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 investigation , borax (B) (additive I) and chlorinated paraffin (CP.) (additive II) ,were used as flame retardants for each of epoxy and unsaturated polyester resins in the weight ratios of 2,4,6, & 8% by preparing films of (130×130×3) mm dimensions. Also films of these resins with a mixture of [50%(B.)+50%(CP.)] (additive III) in the same weight ratios were prepared in order to study the synergistic effect of these additives on the flammability of the two resins . Three standard test methods were used to measure the flame retardation which are : 1-ASTM : D-2863 2-ASTM : D-635 3-ASTM : D-3014

Background: One of the most common and prevalent oral diseases among adolescents is periodontal disease particularly gingivitis, however enamel anomalies and dental trauma could occur. Aims of the study: This study was conducted among 14-15 years intermediate school male students in urban area of Al-Khalis city to assess the oral hygiene (dental plaque) and to estimate the prevalence and severity of gingivitis, enamel anomalies, as well as traumatic dental injuries, furthermore to show the significant difference between these two ages concerning these oral problems. Materials and methods: In this study the total sample consisted of 735 students (397 aged 15 years and 338 aged 14 years ). In present study dental plaque was recorded accord

This study investigates the complex challenges of managing heritage sites in Iraq, focusing on the Prophet Tho Al-Kifl Shrine in Babylon due to its religious, historical, and architectural significance. The site exemplifies critical management issues, including institutional fragmentation, limited technical and financial resources, and insufficient legislative frameworks. Left unaddressed, these challenges threaten the site's material integrity and symbolic identity through uncoordinated interventions and neglect. The research aims to propose a context-sensitive framework for sustainable heritage management by combining theoretical perspectives with practical analysis. Using a case study methodology, the study draws on field observations, h

This study included estimation of glutathione (GSH) and Malondialdehyde (MDA) levels in the serum of diabetic patients type II who are treated with a polyherbs mixture (Nigella sativa, Trigonella foenum-graeum, Cyperus rotundus and Teucrium polium) for three months of treatments. Seventy samples of diabetic patients Type II male and females with age about (35-60) years were taken including 44 samples for group one (24 male, 20 female) who used herbs accompanied with chemical treatment (drugs) and 26 samples for the second group (13male and 13 female) who used herbs only. These groups were compared with 60 samples obtained from healthy persons (29 male, 31 female) at the same age of patients as a control group. Effect of age and treatment fo

The planning for the formation of administrative policies and guidance through leadership are important things for managing administrative processes and sporting activities. As both contribute in the stability of the administrative conditions, and their development in the sport federations, whether they both were attentive about team and individual Olympic Games. The two researchers observe that, there is a variation in the correct way of application. Particularly in the formulation of administrative policies and leadership describing it as, modern management standards for both team and individual Olympic Games in the Iraqi National Olympic Committee. That led to cause a misconception and lack of clarity for some administrators of those uni

This deals with estimation of Reliability function and one shape parameter (?) of two- parameters Burr – XII , when ?(shape parameter is known) (?=0.5,1,1.5) and also the initial values of (?=1), while different sample shze n= 10, 20, 30, 50) bare used. The results depend on empirical study through simulation experiments are applied to compare the four methods of estimation, as well as computing the reliability function . The results of Mean square error indicates that Jacknif estimator is better than other three estimators , for all sample size and parameter values

The research aims Modifying the accuracy test for the diagonal and straight high smash skill from center (4) according to the body position of the Premier League volleyball players and extracting the grades and standard levels. To achieve the two objectives of the research: the descriptive approach with the survey method was adopted, because it agrees in solving the research problem. As for the research sample, it consisted Of the players in the Premier League for volleyball clubs for the 2023-2024 season, the researcher chose central players (4)(2) because their skill abilities are compatible with the skill of hitting the diagonal and straight smashes, and they numbered (90) players (6 players from each team), and then the researche