Some classes of sets of vectors of natural numbers are introduced as generalizations of the semi-linear sets, among them the ‘simple semi-polynomial sets.’ Motivated by verification problems that involve arithmetical constraints, we show results on the intersection of such generalized sets with semi-linear sets, singling out cases where the nonemptiness of intersection is decidable. Starting fr...

In this paper, minimal γ-semi-open sets in topological spaces introduce and discuss. Also some properties of pre γ-semi-open sets using properties of minimal γ-semi-open sets obtain. As an application of a theory of minimal γ-semi-open sets, I obtain a sufficient condition for a γ-semi-locally finite space to be a pre γ-semi-T2 space.

We introduce and study the concept of $alpha $-semi short modules.Using this concept we extend some of the basic results of $alpha $-short modules to $alpha $-semi short modules.We observe that if $M$ is an $alpha $-semi short module then the dual perfect dimension of $M$ is $alpha $ or $alpha +1$.%In particular, if a semiprime ring $R$ is $alpha $-semi short as an $R$-module, then its Noetheri...

In this paper, we computed general interval indicators of availability and reliability for systems modelled by time non-homogeneous semi-Markov chains. First, considered duration-dependent extensions the Interval Reliability then, determined an explicit formula with a given window containing point. To make computation availability, was derived involving transition probabilities function. Both f...

Let X be a smooth projective surface, Coh(X) the abelian category of coherent sheaves on X, and D(X) the bounded derived category of coherent sheaves on X. We study the Bridgeland stability conditions on D(X) and see that for some stability conditions on D(X) the moduli spaces of (semi)stable objects in D(X) coincide with the moduli spaces of (semi)stable coherent sheaves, while for some other ...