The terminology and notation used here have been introduced in the following articles: [9], [4], [13], [12], [10], [8], [2], [3], [1], [14], [7], [11], [5], and [6]. Let M be a metric structure, and let x, y be elements of the carrier of M . The predicate x ≈ y is defined by: (Def.1) ρ(x, y) = 0. Let M be a metric structure, and let x be an element of the carrier of M . The functor x yielding a...

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.

computation of the second order delay in rc-tree based circuits is important during the design process of modern vlsi systems with respect to having tree structure circuits. calculation of the second and higher order moments is possible in tree based networks. because of the closed form solution, computation speed and the ease of using the performance optimization in vlsi design methods such as...

Keywords: Implicit iterative algorithm Asymptotically quasi-nonexpansive mappings Common fixed point Convex metric space a b s t r a c t In this paper, we consider an implicit iteration process to approximate the common fixed points of two finite families of asymptotically quasi-nonexpansive mappings in convex metric spaces. As a consequence of our result, we obtain some related convergence the...

We show that any quantum family of maps from a non commutative space to a compact quantum metric space has a canonical quantum semi metric structure.

‎In this study‎, ‎we investigate topological properties of fuzzy strong‎ b-metric spaces defined in [13]‎. ‎Firstly‎, ‎we prove Baire's theorem for‎ ‎these spaces‎. ‎Then we define the product of two fuzzy strong b-metric spaces‎ ‎defined with same continuous t-norms and show that $X_{1}times X_{2}$ is a‎ ‎complete fuzzy strong b-metric space if and only if $X_{1}$ and $X_{2}$ are‎ ‎complete fu...

In this paper we examine the basic structure of metric trees and prove fixed point theorems for uniformly Lipschitzian mappings in metric trees.

We prove that the L Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold induces a metric space structure. As the L metric is a weak Riemannian metric, this fact does not follow from general results. In addition, we prove several results on the exponential mapping and distance function of a weak Riemannian metric on a Hilbert/Fréchet ...

Motivated by the classical statements of Mirror Symmetry, we study certain Kähler metrics on the complexified Kähler cone of a Calabi– Yau threefold, conjecturally corresponding to approximations to the Weil– Petersson metric near large complex structure limit for the mirror. In particular, the naturally defined Riemannian metric (defined via cup-product) on a level set of the Kähler cone is se...

The usual form of the C-metric has the structure function G(ξ) = 1 − ξ 2 − 2mAξ 3 , whose cubic nature can make calculations cumbersome, especially when explicit expressions for its roots are required. In this paper, we propose a new form of the C-metric, with the explicitly factorisable structure function G(ξ) = (1 − ξ 2)(1 + 2mAξ). Although this form is related to the usual one by a coordinat...