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

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.

The family Ormyridae has been very much neglected by workers and only two species has been recorded so far from Iraq. The present study, based mainly on my collection, deals with five species, of which one is new to science. The new species is described together with notes on locality data, host records, distribution and taxonomical remarks for all the species.

fields of the College of Agricultural Engineering Sciences, University of Baghdad/Al-Jadriya, in the fall season 2021-2022. With three sowing dates (26 July, 4 August, 12 August), The experiment was implemented according to a randomized complete block design (RCBD) with three replications. The aim is to detect the expression of the INCW1 gene associated with sucrose-to-glucose analysis, which is critical for many metabolic functions in different sink tissues, and determine the amount of fold gene expression to find out which of the genotypes contain the invertase gene, and which ones have a high level of gene expression based on the fold of gene expression. The results showed significant differences in the invertase enzyme activity for the

The research consists of five chapters and aims to explore the administrative skills of leaders in physical education colleges and their relationship with administrative reform. The study sample included (deans, vice deans, and heads of departments) from physical education colleges for the academic year 2012-2013, with a total of 61 individuals. They were selected using the purposive sampling method, and the researcher distributed questionnaires to them, collecting 60 valid responses and excluding one due to its invalidity. After defining the concepts of administrative skills and administrative reform and redownloading relevant literature and previous studies, as well as consulting with a group of experts in management and psychology, the r

The main topic of this study is central around the independence of Jordanian central bank and the extent of the effectiveness at the bank in leading the monetary policy without interferences or pressures from side of the government.  the degree of independence of Jordanian central bank was  based on the following based hypothesis following ,there is relationship between the independence of the central bank and the legislative and economical indices. the most important recommendations are degree of independence of the Jordan central bank 43.5% is a good one, but it possible to reach a higher degree than this one by to making some modification on the Jordanian central bank law and by the central bank should be more rigid

The principal forms of radiation dosage for humans from spontaneous radiation material are being recognized as radon and its progenitors in the interior environment. Radiation-related health risks are caused by radon in water supply, which can be inhaled or ingested. Materials and Methods: The solid-state CR-39 nuclear trace detectors method was using in this research for measuring accumulation of radioactivity in water supply in different locations of Iraq's southwest corner of Baghdad. In Baghdad district, 42 samples were selected from 14 regions (3 samples out of each region) and put in dosimeters for 50 days. Results: The mean radon concentration was 49.75 Bq/m3, that is lower than the internationally recognized limit of 1100 Bq /m3. Th

Discussed the research variables are important, privatization options and strategic analysis of the external environment, and that the purpose of the research is the trade-off between privatization options and choose the most appropriate alternative in proportion to the external environment, the research aims to determine the privatization the most appropriate option for companies and public contracting, showing the importance of the study provide the privatization of public companies as a strategy can all its way public sector organizations from the transfer of work practices or private sector organizations and mechanisms to it as contributing to improving the level of skills Develop the current and future level of performance,