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

A new type of solar air heater was designed, fabricated, and tested in Baghdad, Iraq winter conditions. The heater consists of two main parts. The horizontal section was filled with the black colored iron chip while the vertical part has five pipes filled with Iraqi paraffin wax. A fan was fixed at the exit of the air. Two cases were studied: when the air moved by natural convection and when forced convection moved it. The studied air heater has proven its effectiveness as it heated the air passing through it to high temperatures. The results manifest that using little air movement makes the temperatures, stored energies, and efficiencies of the two studied cases converge

In the current study, different concentrations of miltefosine drug, which is the first effective and safe oral treatment for visceral leishmaniasis, was evaluated against L. donovani promastigotes in comparison with pentosam drug. Direct counting microscopic assay was used to find 50% inhibitory concentration (IC50) of miltefosine and pentostam against L. donovani promastigotes. The IC50 of miltefosine drug was 45.42μg/ml, 46.76μg/ml and 36.68μg/ml after 24 hr, 48hr and 72hr respectively, In comparison with IC 50 of pentostam drug was 75.39 μg/ml after 72hr. There were significant differences (P˂0.05) between IC50 values of miltefosine and pentostam drugs from first day to third day.

Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an ef

During the period October 2003 till July 2004, about (253) urine samples have been collected from urinary tract infection. The study has shown that the bacterium Proteus mirabilis is the responsible for (11.85%) of the urinary tracts infections. Also, the study has declared that the ratio of separation this bacterium from women was (7.51%) and it is higher than the ratio of separation in both men and children which ranged (1. 58%) and (2.76%) respectively . About (30) samples of stool have been collected from children and the ratio of isolation this bacterium has been showen to be( 30%) from children aged bellow 3 years,as well as, we have got bacterial cultures related to P.mirabilis isolated from the infections of middle-ear and b

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

Background : Knee flexors tightness has been documented in apparently healthy adults and in those with musculoskeletal problems, but the influence of age on the tightness has not been studied in Iraq. This study was therefore designed to determine the influence of age on knee flexors tightness in apparently healthy subjects.Methods: Knee flexors tightness was measured using the active knee extension test (AKET) in 200 apparently healthy male and female subjects, aged 13 to 59 years. The subjects were recruited into 5 age groups using the purposive sampling technique.Knee flexors tightness was compared across the age groups using one-way analysis ofvariance (ANOVA). The independent t-test was used to compare knee flexors tightness on both

After studying the reality of application to occupational safety in new Iraqi building projects and sampling the situation wilt that in developed and neighboring countries, researcher found that there is a big gap in the level of safety application conditions, this indicates the need fora quick and clear reference for local engineers to use it on site for safety conditions in their projects . As a case study the monitors work the researcher studied a huge project in the United Arab Emirates.This project considered for safety requirements to highest grades. This case study may be far away from the projects in Iraq, but we hope to rise the Iraqi work level in the near future. After seeing the way of administration work and how they were ra