Connes’ functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d’Alembert operator and the causal functions of a globally hyperbolic spacetime. As a step of the presented machinery, a proof of the almosteverywhere smoothness of the Lorentzian distance considered as a function of one of the two arguments is given. Afterwar...

Euclidean distance matrices (EDM) are symmetric nonnegative with several interesting properties. In this article, we introduce a wider class of called generalized (GEDMs) that include EDMs. Each GEDM is an entry-wise matrix. A not unless it EDM. By some new techniques, show many significant results on can be extended to matrices. These contain about eigenvalues, inverse, determinant, spectral r...

Recently, a new kind of distance has been introduced for the graphs two point-to-set operators, one which is maximally monotone. When both operators are subdifferential proper lower semicontinuous convex function, this specializes under modest assumptions to classical Bregman distance. We name generalized distance, and we shed light on it with examples that utilize other most natural representa...

In this paper, we introduce a new concept on a complete generalized D∗-metric space by using the concept of generalized D∗-metric space (D∗-cone metric space) called ∇∗∗-distance and, by using the concept of the ∇∗∗-distance we prove some new fixed point theorems in complete partially ordered generalized D∗-metric space which is the main result of our paper. c ©2015 All rights reserved.

a r t i c l e i n f o a b s t r a c t We propose a generalized version of the Granularity-Enhanced Hamming (GEH) distance for use in k-NN queries in non-ordered discrete data spaces (NDDS). The use of the GEH distance metric improves search semantics by reducing the degree of non-determinism of k-NN queries in NDDSs. The generalized form presented here enables the GEH distance to be used for a ...

In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1, . . . , mr&minus1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are co...

this study aimsto investigate an aspect of marital interactions, distance. by applying aqualitative method and conducting 43 in-depth semi-structured interviews, including 22women and 21 men, women and men experiences of distance were investigated based on theirown narratives.the results of the study suggested different forms of distance in couples' relationships,which can be classified to...

In this paper, we give the idea of a generalized c-distance in a cone b-metric space. Then, we prove some common fixed point and fixed point theorems in cone b-metric spaces by using the distance.