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.

Three species of nematodes are recorded from alimentary tracts of some Iraqi bats for the first tithe, while reporting Thelandros alatus constitutes first record of this species from mammals. Information on infection rate, distribution and halts are provided along with some relevant remarks.

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise closure topological spaces, fibrewise wake topological spaces, fibrewise strong topological spaces over B. Also, we introduce the concepts of fibrewise w-closed (resp., w-coclosed, w-biclosed) and w-open (resp., w-coopen, w-biopen) topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

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

In this work, we introduce a new kind of perfect mappings, namely j-perfect mappings and j-ω-perfect mappings. Furthermore we devoted to study the relationship between j-perfect mappings and j-ω-perfect mappings. Finally, certain theorems and characterization concerning these concepts are studied; j = , δ, α, pre, b, β

The study aimed to identify the use of the electronic concept maps method in learning some of the skills of the floor exercises in the artistic gymnastics for third graders ,as well as to identify the best group between the two research groups (experimental And the officer to learn and retain some of the skills of the floor exercises in the artistic gymnastics of the research subject , and the experimental method was used and included the sample research on students of the collage of Physical Education and Sports Sciences/University of Baghdad, third grade, and has selected (10) Students for each group of The experimental and controlling groups randomly by lottery and after the completion of the period of implementation of the experiment wh

       The present article discusses innovative word-formation processes in Internet texts, the emergence of new derivative words, new affixes, word-formation models, and word-formation methods. Using several neologisms as an example, the article shows both the possibilities of Internet word-making process and the possibilities of studying a newly established work through Internet communication. The words selected for analysis can be attributed to the keywords of the current time. (In particular, the words included in the list of "Words of 2019") there are number of words formed by the suffix method, which is the traditional method of the Russian word formation. A negation of these words is usually made thro

The child realize that the meals time provide golden opportunities to get the attention the child needs. However, many difficulties that may appear about eating food can be avoided, if the family used the right way in dealing with this problem. The study aims, in this case, at searching for the reasons that lies behind the child's obstinacy in eating his food and the attempt to study some variables that is related to the research topic.

The results are summed up as follows:

• The number of the sample children is 3 of both sexes between the ages of 3 to 6 years