we prove that every r-quadratic metric of scalar flag curvature with a dimension greater than twois of constant flag curvature. then we show that generalized douglas-weyl metrics contain r-quadraticmetrics as a special case, but the class of r-quadratic metric is not closed under projective transformations

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

the sequential $p$-convergence in a fuzzy metric space, in the sense of george and veeramani, was introduced by d. mihet as a weaker concept than convergence. here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. in such a case $m$ is called an $s$-fuzzy metric. if $(n_m,ast)$ is a fuzzy metri...

equality of -curvatures of the berwald and cartan connections leads to a new class of finsler metrics, so-called bc-generalized landsberg metrics. here, we prove that every bc-generalized landsberg metric of scalar flag curvature with dimension greater than two is of constant flag curvature.

Introduction: Appropriate definition of the distance measure between diffusion tensors has a deep impact on Diffusion Tensor Image (DTI) segmentation results. The geodesic metric is the best distance measure since it yields high-quality segmentation results. However, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. The main goal of this ...

The Skorokhod distance is a natural metric on traces of continuous and hybrid systems. For two traces, from [0, T ] to values in a metric space O, it measures the best match between the traces when allowed continuous bijective timing distortions. Formally, it computes the infimum, over all timing distortions, of the maximum of two components: the first component quantifies the timing discrepanc...

We introduce a novel geometric framework for separating the phase and the amplitude variability in functional data of the type frequently studied in growth curve analysis. This framework uses the Fisher-Rao Riemannian metric to derive a proper distance on the quotient space of functions modulo the time-warping group. A convenient square-root velocity function (SRVF) representation transforms th...

recently, rahimi et al. [comp. appl. math. 2013, in press] dened the conceptof quadrupled xed point in k-metric spaces and proved several quadrupled xed pointtheorems for solid cones on k-metric spaces. in this paper some quadrupled xed point resultsfor t-contraction on k-metric spaces without normality condition are proved. obtainedresults extend and generalize well-known comparable result...

The purpose of the present study was to identify any significant relationship between critical thinking ability, L2 vocabulary knowledge, and L2 vocabulary learning strategies of Iranian EFL learners. To this aim, the productive vocabulary levels test was administered to measure the learner’s L2 vocabulary knowledge and observe homogeneity in terms of vocabulary knowledge. At the second stage, ...