Let G denote a locally compact abelian topological group (an l.c.a. group) with dual group C\ We will denote by A7(G) the Banach algebra of bounded regular Borel measures on G under convolution multiplication and by L(G) the algebra of bounded measures absolutely continuous with respect to Haar measure on G (for discussions of these Banach algebras cf. [1], [2], and [5]). In this paper we shall...

A significant cue for visual perception is the occlusion pattern in 2-D images projected onto biological or digital retinas, which allows humans or robots to successfully sense and navigate the 3-D environments. There have been many works on modeling and studying the role of occlusion in image analysis and visual perception, mostly from analytical or statistical points of view. The current pape...

A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of βN, or it is a “tame” topological space whose topology is determined by the convergence of sequences. In the latter case the dynamical system is called tame. We use the structure theory of minimal dynamical systems to s...

Consider a simple graph G with vertex set V(G) and edge E(G). A invariant for is number related to the structure of G, which under symmetry G. The Sombor index new defined as SO(G)=∑uv∈E(G)(du)2+(dv)2. In this work, we connected theory abstract algebra. We computed topological over tensor Cartesian products monogenic semigroup by presenting two different algorithms; obtained results are illustr...

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

Let iX, T) be a transformation group with compact Hausdorff phase space X. The points x and y of A" are said to be proximal provided, whenever ß is a member of the unique compatible uniformity of X, there exists i£ T such that (x/, yt) GßIf x and y are not proximal, they are said to be distal. Let P denote the proximal relation in X. P is a reflexive, symmetric, T invariant relation, but is not...

The Fourier and Fourier-Stieltjes algebras A(G) and B(G) of a locally compact group G are introduced and studied in 60’s by Piere Eymard in his PhD thesis. If G is a locally compact abelian group, then A(G) ≃ L(Ĝ), and B(G) ≃ M(Ĝ), via the Fourier and Fourier-Stieltjes transforms, where Ĝ is the Pontryagin dual of G. Recently these algebras are defined on a (topological or measured) groupoid an...

A toric face ring, which generalizes both Stanley-Reisner rings and affine semigroup rings, is studied by Bruns, Römer and their coauthors recently. In this paper, under the “normality” assumption, we describe a dualizing complex of a toric face ring R in a very concise way. Since R is not a graded ring in general, the proof is not straightforward. We also develop the squarefree module theory o...