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Jan Chvalina and Šárka Hošková-Mayerová

Abstract

The contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup on the power set of the mentioned differential operators. Constructions of investigated hypergroups are based on the so called “Ends-Lemma” applied on ordered groups of differnetial operators. Moreover, there is also obtained a regularly preordered transpositions hypergroup of considered partial differntial operators.

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Jan Chvalina, Štěpán Kŕehlík and Michal Novák

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.

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Jan Chvalina, Šárka Hošková-Mayerová and A. D. Nezhad

Abstract

The aim of this paper is to investigate useful generalizations of the classical concept of a quasi-automaton without outputs or a discrete dynamical system, which are also called actions of semigroups or groups on given phase sets. The paper contains also certain applications of presented concepts and examples from various areas of mathematics.