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 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

الخلاصة: الحكة اليوريمية لدى مرضى غسيل الكلى يؤثر على أكثر من 40٪ من المرضى. وربما ترتبط الحكة المستمرة بمستويات عالية من الإنترلوكين 31. الاهداف: النظر إلى مستويات مصل إنترلوكين 31 لدى مرضى غسيل الكلى المصابين بمرض الكلى في المرحلة النهائية، سواء مع أو بدون حكة يوريمية. النتائج: لم يكن مستوى المصل [الوسيط (] لـ IL-31 في المرضى الذين يعانون من الحكة اليوريميةأو بدون حكة في عينة مصل ما قبل غسيل الكلى مختلفًا بشكل م

An essential issue in obstetrics is the prevalence of maternal and fetal complications in pregnant women with polycystic ovary syndrome (PCOS). The purpose of the present study was to investigate the prevalence of pregnancy complications among various phenotypes of pregnant women with PCOS.

Background: This in vitro study evaluated the fracture resistance of weakened endodontically treated premolars with class II MOD cavities restored with different composite restorations (Low-shrinkage Filtek P90, nanohybrid Filtek Z250 XT and SDR bulk fill). The type and mode of fracture were also assessed for all the experimental groups. Materials and Method: Fifty human adult maxillary premolar teeth were selected for this study. Standardized extensive class II MOD cavities with endodontic treatment were prepared for all teeth, except those that were saved as intact control. The teeth were divided into five groups of ten teeth each (n=10): (Group 1) intact control group, (Group 2) unrestored teeth with endodontic treatment, (Group 3) resto