x = niabcfghpqr, y = nigh(af) 2 p*, z = mca(bg) 2 q s , w = tnbf{ch) 2 r z , where the parameters m, • • • , r may be restricted by the G.CD. conditions 1 = (o,f) = (b,g) = (c,h), 1 = (afp, bcqr) = (bgq, hfrp) = (chr, agpq). The most immediate application of this is to the solution of # 3 +/(:y> £> «0 = 0> where ƒ (y, z, w) is any ternary cubic factorable into 3 linear, homogeneous factors whos...

Based on previous results that study the completion of fuzzy metric spaces, we show that every intuitionistic fuzzy quasi-metric space, using the notion of fuzzy metric space in the sense of Kramosil and Michalek to obtain a generalization to the quasi-metric setting, has a bicompletion which is unique up to isometry.

The aim of this paper is to introduce the concepts of compatible mappings and compatible mappings of type (R) in non-Archimedean Menger probabilistic normed spaces and to study the existence problems of common fixed points for compatible mappings of type (R), also, we give an applications by using the main theorems.

It will be shown that according to theorems of K. Menger, every neuron grid if identified with a curve is able to preserve the adopted qualitative structure of a data space. Furthermore, if this identification is made, the neuron grid structure can always be mapped to a subset of a universal neuron grid which is constructable in three space dimensions. Conclusions will be drawn for established ...

We study when the product of separable metric spaces has the selective screenability property, the Menger property, or the Rothberger property. Our results imply The product of a Lusin set and (1) a Sierpinski set always has the Menger property (Corollary 12); (2) a γ-set always has the Rothberger property (Corollary 13). All topological spaces considered in this paper are assumed to be separab...

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

Automatically generated playlists have become an important medium for accessing and exploring large collections of music. In this paper, we present a probabilistic model for generating coherent playlists by embedding songs and social tags in a unified metric space. We show how the embedding can be learned from example playlists, providing the metric space with a probabilistic meaning for song/s...

‎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...

We present an algebraic account of the Wasserstein distances Wp on complete metric spaces. This is part of a program of a quantitative algebraic theory of effects in programming languages. In particular, we give axioms, parametric in p, for algebras over metric spaces equipped with probabilistic choice operations. The axioms say that the operations form a barycentric algebra and that the metric...