Linear Diophantine fuzzy sets were recently introduced as a generalized form of sets. The aim this paper is to shed the light on relationship between algebraic hyperstructures and linear through polygroups. More precisely, we introduce concepts subpolygroups polygroup, normal anti-fuzzy polygroup. Furthermore, study some their properties characterize them in relation level ceiling

With my appreciation, I wish to thank my advisor Prof. Hillel Furstenberg for his guidance, support and encouragement during these unforgettable years of learning and research Abstract We associate ergodic properties to some subsets of the natural numbers. For any given family of subsets of the natural numbers one may study the question of occurrence of certain " algebraic patterns " in every s...

It is known that finding the shortest solution for a linear Diophantine equation is a NP problem. In this paper we have devised a method, based upon the basis reduction algorithm, to obtain short solutions to a linear Diophantine equation. By this method we can obtain a short solution (not necessarily the shortest one) in a polynomial time. Numerical experiments show superiority to other method...

The rules for unification in a simple syntactic theory, using Kirchner’s mutation [15, 16] do not terminate in the case of associativecommutative theories. We show that in the case of a linear equation, these rules terminate, yielding a complete set of solved forms, each variable introduced by the unifiers corresponding to a (trivial) minimal solution of the (trivial) Diophantine equation where...

The polyhedron model provides one possible approach to model-based program analysis and transformation. Over the years, it has undergone many improvements in order to handle a still growing class of programs. A recent approach enabled the use of non-linear parameters, which was in that generality not possible before. While this new framework uses real quantifier elimination, the present work ex...

Let be a strictly positive monotonically decreasing function deened on the set of positive integers. Given real numbers and , consider the solubility of the following two inequalities jq + pj < (q); (1) jq + p + j < (q) (2) for integers p and q. The rst problem is said to be homogeneous and the second inho-mogeneous (see 2]). The well known theorem of Khintchine 2, 4] asserts that for almost al...