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. ‎

Friction stir welding (FSW) of Tee-joints is obtained by inserting a specially designed rotating pin into the clamped blanks, through top plate (skin) to bottom plate (stringer), and then moving it along the joint, limiting the contact between the tool shoulder and the skin. The present work aims to investigate the defects occur for Tee-joint of an Aluminum alloy (Al 5456) with dimensions (180mm x 70mm) for the skin plate, (180mm x 30mm) for stringer plate and thickness of (4mm).
The effects of welding parameters such as rotational speed, linear speed, plunging depth, tool tilting, and die radii of welding fixture on the welding quality of Aluminum Alloy will be studied. Weld defects had been summarized and studied, and then the best

The subject of an valuation of quality of construction projects is one of the topics which it becomes necessary of the absence of the quantity standards in measuring the control works and the quality valuation standards in constructional projects. In the time being it depends on the experience of the workers which leads to an apparent differences in the valuation.

The idea of this research came to put the standards to evaluate the quality of the projects in a special system depending on quantity scale nor quality specifying in order to prepare an expert system “ Crystal “ to apply this special system to able the engineers to valuate the quality of their projects easily and in more accurate ways.

In this work, the effect of different particle size on the nonlinear optical properties of silver nanoparticles in de-ionized water was studied. The experimental observation of the far field diffraction patterns by CCD camera in two and three dimensions. The maximum change of nonlinear refractive index and the relative phase shift were calculated. The self-defocusing technique was used with a continuous-wave radiation from DPSS Blue laser .The wavelength is 473 nm with an output power of 270 mW. All the Ag colloids samples containing the sizes 15, 30, 50, and 70 nm of silver nanoparticles used in the study were chemically prepared. It was found that the nonlinear refractive index is a particle size dependent and of the order of 10-7 cm2/

Objective: the aim of this study is to invest age and determine the effect of using (2) packing
technique (conventional and new tension technique) on hardness of (2) types of heat cure acrylic
resin which are (Ivoclar and Qual dental type).
Methodology : this study was intended the using of two types of heat cure acrylic (IVoclar and
Qual dental type) which are used in construction of complete denture which packed in two different
packing technique (conventional and new tension technique) and accomplished by using a total of
(40) specimens in diameter of ( 2mm thickness, 2 cm length and 1 cm width) . This specimens were
sectioned and subdivide into (4) group each (10) specimens for one group , then signed as (A, Al B

       The study aimed to reach the best rating for the views and variables in the totals characterized by qualities and characteristics common within each group and distinguish them from aggregates other for the purpose of distinguishing between Iraqi provinces which suffer from deprivation, for the purpose of identifying the status of those provinces in the early allowing interested parties and regulators to intervene to take appropriate corrective action in a timely manner. Style has been used cluster analysis Cluster analysis to reach the best rating to those totals from the provinces that suffer from problems, where the provinces were classified, based on the variables (Edu

Spatial data observed on a group of areal units is common in scientific applications. The usual hierarchical approach for modeling this kind of dataset is to introduce a spatial random effect with an autoregressive prior. However, the usual Markov chain Monte Carlo scheme for this hierarchical framework requires the spatial effects to be sampled from their full conditional posteriors one-by-one resulting in poor mixing. More importantly, it makes the model computationally inefficient for datasets with large number of units. In this article, we propose a Bayesian approach that uses the spectral structure of the adjacency to construct a low-rank expansion for modeling spatial dependence. We propose a pair of computationally efficient estimati