Numerous researches have been investigated on the mass transfer phenomena and hydrodynamics for the fluid in the vicinity of the membrane surface by the mathematical modelling and simulation. Due to complexities involved in solving transport phenomena within membranes, the application of CFD simulation study for determining the concentration polarization (CP) profile in the membrane channel is ...

In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going down theorems for modules.

‎In this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  It shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull's intersection theorem of fuzzy ideals by using concept $mu$-adic comp...

A module M is called epi-retractable if every submodule of M is a homomorphic image of M. Dually, a module M is called co-epi-retractable if it contains a copy of each of its factor modules. In special case, a ring R is called co-pli (resp. co-pri) if RR (resp. RR) is co-epi-retractable. It is proved that if R is a left principal right duo ring, then every left ideal of R is an epi-retractable ...

The extraction of oil and gas from deep water is one of the most important challenges of the oil and gas industry today. FPSO is one of the leading platforms for deep waters. This study discussed the performance of FPSO deck modules under loads exerted on the hull of the ship. Modeling of the studied module was executed by SACS software and the effect of support using neoprene in the function o...

Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module with $S=$ End$_R(M)$. The module $M$ is called {it Rickart} if for any $fin S$, $r_M(f)=Se$ for some $e^2=ein S$. We prove that some results of principally projective rings and Baer modules can be extended to Rickart modules for this general settings.

the class of ads modules with the sip (briefly‎, ‎$sa$-modules) is studied‎. ‎various conditions for a module to be $sa$-module are given‎. ‎it is proved that for a quasi-continuous module $m$‎, ‎$m$ is a uc-module if and only if $m$ is an $sa$-module‎. ‎also‎, ‎it is proved that the direct sum of two $sa$-modules as $r$-modules is an $sa$-module when $r$ is the sum of the annihilators of these...

The paper describes an approach to developing an interactive MT system for translating technical texts on the example of translating patent claims between Russian and English. The approach conforms to the human-aided machine translation paradigm. The system is meant for a source language (SL) speaker who does not know the target language (TL). It consists of i) an analysis module which includes...

let $r$ be a commutative ring and let $m$ be an $r$-module. we define the small intersection graph $g(m)$ of $m$ with all non-small proper submodules of $m$ as vertices and two distinct vertices $n, k$ are adjacent if and only if $ncap k$ is a non-small submodule of $m$. in this article, we investigate the interplay between the graph-theoretic properties of $g(m)$ and algebraic properties of $m...

This paper presents a mechanistic, fully dynamic, internally mixed, sectional aerosol module, the UCD Aerosol Module, which evolves from the Aerosol Inorganic Model (AIM). The UCD Aerosol Module employs three gas-to-particle mass transport schemes, replacement, coupled and uncoupled, and simplified aerosol thermodynamics to predict gas–particle partitioning, aerosol phase state and water conten...