The class of  $n$-ary polygroups is a certain subclass of $n$-ary hypergroups, a generalization of D{"o}rnte $n$-arygroups and  a generalization of polygroups. The$beta^*$-relation and the $gamma^*$-relation are the smallestequivalence relations on an $n$-ary polygroup $P$ such that$P/beta^*$ and $P/gamma^*$ are an $n$-ary group and acommutative $n$-ary group, respectively. We use the $beta^*$-...

In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $\Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (clo...

There is growing evidence that long and hard gamma-ray bursts (GRBs), discovered at redshifts between 0.4 and 3.4, are related to some type of supernova (SN) explosions. The GRB ejecta are ultra-relativistic, and possibly beamed. There is a possibility that some SN ejecta are also beamed and/or relativistic. Prospects for farther advances guided by expected and unexpected observational developm...

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

‎Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$‎. ‎In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$‎, ‎where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$‎. ‎We introduce a new graph determined ...

Working within the deep-MOND limit (DML), I describe spherical, self-gravitating systems governed by a polytropic equation of state, $P=\mathcal{K}\rho^\gamma$. As self-consistent structures, such can serve as heuristic models for DML, astronomical systems, dwarf spheroidal galaxies, low-surface-density elliptical galaxies and star clusters, diffuse galaxy groups. They also testing ground vario...

In this Letter we show that there is a redshift degeneracy in the Eiso −Epeak relation of gamma-ray bursts (GRBs). If a GRB has a redshift solved from the Eiso − Epeak relation that lies in the range of 0.9 < z < 20, a GRB that has the same observed fluence and peak spectral energy but is at a different redshift in that range also satisfies the Eiso − Epeak relation within 1-σ error, implying a...

This paper deenes a congruence relation on Gamma programs. Based on this congruence relation, laws for transforming programs are derived. We deene an axiomatic semantics for Gamma based on Brookes' transition assertions. The deenition of the congruence is in terms of provable satissability of such assertions. We consider the relationship between our congruence and other orderings that have been...