generalized trigonometry that had been known for years, to introduce new facts …

If∈(X), then we say that is an average distance for X (abbreviated:(AD)). Let F∈ F (S); if 1
(X)¡ 2 (X) and∈(1 (X); 2 (X))⊂(1 (F); 2 (F)), then there exists xF∈ S (X) such that (F; xF)=. If …

This paper presents a bibliography of about 1450 references related to the computer
processing of pictorial information, arranged by subject matter. Coverage is restricted, for the …