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.

Through this study, the following has been proven, if  is an algebraically paranormal operator acting on separable Hilbert space, then  satisfies the ( ) property and  is also satisfies the ( ) property for all . These results are also achieved for  ( ) property.    In addition, we prove that for a polaroid operator with finite ascent then after the property ( ) holds for  for all.

This study is due to insufficient development of the issues of initial training in tennis at youthful (student) age. Objective: development of a methodological and scientific-methodological base of students' tennis with current trends in tennis. Summing up the best practices of modern tennis, we came to the conclusion that the formation of the art of reflection backhands in teaching beginner students of sports specialization to achieve future success. In modern conditions in the development of Russian tennis student opens the possibility of using new technologies and programs. Using these approaches, we have developed a training program and tested students' tennis in the pedagogical experiment, which resulted in its effectiveness.

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

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.

Aphid Aphis spp (Hemiptera:Aphididae) and Thrips Thrips spp (Thysanoptera: Thripidae) an economically important pests on several crops in the world and Iraq, that transfer many viruses diseases to it. Field studies were conducted to assessment the population density of these insects and susceptibility of six varieties (Barin, Revera, Divela, Rudlph, Alazata and Pleny) to infestation during 2013 spring season. The results were showed that all Potato varieties were infested by Aphis and Thrips on spring plantation but with different percentage. The Divela variety was higher percentage of infestation and high population density of aphid which averaged 1.47 insect/ leaf while in Alazata was the lower population density which averaged 1.02 in

<em>The aim of the research is to set a set of BioKinematic variables for the step of crossing barriers (3–6–9) in a 110-meter barrier for young runners. The researchers concluded the study by interpreting and discussing the results that the most important variables must be relied upon when training and selecting runners that got the best saturation on their factors: 1-The first factor which refers to the total distance of the plan to pass the third barrier + the total distance of the plan to pass the ninth barrier + the total distance Plan to cross the sixth barrier. 2-The second factor which refers to the total vertical speed before passing the third barrier + the total vertical speed before the sixth barrier + the total vertica

The impact of mental training overlap on the development of some closed and open skills in five-aside football for middle school students, Ayad Ali Hussein, Haidar Abedalameer Habe

The job that confronts players with the effectiveness of shooting with an air rifle is high, so it requires necessary functional adaptations that differ in their degrees from other sports. Regular training in air rifle shooting leads to physiological changes in most of the body's internal systems, and changes and responses can be identified. The functional accompanying physical activity through the presence of body components that reflect these physiological changes in the form of changes in some components, and the importance of research lies in studying the physiological changes accompanying the maximum physical effort and the consequent development of the level of achievement in the effectiveness of shooting with air rifle and body