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

In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

The objective of an Optimal Power Flow (OPF) algorithm is to find steady state operation point which minimizes generation cost, loss etc. while maintaining an acceptable system performance in terms of limits on generators real and reactive powers, line flow limits etc. The OPF solution includes an objective function. A common objective function concerns the active power generation cost. A Linear programming method is proposed to solve the OPF problem. The Linear Programming (LP) approach transforms the nonlinear optimization problem into an iterative algorithm that in each iteration solves a linear optimization problem resulting from linearization both the objective function and constrains. A computer program, written in MATLAB environme

     Recognizing cars is a highly difficult task due to the wide variety in the appearance of cars from the same car manufacturer. Therefore, the car logo is the most prominent indicator of the car manufacturer. The captured logo image suffers from several problems, such as a complex background, differences in size and shape, the appearance of noise, and lighting circumstances. To solve these problems, this paper presents an effective technique for extracting and recognizing a logo that identifies a car. Our proposed method includes four stages: First, we apply the k-medoids clustering method to extract the logo and remove the background and noise. Secondly, the logo image is converted to grayscale and also converted to a binary imag

(4R)-2, 3-(2`-chloro-2`- carboxyl)-1, 3-dioxolano-4- (2- dimethyl –dioxolane -yl) ascorbic acid (HL), a derivative of L-ascorbic acid was prepared by the reaction of 5,6-O-isopropylidene–L-ascorbic acid with trichloroacetic acid in alkaline medium. Seven new metal ion complexes of this ligand (HL) were prepared through its direct reaction with the chlorides of Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II) ions respectively. The new ligand and its ion metal complexes were characterized applying elemental analyses,1H and 13C NMR, IR as well as UV-Visible spectra. Spectroscopic data showed that the ligand (C11H11O8Cl) was coordinated to the metal ions through the two oxygen atoms of the carboxyl group as abidentate ligan

In this research two series of the new derivatives of Trimethoprim and paracetamol drugs have been prepared which known as a high medicinal effectiveness. Series (A) is including the interaction of diazonium salt of trimethoprim and coupling with some substituted phenol compounds (2-amino phenol, 3-ethyl phenol, 1-naphthol, 2-nitro phenol, Salbutamol). Series (B) is including the interaction coupling alkali solution of paracetamol with diazonium salt of some substituted aniline compounds (Benzedine, 2, 3-di chloro aniline, Trimethoprim, Anilinium chloride, 2-nitro- 4-chloro aniline).Chemical structures of all synthesized compounds were confirmed by UV-visible and FTIR spectroscopy.

Abstract-Servo motors are important parts of industry automation due to their several advantages such as cost and energy efficiency, simple design, and flexibility. However, the position control of the servo motor is a difficult task because of different factors of external disturbances, nonlinearities, and uncertainties. To tackle these challenges, an adaptive integral sliding mode control (AISMC) is proposed, in which a novel bidirectional adaptive law is constructed to reduce the control chattering. The proposed control has three steps to be designed. Firstly, a full-order integral sliding manifold is designed to improve the servo motor position tracking performance, in which the reaching phase is eliminated to achieve the invariance of