The paper establishes explicit representations of the errors and residuals of approximate
solutions of triangular linear systems by Jordan elimination and of general linear algebraic
systems by Gauss-Jordan elimination as functions of the data perturbations and the rounding
errors in arithmetic floating-point operations. From these representations strict optimal
componentwise error and residual bounds are derived. Further, stability estimates for the
solutions are discussed. The error bounds for the solutions of triangular linear systems are
compared to the optimal error bounds for the solutions by back substitution and by Gaussian
elimination with back substitution, respectively. The results confirm in a very

This paper studies a novel technique based on the use of two effective methods like modified Laplace- variational method (MLVIM) and a new Variational method (MVIM)to solve PDEs with variable coefficients. The current modification for the (MLVIM) is based on coupling of the Variational method (VIM) and Laplace- method (LT). In our proposal there is no need to calculate Lagrange multiplier. We applied Laplace method to the problem .Furthermore, the nonlinear terms for this problem is solved using homotopy method (HPM). Some examples are taken to compare results between two methods and to verify the reliability of our present methods.

Signal denoising is directly related to sample estimation of received signals, either by estimating the equation parameters for the target reflections or the surrounding noise and clutter accompanying the data of interest. Radar signals recorded using analogue or digital devices are not immune to noise. Random or white noise with no coherency is mainly produced in the form of random electrons, and caused by heat, environment, and stray circuitry loses. These factors influence the output signal voltage, thus creating detectable noise. Differential Evolution (DE) is an effectual, competent, and robust optimisation method used to solve different problems in the engineering and scientific domains, such as in signal processing. This paper looks

In this paper we used frequentist and Bayesian approaches for the linear regression model to predict future observations for unemployment rates in Iraq. Parameters are estimated using the ordinary least squares method and for the Bayesian approach using the Markov Chain Monte Carlo (MCMC) method. Calculations are done using the R program. The analysis showed that the linear regression model using the Bayesian approach is better and can be used as an alternative to the frequentist approach. Two criteria, the root mean square error (RMSE) and the median absolute deviation (MAD) were used to compare the performance of the estimates. The results obtained showed that the unemployment rates will continue to increase in the next two decade

In this paper, a self-tuning adaptive neural controller strategy for unknown nonlinear system is presented. The system considered is described by an unknown NARMA-L2 model and a feedforward neural network is used to learn the model with two stages. The first stage is learned off-line with two configuration serial-parallel model & parallel model to ensure that model output is equal to actual output of the system & to find the jacobain of the system. Which appears to be of critical importance parameter as it is used for the feedback controller and the second stage is learned on-line to modify the weights of the model in order to control the variable parameters that will occur to the system. A back propagation neural network is appl

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

Many researchers used different methods in their investigations to enhance the heat transfer coefficient, one of these methods is using porous medium. Heat transfer process inside closed and open cavities filled with a fluid-saturated porous media has a considerable importance in different engineering applications, such as compact heat exchangers, nuclear reactors and solar collectors. So, the present paper comprises a review on natural, forced, and combined convection heat transfer inside a porous cavity with and without driven lid. Most of the researchers on this specific subject studied the effect of many parameters on the heat transfer and fluid field inside a porous cavity, like the angle of inclination, the presenc

Objective: To conduct a standardized method for cavity preparation on the palatal surface of rat maxillary molars and to introduce a standardized method for tooth correct alignment within the specimen during the wax embedding procedure to better detect cavity position within the examined slides. Materials and methods: Six male Wistar rats, aged 4-6 weeks, were used. The maxillary molars of three animals were sectioned in the frontal plane to identify the thickness of hard tissue on the palatal surface of the first molar which was (250-300µm). The end-cutting bur (with a cutting head diameter of 0.2mm) was suitable for preparing a dentinal cavity (70-80µm) depth. Cavity preparation was then performed using the same bur on the tooth surf

Objective: To conduct a standardized method for cavity preparation on the palatal surface of rat maxillary molars and to introduce a standardized method for tooth correct alignment within the specimen during the wax embedding procedure to better detect cavity position within the examined slides. Materials and methods: Six male Wistar rats, aged 4-6 weeks, were used. The maxillary molars of three animals were sectioned in the frontal plane to identify the thickness of hard tissue on the palatal surface of the first molar which was (250-300µm). The end-cutting bur (with a cutting head diameter of 0.2mm) was suitable for preparing a dentinal cavity (70-80µm) depth. Cavity preparation was then performed using the same bur on the tooth

The production function forms one of the techniques used in evaluation the  production the process for any establishment or company, and to explain the importance of contribution of element from the independent variable and it's affect on the dependent variable. Then knowing the elements which are significant or non-significant on the dependent variable.

    So the importance of this study come from estimating the Cobb-Douglas production function for Al- Mansoor General Company for Engineering industries in Iraq during the period (1989-2001)

     To explain the importance which effects the independent variable such as
(N