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.

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.

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

In this study Oscillatoria limnetica and Chroococus minor were isolated ?purified and identification from water canal around Baghdad University Campus. The water of this canals originally from Tigris River. BG-11 culture media was used for their cultivation in suitable laboratory conditions (25c°, 200µE/m2/sec) for 16:8 hrs. Light: dark. Each culture was harvested at the end of exponential phase .Organic solvents used for extraction were Ethanol? Hexane and Methanol 95% to extract the crude active Intracellular and Extracellular substances, and evaporated down to dryness .Antibacterial and antifungal activity of these different extracts were evaluated against 6 strains of gram positive bacteria and gram negative bacteria in additi

This research deals with the case of the Iraqi joint-stock companies listed on the Iraq Stock Exchange study in terms of compliance with the requirements of IAS 33 "Earnings per share" and the research problem Alrtash concentrated in a statement the commitment of those companies the requirements of the International Standard 33, which may adversely affect the quality of financial reporting where and in particular the quality of accounting information and content of the primary and secondary characteristics make them be of interest to the decisions of its users, so the aim of this research to the statement of financial reporting earnings per share on the quality of financial reporting in listed shareholding in Iraq Stock Exchange

The main objective of the research is to identify the role of strategic training and its effect on enhancing the self-growth of the individual. Stratigic training represents a contemporary tendency. that is adopted by business organizations in carrying out their activities and tasks.

It is worth to mention, that self-growth of the individual is one of the indictors used to determine the ability of organization to a achieve its goals. 

The problem of the research has pointed out to the minimum awareness of the important role played by training strategy in enhancing the self-growth of the individual. The researcher has adopted an analytical approach, in collecting and analyses