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.

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,...

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 ...

Introduction: In this study the effect of Matricaria recutita extract on acute pain in the presence and absence of flumazenil (antagonist of benzodiazepine) and lesioned paragigantocellularis (PGi) nucleus was investigated. Method: Wistar male rats (250±20 g) were used. Animals were grouped randomly into intact, sham and bilateral lesion of PGi nucleus. Intact and lesioned animals, each...

The concept of gyrogroups, with a weaker algebraic structure without associative law, was introduced under the background c -ball relativistically admissible velocities Einstein velocity addition. A topological gyrogroup is just endowed compatible topology such that multiplication jointly continuous and inverse continuous. This generalizes groups. In this paper, we are going to establish for lo...

Broad nervous circuits originate from the hypothalamic arcuate nucleus project to many parts of the brain which are related to pain perception. Insulin receptors have been found in the arcuate nucleus. Since nociception may be affected in type 1 diabetes, the present study aimed to investigate the intra-arcuate nucleus insulin role in pain perception in STZ-induced diabetic and healthy rats. Fo...