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...

By using anholonomic frames in (pseudo) Riemannian spaces we define anisotropic extensions of Euclidean Taub–NUT spaces. With respect to coordinate frames such spaces are described by off-diagonal metrics which could be diagonalized by corresponding anholonomic transforms. We define the conditions when the 5D vacuum Einstein equations have as solutions anisotropic Taub–NUT spaces. The generaliz...

We study solvability for a model elliptic pseudo-differential equation with an additional integral condition in Sobolev–Slobodetskii spaces certain conical domains Euclidean space. . Using the wave factorization symbol we construct solution this boundary value problem and behavior of when parameters cones tend to their extremal values. It was shown that such need besides presented condition.

This work is devoted to the study of analytic wormhole solutions within framework f ( R ) $f(R)$ gravity theory. To check possibility having structures satisfying energy conditions, by means class I approach pair { Φ r , b } $\lbrace \Phi (r), b(r)\rbrace$ describing geometry has been obtained. Then, in conjunction with a remarkably model, satisfaction null and weak conditions at throat its nei...

The evolute of a conic in the pseudo-Euclidean plane is locus centers all its osculating circles. It’s curve order six and class four general case. In this paper we discuss compute evolutes different types conics. We will highlight those cases that have no analogy Euclidean plane.

Non-metric dissimilarity measures may arise in practice e.g. when objects represented by sensory measurements or by structural descriptions are compared. It is an open issue whether such non-metric measures should be corrected in some way to be metric or even Euclidean. The reason for such corrections is the fact that pairwise metric distances are interpreted in metric spaces, while Euclidean d...

It is reasonably well-known that birefringent crystal optics can to some extent be described by the use of pseudo–Finslerian spacetimes (an extension of the natural pseudo-Riemannian Minkowski spacetime one encounters in mono-refringent situations). What is less commonly appreciated is that there are two separate and quite disjoint pseudo–Finsler structures for the two photon polarizations, and...