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.

The historical person study as a personality to the AL- Bazargan, one of the important
studies, is the shed light on the character had an effect of the political life in Iraq, an important
historical era involved many events, coincided with a national and historical by this personal
at the events successive positions that stage of the history of Iraq, especially if we know,
strongly his loyalty to the homeland and the earth, and intense hatred for any occupation or
colonization desecrate the land...
This was evident during his participation and his supervisor in 1920 liberal revolution
against the British occupation, and urged the need for adherence to the principles of
independence, and the emphasis on the nation

The Objective of the research is to identify the Strategic Vigilance and effect in the Managerial Decision Quality, by knowing the interest of the organization influence the Strategic Vigilance in the Managerial Decision Quality, adopted four dimensions of the Strategic Vigilance is (Environmental Vigilance, Commercial, Competitiveness & Technology) to indicate the extent individually and collectively impact in the Managerial Decision Quality, The questionnaire was used as a main tool to survey the views of a sample of 45 managers, was named Supreme Judicial Council society for research, and the statistical program SPSS, and research found a clear positive impact dimensions Strategic Vigilance in the Manageri

Institutions and companies are looking to reduce spending on buildings and services according to scientific methods, provided they reach the same purpose but at a lower cost. On this basis, this paper proposes a model to measure and reduce maintenance costs in one of the public sector institutions in Iraq by using performance indicators that fit the nature of the work of this institution and the available data. The paper relied on studying the nature of the institution’s work in the maintenance field and looking at the type of data available to know the type and number of appropriate indicators to create the model. Maintenance data were collected for the previous six years by reviewing the maintenance and financial dep

The aim of this research is to show the level of banking leadership trends in the importance of  organizational  confidence and its reflection in the dimensions of the strategic position the research was applied in a bank (Al- Mansour Investment, Business Bay), and the Questionnaire Was adopted as a tool to collect data and information from the number of the sample (15) who are in allocation (Department Manager, Department Manager Department Manager, Division Officer, Unit Officer) and he used the statistical program (spss) to calculate (standard deviation, arithmetic mean, percentages, regression, analysis,F-test coefficient of determination R2, Coefficieent, square Kay and the research reached a number of conclusions, the mos

Require senior management of the state when developing the strategy the general budget to the clarity of the reasons that are based upon the ministries in the preparation of estimates of expenditure for the next year to justify the spending, and in the absence of targets, the ministry or government unit would not be in front, but be guided by the size of expenditure for the last year in addition to the percentage of represented an increase of appropriations required for the next year in light of the fiscal policy of the state, so the requested increase in appropriations to meet the desired increase in some of its activities and to meet the increase in salaries and prices. So must be available to the Ministry of criteria that coul

This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

this research aims to identify the impact of teaching with ana logies in collection of chemistry students grade average.And direction in order to verify to the zero hypothesis has been formulated and validated,The researcher conducted experiment lasted a full semester as experimental design was chosen (exactly)two equal one pilot and another officer.The research community has been  selected one of intentional Middle School of the Education Directorate in B aghdad Karkh second either search sample consisted of (68) students from second grade average (34 ) Students for each group randomly selected research groups was equal to the following variables (lifetime months,parent of first grade chemistry degrees average test informat

Abstract The strategic performance of the United States depends on dealing with the Middle East countries and its variants on several bases and motives that enabled them to achieve American hegemony and invest its interests at the expense of the region countries. Within this performance, the administration of the United State President Donald Trump presented the Strategic Document on December 18, 2017, which focused on the principle of "America First", to determine the direction of future US strategic performance in the formulation of means of cooperation and intersections or hostility in addition to interests and threats.The future vision of the Arab region and the Middle East as a whole, this strategy is based on the fact that