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

The definition of the role of any institution in society is achieved through its objectives, The same is true for the military and how to deal with security threats in the humanitarian field ,Terrorism, which has almost replaced the traditional pattern of war, has waged a street war and intimidated individuals, families and society ,On the other hand, he found someone to meet him from a popular crowd of volunteers to defend their homeland from different sects, sects and religions,  Thus, our study will be exposed to the role of popular mobilization in human security from a sociological point of view in Samarra, a field study of 100 male and female respondents.

Five levels of Zn-EDTA fertilizer and foliar application of boron were used to study the local rice response through studying of some vegetative and reproductive growth characters, by conducting two field experiments at Kanipanka Agricultural Research Station during the summer season of 2004 by using RCBD with three replications. Significant differences were found in studied characters, there were increase in the number of days from seeding to 50% flowering (94.330-96.233) days, from 50% flowering to physiological maturity (37.50-38.28) days, plant height (82.50-91.423) cm and LAI (5.441-7.525). Reproductive characters such as number of grains panicle-1 (74.11-85.88), number of panicles m-2 (321.00-426.083), biological yield (8166.166-11082

The synthesis of zeolite NaX from locally available kaolin has been studied. The operating conditions for zeolite NaX production from kaolin with good crystallinity were as follows; a gel formation step of metakaolin in alkaline medium in presence of additional silica to crystallize the zeolite was achieved at 60 oC for 1 hr,and with stirring. In ageing step of the reactants at room temperature for 5 days and crystallization step at 87±2 oC for 24 hr. The catalytic activity of catalyst prepared from local kaolin was studied by using cumene cracking as a model for catalytic cracking and compared with standard HY zeolite and HX zeolite catalysts. The activity test was carried out in a laboratory continuous flow unit with fixed bed reactor

The effect of using grinded rocks of (quartzite and porcelanite) as powder of (10 and 20) % replacement by weight of cement for self-compacting concrete slabs was investigated in this study. Five slabs with 15 concrete cubes were tested experimentally at 28 days to study the compressive strength, ultimate load, ultimate deflection, ductility, crack load and steel strain. The test results show that, the compressive strength improvement when replacement of local rock powder reached to (7.3, 4.22) % for (10 and 20) % quartzite powder and (11.3, 16.1) % for (10 and 20) % porcelanite powder, respectively compared to the reference specimen. The ultimate load percentage increase for slabs with (10 and 20) % rep

The focus of this work is on systematically understanding the effects of packing density of the sand grains on both the internal and bulk mechanical properties for strip footing interacting with granular soil. The studies are based on particle image velocimetry (PIV) method, coupled with a high resolution imaging camera. This provides valuable new insights on the evolution of slip planes at grain-scale under different fractions of the ultimate load. Furthermore, the PIV based results are compared with finite element method simulations in which the experimentally characterised parameters and constitutive behaviour are fed as an input, and a good level of agreements are obtained. The reported results would serve to the practicing engineers, r

Each book has a specific style in which its author walks on it from its beginning to its end, and the Holy Qur’an is a book that compiled many methods that were indicative of its miracle, and that it is one unit even though it has been astrologer for twenty-three years.
There is no doubt that knowledge of the Qur’anic methods is one of the pillars of the approach that deals with any of the Qur’an, and the multiplicity of Qur’anic methods is a fact that has many causes. It has been expressed by the Qur’anic discharge and the conjugation of verses to bring them to different methods, and on multiple forms such as nominal, actual, singular Qur’an, presentation, delay, deletion, mention, abbreviation and redundancy. The Qur'ani