alzheimer’s disease (ad) is a uniquely human disorder. although the pathogenesis of ad is not fully understood, growing evidence indicates that the deposition of beta-amyloid (aβ) and the local reactions of various cell types to this protein play major roles in the development of the disease. in the present study transgenic mice expressing mutant amyloid precursor protein (app) has been used. t...

In this paper we consider the conformal group of the unit sphere S, the proper Lorentz group Spin(1, n), for the study of spherical continuous wavelet transforms. The parameter space is determined by the factorization of the gyrogroup of the unit ball by an appropriate gyro-subgroup. We study two families of sections that give rise to anisotropic conformal dilation operators for the unit sphere...

In this paper, we have studied the properties of associated gyrogroup °G a given group G nilpotency class 3. We proved that if 3 does not divide order G, then ni...

In this study, we investigate Hamiltonian cycles in the right-Cayley graphs of gyrogroups. More specifically, give a gyrogroup version factor group lemma and show that some certain gyrogroups are Hamiltonian.

A space X is submaximal if any dense subset of open. In this paper, we prove that every topological gyrogroup non-measurable cardinality strongly ?-discrete. Moreover, hereditarily paracompact.

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 concept of topological gyrogroups is a generalization group. In this work, ones prove that gyrogroup G metrizable iff has an {\omega}{\omega}-base and Frechet-Urysohn. Moreover, in gyrogroups, every (countably, sequentially) compact subset being strictly (strongly) Frechet-Urysohn having are all weakly three-space properties with H closed L-subgyrogroup

‎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 spaces‎, ‎which are the Einstein and M"{o}bius gyrovector spaces‎. ‎We introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and explore its...