Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

Abstract

There has been a heated controversy over the role the financial policy plays and how sufficient   it   is   in affording   the   financial   burden. This   burden   is   known as the operational   current expenses   which   the   governments   of   various countries mainly afford,   despite the   discrepancy   in   the   government’s   economic   policy.   After   the deterioration and deficit in the state budget in all countries nowadays, it was necessary to find an appropri

The results of analyzing BVRI CCD photometry of the spiral galaxies NGC 7339, NGC 7537, and NGC 7541 are presented using the observations acquired with the 1.88m Kottamia telescope (Egypt). The overall structure of the galaxies is analyzed together with isophotal contour maps. The surface brightness profiles of the galaxies are decomposed to bulge and disk components by fitting a de Vaucouleurs law for the bulge and an exponential law for the disk to obtain photometric parameters for each component. The corrected total and absolute magnitudes and integrated color are also obtained and found to be close to the published values. The radial profiles of ellipticity, major-axis position angle, and color are also obtained and discussed.

The research aims to measure the net nominal protection coefficients for the products table eggs and poultry meat and the extent of its impact on domestic production volume for the period of 1990- 2013 has been the use of mathematical formulas simplified in the calculation of the transaction process with a view to the extent of support and protection offered by the state pricing policy for products Resources Sector Animal in Iraq and reach search Highlights and most important, there are volatile price state policy with regard to eggs and poultry meat, as it ranged net nominal protection coefficients between the larger and less than the right one, which means that values are unstable to support local producers or consumers, and can be The

Background: Masseter muscle is one of the most obvious muscles of mastication and considered as one indicator of jaw muscle activity. It has a major influence on the transverse growth of the midface and the vertical growth of the mandible. This study undertaken to determine the role of cephalometric analysis for discrimination between Cl I and Cl III skeletal relationships, determine the role of ultrasonography in determination of masseter muscle thickness, compare masseter muscle thickness between Cl I and Cl III skeletal relationships, and determine the effect of gender on masseter muscle thickness. Material and Method: The sample of the current study consisted of 70 Iraqi subjects 40 males and 30 females with age ranging 18-25 years. The

In this work, electrochemical process was presented to polymerized eugenol on Gr.2 and Gr.5 titanium alloys before and after treated by Micro Arc Oxidation (MAO), where Gr.2 is commercial pure titanium and Gr.5 is Ti-6Al-4V dental alloys. The deposited layers were characterized by scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD), and Fourier transform infrared spectroscopy (FTIR). The adhesion strength of polymeric thin-film was estimation by using pull-off adhesion test and the result was the adhesion strength of PE was (1.23 MPa) on Gr.2 before MAO and increase to (1.98 MPa) on Gr.2 after MAO treatment. The corrosion behavior of Gr.2 and Gr.5 alloy in artificial saliva environment at

This paper investigates the performance evaluation of two state feedback controllers, Pole Placement (PP) and Linear Quadratic Regulator (LQR). The two controllers are designed for a Mass-Spring-Damper (MSD) system found in numerous applications to stabilize the MSD system performance and minimize the position tracking error of the system output. The state space model of the MSD system is first developed. Then, two meta-heuristic optimizations, Simulated Annealing (SA) optimization and Ant Colony (AC) optimization are utilized to optimize feedback gains matrix K of the PP and the weighting matrices Q and R of the LQR to make the MSD system reach stabilization and reduce the oscillation of the response. The Matlab softwar

       Despite the multiplicity of institutions contributing to the decision-making process in the United States of America, they interact to crystallize positions regarding international and strategic situations. The formulation of the national security policy depends on a number of institutions that complement each other in order to achieve an advanced security situation. Thus, the decision reflects the process of interaction of the existing regulatory institutions. This is because the essence of the national security and achieving its requirements also stems from the existence of a coherent system of shared beliefs and principles in the American society. Besides, these elements are the bases for achieving