Quality design of websites implies that among other factors, hypelinks’ structure should allow the users to reach the information they seek with the minimum number of clicks. This paper utilises the fuzzy equivalence relation based clustering in adapting website hyperlinks’ structure so that the redesigned website allows users to meet as effectively as possible their informational and navigatio...

It has been established recently that there is an interesting thermodynamic ‘‘equivalence’’ between noninteracting Bose and spinless Fermi gases in two dimensions, and between onedimensional Bose and Fermi systems with linear dispersion, both in the grand-canonical ensemble. These are known to be special cases of a larger class of equivalences of noninteracting systems having an energy-independ...

Consider a standard probability space (X,μ), i.e., a space isomorphic to the unit interval with Lebesgue measure. We denote by Aut(X,μ) the automorphism group of (X,μ), i.e., the group of all Borel automorphisms of X which preserve μ (where two such automorphisms are identified if they are equal μ-a.e.). A Borel equivalence relation E ⊆ X is called countable if every E-class [x]E is countable a...

In the study of quantum process algebras, researchers have introduced different notions of equivalence between quantum processes like bisimulation or barbed congruence. However, there are intuitively equivalent quantum processes that these notions do not regard as equivalent. In this paper, we introduce a notion of equivalence named observational equivalence into qCCS. Since quantum processes h...

Similarity concept, finding the resemblance or classifying some groups of objects and study their common properties has been the interest of many researchers. Basically, in the studies the similarity between two objects or phenomena, 2-similarity in our words, has been discussed. In this paper, we consider the case when the resemblance or similarity among three objects or phenomena of a set, 3-...

We describe a generalization of equivalence between constraint sets, called weak equivalence. This new equivalence relation takes into account that not all variables have the same function in a constraint set and therefore distinguishes between restriction variables and intermediate variables. We explore the properties of weak equivalence and its underlying notion of weak implication with an ax...

We present a logical relation for proving contextual equivalence in a probabilistic programming language (PPL) with continuous random variables and with a scoring operation for expressing observations and soft constraints. Our PPL model is based on a big-step operational semantics that represents an idealized sampler with likelihood weighting. The semantics treats probabilistic non-determinism ...

In the topological classification of phase portraits no distinctions are made between a focus and a node and neither are they made between a strong and a weak focus or between foci of different orders. These distinctions are however important in the production of limit cycles close to the foci in perturbations of the systems. The distinction between the one direction node and the two directions...

The purpose of this paper is the study of direct limits in category of Krasner (m, n)-hyperrings. In this regards we introduce and study direct limit of a direct system in category (m, n)-hyperrings. Also, we consider fundamental relation , as the smallest equivalence relation on an (m, n)-hyperring R such that the quotient space is an (m, n)-ring, to introdu...

in this paper we classify fuzzy subgroups of a rank-3 abelian group $g = mathbb{z}_{p^n} + mathbb{z}_p + mathbb{z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. we present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...