A finitely generated $R$-module is said to be a module of type ($F_r$) if its $(r-1)$-th Fitting ideal is the zero ideal and its $r$-th Fitting ideal is a regular ideal. Let $R$ be a commutative ring and $N$ be a submodule of  $R^n$ which is generated by columns of  a matrix $A=(a_{ij})$ with $a_{ij}in R$ for all $1leq ileq n$, $jin Lambda$, where $Lambda $ is a (possibly infinite) index set.  ...

based on the carnahan and starling hard sphere equation of compressibility, an equation of state has been derived. conditions that must be met by all equations of state are applied in order to obtain attractive term or non - ideal compressibility term of the equation. second virial coefficient and acentric factor arc used in the derivation of the equation of state. in this equation, compressibi...

in this paper, presenting two simple methods for ranking of efficient dmus in dea models that included to add one virtual dmu as ideal dmu and is using the additive model. note that, we use an ideal point just for comparing efficient dmus with. although these methods are simple, they have ability for ranking all efficient dmus, extreme points and the others, also they are capable of ranking the...

In this note we study the fibers of a rational map from an algebraic point of view. We begin by describing two interpretations of the word ‘fiber’. Let S = k[x0, . . . , xn] be a polynomial ring over an infinite field k, I ⊂ S an ideal generated by an r+1-dimensional vector space W of forms of the same degree, and φ the associated rational map P → P = P(W ). We will use this notation throughout...

Background: In recent years, there has been an increased interest toward non-lead radiation shields consisting of small-sized filler particles doped into polymer matrices. In this paper, we study a new polyvinyl alcohol (PVA)/WO3 composite in the presence of high-energy gamma photons through simulation via the Monte Carlo N-Particle (MCNP) simulation code. Materia...