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.

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 family Ormyridae has been very much neglected by workers and only two species has been recorded so far from Iraq. The present study, based mainly on my collection, deals with five species, of which one is new to science. The new species is described together with notes on locality data, host records, distribution and taxonomical remarks for all the species.

The research demonstrates new species of the games by applying separation axioms via  sets, where the relationships between the various species that were specified and the strategy of winning and losing to any one of the players, and their relationship with the concepts of separation axioms via  sets have been studied.

ABSTRACT

The research aims to clarify the role of electronic marketing and what it can achieve in promoting the products of the national industry in Iraq. Marketing channel depends on modern communication and information technology that industrial and metal companies can use in promoting and selling their products along with traditional marketing outlets. To achieve the objectives of the research, a questionnaire was used, which consists of three axes, the first includes the personal data of the sample (gender, age, educational attainment, place of residence, marital status, income level), while the second axis includes various questions about the products of the national industry. Third axis includes que

This study focused on the role and importance of alkaloid compounds in Punica granatum peels which is one of many wide distribution medicinal fruits. Two kinds of pathogenic fungi were isolated from patients in Baghdad to be tested, also a type of extracts was prepared, alkaloids were isolated and partially purified and detected by two ways, a classic depended technique also used for determine these alkaloids, results showed an observed differences among extracts or treatments towards the fungi samples. So this study was one of the scientific applications to find natural alternative compounds that inhibit the growth of several pathogenic organisms that cause dangers and harms for human health.

The pervaporation using a commercial hydrophilic ceramic membrane supplied from PERVATECH was conducted. The dehydration of ethanol/ water system was used as a model for the pervaporation study. Pervaporation experiments of ethanol/water system were carried out in the temperature range of 303-343K, ethanol concentration in the feed 10-90 vol. % and the feed flow rate in the range of 0.5-10 L/min.  In this work, the effect of operation parameters on permeates fluxes as well as permeates separation factors have been studied. The Water flux is strongly dependent on the temperature; it increased with increasing in temperature, which in turn decreased the selectivity of membrane to water molecules.

In addition water flux was decr