Michal Novák

On E L -semihypergroups

This paper is a contribution to the investigation of hyperstructures in connection with binary relations, i.e. to one of the areas covered by canonical books on hyperstructure theory. We use a construction of hyperstructures from quasi- or partially ordered semigroups and study cases which result in semihypergroups such that the reproductive law does not hold. First, such cases are identified. Then we study some of their properties. Examples as well as some applications on isolated particular results obtained earlier without the theoretical background of this paper are included.

n–ary hyperstructures constructed from binary quasi–ordered semigroups

Abstract Based on works by Davvaz, Vougiouklis and Leoreanu-Fotea in the field of n–ary hyperstructures and binary relations we present a construction of n–ary hyperstructures from binary quasi-ordered semigroups. We not only construct the hyperstructures but also study their important elements such as identities, scalar identities or zeros. We also relate the results to earlier results obtained for a similar binary construction and include an application of the results on a hyperstructure of linear differential operators.

Cartesian composition and the problem of generalizing the MAC condition to quasi-multiautomata

Abstract When we assume that the input-set of an automaton without output is a semihypergroup instead of a monoid, we talk about quasi-multiautomata. Even though cartesian composition of quasi-automata is a commonly used concept, the cartesian composition of quasi-multiautomata has not been successfully constructed yet. In our paper we show that the straightforward transfer of the deffinition into the multivariate context fails. We suggest two possible solutions of this problem.

EL-hyperstructures revisited

In the paper we study ordered sets in which multi-valued aspects are important. To be more precise, we focus on EL-hyperstructures, i.e. semihypergroups constructed from partially ordered semigroups. We show that when certain slight modifications of the concept (motivated by real-life situations) are introduced, the applicability of this model increases as we are able to reduce the number of its assumptions, bypass some existing problems and at the same time apply the idea in a greater number of contexts.

From lattices to H_v - matrices

Abstract In this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices. First of all, we define hyperoperations similar to those used when constructing hyperstructures from quasi-ordered semigroups. This then enables us to show that if entries of matrices are elements of lattices, these considerations provide a natural link between matrices, some basic concepts of the hyperstructure theory including Hv-rings and Hv-matrices and also one recent construction of hyperstructures.

A hyperstructure model of underwater wireless sensor network (UWSN) design

We discuss some challenges of underwater wireless sensor networks (UWSN) and show that in the architecture of commonly used types of UWSNs certain hyperstructure concepts, which make use of ordering, can be naturally identified.We discuss some challenges of underwater wireless sensor networks (UWSN) and show that in the architecture of commonly used types of UWSNs certain hyperstructure concepts, which make use of ordering, can be naturally identified.