EP elements are important research objects in the ring theory. This paper mainly gives sufficient and necessary conditions for an element a to be element, partial isometry, strongly by using solutions of certain equations.

In this paper, we give a probabilistic counterpart of  Mazur-Ulam theorem  in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.

The separability of the Hamilton-Jacobi equation has a well-known connection to existence Killing vectors and rank-two tensors. This paper combines this with detailed knowledge compactification metrics consistent truncations on spheres. fact that both inverse metric such compactifications, as well tensors can be written in terms bilinears underlying "round metric," enables us perform analyses f...

An atomic decomposition is proved for Banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process. This is then applied to yield, under appropriate assumptions, geometric characterizations, up to isometry, of the unit ball of the dual space of a JB∗-triple, and up to complete isometry, of one-sided ideals in C∗-algebras.

In this article we prove the problem on isometric mappings of S posed by Th. M. Rassias. We prove that any map f : S → S, p ≥ n > 1, preserving two angles θ and mθ (mθ < π, m > 1) is an isometry. With the assumption of continuity we prove that any map f : S → S preserving an irrational angle is an isometry.

In this paper we investigatet the efficiency of the Orthogonal Matching Pursuit for random dictionaries. We concentrate on dictionaries satisfying Restricted Isometry Property. We introduce a stronger Homogenous Restricted Isometry Property which is satisfied with overwhelming probability for random dictionaries used in compressed sensing. We also present and discuss some open problems about OMP.