Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.

‎A module $M$ is lifting if and only if $M$ is amply supplemented and‎ ‎every coclosed submodule of $M$ is a direct summand‎. ‎In this paper‎, ‎we are‎ ‎interested in a generalization of lifting modules by removing the condition‎"‎amply supplemented‎" ‎and just focus on modules such that every non-cosingular‎ ‎submodule of them is a summand‎. ‎We call these modules NS‎. ‎We investigate some gen...

An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

Let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $R$.  In this paper we  study the relationship between an$R$-module $M_R$ and the  general polynomial module  $M[x]$ over theskew polynomial ring $R[x;alpha,delta]$. We introduce the notionsof skew-Armendariz modules and skew quasi-Armendariz modules whichare generalizations of $alpha$-Armendariz modules and extend thecla...

The paper uses a new approach to investigate prime submodules and minimal prime submodules of certain modules such as Artinian and torsion modules. In particular, we introduce a concrete formula for the radical of submodules of Artinian modules.

A micro-channel heat exchanger reactor with different micro-baffle shapes has been studied numerically. Governing equations were solved base on the finite volume method with FLUENT software. In upper section, oxidation reaction of methanol was occurred and in lower section, steam reforming of methanol was done. Two sections were separated with solid part which played as heat exchanger and trans...

In marine storage and transportation, the sloshing of liquid oxygen disturbs thermodynamic equilibrium induces stress on tank walls. Numerous problems are associated with mechanism demand a detailed investigation. this study, numerical model is developed by coupling Eulerian framework algebraic interface area density (AIAD) method while considering interphase drag force to investigate thermal b...

Sloshing refers to a certain kind of fluid movement that changes as it progresses. It possesses properties are both nonlinear and exceedingly unpredictable, these affect the tank wall. This effect may lead structural wear, which in turn can cause fail. Benzene gasoil liquids used test sloshing liquid accompanying pressure on wall caused by baffles partially full tanks. To attain this, modeling ...