Some applications of the point-open subbase game

extensions of some polynomial inequalities to the polar derivative

توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی

The lex game and some applications

Let F be a field, V a finite subset of F. We introduce the lex game, which yields a combinatorial description of the lexicographic standard monomials of the ideal I(V ) of polynomials vanishing on V . As a consequence, we obtain a fast algorithm which computes the lexicographic standard monomials of I(V ). We apply the lex game to calculate explicitly the standard monomials for special types of...

Some Applications of Fixed Point Theorems

Some Applications of Minimal Open Sets

We characterize minimal open sets in topological spaces. We show that any nonempty subset of a minimal open set is pre-open. As an application of a theory of minimal open sets, we obtain a sufficient condition for a locally finite space to be a preHausdorff space. 2000 Mathematics Subject Classification. 54A05, 54D99.

Applications of fuzzy $e$-open sets

The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated via fuzzy $e$-open sets.