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.

fields of the College of Agricultural Engineering Sciences, University of Baghdad/Al-Jadriya, in the fall season 2021-2022. With three sowing dates (26 July, 4 August, 12 August), The experiment was implemented according to a randomized complete block design (RCBD) with three replications. The aim is to detect the expression of the INCW1 gene associated with sucrose-to-glucose analysis, which is critical for many metabolic functions in different sink tissues, and determine the amount of fold gene expression to find out which of the genotypes contain the invertase gene, and which ones have a high level of gene expression based on the fold of gene expression. The results showed significant differences in the invertase enzyme activity for the

يهدف البحث الى أعداد بعض تمرينات الاساسية لسلاح الشيش بأستخدام المرايا في تطوير قدرة مستوى تعلم الطالبات في المبارزة ومعرفة الفروق بين المجموعتين التجريبي والضابطة بتأثير استخدام المرايا في مستوى اداء بعض مهارات سلاح الشيش لطالبات المرحلة الثالثة , وقد أستخدمت الباحثتان المنهج التجريبي على عينة من طالبات المرحلة الثالثة , وقد بلغ عددهم (45) طالبة , وقد خرجت الباحثتين بعدة أستنتاجات وهي:- - أن المنهاج التعليمي

The study aims to identify the effect of training with weight added to different parts of the body in improving the biomechanical variables of the last step and upgrading the high jump for young people, the research was applied to one of the elite high jumpers for young people, and video imaging and kinetic analysis were conducted to extract the variables under study, and then the jumper underwent For the proposed exercises by 3 training units per week for a period of (8) weeks, in which emphasis was placed on improving the rotational forces (moments) of these parts, and then the post-tests were conducted, and the researcher concluded that the exercises applied and the added weights for all parts of the body (leg, thigh, trunk, and arms) le

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fourth order by using the Lyapunov-Krasovskii functional approach; we obtain some conditions of instability of solution of such equation.

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fifth order with delay by using the Lyapunov-Krasovskii functional approach, we obtain some conditions of instability of solution of such equation.

This study was conducted to estimate some heavy metals cadmium, lead, nickel and iron in 15 samples of Iraqi honey with 3 replicates for each sample which were collected from apiaries near potential contamination areas in five Iraqi governorates, including Baghdad, Karbala, Babylon, Diyala and Salah al-Din. The atomic absorption technique was used to estimate the concentrations of heavy metals, the results showed that there were significant differences at (P≤0.05) between the concentrations of these elements in the honey samples, the highest concentrations of cadmium 0.123 mg/kg were recorded in Baghdad, near the petrochemical production complex, lead 4.657 mg/kg and nickel 0.023 mg/kg in Babylon near the power plant, iron was