The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.

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. ‎

This paper presents a hybrid approach for solving null values problem; it hybridizes rough set theory with intelligent swarm algorithm. The proposed approach is a supervised learning model. A large set of complete data called learning data is used to find the decision rule sets that then have been used in solving the incomplete data problem. The intelligent swarm algorithm is used for feature selection which represents bees algorithm as heuristic search algorithm combined with rough set theory as evaluation function. Also another feature selection algorithm called ID3 is presented, it works as statistical algorithm instead of intelligent algorithm. A comparison between those two approaches is made in their performance for null values estima

In the current study, haemoglobin analytes dissolved in a special buffer (KH₂PO₄(1M), K₂HPO₄(1M)) with pH of 7.4 were used to record absorption spectra measurements with a range of concentrations from (10^-8 to 10^-9) M and an absorption peak of 440nm using Broadband Cavity Enhanced Absorption Spectroscopy (BBCEAS) which is considered a simple, low cost, and robust setup. The principle work of this technique depends on the multiple reflections between the light source, which is represented by the Light Emitting Diode 3 W, and the detector, which is represented by the Avantes spectrophotomer. The optical cavity includes two high reflectivity  ≥99%  dielectric mirrors (dia

The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.

This work aimed to study the effect of laser surface treatment on the mechanical characteristics and corrosion behaviour of grey cast iron type A159. Many technical applications used conventional surface treatment, but laser surface hardening has recently been used to enhance the surface properties of many alloys. The mechanical characteristics, including microstructure, microhardness, and wear resistance of A159 grey cast iron, were studied, in addition to corrosion behaviour. The experimental laser parameters in this work were 0.9, 1.2, and 1.5 KW power with continuous wave carbon dioxide lasers with scanning speeds of 10 and 12 mm/s were used. The results found that phase-transitional alterations in microstructure were influenced by lase

This study assessed the effect of co-substitution of strontium (Sr) and magnesium (Mg) ions into the hydroxyapatite (HA) coating which was deposited on Ti–6Al–4V dental alloys by an electrochemical deposition process. The deposited layers were examined using energy-dispersive X-ray spectroscopy, scanning electron microscopy, Fourier transform infrared spectroscopy, atomic force microscopy and X-ray diffraction. The corrosion behavior of Ti–6Al–4V alloys in an artificial saliva environment was studied through potentiodynamic polarization technique and electrochemical impedance spectroscopy. The results indicated that the substituted Sr and Mg ions in HA improved the HA coating, where the protection efficiency percentage (PE%) for Ti