Let R be a commutative ring with identity, and M be a left untial module. In this paper we introduce and study the concept w-closed submodules, that is stronger form of the concept of closed submodules, where asubmodule K of a module M is called w-closed in M, "if it has no proper weak essential extension in M", that is if there exists a submodule L of M with K is weak essential submodule of L then K=L. Some basic properties, examples of w-closed submodules are investigated, and some relationships between w-closed submodules and other related modules are studied. Furthermore, modules with chain condition on w-closed submodules are studied.   

     This research aims to present some  results for  conceptions of  quasi -hyponormal operator defined on Hilbert space . Signified by the -operator, together with some significant characteristics of this operator and various theorems pertaining to this operator are discussed, as well as, we discussed the null space and range of these  kinds of operators.

The purpose of this paper is to investigate the concept of relative quasi-invertible submodules motivated by rational submodules and quasi-invertible submodules. We introduce several properties and characterizations to relative quasi-invertiblity. We further investigate conditions under which identification consider between rationality, essentiality and relative quasi-invertiblity. Finally, we consider quasiinvertiblity relative to certain classes of submodules

In this paper, we introduce a class of operators on a Hilbert space namely quasi-posinormal operators that contain properly the classes of normal operator, hyponormal operators, M–hyponormal operators, dominant operators and posinormal operators . We study some basic properties of these operators .Also we are looking at the relationship between invertibility operator and quasi-posinormal operator .

The present study involves experimental analysis of the modified Closed Wet Cooling Tower (CWCT) based on first and second law of thermodynamics, to gain a deeper knowledge in this important field of engineering in Iraq. For this purpose, a prototype of CWCT optimized by added packing under a heat exchanger was designed, manufactured and tested for cooling capacity of 9 kW. Experiments are conducted to explore the effects of various operational and conformational parameters on the towers thermal performance. In the test section, spray water temperature and both dry bulb temperature and relative humidity of air measured at intermediate points of the heat exchanger and packing. Exergy of water and air were calculated by applying the exergy

     Terrorist operations disturbed societies and threatened their existence due to destructive ideas carried by those groups that believe in radical change and the use of multiple methods to implement their ideas, as well as taking methods of concealment among society, so it has become difficult to detect them. The study's purpose is to locate sleeper cells of terrorist operations in areas dense with various human activities using remote sensing techniques and geographic information systems programs. The programs were used to analyze the group of terrorist incidents data that occurred in Baghdad in 2011 and study how to limit the crimes spreading in Baghdad. The study included building a model in spatial information systems for site

      In this paper, we introduce and study the notation of approximaitly quasi-primary submodules of a unitary left -module  over a commutative ring  with identity. This concept is a generalization of prime and primary submodules, where a proper submodule  of an -module  is called an approximaitly quasi-primary (for short App-qp) submodule of , if , for , , implies that either  or , for some . Many basic properties, examples and characterizations of this concept are introduced.

The concept of a 2-Absorbing submodule is considered as an essential feature in the field of module theory and has many generalizations. This articale discusses the concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules and their relationship to the 2-Absorbing submodule, Quasi-2-Absorbing submodule, Nearly-2-Absorbing submodule, Pseudo-2-Absorbing submodule, and the rest of the other concepts previously studied. The relationship between them has been studied, explaining that the opposite is not true and that under certain conditions the opposite becomes true. This article aims to study this concept and gives the most important propositions, characterizations, remarks, examples, lemmas, and observations related to it. In the en

Let  be a commutative ring with identity, and  be a unitary left -module. In this paper we introduce the concept pseudo weakly closed submodule as a generalization of -closed submodules, where a submodule  of an -module  is called a pseudo weakly closed submodule, if for all , there exists a -closed submodule  of  with  is a submodule of  such that . Several basic properties, examples and results of pseudo weakly closed submodules are given. Furthermore the behavior of pseudo weakly closed submodules in class of multiplication modules are studied. On the other hand modules with chain conditions on pseudo weakly closed submodules are established. Also, the relationships of  pseudo weakly closed

Sufficient conditions for boundary controllability of nonlinear system in quasi-Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and some techniques of nonlinear functional analysis, such as, fixed point theorem and quasi-Banach contraction principle theorem. Moreover, we given an example which is provided to illustrate the theory.