TCHEBYCHEV

Tchebychev nets on spheres

On the Existence of Global Tchebychev Nets

Let S be a complete, open simply connected surface. Suppose that the integral of the Gauss curvature over arbitrary measurable sets is less than tt/2 in magnitude. We show that the surface admits a global Tchebychev net.

Orthogonalizing Weights of Tchebychev Sets of Polynomials

We characterize distributions with respect to which the members of a Tchebychev set of polynomials are orthogonal when they satisfy differential equations with polynomial coefficients. As an application, we find a real weight of bounded variation with support in [0, oo) for Bessel polynomials.

The three-dimensional Fermat-Weber problem with Tchebychev distances

The three-dimensional Fermat-Weber facility location problem with Tchebychev distances is investigated. Expanding on previous research for the analogous two-dimensional problem, this study presents a new algorithm for solving the elusive three-dimensional case. The algorithm presented herein finds near optimal solutions in practical computational times. Some experimental results are also convey...

Certain Combinatorial Identities of Twin Pairs Related to Tchebychev Polynomials

In the present paper, a twin pair (xn, yn) and (Xn, Yn) of numbers related to one and two variable Tchebychev polynomials of first and second kinds are proposed. Certain Combinatorial Identities of the twin pairs are stated and proved.