On Certain Proximities and Preorderings on the Transposition Hypergroups of Linear First-Order Partial Differential Operators

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.

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

“…For details regarding this condition see e.g. [3,4,5,6]. Notice that a semihypergroup is an associative hypergroupoid.…”

“…Also Chvalina proposed and with Chvalinová, Hošková or Dehghan Nezhad studied [3,4,5,6] generalization of the concept. In papers such as [3,4,5,6] the GMAC condition, i.e. a condition which the transition function must fulfil in quasi-multiautomata, is studied.…”

“…We suggest two extensions of this condition and show various aspects of their use and application. When constructing specific quasimultiautomata we expand results of [3,4,5,6] and make use of hyperstructures and sets of differential operators motivated by functions used to model specific time processes in electrical engineering.…”

Distributive and Dual Distributive Elements in Hyperlattices

“…Some applications can be found also in e.g. in [4,5,8,10,16,17]. The theory of hyperlattices was introduced by Konstantinidou in 1977 [13].…”

C-Γ-hyperideal Theory in Ordered Γ-semihypergroups

“…In [21], some properties of hyperlattices are studied and the relationship between prime ideals and prime filters in hyperlattices is discussed. Motivation of compatibility of orderings with hyperoperations can be found in [22,23]. In 2010, Davvaz, et al [24][25][26] introduced the notion of the Γ-semihypergroup as a generalization of a semigroup, a generalization of a semihypergroup and a generalization of a Γ-semigroup.…”