In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

Laboratory model tests were performed to investigate the behavior of shallow and inclined skirted foundations placed on sandy soil with R.D%=30 and the extent of the impact of the positive and negative eccentric-inclined loading effect on them. To achieve the experimental tests, it was used a box of (600×600) mm cross-sectional and 600mm in height and a square footing of (50*50) mm and 10 mm in thickness attached to the skirt with Ds=0.5B and various an angle of (10°, 20°, 30°). The results showed that using skirts leads to a significant improvement in load-carrying capacity and decreased settlement. In addition, when the skirt angle increased, the ultimate load improved. Load-carrying capacity decreased with increasing eccentri

In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

Atmospheric transmission is disturbed by scintillation, where scintillation caused more beam divergence. In this work target image spot radius was calculated in presence of atmospheric scintillation. The calculation depend on few relevant equation based on atmospheric parameter (for Middle East), tracking range, expansion ratio of applied beam expander's, receiving unit lens F-number, and the laser wavelength besides photodetector parameter. At maximum target range Rmax =20 km, target image radius is at its maximum Rs=0.4 mm. As the range decreases spot radius decreases too, until the range reaches limit (4 km) at which target image spot radius at its minimum value (0.22 mm). Then as the range decreases, spot radius increases due to geom

Each school of Islamic jurisprudence has principles and rules upon which the diligent work in these schools is based. This is due to the view of sanctification of these rulings, as they are divine rulings. Therefore, the goal is to reach a ruling that represents the intent of the legislator as much as possible.
Hence, these schools of thought established rules for issuing fatwas with the intention of restricting the performance of a fatwa to the hands of those who are qualified for it and have met its conditions, so they gave priority to the most knowledgeable person over others to perform the fatwa. In the Hanafi school of thought, for example, the saying of Imam Abu Hanifa (may God have mercy on him) is given precedence over others,

In the literature, several correlations have been proposed for bubble size prediction in bubble columns. However these correlations fail to predict bubble diameter over a wide range of conditions. Based on a data bank of around 230 measurements collected from the open literature, a correlation for bubble sizes in the homogenous region in bubble columns was derived using Artificial Neural Network (ANN) modeling. The bubble diameter was found to be a function of six parameters: gas velocity, column diameter, diameter of orifice, liquid density, liquid viscosity and liquid surface tension. Statistical analysis showed that the proposed correlation has an Average Absolute Relative Error (AARE) of 7.3 % and correlation coefficient of 92.2%. A

Background: one of the complications of power bleaching is surface roughness of enamel which increases the possibility of post bleaching teeth discoloration. The aim of the present study is to evaluate the effect of toothpaste containing nano hydroxyapatite, NovaMin and kin sense fluoride on surface roughness of human tooth enamel after laser bleaching with 35% hydrogen peroxide bleaching gel. Materials and Methods: Twenty human enamel incisors were cleaned and their labial surface polished up to #1200, then categorized into four equal groups; first group kept without bleaching as a control group, while the remaining three experimental groups were bleached with 35% hydrogen peroxide, and each group treated with a restore paste containing o

This study aimed at accounting for the role of talents management in consolidating organizational learning process at the Yemeni General Corporation For telecommunication. To achieve the objective of the study, the researcher designed a questionnaire and administered it. The sample of the study consisted of (166) employees (General Manager, Manager and Department Head). They were selected randomly out of a total Population of (291) employees during the Year 2019. The descriptive analytic approach was used t reach conclusions.

The finding of the study revealed existence of effect of talents management dimensions, all together and alone, (talents polarization, talents development, talents maintenance and ma