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

Films of silver oxide of different thickness have been prepared by the chemical spray paralysis. Transmission and absorption spectra have recorded in order to study the effect of increasing thickness on some optical parameter such as reflectance, refractive index , and dielectric constant in its two parts . This study reveals that all these paramters affect by increasing the thickness .

Forty eight isolates (41.02%) were obtained from 117 wound and burn samples. The isolates that showed high resistance for both antibiotic was two only that represent 4,1% from all isolates. The result of PCR product electrophoresis was referred that the gene is VIM gene. Lactose and raffinose showed double increasing in diameter of inhibition zone of imipenem with 1% that mean showed highest susceptibility that decreased with the concentration increasing, the same result were with meropenem. But no effect were detected on meropenem inhibition zone diameter. Mannose have no effect on the resistance in 1%, 3% and 7%. Results showed that only three case that increase the expression of gene, they were lactose at 1% concentration that increased

This study was conducted in a laboratory experiment at the University of Baghdad, College of Science, computing Department, 5 km from the center of Baghdad city, in 2021 to evaluate the sorting method for the tomato crop. The experiments were conducted in a factorial experiment under a complete randomized design with three replications and using SAS analysis, artificial neural network, image processing, the study of external characteristics, and physical features; fruit surface area and fruit circumference were 1334.46 cm2,57.53 cm2 and free diseases. The error value was less than zero, while training with outputs recorded the highest value and which was 5. The neural network's performance between the input and the mean square of th

This research aims at building a proposed training program according to the self-regulated strategies for the mathematics teachers and to identify the effect of this program on relational Mathematics of teachers. The sample of the research was (60) Math teachers; (30) teachers as experimental group and (30) teachers as control group. The results of the current research reacheded that the proposed training program according to some self-managed learning strategies, meets the needs of trainees with remarkable effectiveness to improve the level of their teaching performance to achieve the desired goals. Training teacher according to self-managed learning strategies is effective in bringing about the transition of training to their students

Introduction: Attention is a fundamental cognitive function in sports, particularly in volleyball, where players must process multiple stimuli and make rapid decisions. Effective attentional control can enhance an athlete’s ability to react to dynamic game situations. The nomination of ideas strategy. Objective: This study aims to examine the effectiveness of the nomination of ideas strategy in enhancing divided and selective attention and its subsequent impact on volleyball skill performance. Methodology: A controlled experimental design was employed, involving volleyball players divided into an experimental group and a control group. The experimental group integrated the nomination of ideas strategy into their training sessions,