Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

polyvinylidene fluoride/polyvinylpyrrolidone (pvdf/pvp) hollow fiber membranes were fabricated by dry-jet wet-spinning process. the correlated effects of the air gap length and pvp concentration ((1) the air gap length effect at the low and high pvp concentration in the dope solutions, as well as (2) the effect of the pvp concentration at the same air gap length) on the cross-section structure ...

this paper investigates hollow and porous alumina nanospheres that were previously synthesized to be used for the dehydration of methanol to dimethyl ether (dme). as hollow nanostructures possess characteristics such as low density and high surface to volume ratio, their catalytic activity between hollow and porous structure is compared. for this purpose, three most important parameters (acidit...

A mass transfer model is proposed for prediction of permeate concentration and percent rejection at different inlet pressures and feed dye concentrations in membrane ultrafiltration. A differential equation in cylindrical co-ordinates considering the spiral wound membrane equivalent to a cylindrical module is derived which coupled with mass balance and permeate flux equations are solved to yiel...

$r$-module. in this paper, we explore more properties of $max$-injective modules and we study some conditions under which the maximal spectrum of $m$ is a $max$-spectral space for its zariski topology.

2,6-di(5,6-dipropyl-1,2,4-triazin-3-yl)pyridine (n-Pr-BTP), first developed in our laboratory, is a very promising extractant for the effective separation of actinides(III) from lanthanides(III). It is able to extract actinides(III) with usable distribution coefficient from 1-2 molar nitric acid selectively over lanthanides(III). The Am(III)/Eu(III) separation factor is approx. 135. The perform...

In this study, simulation of Fitzhugh nagumo model in order to generation and propagation of the wave of action potential over the length the of the squid giant axon and survey the passage of time effect in wave propagation have been explored. Simulation has been performed by using the Comsol Multiphysics 3.5 a software. So that, in this simulation, squid giant axon is intended to form hollow c...

let $r$ be a ring and $m$ a right $r$-module with $s=end_r(m)$. a module $m$ is called semi-projective if for any epimorphism $f:mrightarrow n$, where $n$ is a submodule of $m$, and for any homomorphism $g: mrightarrow n$, there exists $h:mrightarrow m$ such that $fh=g$. in this paper, we study sgq-projective and$pi$-semi-projective modules as two generalizations of semi-projective modules. a m...

let $r$ be a commutative ring with identity and $m$ be a unitary$r$-module. the primary-like spectrum $spec_l(m)$ is thecollection of all primary-like submodules $q$ such that $m/q$ is aprimeful $r$-module. here, $m$ is defined to be rsp if $rad(q)$ isa prime submodule for all $qin spec_l(m)$. this class containsthe family of multiplication modules properly. the purpose of thispaper is to intro...

We are developing a new method using ultrasonic longitudinal and torsional vibration of a hollow-type stepped horn for hole machining. We foresee that the equipment can be simplified and miniaturized. In this paper, ultrasonic vibration sources of a hollow-type stepped horn without a diagonal slits vibration converter and with a diagonal slits vibration converter are used. The longitudinal and ...