The main purpose of this paper is to introduce a concept of$L$-fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$-fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$-fuzzifying neighborhoo...

Abstract. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also le...

A set of fundamental yet ill understood phenomena in uid dynamics involves changes in the topology of interfaces between partially miscible or nominally immiscible uids Such changes occur for example when continuous jets pinch o into droplets when sheared interfaces atomize and when droplets of one uid reconnect with one another These topological transitions occur in many practical applications...

Suppose (S, ∗) is a mathematical structure on a set S. As examples, (S, ∗) might be a topological space on S, a topological group on S, an n-ary operator on S, an n-ary relation on S or a Steiner triple system on S. A similarity mapping on (S, ∗) is a permutation on S that preserves the structure of (S, ∗). Such mappings f : (S, ∗) → (S, ∗) are called by different names. As examples, f might be...

Motivation. In the past, molecular similarity spaces have been developed from arbitrary sets of molecular properties or theoretical descriptors and the results of property estimation based on these methods have always been inferior to SAR and QSAR models. Tailored QMSA methods attempt to create similarity spaces specific for a property of interest, rather than being purely arbitrary spaces char...

Feature-based similarity retrieval has become an iniportant research issue in multimedia database systems. The features of multimedia data are useful for discriminating between multimedia objects (e.g., documents, images, video, music score, etc.). For example, images are represented by their color histograms, texture vectors, and shape descriptors. A feature vector is a vector that represents ...

Measures of graph similarity have a broad array of applications, including comparing chemical structures, navigating complex networks like the World Wide Web, and more recently, analyzing different kinds of biological data. This thesis surveys several different notions of similarity, then focuses on an interesting class of iterative algorithms that use the structural similarity of local neighbo...

In this paper we give some characterizations of topological extreme amenability. Also we answer a question raised by Ling [5]. In particular we prove that if T is a Borel subset of a locally compact semigroup S such that M(S)* has a multiplicative topological left invariant mean then T is topological left lumpy if and only if there is a multiplicative topological left invariant mean M on M(S)* ...