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

Chronic liver disease (CLD) can potentially cause disruptions in the normal functioning of various endocrine organs responsible for producing hormones. As a result, individuals suffering from CLD may experience fluctuations or imbalances in the levels of certain hormones within their bodies. As well as they frequently have suppressed immune systems making them more vulnerable to parasite infections. The primary objective of this study was to investigate the association between Toxoplasma gondii infections and liver function by analyzing the interplay between these parasites and hormones. This study was conducted in Baghdad, Iraq from December 2021 to May 2022. One hundred and twenty male patients with Chronic liver disease (CLD) (ag

Water produced from power plants is one of the most important sources of water pollution, especially for areas like Baghdad, Contaminated industrial wastewater is a major environmental challenge due to the rapid growth of industries, leading to increased accumulation of harmful pollutants in water resources, the work is intended to study the impact of water generated from a power plant in the south on the level of heavy metals before and after the treatment process and after its discharge to the Tigris River. Objective is to determine the extent of heavy metals such as iron, copper, chromium, and zinc concentration in water extracted from various points and subsequently study the monthly variations of these elements with a view to assessmen

Sludge from stone-cutting (SSC) factories and stone mines cannot be used as decorative stones, stone powder, etc. These substances are left in the environment and cause environmental problems. This study aim is to produce artificial stone composite (ASC) using sludge from stone cutting factories, cement, unsaturated resin, water, silicon carbide nanoparticles (SiC-NPs), and nano-graphene oxide (NGO) as fillers. Nano graphene oxide has a hydrophobic plate structure that water is not absorbed due to the lack of surface tension on these plates. NGO has a significant effect on the properties of artificial stone due to its high specific surface area and low density in the composite. Its uniform distribution in ASC is very low due to its hydropho

The aim of this research is to study the effect of welded joint design (Butt joint and lap joint) on thejoint strength during tension and fatigue loading with different current of welding (40,50,60,70,80) ^per, and different type of wire welding. The result of this research is showed that the effect of fatigue loading on the type of joint is more than the effect of tension loading on it. And the butt joint welding is better than the lap joint welding during the fatigue loaded.The experimental results of the effect of W'elding current showed that more increasing and more decreasing the value of the heat input, during the welding was found to produce mechanical brittleness on the buttjoint welding during the static and dynamic loading. Also i

In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.