the only justification for the einstein velocity addition law appeared to be its empirical adequacy, so that the intrinsic beauty and harmony in einstein addition remained for a long time a mystery to be conquered. accordingly, the aim of this expository article is to present (i) the einstein relativistic vector addition, (ii) the resulting einstein scalar multiplication, (iii) the einstein rel...

the only justification for the einstein velocity addition law appeared to be its empirical adequacy, so that the intrinsic beauty and harmony in einstein addition remained for a long timea mystery to be conquered. accordingly, the aim of this expository article is to present(i) the einstein relativistic vector addition,(ii) the resulting einstein scalar multiplication,(iii) the einstein relativ...

in this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. we characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. we also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

The concept of gyrogroups is a generalization groups which do not explicitly have associativity. Recently, Atiponrat extended the idea topological (paratopological) to gyrogroups. In this paper, we prove that every regular (Hausdorff) locally gyroscopic invariant paratopological gyrogroup G completely (function Hausdorff). These results improve theorems Banakh and Ravsky for groups. Also, exten...

in this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional euclidean space, which are the einstein and möbius gyrovector spaces. we introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and see its interest...

the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

Résumé. Dans cet article, nous proposons un système de classification des comptes-rendus mammographiques, reposant sur une ontologie radiologique décrivant les signes radiologiques et les différentes classes de la classification ACR des systèmes BIRADS dans le langage OWL. Le système est conçu pour, extraire les faits issus des textes libres de comptes-rendus en étant dirigé par l’ontologie, pu...

Suppose that (T;*) is a groupoid with left identity such each element 2 T has inverse. Then called gyrogroup if and only (i) there exists function gyr : x -Aut(T) for all a; b; c T, * (b c) = (a b) ? gyr[a; b]c, where b]c gyr(a; b)(c); (ii) b b] gyr[a b]. In this paper, the structure of normal subgyrogroups certain gyrogroups are investigated.

Using Klein's approach, geometry can be studied in terms of a space points and group transformations that space. This allows us to apply algebraic tools studying mathematical structures. In this article, we follow approach study the $(G, \mathcal{T})$, where $G$ is an abstract gyrogroup $\mathcal{T}$ appropriate containing all gyroautomorphisms $G$. We focus on $n$-transitivity gyrogroups also ...