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.

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

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.

In this work, we study several features of the non-zero divisor graphs (ℵZD- graph) for the ring Zn of integer modulo n. For instance, the clique number, radius, girth, domination number, and the local clustering coefficient are determined. Furthermore, we present an algorithm that calculates the clique number and draws the non-zero divisor for the ring Zn.

Abstract The purpose of the study is to develop self-attendance fear measures for table tennis players and tennis players with disabilities, as well as to gauge how severe these fears are in both groups. The authors propose that there are no statistically significant differences in the level of fear of self-attendance for players of ground tennis and table tennis for the disabled between the arithmetic mean and the hypothetical mean. In keeping with the nature of the current study, we adopted a descriptive methodology, and the sample comprised 62 players of table tennis and tennis for the disabled. The authors make use of the Al-Taei prepared scale (fears of selfattendance). The statistical package for educational sciences (spss v 26)

This study investigated athletic Affiliation among male and female racket sports players (tennis, table tennis, and badminton). Athletic Affiliation Scale designed by (El-Shahat, 2021). The problem of the study comes from the extent to which players are affiliated with these sports. The researchers identified the scientific foundations of the scale. After verifying its validity, a random sample was selected from the Baghdad Governorate, including (49) players for the main experiment and (10) players for the pilot sample, distributed among the three sports from the original community 140 players (male and female) registered in the official federations of the games. The researchers adopted a descriptive approach using the survey metho