Let $G$ be a graph with $p$ vertices and $q$ edges. The graph $G$ is said to be a super pair sum labeling if there exists a bijection $f$ from $V(G)cup E(G)$ to ${0, pm 1, pm2, dots, pm (frac{p+q-1}{2})}$ when $p+q$ is odd and from $V(G)cup E(G)$ to ${pm 1, pm 2, dots, pm (frac{p+q}{2})}$ when $p+q$ is even such that $f(uv)=f(u)+f(v).$ A graph that admits a super pair sum labeling is called a {...

in this work, using eigenvalues and eigenvectors of unitary cayley graphs over finite local rings and elementary linear algebra, we characterize which local rings allowing pst occurring in its unitary cayley graph. moreover, we have some developments when $r$ is a product of local rings.

in this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. next, we investigate some properties of such rings. we prove that mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.

We introduce the class of “right almost V-rings” which is properly between the classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-rin...

The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings.  In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rxcap Ry = Rxy$.  In Section 2 of this articl...

introduction: hydrogen sulfide (h2s) plays a key role in the regulation of vascular tone and protection of blood vessels against endothelial dysfunction. since the mechanism of salt impairing h2s-induced vascular relaxation is not fully clear, therefore this study was designed to investigate the role of potassium (k+) channels in the vasodilatory effects of exogenous h2s in rat aortic rings. ma...

Do recent declines in first marriage rates signal that an increasing proportion of women will remain single their entire lives, or merely that they are postponing marriage to older ages? Our forecasts for cohorts born in the 1950s and 1960s suggest that marriage will remain nearly universal for American women—close to 90 percent of women are predicted to marry. However, separate forecasts by ed...

In this research, a model for optimal PM planning based on reliability is developed and solved for multi-component systems. In the proposed model, the type of PM actions for each inspection period is determined in such manner that the total weighted related costs are minimized while a minimum required system reliability is maintained. The planning horizon is divided into some inspections interv...

Porous media has interesting features in compared with free flame combustion due to the extended of the lean flammability limits and lower emissions. Advanced new generation of internal combustion (IC) engines are expected to have far better emissions levels both gaseous and particulate matter, at the same time having far lower fuel consumption on a wide range of operating condition. These c...