Let R be a commutative ring with 1 and M be a left unitary R-module. In this paper, we give a generalization for the notions of compressible (retractable) Modules. We study s-essentially compressible (s-essentially retractable). We give some of their advantages, properties, characterizations and examples. We also study the relation between s-essentially compressible   (s-essentially retractable modules) and some classes of modules.

Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of

In this paper, we introduce a new concept named St-polyform modules, and show that the class of St-polyform modules is contained properly in the well-known classes; polyform, strongly essentially quasi-Dedekind and ?-nonsingular modules. Various properties of such modules are obtained. Another characterization of St-polyform module is given. An existence of St-polyform submodules in certain class of modules is considered. The relationships of St-polyform with some related concepts are investigated. Furthermore, we introduce other new classes which are; St-semisimple and ?-non St-singular modules, and we verify that the class of St-polyform modules lies between them.

In this research, we introduce a small essentially quasi−Dedekind R-module to generalize the term of an essentially quasi.−Dedekind R-module. We also give some of the basic properties and a number of examples that illustrate these properties.

The main goal of this paper is introducing and studying a new concept, which is named H-essential submodules, and we use it to construct another concept called Homessential modules. Several fundamental properties of these concepts are investigated, and other characterizations for each one of them is given. Moreover, many relationships of Homessential modules with other related concepts are studied such as Quasi-Dedekind, Uniform, Prime and Extending modules.

Let R be an associative ring with identity, and let M be a unital left R-module, M is called totally generalized *cofinitely supplemented module for short ( T G*CS), if every submodule of M is a Generalized *cofinitely supplemented ( G*CS ). In this paper we prove among the results under certain condition the factor module of T G*CS is T G*CS and the finite sum of T G*CS is T G*CS.

Non-prismatic reinforced concrete (RC) beams are widely used for various practical purposes, including enhancing architectural aesthetics and increasing the overall thickness in the support area above the column, which gives high assurance to services that this will not result in the distortion of construction features and can reduce heights. The hollow sections (recess) can also be used for the maintenance of large structural sections and the safe passage of utility lines of water, gas, telecommunications, electricity, etc. They are generally used in large and complex civil engineering works like bridges. This study conducted a numerical study using the commercial finite element software ANSYS version 15 for analysing RC beams, hol

   Pressure retarded osmosis (PRO) can be considered as one of the methods for utilizing osmotic power, which is a membrane-based technology. Mathematical modeling plays an essential part in the development and optimization of PRO energy-generating systems. In this research, a mathematical model was developed for the hollow fiber module to predict the power density and the permeate water flux theoretically. Sodium chloride solution was employed as the feed and draw solution. Different operating parameters, draw solution concentration (1 and 2 M), the flow rate of draw solution (2, 3, and 4 L/min), and applied hydraulic pressure difference (0 - 90 bar) was used to evaluate the performance of PRO process of a hollow fiber module. The eff