A set of n weighted points in general position in Rd defines a unique regular triangulation. This paper proves that if the points are added one by one, then flipping in a topological order will succeed in constructing this triangulation. If, in addition, the points are added in a random sequence and the history of the flips is used for locating the next point, then the algorithm takes expected ...

In this paper, we consider an algebraic additive Schwarz iteration scheme for solving the nite-dimensional linear complementarity problem that involves an M-matrix. The scheme contains some existing algorithms as special cases. We establish monotone convergence of the iteration scheme under appropriate conditions. Moreover, using the concept of weak regular splitting, we estimate weighted max-n...

We introduce the notion of weighted A-statistical convergence of a sequence, where A represents the nonnegative regular matrix. We also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence. Further, we give a rate of weighted A-statistical convergence and apply the classical Bernstein polynomial to construct an illustrative example in support of our...

Notation: A power diagram for a weighted point set (X = {xi},W = {wi}) is a partition of a domain D into convex cells V i such that V i = {x ∈ D | ‖x − xi‖ − wi ≤ ‖x − xj‖ − wj ,∀j}. The dual of power diagram defines the regular triangulation of (X,W ). We denote by eij the regular edge between two adjacent points xi and xj , and by eij the dual (orthogonal and clipped byD) edge separating the ...

Brouwer, Cohen, and Neumaier found that the intersection numbers of most known families of distance-regular graphs could be described in terms of four parameters (d, b, :, ;) [2, pp. ix, 193]. They invented the term classical to describe those graphs for which this could be done. All classical distance-regular graphs with b=1 are classified by Y. Egawa, A. Neumaier, and P. Terwilliger in a sequ...

Let (G,B,N, S) be a Tits system. Some aspects of intersections of conjugacy classes ofG with Bruhat cellsBẇB have been investigated by several authors (see e.g., [St1], [K], [V] and [VS]). Here w ∈ W = N/(B ∩N) and ẇ ∈ N is a preimage of w with respect to the natural surjection N → W . In particular, it is desirable to learn how a conjugacy class C of G is related to those conjugacy classes Cw ...

In our paper we introduce Grammatically Aware Regular expression (GARE) and describe its usage using examples from moral consequences retrieval task. GARE is an extension to the regular expression concept that overcomes many of the difficulties with traditional regexp by adding Normalization (e.g., searching all grammatical forms with basic form of a verb or adjective is possible) or POS awaren...

Suppose X is a (smooth projective irreducible algebraic) curve over a finite field k. Counting the number of points on X over all finite field extensions of k will not determine the curve uniquely. Actually, a famous theorem of Tate implies that two such curves over k have the same zeta function (i.e., the same number of points over all extensions of k) if and only if their corresponding Jacobi...

We study the problem of computing geometric spanners for (additively) weighted point sets. A weighted point set is a set of pairs (p, r) where p is a point in the plane and r is a real number. The distance between two points (pi, ri) and (pj , rj) is defined as |pipj | − ri − rj . We show that in the case where all ri are positive numbers and |pipj | ≥ ri + rj for all i, j (in which case the po...