let $r$ be a commutative ring with identity and $m$ an $r$-module. in this paper, we associate a graph to $m$, say ${gamma}({}_{r}m)$, such that when $m=r$, ${gamma}({}_{r}m)$ coincide with the zero-divisor graph of $r$. many well-known results by d.f. anderson and p.s. livingston have been generalized for ${gamma}({}_{r}m)$. we show that ${gamma}({}_{r}m)$ is connected with ${diam}({gamma}({}_...

Consider a Markovian Petri net with race policy. The marking process has a " product form " stationary distribution if the probability of viewing a given marking can be decomposed as the product over places of terms depending only on the local marking. First we observe that the Deficiency Zero Theorem of Feinberg, developped for chemical reaction networks, provides a structural and simple suffi...

for an arbitrary ring $r$, the zero-divisor graph of $r$, denoted by $gamma (r)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $r$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. it is well-known that for any commutative ring $r$, $gamma (r) cong gamma (t(r))$ where $t(r)$ is the (total) quotient ring of $r$. in this...

nutrition is an important factor that influences immunity, and nutritional deficiencies can impair resistance to infections. malnutrition is the most common cause of immunodeficiency worldwide. trace elements such as zinc, selenium, iron, and copper can influence several components of immunity. primary antibody deficiency disorders are a group of disorders characterized by an unusual susceptibi...

since early works on isolation and characterization of vitamin d by elmer verner mccollum and edward mellanby in 1900s, this molecule still seems mysterious (1-2). after several decades since discovery of the miraculous effect of cod liver oil in treatment of nutritional rickets, escalating number of reports provide a huge body of evidence for various effects of vitamin d on human body (3). the...

a research was carried out to determine the factors affecting knowledge, attitude and practice of secnodary school girls concerning iron deficiency anemia, in quazvin city. the study population consists of 218 students who were randomly selected form ten secondary schools in a selected area. aquestionnaire was prepared to collect the data and statistical tests of x2 and regression were employed...

abstract background: cut380a intra uterine device intra uterine device (iud) is used in the health system of iran. the most important and frequent side effects of the iuds are hypermenorrhea and polymenorrhea. in iran, iron supplement are not prescribed for the iud users and there are no documents indicating their iron reservation status. this study was performed to determine the iron status in...

The notion of strongly Lie zero-product preserving maps on normed algebras as a generalization of Lie zero-product preserving maps are dened. We give a necessary and sufficient condition from which a linear map between normed algebras to be strongly Lie zero-product preserving. Also some hereditary properties of strongly Lie zero-product preserving maps are presented. Finally the second dual of...

Orthogonal zero interpolants (OZI) are polynomials which interpolate the “zero-function” at a finite number of pre-assigned nodes and satisfy orthogonality condition. OZI’s can be constructed by the 3-term recurrence relation. These interpolants are found useful in the solution of constrained approximation problems and in the structure of Gauss-type quadrature rules. We present some theoretical...