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

Background: Polymorphisms in the TNF-α gene affect the development and progression of rheumatoid arthritis. Objective: To investigate the associations between (-806 T/C) and (-857 T/C) SNPs with rheumatoid arthritis severity and susceptibility in a sample of Iraqi patients. Methods: A case-control study was conducted in Baghdad, Iraq. Twenty healthy controls and 63 patients confirmed to be newly diagnosed with rheumatoid arthritis were included. Those are divided into two groups (patients and controls), and the patients were further subdivided into severe and mild-moderate groups. Samples from those participants were analyzed for clinical and inflammatory parameter measurements. Genotyping by the Sanger method was performed to stu

Citrus fruit contain variety of flavonoids such as Hesperidin (the principal flavonoid in oranges and grapefruit). Hesperidin is found in high concentration in fruit peel of oranges and in substantially lower concentration in juice of these fruits. Hesperidin was extracted from oranges peel by treating the peels with calcium hydroxide. HPLC technique was used to determine hesperidin. Hesperidin was saperated and purified in a purity of about 90.1-95.7% and yield about 1.5 %w/w from oranges peel dry powder. Both hesperidin and oranges peel extract showed significan antibacterial activity. Sensitivity to hesperidin and oranges peel extracts were not similar for the chosen bacteriaCrude orange peel extract gave a various antimicro

The aim of this study to conduct the effects of fimbrial and lipopolysacchride (LPS) immunization is on the pathohistological changes in rabbits, Fifteen rabbits of both sexes (Weight 1500-2000 gm) divided into three groups (5 animals of each group). The first group was immunized by 1ml (200µg /animal) of fimbrial subcutaneously the second group gave 1 ml ( 200 µg /animal) LPS while the third group was left as negative control group that injected 1 ml phosphate buffer control subcutaneously. First and second groups recived the same dose after two weeks give as booster dose. All animals challenged after 5 weeks of immunization by5X107CFU/ml Proteus vulgaris intra peritoneally .After 7 days from challenge all the animals, sacrificed for hi

The study of biomechanical indicators in the arc of the run and the upgrading stage is one of the important variables that affect the nature of the upgrading and thus affect the result of the race due to the importance of these stages and the consequent variables during the last steps. That’s why, the jump-trainings based on assistant means or body weight positively affect the step-time for each of the three steps in the acceleration arc. As well as, it focuses on the momentary strength of each step at this stage. It also significantly affects the speed of motor performance to suit the activity in which the runner needs to perform perfect steps with high flow in order to convert the horizontal speed to a vertical one. This is achieved thr