We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular motion in polygons is taken within the alternative deterministic and stochastic frameworks. The analysis is developed in terms of the billiard-wall collision...

Capabilities of detecting temporal relations between two events can benefit many applications. Most of existing temporal relation classifiers were trained in a supervised manner. Instead, we explore the observation that regular event pairs show a consistent temporal relation despite of their various contexts, and these rich contexts can be used to train a contextual temporal relation classifier...

In the present paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, and investigate some of their properties. It was proved that a pairwise weakly Lindelof property is not a hereditary property.

In this paper, we study the concept of weakly almost periodic functions on Fréchet algebras. For a algebra [Formula: see text], show that text]. We also text] is Arens regular if and only both are regular. Finally, for sequence algebras prove regualr each

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...