Let (W,d) be a metric space and S = {s1 . . . sk} an ordered list of subsets of W . The distance between p ∈ W and si ∈ S is d(p, si) = min{ d(p, q) : q ∈ si }. S is a resolving set forW if d(x, si) = d(y, si) for all si implies x = y. A metric basis is a resolving set of minimal cardinality, named the metric dimension of (W,d). The metric dimension has been extensively studied in the literatur...

+ Corresponding author. Abstract— A novel metric for full-reference image quality assessment (IQA) is proposed in this paper. Based on the sparse representation in independent component analysis (ICA) domain, the image basis is generated from natural images adaptively, which coincides with the characteristics of human vision system (HVS). In order to extract the feature vector, a hybrid norm op...

In the present paper, we give a new approach to Caristi's fixed pointtheorem on non-Archimedean fuzzy metric spaces. For this we define anordinary metric $d$ using the non-Archimedean fuzzy metric $M$ on a nonemptyset $X$ and we establish some relationship between $(X,d)$ and $(X,M,ast )$%. Hence, we prove our result by considering the original Caristi's fixedpoint theorem.

The purpose of this paper is to describe a practical view of software measurement that formed the basis for a company-wide software metrics initiative within Motorola. A multi-dimensional view of measurement is provided by identifying different dimensions (e.g., metric usefulness/utility, metric types or categories, metric audiences, etc.) that were considered in this company-wide metrics imple...

We introduce and study a metric notion for trees and relate it to a conjecture of Shelah [10] about the existence of a finite basis for a class of linear orderings.

Projection-based model reduction techniques rely on the definition of a small dimensional subspace in which the solution is approximated. Using local subspaces reduces the dimensionality of each subspace and enables larger speedups. Transitions between local subspaces require special care and updating the reduced bases associated with each subspace increases the accuracy of the reduced-order mo...

We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this ”independence” approach delivers an increased flexibility its downside is the considerable risk of overfitting. We present a new parametric local metric learning method in which we learn a smooth metric matrix func...

in this paper, we introduce intuitionistic fuzzy contraction mappingand prove a fixed point theorem in intuitionistic fuzzy metric spaces.

we consider the concept of ω-distance on a complete partially ordered g-metric space and prove some common fixed point theorems.

In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...