In this research note approximately prime submodules is defined as a new generalization of prime submodules of unitary modules over a commutative ring with identity. A proper submodule  of an -module  is called an approximaitly prime submodule of  (for short app-prime submodule), if when ever , where , , implies that either  or . So, an ideal  of a ring  is called app-prime ideal of  if   is an app-prime submodule of -module . Several basic properties, characterizations and examples of approximaitly prime submodules were given. Furthermore, the definition of approximaitly prime radical of submodules of modules were introduced, and some of it is properties were established.

     The concept of a small f- subm was presented in a previous study. This work introduced a concept of a hollow f- module, where a module is said to be hollow fuzzy when every subm of it is a small f- subm. Some new types of hollow modules are provided namely, Loc- hollow f- modules as a strength of the hollow module, where every Loc- hollow f- module is a hollow module, but the converse is not true. Many properties and characterizations of these concepts are proved, also the relationship between all these types is researched. Many important results that explain this relationship are demonstrated also several characterizations and properties related to these concepts are given.

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

Suppose R has been an identity-preserving commutative ring, and suppose V has been a legitimate submodule of R-module W. A submodule V has been J-Prime Occasionally as well as occasionally based on what’s needed, it has been acceptable: x ∈ V + J(W) according to some of that r ∈ R, x ∈ W and J(W) an interpretation of the Jacobson radical of W, which x ∈ V or r ∈ [V: W] = {s ∈ R; sW ⊆ V}. To that end, we investigate the notion of J-Prime submodules and characterize some of the attributes of has been classification of submodules.

Abstraet

Students dropout from the Education has a negative phenomena on individual and society and even on different aspects of life especially on the economic aspect , Thus our research tries studying and analyzing the relation between the size of dropout and human development level in Iraq and as (research sample) the first decade of this century as a studying period, the study includes the dropout in Secondary schools and depending the formal records as a main source to evaluate the size of this problem in Iraq , which shows an increase in the size of dropout in this period in comparison with the last decades of the twentieth century, this produces a negative effect on human developme

The present work presents design and implementation of an automated two-axis solar tracking system using local materials with minimum cost, light weight and reliable structure. The tracking system consists of two parts, mechanical units (fixed and moving parts) and control units (four LDR sensors and Arduino UNO microcontroller to control two DC servomotors). The tracking system was fitted and assembled together with a parabolic trough solar concentrator (PTSC) system to move it according to information come from the sensors so as to keep the PTSC always perpendicular to sun rays. The experimental tests have been done on the PTSC system to investigate its thermal performance in two cases, with tracking system (case 1) and without trackin

Abstract

 This work involves studying the effect of adding some selective organic component mixture on corrosion behavior of pure Al and its alloys in condensed synthetic automotive solution (CSAS) at room temperature. This mixture indicates the increasing of octane number in previous study and in this study show the increasing in corrosion resistance through the decreasing in corrosion rate values.

Electrochemical measurements were carried out by potentiostat at 3 mV/sec to estimate the corrosion parameters using  Tafel extrapolation method, in addition to cyclic polarization test to know the pitting susceptibility of materials in tested medium.

The cathodic Tafel slope

In this study, a packed bed was used to remove pathogenic bacteria from synthetic contaminated water. Two types of packing material substrates, sand and zeolite, were used. These substrates were coated with silver nanoparticles (AgNPs), which were prepared by decomposition of Ag ions from AgNO3 solution. The prepared coated packings were characterized using scanning electron microscopy, energy-dispersive X-ray spectroscopy and transmission electron microscopy. The packed column consisted of a PVC cylinder of 2 cm diameter and 20 cm in length. The column was packed with silver nanoparticlecoated substrates (sand or zeolite) at a depth of 10 cm. Four types of bacteria were studied: Escherichia coli, Shigella dysenteriae, Pseudomonas aerugi