Let K be a locally compact hypergroup. In this paper we initiate the concept of fundamental domain in locally compact hypergroups and then we introduce the Borel section mapping. In fact, a fundamental domain is a subset of a hypergroup K including a unique element from each cosets, and the Borel section mapping is a function which corresponds to any coset, the related unique element in the fun...

Based on different cognitive tasks and mapping methods, the human intraparietal sulcus (IPS) has been subdivided according to multiple different organizational schemes. The presence of topographically organized regions throughout IPS indicates a strong location-based processing in this brain region. However, visual short-term memory (VSTM) studies have shown that while a region in the inferior ...

We introduce the notion of multiendomorphism in a hypergroupoid and the notion of G-semiring. We show that, if (H, ∗) is a commutative semi-hypergroup, these multiendomorphisms form a G-semiring (E,+, ◦,≤), where the operation + is induced by ∗, ◦ is the usual composition of maps ◦ and ≤ is the usual inclusion of maps. Moreover, we show under which conditions the G-semiring (E,+, ◦,≤) is, in fa...

It was recently shown by the authors that deformations of hypergroup convolutions w.r.t. positive semicharacters can be used to explain probabilistic connections between the Gelfand pairs (SL(d, C), SU(d)) and Hermitian matrices. We here study connections between general convolution semigroups on commutative hypergroups and their deformations. We are able to develop a satisfying theory, if the ...