In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study weakly prime ideals. We investigate rings in which all graded...

We develop a new Approximate Dynamic Programming (ADP) method for infinite horizon discounted reward Markov Decision Processes (MDP) based on projection onto a subsemimodule. We approximate the value function in terms of a (min,+) linear combination of a set of basis functions whose (min,+) linear span constitutes a subsemimodule. The projection operator is closely related to the Fenchel transf...

In this paper we have generalized the concepts of   q   , -fuzzy ideals,   q   , -fuzzy quasi-ideals and   q   , -fuzzy bi-ideals by introducing the concepts of   k q   , -fuzzy ideals,   k q   , -fuzzy quasiideals and   k q   , -fuzzy bi-ideals in ternary semigroups and several related properties are investigated. Different characterizations of regular and weakly ...

Our initial problem is to represent classes $$m$$ modulo $$q$$ by a sum of three terms, two being taken from rather small sets $$\mathcal A$$ and B$$ the third one having an odd number prime factors (the so-called irregular numbers in S. Ramanujan’s terminology) lying interval $$[q^{20r},q^{20r}+q^{16r}]$$ for some given $$r\ge1$$ . We show that it always possible do so provided $$|\mathcal A|\...