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.

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.

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

The weight of larvae virgins and Alcamlat for males more than the weight of females of the roles themselves that the highest rate of loss in weight of larvae developed to virgins when field conditions were (21.5,22,21.3) mg during June and July and August respectively, recorded the highest degrees of heat and less attributed to moisture

The present study aimed to examine the effect of endosulfan insecticide on some molecular and biochemical parameters in white mice. Thirty mice were separated randomly into three groups for treatment with endosulfan. One group (G1) served as the control, while the other two groups received intraperitoneal injections of endosulfan G2 (3 mg/kg) and G3 (17 mg/kg) twice a week for 21 and 45 days, respectively. A biochemical study by measuring liver  function parameters, including (alanine aminotransferase (ALT) and aspartate aminotransferase (AST)) and kidney function parameters, including (Blood Urea and Creatinine) and malondialdehyde (MDA), catalase activity (CAT). This study also tested DNA damage by comet assay (normal%, low%, med

Background: Poly (methylmethacrylate) is the most widely used material in denture fabrication. The characteristics of acrylic resin which support microorganism development can threaten the oral health of denture users. This study was assigned to prepareand incorporate Ag-Zn zeolite powder into heat cured denture base material as antimicrobial material and to investigate its effect on some properties of heat cured acrylic denture base materials. Materials and methods: Sliver –zinc zeolite was prepared by ion exchange method and characterized then incorporated into poly (methylmethacrylate) powder in0.5% by weight. Specimens were constructed and divided into 6 groups according to the using tests; each group was subdivided into 2 groups

Background: The geriatric patients wearing removable partial dentures are increasing in proportion. At the same time, the root caries prevalence accompanied by gingival recession is increasing. A variety of vehicles can deliver fluoride into the oral cavity, including fluoride mouth-rinse, fluoride dentifrice, topical fluoride, and fluoride-releasing restorative materials, all of which effectively prevent root caries and suppress recurrent caries. This study aimed to evaluate the effect of sodium fluoride addition on some mechanical properties of heat cure acrylic denture base material. Material and method: A total of 90 samples were prepared in this study, then divided into three main groups according to the type of test used (hardness, te

In this work, varying compositions of SiO₂ micro filler were added
with the Polyvinyl Chloride (PVC) and samples have been prepared
using film casting technique. The results have been analyzed and
compared for PVC samples with (1 wt%, 3 wt%, 5 wt% and 10 wt%)
SiO2 micro filler. Mechanical characteristics such as tensile strength,
elongation at break and Young`s modulus were measured for all the
samples, where the tensile strength was increased from 8.39 Mpa for
purified PVC to 16 Mpa for 3% SiO₂/PVC composite. Also, thermal
conductivity measurement values illustrated that composite materials
have a good thermal insulation at 10 wt. %, thermal conductivity was
decreased from 0.1684 W/m.