To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was ‎proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the ‎exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the ‎modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact ‎solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which ‎shows the reliability and applicability of the proposed approach. ‎

           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

      Face Detection by skin color in the field of computer vision is a difficult challenge. Detection of human skin focuses on the identification of pixels and skin-colored areas of a given picture. Since skin colors are invariant in orientation and size and rapid to process, they are used in the identification of human skin. In addition features like ethnicity, sensor, optics and lighting conditions that are different are sensitive factors for the relationship between surface colors and lighting (an issue that is strongly related to color stability). This paper presents a new technique for face detection based on human skin. Three methods of Probability Density Function (PDF) were applied to detect the face by skin color; these ar

In this paper, the homotopy perturbation method is presented for solving the second kind linear mixed Volterra-Fredholm integral equations. Then, Aitken method is used to accelerate the convergence. In this method, a series will be constructed whose sum is the solution of the considered integral equation. Convergence of the constructed series is discussed, and its proof is given; the error estimation is also obtained. For more illustration, the method is applied on several examples and programs, which are written in MATLAB (R2015a) to compute the results. The absolute errors are computed to clarify the efficiency of the method.

     We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed  (LSD)

The proposed method is sensitive, simple , fast for the determination of mebeverine hydrochloride in pure form or in pharmaceutical dosage . Using Homemade instrument fluorimeter continuous flow injection analyser with solid state laser (405 nm) as a source. Where it is based upon the fluorescence of fluorescein sodium salt and quenching effect of fluorescence by mebeverine in aqueous medium. The calibration graph was linear in the concentration range 0.05 to10 mMol.L-1 (r= 0.9629) with relative standard deviation (RSD%) for 1 mMol.L-1mebeverine solution was lower than 3% (n=6). Three pharmaceutical drugs were used as an application for the determination of mebeverine. A comparison was made between the newly developed method of analysis wit

A new Turbidimetric method characterized by simplicity, accuracy and speed for determination of Hydronium ion by continuous flow injection analysis. The method was based on the formation of complex Zn3[Fe(CN)6] for Zinc(II) that was eluted by Hydronium ion from cation exchanger column with Potassium hexacyanoferrate(III) for the formation of a pale yellow precipitate and this precipitate was determined using homemade Linear Array Ayah-5SX1-T-1D continuous flow injection analyser. The optimum parameters were 2.7 mL.min-1 flow rate using H2O as a carrier stream, 1.7 mL.min-1 reagent stream, 110 L sample volume and open valve for the purge of the sample segment. Data treatment shows that linear range 0.01-0.1 mol.L-1 for each acids (HClO

A new Turbidimetric method characterized by simplicity, accuracy and speed for determination of Hydronium ion by continuous flow injection analysis. The method was based on the formation of complex Zn3[Fe(CN)6] for Zinc(II) that was eluted by Hydronium ion from cation exchanger column with Potassium hexacyanoferrate(III) for the formation of a pale yellow precipitate and this precipitate was determined using homemade Linear Array Ayah-5SX1-T-1D continuous flow injection analyser. The optimum parameters were 2.7 mL.min-1 flow rate using H2O as a carrier stream, 1.7 mL.min-1 reagent stream, 110 L sample volume and open valve for the purge of the sample segment. Data treatment shows that linear range 0.01-0.1 mol.L-1 for each acids (HClO