This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

In this paper, various aspects of smart grids are described. These aspects include the components of smart grids, the detailed functions of the smart energy meters within the smart grids and their effects on increasing the awareness, the advantages and disadvantages of smart grids, and the requirements of utilizing smart grids. To put some light on the difference between smart grids and traditional utility grids, some aspects of the traditional utility grids are covered in this paper as well.

The increase in obesity and the many accompanying diseases is attributed to the increased production and consumption of foods made of non-nutritive sweeteners without regard to the risks of consuming additional calories, and this in turn leads to hormonal imbalance and metabolic disorders and the resulting imbalance and ill health that have spread to all segments of society. During the research, 0.01, 0.02, 0.03, 0.04 and 0.05 % of stevia sweetener was added to the cream instead of the sugar used. Physical and chemical tests were performed for the stevia extract and the microbial content in the cream, as well as the sensory evaluation. It was noted that fortifying the cream with calorie-free stevia sugar led to the production of

The aim of this study is to identify the effect of enabling the effectiveness of the work of the audit committees in private commercial banks and to identify the extent of awareness of the importance of empowerment in the work of these committees, especially as it is known that these committees, especially the inspection committees that go to private banks and from various sources including committees of the Central Bank of Iraq Committees of the Securities Commission and finally committees of the external audit offices, through an analysis of the determinants of empowerment in the performance of the most important work of the audit committees, namely: supervising the process of preparing reports, supervising the system of intern

This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

Background: Cytology is one of the important diagnostic tests done on effusion fluid. It can detect malignant cells in up to 60% of malignant cases. The most important benign cell present in these effusions is the mesothelial cell. Mesothelial atypia can be striking andmay simulate metastatic carcinoma. Many clinical conditions may produce such a reactive atypical cells as in anemia,SLE, liver cirrhosis and many other conditions. Recently many studies showed the value of computerized image analysis in differentiating atypical cells from malignant adenocarcinoma cells in effusion smears. Other studies support the reliability of the quantitative analysisand morphometric features and proved that they are objective prognostic indices. Method

The automatic liquid filling system is used in different applications such as production of detergents, liquid soaps, fruit juices, milk products, bottled water, etc. The automatic bottle filling system is highly expensive. Where, the common filling systems required to complex changes in hardware and software in order to modify volume of liquid. There are many important variables in the filling process such as volume of liquid, the filling time, etc. This paper presents a new approach to develop an automatic liquid filling system. The new proposed system consists of a conveyor subsystem, filling stations, and camera to detect the level of the liquid at any instant during the filling process. The camera can detect accurately the leve

There are great figures in our nation, who are famous for their encyclopedia in their sciences, and their fame spreads across the horizons for what they presented to their religion and nation.
So they became torches of guidance, advocates of goodness, and treasuries of knowledge until God inherits the earth and those on it.
Among these imams is Imam al-Qurtubi, who died in the year (671 AH), after whom he left a great legacy of valuable books, including this one, which is the subject of my research, his valuable interpretation (Al-Jami’ Li Ahkam Al-Qur’an). Taking from him and his approach in interpreting the verses of judgment, following the method of extrapolation, investigation and deduction to know his style, which he used