We study observed correlations between supermassive black hole (BHs) and the properties of their host galaxies, and show that the observations define a BH “fundamental plane” (BHFP), of the form MBH ∝ σ3.0±0.3 R0.43±0.19 e or MBH ∝ M 0.54±0.17 ∗ σ 2.2±0.5, analogous to the FP of elliptical galaxies. The BHFP is preferred over a simple relation between MBH and any of σ, M∗, Mdyn, or Re alone at ...

Algebraic hyperstructures have many applications in various sciences. The main purpose of this paper is to provide a new application of weak hyperstructures in Chemistry. More precisely, we present three different examples of hyperstructures associated to electrochemical cells. In which we prove that our hyperstructures are Hv-semigroups and we present some interesting results.

The purpose of this paper is the study of Cayley graph associated to a semihypergroup(or hypergroup). In this regards first  we associate a Cayley graph to every semihypergroup and then we study theproperties of this graph, such as  Hamiltonian cycles in this  graph.  Also, by some of examples we will illustrate  the properties and behavior of  these Cayley  graphs, in particulars we show that ...

In this paper we will call this the fundamental algebra and the single relation will be called the fundamental relation or equation. This relation arises naturally from attempts to find representations of the braid group. Representations of the fundamental algebra as matrices can be used to define representations of the virtual braid group and invariants of virtual knots and links. In [BuF] we ...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ...

Alzheimer's disease (AD), the most ordinary form of dementia and extracellular accumulation of Amyloid-β (Aβ) in senile plaques, is an important and a main event in the pathogenesis of AD. Deposition of Aβ Peptide initiates a spectrum of cellular responses that are interposed by the resident neuroimmune cells of the brain, the microglia. Recently, a novel inflammasome signaling&n...

The purpose of this paper is to define a new equivalence relation τ∗ on divisible hypergroups and to show that this relation is the smallest strongly regular relation (the fundamental relation) on commutative divisible hypergroups. We show that τ∗ ̸= β∗, τ∗ ̸= γ∗ and, we define a divisible hypergroup on every nonempty set. We show that the quotient of a finite divisible hypergroup by τ∗ is the tr...

Let $ { mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree  version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates us to present the pointfree  version of $C_c(X).$The main aim of this paper is to present t...