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 purpose of this study is to avoid delays and cost changes that occur in emergency reconstruction projects especially in post disaster circumstances. This study is aimed to identify the factors that affect the real construction period and the real cost of a project against the estimated period of construction and the estimated cost of the project. The case study is related to the construction projects in Iraq. Thirty projects in different areas of construction in Iraq were selected as a sample for this study. Project participants from the projects authorities provided data about the projects through a data collection distributed survey made by the authors. Mathematical data analysis was used to construct a model to predict change

The flow measurements have increased importance in the last decades due to the shortage of water resources resulting from climate changes that request high control of the available water needed for different uses. The classical technique of open channel flow measurement by the integrating-float method was needed for measuring flow in different locations when there were no available modern devices for different reasons, such as the cost of devices. So, the use of classical techniques was taken place to solve the problem. The present study examines the integrating float method and defines the parameters affecting the acceleration of floating spheres in flowing water that was analyzed using experimental measurements. The me

The non static chain is always the problem of static analysis so that explained some of theoretical work, the properties of statistical regression analysis to lose when using strings in statistic and gives the slope of an imaginary relation under consideration.  chain is not static can become static by adding variable time to the multivariate analysis the factors to remove the general trend as well as variable placebo seasons to remove the effect of seasonal .convert the data to form exponential or logarithmic , in addition to using the difference repeated d is said in this case it integrated class d. Where the research contained in the theoretical side in parts in the first part the research methodology ha

Knowledge of permeability, which is the ability of rocks to transmit the fluid, is important for understanding the flow mechanisms in oil and gas reservoirs.
Permeability is best measured in the laboratory on cored rock taken from the reservoir. Coring is expensive and time-consuming in comparison to the electronic survey techniques most commonly used to gain information about permeability.
Yamama formation was chosen, to predict the permeability by using FZI method. Yamama Formation is the main lower cretaceous carbonate reservoir in southern of Iraq. This formation is made up mainly of limestone. Yamama formation was deposited on a gradually rising basin floor. The digenesis of Yamama sediments is very important due to its direct

Drag reduction (DR) techniques are used to improve the flow by spare the flow energy. The applications of DR are conduits in oil pipelines, oil well operations and flood water disposal, many techniques for drag reduction are used. One of these techniques is microbubbles.  In this work, reduce of drag percent occurs by using a small bubbles of air pumped in the fluid transported. Gasoil is used as liquid transporting in the pipelines and air pumped as microbubbles. This study shows that the maximum value of drag reduction is 25.11%.

The process of risk assessment in the build-operate transfer (BOT) project is very important to identify and analyze the risks in order to make the appropriate decision to respond to them. In this paper, AHP Technique was used to make the appropriate decision regarding response to the most prominent risks that were generated in BOT projects, which includes a comparison between the criteria for each risk as well as the available alternatives and by mathematical methods using matrices to reach an appropriate decision to respond to each risk.Ten common risks in BOT contracts are adopted for analysis in this paper, which is grouped into six main risk headings.The procedures followed in this paper are the questionnaire method

Flexible paving is the most popular type of paving used in road building and one of the biggest problems facing the world's paving business is the rising demand for scarce natural resources. Uncontrolled. Numerous studies have shown that secondary materials reduce the need for traditional materials, offer efficient waste disposal technology and lower the overall cost of paving. The current study aimed to evaluate the efficiency of both fibers and dust on the sustainability and cost of flexible pavement by studying each of polyester fibers as a waste of the textile industry and fibers or rubber particles as one of the rubber waste products, in addition to studying the efficiency of using cement dust and marble dust on the paving proc