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 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.

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 research, the influence of the fermentation treatments and baking in Iraqi’s flour type (Ibaa 99, Al-rashed, Tamus, Abu-grabe) and Turkish flour type (Muaamel) on phytic acid was investigated. In whole wheat flour, the phytic acid was (1500, 1290, 1450, 1230, 1440 ( mg/ 100 g flour respectively, and the inorganic phosphorous was (29.18, 25.15, 23.89, 20.85, 22.83) mg/100 g flour respectively. The dough prepared from flour with a higher phytic acid content also contained higher amount of phytic acid. During fermentation, degradation of phytic acid occurred. The cumulative loss of phytic acid after fermentation in all type of dough was ~ 23, 22, 34, 26 and 27% respectively،While increased of inorganic phosphorous occurred. The c

Abstract

The current research aims to examine the effect of the Adi and Shayer model on the achievement of fifth-grade students and their attitudes toward history. To achieve the research objective, the researcher has adopted two null hypotheses. 1) there is no statistically significant difference at the level of (0.05) between the average score of students of the experimental group who study the history of Europe and modern American history according to the model of Addie and Shayer, and the average scores of the students of the control group who study the same subjects according to the traditional method in the test of post-achievement. 2) There was no statistically significant difference at the level (

The functional properties of the defatted powder and protein isolate of germinated mung bean seeds were studied and the estimation of the amino acids was carried out. The results showed a significant increase in the values of the amino acids leucine, lysine, phenylalanine and valine. The results of studying the functional properties of the protein isolate and defatted powder showed that there were significant differences between the sample The defatted and protein isolate, if the water absorption capacity of the defatted mung powder was 2.5% water/gm protein and the water absorption capacity of the protein isolate was 3%ml water/g protein, the fat binding capacity of the defatted powder was 0.3 ml fat/g protein and the isolate The ratio was

Thick films of poly(vinyl chloride)(PVC)& PVC doped with Zn(etx)2 salt complex have been prepared by cast method with fixed thickness almost (120±5) Microns. Optical studies were carried out in the wavelengths region(200-900)nm based on absorption & transmition measurement. Optical parameters such as absorption coefficient(?) ,refraction index(n) and extinction coefficient(K) were observed to be effected by adding the dopant.Electrical parameters such as real(?)& imaginary(?) part of dielectric constant were also calculated part of dielectric constant were also calculated from the optical parameters using Maxwell equation.