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 definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X , ï´ ) be a topological space, and let A ⊆, then A is called semi-preopen set if ⊆∘ . In this paper, we study the properties of semi-preopen sets but by another definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.
The structure of this paper includes an introduction to the definition of the nano topological space, which was defined by M. L. Thivagar, who defined the lower approximation of G and the upper approximation of G, as well as defined the boundary region of G and some other important definitions that were mentioned in this paper with giving some theories on this subject. Some examples of defining nano perfect mappings are presented along with some basic theories. Also, some basic definitions were presented that form the focus of this paper, including the definition of nano pseudometrizable space, the definition of nano compactly generated space, and the definition of completely nano para-compact. In this paper, we presented images of nan
... Show MoreCzerwi’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 Kn, Complete bipartite graph Km,n and Complete tripartite graph Kl,m,n. It has also been studied how the lucky number changes whi
... Show MoreThe definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X , ï´ ) be a topological space, and let A ⊆, then Ais called semi-preopen set if ⊆∘ . In this paper, we study the properties of semi-preopen sets but by another definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.
In this paper we define and study new concepts of functions on fibrewise topological spaces over B namely, fibrewise weakly (resp., closure, strongly) continuoac; funttions which are analogous of weakly
(resp., closure, strongly) continuous functions and the main result is : Let <p : XY be a fibrewise closure (resp., weakly, closure, strongly, strongly) continuous function, where Y is fibrewise topological space over B and X is a fibrewise set which has the
in
... Show MoreThe research consists of five chapters, and in the first chapter, it addresses the introduction and importance of the research, where the researcher explained the importance of bio-motor abilities and their role in achieving a high level through their connection to the skill performance of standing on the hands followed by the forward roll, and the research problem: Do these bio-motor abilities have an impact on the level of skill performance? Handstand followed by forward roll.
The predisposing factors and their effect on the increasing of vulvovaginal Candidiasis have been studied in this research. The result indicated that the highest of infection with vaginal Candidias was in the age of women with age of (21-30years) with vaginal itching and discharge, also the results revealed that the pregnancy was the main predisposing factor. The percentage of the infected pregnant Ladies was 33.7% followed by the women who used the IUCD and OCP 22.1%, those who used steroids 5.2% comparing with control women (without predisposing factors).The results also indicated that the most cases of infection were during the third trimester of pregnancy (where the rate of infedion) was 53.9%.-OCP- Oral Contraceptive Pills-IUCD- Intrr
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