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...

Hyperstructure theory was born in 1934 when Marty [19] defined hypergroups as a generalization of groups. Let H be a non-empty set and let ℘∗(H) be the set of all non-empty subsets of H. A hyperoperation on H is a map ◦ : H ×H −→ ℘∗(H) and the couple (H, ◦) is called a hypergroupoid. If A and B are non-empty subsets of H, then we denote A◦B = ∪ a∈A, b∈B a◦b, x◦A = {x}◦A and A◦x = A◦{x}. Under c...

The theory of hyperstructures has been introduced byMarty in 1934 during the 8th Congress of the Scandinavian Mathematicians [4]. Marty introduced the notion of a hypergroup and since then many researchers have worked on this new topic of modern algebra and developed it. The notion of a hyperfield and a hyperring was studied first by Krasner [2] and then some authors followed him, for example, ...

Sertoli cells constitute the structural framework in testis and provide an immune-privileged environment for germ cells. Induced pluripotent stem cells (iPS cells) resemble embryonic stem cells (ES cells) and are generated from somatic cells by expression of specific reprogramming transcription factors. Here, we used C57BL/6 (B6) Sertoli cells to generate iPS cells (Ser-iPS cells) and compared ...

Conformal inclusions of chiral conformal field theories, or more generally quantum are described in the von Neumann algebraic setting by nets subfactors, possibly with infinite Jones index if one takes non-rational theories into account. With this situation mind, we study a purely subfactor theoretical context certain class braided discrete subfactors an additional commutativity constraint, tha...