In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDE_s). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDE_s) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDE_s) by the assistance of Matlab10.   

      The present paper concern with minimax shrinkage estimator technique in order to estimate Burr X distribution shape parameter, when prior information about the real shape obtainable as original estimate while known scale parameter.

 Derivation for Bias Ratio, Mean squared error and the Relative Efficiency equations.

 Numerical results and conclusions for the expressions mentioned above were displayed. Comparisons for proposed estimator with most recent works were made.

     An Alternating Directions Implicit method is presented to solve the homogeneous heat diffusion equation when the governing equation is a bi-harmonic equation (X) based on Alternative Direction Implicit (ADI). Numerical results are compared with other results obtained by other numerical (explicit and implicit) methods. We apply these methods it two examples (X): the first one, we apply explicit when the temperature .

Active Magnetic Bearings (AMBs) are progressively being implemented in a wide variety of applications. Their exclusive appealing features make them suitable for solving traditional rotor-bearing problems using novel design approaches for rotating machinery.  In this paper, a linearized uncertain model of AMBs is utilized to develop a nonlinear sliding mode controller based on Lyapunov function for the electromechanical system. The controller requires measurements of the rotor displacements and their derivatives. Since the control law is discontinuous, the proposed controller can achieve a finite time regulation but with the drawback of the chattering problem. To reduce the effect of this problem, the gain of the uni

    Tissue culture of Catharanthus  roseus  was established under many parameters to insure good results for detection of the alkaloids present in this plant . It was found that NItsch and Nitsch medium containing 8µM Benzyladeninpurine plus Naphalene acetic acid were the best and the callus of C.roseus left to grow in the dark and had much better influence for the production of Alkloids. The precursor phenylalanine showed a better result than other precursor( tryptophan ) . Abscisic acid has an inhibitory effect on the production of Alkaloid

Background: Autoimmune hepatitis (AIH) is a rare chronic liver disease of known etiology, characterized by hypergammaglobulinemia, characteristic auto antibodies, and a favorable response to immunosuppressive treatment.Strong circumstantial evidences denoted that there is quite long list of environmental factors such as (food additives and drugs), viruses and toxins which play an important role in precipitating this disease.<br />Patients and Methods: the study was performed on 13 Iraqi patients with acute viral hepatitis, attending the Teaching Hospital for Gastroenterology and Liver Disease and Al-Khadymia Teaching Hospital in the period between November 2003 and July 2005. ANA, SMA and anti-LKM 1 were detected by immunoflurescen

In this paper, we present an approximate method for solving integro-differential equations of multi-fractional order by using the variational iteration method.
First, we derive the variational iteration formula related to the considered problem, then prove its convergence to the exact solution. Also we give some illustrative examples of linear and nonlinear equations.

Background: P53 is an important tumor marker in many malignancies, the P53 gene is a tumor suppressor gene that plays a key role in the regulation of the cell cycle.

This paper addresses the use of adaptive sliding mode control for the servo actuator system with friction. The adaptive sliding mode control has several advantages over traditional sliding mode control method. Firstly, the magnitude of control effort is reduced to the minimal admissible level defined by the conditions for the sliding mode to exist. Secondly, the upper bounds of uncertainties are not required to be known in advance. Therefore, adaptive sliding mode control method can be effectively implemented. The numerical simulation via MATLAB 2014a for servo actuator system with friction is investigated to confirm the effectiveness of the proposed robust adaptive sliding mode control scheme. The results clarify, after