Bárány, Hubard, and Jerónimo recently showed that for given well separated convex bodies S1, . . . , Sd in R and constants βi ∈ [0, 1], there exists a unique hyperplane h with the property that Vol(h ∩Si) = βi·Vol(Si); h is the closed positive transversal halfspace of h, and h is a “generalized ham-sandwich cut”. We give a discrete analogue for a set S of n points in R which is partitioned into...

The six Painlevé transcendents PI -PV I have both applications and analytic properties that make them stand out from most other classes of special functions. Although they have been the subject of extensive theoretical investigations for about a century, they still have a reputation for being numerically challenging. In particular, their extensive pole fields in the complex plane have often bee...

In this paper we exhibit a condition on the syntax of the logic programs with negation, the semi-strictness property, which assures the equivalence of the well founded semantics and the stable semantics: so, for semi-strict programs the well founded model is total if and only if the program has an unique stable model.

In this preliminary work, left and right conjugate vectors are deened for nonsymmetric, nonsin-gular matrices A and some properties of these vectors are studied. A left conjugate direction (LCD) method for solving nonsymmetric systems of linear equations is proposed. The method reduces to the usual conjugate gradient method when A is symmetric positive deenite. A nite termination property of th...

We present some properties regarding diffusion and semi-convexity for fuzzy set multifunctions defined on a ring of subsets of an abstract nonvoid space and taking values in the family of all nonvoid closed subsets of a real normed space. Key–Words: diffused, semi-convex, fuzzy set multifunction, non-atomicity, Darboux property, regular, multimeasure, null-additive.

A property is persistent if for any many-sorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property . In this paper, we show that weak normalization is persistent for term rewriting systems. Furthermore we obtain that semi-completeness is persistent for term rewriting systems and we give the exampl...

This chapter aims to further explore the capabilities of the Higher Order Neural Networks class and especially the Pi-Sigma Neural Networks. The performance of Pi-Sigma Networks is evaluated through several well known neural network training benchmarks. In the experiments reported here, Distributed Evolutionary Algorithms are implemented for Pi-Sigma neural networks training. More specifically,...

Let I = {i1, . . . , in} be a set of voters (players) and A = {a1, . . . , ap} be a set of candidates (outcomes). Each voter i ∈ I has a preference Pi over the candidates. We assume that Pi is a complete order on A. The preference profile P = {Pi, i ∈ I} is called a situation. A situation is called war if the set of all voters I is partitioned in two coalitions K1 and K2 such that all voters of...

We show that for a sequence in a Banach space, the property of being stable under large perturbations characterizes the property of being equivalent to the unit vector basis of l1. We show that a normalized unconditional basic sequence in l1 that is semi-normalized in l∞ is equivalent to the standard unit vector basis of l1.