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.

Czerwi’nski et al. introduced Lucky labeling in 2009 and Akbari et al and A.Nellai Murugan et al studied it further. Czerwi’nski defined Lucky Number of graph as follows: A labeling of vertices of a graph G is called a Lucky labeling if  for every pair of adjacent vertices u and v in G where . A graph G may admit any number of lucky labelings. The least integer k for which a graph G has a lucky labeling from the set 1, 2, k is the lucky number of G denoted by η(G). This paper aims to determine the lucky number of Complete graph K_n, Complete bipartite graph K_m,n and Complete tripartite graph K_l,m,n. It has also been studied how the lucky number changes whi

     In this article, the lattice Boltzmann method with two relaxation time  (TRT)  for the  D2Q9 model is used to investigate numerical results for 2D flow. The problem is performed to show the dissipation of the kinetic energy rate and its relationship with the enstrophy growth for 2D dipole wall collision. The investigation is carried out for normal collision and oblique incidents at an angle of . We prove the accuracy of moment -based boundary conditions with slip and Navier-Maxwell slip conditions to simulate this flow. These conditions are under the effect of Burnett-order stress conditions that are consistent with the discrete Boltzmann equation. Stable results are found by using this kind of boundary condition where d

This paper set forth the spatial suitability of the informal settlement supposed to be distributed by the Iraqis government to poor people. The Iraqi government identified 9 locations of informal settlement in Baghdad city and acceptance it as a reality as a help for them to getting home. In this paper I discovered the suitability of those locations which one will be suitable more than others for living. The analysis process was applied using the GIS environment – spatial analysis. According to the results, It has been identified as the most important measures to identify which one of these areas suitable for development for housing by using some criteria (Distance from the city center, Proximity from transport routes, Proximity of high v

A new series of Fe (III) , Co (II) , Ni (II) and Cu (II) complexes of the Schiff base, 5 (2-hydroxy benzylidine) -2-thio ether -1, 3, 4-thiadiazole were prepared and characterized .The imine behaves as a bidentate. The nature of bonding and the stereochemistry of the complexes were deduced from metal analyses, infrared, electronic spectra,magnetic susceptibility and conductivity measurements, an octahedral geometry was suggested for all complexes except the copper complex has a square planar geometry .preliminary in vitro tests for antimicrobial activity show that all the prepared compounds except iron complex display good activity to gram positive Staphelococcus aures and gram negative Escherchia coli.

تعد لعبة كرة السلة من الألعاب الرياضية التي تحتاج متطلبات بدنية ووظيفية خاصة بها، وذلك من خلال الانتقال داخل الملعب بالكرة أو بدونها والسبل للتخلص من ملاحقة الخصم أثناء الدفاع وكيفية المناورة أثناء الهجوم مع إجادة التصويب بكافة أنواعه داخل الملعب، ومن هنا تكونت مشكلة البحث في كيفية تطوير تلك العوامل الوظيفية والتي لها الأثر في الارتقاء بمستوى أداء اللاعب أثناء اللعب، وعن طريق استخدام الباحثان لطريقة جهاز ا

A large number of natural or synthetic dyes have been removed from both national and international lists of permitted food colors because of their mutagenic or carcinogenic activity. Therefore, this study aimed to use the Random Amplified Polymorphic DNA-Based Polymerase Chain Reaction (RAPD-PCR) assay as a feasible method to evaluate the ability of some food colors as genotoxin-induced DNA damage and mutations. Lactiplantibacillus plantarum was used as a bioindicator to determine the genotoxic effects by RAPD-PCR using M13 primer after treatment with some synthetic dyes currently used as food color additives, including Sunset Yellow, Carmoisine, and Tartrazine. Besides qualitative analysis, the bioinformatic GelJ software was used for clus

The study aimed at designing compound exercises using added weight on some skill abilities in youth soccer players aged (17 – 19) years old. The researcher sued the experimental method on (30) players aged (17 – 19) years old from Al Zawraa Sport Club. The subjects were divided into three groups and the training program was applied for (8) weeks with (3) training sessions per week. The data was collected and treated using proper statistical operations to conclude that compound exercises with weights between improved the subjects compared to the groups that did not use the added weights. Finally, the researchers recommended the necessity of using compound exercises using added weights during training sessions for youth soccer pla

Abstract The purpose of this paper is preparing exercises according to some biomechanical variables for women with low back pain and identifying the effect of exercise according to some biomechanical variables and relieving lower back pain for women. The researchers used the one-group experimental design. The sample was chosen by the intentional method to provide the necessary conditions for conducting the study, and they represent the research community and its sample. The researchers also excluded (2) of the injured women because they did not adhere to the rehabilitation sessions, and for the purpose of ensuring the homogeneity of the sample members, the researchers used the arithmetic mean, standard deviation, and the torsion coefficient