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In module variety, Riedtmann and Zwara have shown that geometric degeneration by orbit closure is equivalent to algebraic degeneration by exact sequence. In this paper, we define the U-algebraic degeneration by the notion U-exact sequence introduced by Davvas and Parnian-Gramaleky, and we give its relation with geometric degeneration. Moreover, we also explain its relation with virtual and homomorphism...
In this paper we study centroids and derivations of associative algebras. Using a classification result of associative algebras, we describe the centroids and derivations of low-dimensional associative algebras. We review some properties of the centroids in the light of associative algebras and use these properties to categorize the algebras into having small and not small centroids. We also give...
By making use of the generalised derivative operator, a new class of analytic functions is investigated. An upper bound of second Hankel determinant for functions belonging to this class is studied.
A pursuit differential game of two pursuers and one evader in ℝ2 is studied. All players' controls are subjected to coordinate-wise integral constraints. By definition, pursuit is completed if the state of a pursuer coincides with that of the evader at some time. The problem is to find conditions of completion of pursuit. We show that if the energy vector of the evader belongs to a polygon, then pursuit...
In this paper we introduce and study the concept of a bornological semigroup. This generalizes the theory of algebraic semigroup from the algebraic setting to the framework of bornological set. Working with bornological set allows to extend the scope of the latter theory considerably. In this paper we develop and introduce the concept of bornological semigroup and fundamental construction in the class...
The atom-bond connectivity index of a graph G, denoted as ABC(G), is the most important topological indices in chemical graph theory. The ABC index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes. In this note, we prove that the ABC index of a graph increases when three new edges are added.
In this note, singular integration problems of the form equation where equation and fixed point equation is considered. The density function h(x, y) is assumed given, continuous and smooth on the rectangle Ω and belong to the class of functions C2,α(Ω). Cubature formula for double integrals with algebraic singularity on a rectangle is constructed using the modified spline function SΩ(P) of type (0,...
The objective of this research has been devoted to solve linear fuzzy fractional differential equations (FFDEs) of the Caputo sense. The basic idea is to develop a fractional linear multistep method for solving linear FFDEs under fuzzy fractional generalized differentiability. For safely illustrating the advantages and potential of the presented method, a comparison with the fractional Euler method...
In this paper, we introduce new class of Lebesgue quadratic stochastic operators on segment [0,1]. Then, we investigate their limit behaviors and show that these operators are regular transformations.
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