In this paper, we are going to introduce a fundamental relation on \(H_{v}BE\)-algebra and investigate some of properties, also construct new \((H_{v})BE\)-algebras via relation. We show that quotient any regular regulation is an quotient, strongly \(BE\)-algebra. Furthermore consider under what conditions relations transitive.

In this paper, by considering the notion of $Sigma$-hyperalgebras for an arbitrary signature $Sigma$, we study the notions of regular and strongly regular relations on a $Sigma$-hyperalgebra, $mathfrak{A}$. We show that each regular relation which contains a strongly regular relation is a strongly regular relation. Then we concentrate on the connection between the fundamental relation of $mathf...

In this work, the order parameter or average magnetization expressions are obtained for square and honeycomb lattices based on recently relation, $<\sigma_{0,i}>= <\!\!\tanh[ \kappa(\sigma_{1,i}+\sigma_{2,i}+\dots +\sigma_{z,i})+H]\!\!> $. Where, $\kappa$ is coupling strength $z$ number of nearest neighbors. $\sigma_{0,i}$ denotes central spin at $i^{th}$ site while $\sigma_{l,i}$, $l=1,2,\dots...

We consider difference equations y(s+1) = A(s)y(s), where A(s) is an n × n-matrix meromorphic in a neighborhood of ∞ with detA(s) ≡ 0. In general, the formal fundamental solutions of this equation involve gamma-functions which give rise to the critical variable s log s and a level 1. We show that, under a mild condition, formal fundamental matrices of the equation can be summed uniquely to anal...

In this paper, we provide a new approach for computing regular solutions of first-order linear difference systems. We use the setting of factorial series known to be very well suited for dealing with difference equations and we introduce a sequence of functions which play the same role as the powers of the logarithm in the differential case. This allows us to adapt the approach of [5] where we ...

The purpose of this paper is the study of direct limits in category of Krasner (m, n)-hyperrings. In this regards we introduce and study direct limit of a direct system in category (m, n)-hyperrings. Also, we consider fundamental relation , as the smallest equivalence relation on an (m, n)-hyperring R such that the quotient space is an (m, n)-ring, to introdu...