‎in this paper‎, ‎first we develop the duality concept for $g$-bessel sequences‎ ‎and bessel fusion sequences in hilbert spaces‎. ‎we obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎we also expand every $g$-bessel ‎sequence to a frame by summing some elements‎. ‎we define the restricted isometry property for ‎$g$-frames and generalize some resu...

The concept of gyrogroups is a generalization groups which do not explicitly have associativity. In this paper, the notion fuzzy gyronorms on introduced. relations metrics (in sense George and Veeramani), are studied. Also, metric structures normed discussed. Finally completion gyrogroup with an invariant We mainly show that if d G (Gˆ,dˆ) space (G,d); then for any continuous t-norm ⁎, standard...

Due to the nature of multiplicative Rayleigh fading, symmetric space time block codes, and joint estimation and detection schemes, isometry (ambiguities in channel estimation and data detection) degrades MIMO system performances. Training breaks isometry but reduces capacity. Asymmetric space time block code mitigates isometry by replacing training with data-bearing asymmetric codewords. This p...

By local isometries we mean mappings which locally preserve distances. A few of the main results are: 1. For each local isometry / of a compact metric space (M,p) into itself there exists a unique decomposition of M into disjoint open sets, M = Ai g U • • • U Ai>, (0 < n < oo) such that (i) f(M}0) = M!Q, and (ii) f(M{) C M{_x and M< ^ 0 for each i, 1 < i < n. 2. Each local isometry of a metric ...

We show that a finite metric space A admits an extension to a finite metric space B so that each partial isometry of A extends to an isometry of B. We also prove a more precise result on extending a single partial isometry of a finite metric space. Both these results have consequences for the structure of the isometry groups of the rational Urysohn metric space and the Urysohn metric space.

The goal of our work is to develop an efficient, automatic algorithm for discovering point correspondences between surfaces that are approximately and/or partially isometric. Our approach is based on three observations. First, isometries are a subset of the Möbius group, which has low-dimensionality – six degrees of freedom for topological spheres, and three for topological discs. Second, compu...

The aim of this paper is to show that the automorphism and isometry groups of the suspension of B(H), H being a separable infinite dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism, respectively local surjective isometry of C0(R) ⊗ B(H) is an automorphism, respectively a surjective isometry.