The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimizing the degree of error between approximate and exact solutions. The Wang-Ball series has shown its usefulness in solving any real-life scenario model as first- or second-order differential equations (DEs).
Numerical study of separation control on symmetrical airfoil, four digits (NACA
0012) by using rotating cylinder with double steps on its upper surface based on the computation of Reynolds-average Navier- Stokes equations was carried out to find the optimum configuration of unconventional airfoil for best aerodynamics performance. A model based on collocated Finite Volume Method was developed to solve the governing equations on a body-fitted coordinate system. A revised (k-w) model was proposed as a known turbulence model. This model was adapted to simulate the control effects of rotating cylinder. Numerical solutions were performed for flow around unconventional airfoil with cylinder to main stream velocities ratio in the range
... Show MoreThis work introduces a new electrode geometry for making holes with high aspect ratios on AISI 304 using an electrical discharge drilling (EDD) process. In addition to commercially available cylindrical hollow electrodes, an elliptical electrode geometry has been designed, manufactured, and implemented. The principal aim was to improve the removal of debris formed during the erosion process that adversely affects the aspect ratio, dimensional accuracy, and surface integrity. The results were compared and discussed to evaluate the effectiveness of electrode geometry on the machining performance of EDD process with respect to the material removal rate (MRR,) the electrode wear rate (EWR), and the tool wear ratio (TWR). Dimensional features an
... Show MoreBackground: One of the major problems in endodontics is micro-leakage of root canal fillings which might contribute to the failure of endodontic treatment. To avoid this problem, a variety of sealers have been tested. The objective of this, in vitro, study was to evaluate the shear bond strength of four resin based sealers (AH plus, silver free AH26, RealSeal SE and Perma Evolution permanent root canal filling material) to dentin. Materials and Methods: Forty non-carious extracted lower premolars were used. The 2mm of the occlusal surfaces of teeth were sectioned, to expose the dentin surface. The exposed dentin surfaces of teeth were washed with 5ml of 2.5% NaOCl solution followed by 5ml of 17 % EDTA then rinsed by deionized water to remov
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There is a theoretical controversy in the books of Usul al-Fiqh, in the past and the present, about whether the ruling should be attached to its reason (al-Hikmah), or its apparent and stable cause (al-Illah). Looking at the practical cases of the jurists, we found them sometimes attaching rulings to its reason, and sometimes to its cause, so there is a need to know the factors that affect their choices. By extrapolation, the researcher reached at nine factors that affect referring the ruling to its cause or to its reason in jurisprudential cases.
The proposal of nonlinear models is one of the most important methods in time series analysis, which has a wide potential for predicting various phenomena, including physical, engineering and economic, by studying the characteristics of random disturbances in order to arrive at accurate predictions.
In this, the autoregressive model with exogenous variable was built using a threshold as the first method, using two proposed approaches that were used to determine the best cutting point of [the predictability forward (forecasting) and the predictability in the time series (prediction), through the threshold point indicator]. B-J seasonal models are used as a second method based on the principle of the two proposed approaches in dete
... Show MoreDamascus has great importance throughout its history and has increased in the Umayyad period, It was interested the by Caliphs, and became the capital of the Islam, But the late Umayyad era has witness of troubles and political, this led to collapse the Umayyad state and take the Abbasid rule, despite the neglect of the Abbasids for this city and they left to others, but it remains of great concern by some of the Abbasid caliphs.
This study aims at defining the concept of the fragile state, a term that came into existence in 2014, when the states that had internal Problems and external interventions were referred to as the failure states. However, the indicators for their designation and the criteria adopted are 12 indicators that address all aspects of the State’s duties vis-a-vis its citizens. The study examined the reasons that led to the continuation of Iraq within the fragile states, and the selection of the five years within the time limits of the study due to the factors that led to the decline of Iraq and falling back within the most fragile countries. The study dealt with the fragile state challenges to the media reality as a result of the change of it
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