In this study, He's parallel numerical algorithm by neural network is applied to type of integration of fractional equations is Abel’s integral equations of the 1^st and 2^nd kinds. Using a Levenberge – Marquaradt training algorithm as a tool to train the network. To show the efficiency of the method, some type of Abel’s integral equations is solved as numerical examples. Numerical results show that the new method is very efficient problems with high accuracy.

The goal of this paper is to design a robust controller for controlling a pendulum
system. The control of nonlinear systems is a common problem that is facing the researchers in control systems design. The Sliding Mode Controller (SMC) is the best solution for controlling a nonlinear system. The classical SMC consists from two phases. The first phase is the reaching phase and the second is the sliding phase. The SMC suffers from the chattering phenomenon which is considered as a severe problem and undesirable property. It is a zigzag motion along the switching surface. In this paper, the chattering is reduced by using a saturation function instead of sign function. In spite of SMC is a good method for controlling a nonlinear system b

          In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

In this paper, we define two operators of summation and summation-integral of q-type in two dimensional spaces. Firstly, we study the convergence of these operators and then we prove Voronovskaya- type asymptotic formulas for these operators.

Type 2 daibetes mellitus (T2DM) is a global concern boosted by both population growth and ageing, the majority of affected people are aged between (40- 59 year). The objective of this research was to estimate the impact of age and gender on glycaemic control parameters: Fasting blood glucose (FBC), glycated hemoglobin (HbA1C), insulin, insulin resistance (IR) and insulin sensitivity (IS), renal function parameters: urea, creatinine and oxidative stress parameters: total antioxidant capacity (TAC) and reactive oxygen species (ROS). Eighty-one random samples of T2DM patients (35 men and 46 women) were included in this study, their average age was 52.75±9.63 year. Current study found that FBG, HbA1C and IR were highly significant (P<0.01) inc

New tetradentate Schiff base [H2L] namely [2,2׳ -(ethane-1,2- diylbis (azan-1-ylylidene) diacetic acid)] was prepared from condensation of ethylenediamine with  glyoxylic acid  in ethanol as a solvent in presence of drops of 48% HBr .The structure of ligand (H2L) was characterized by,F-IR, U.V-Vis.,1H-,13C-NMR, pectrophotometer,melting point and elemental microanalysis C.H.N.  Metal complexes of the ligand (H2L) in general Molecular formula [M(L)(H2O)2], where M=  Co(II), Ni(II), Cu(II), Mn(II) and Hg(II); L=(C6H8N2O4) were synthesized were characterized by, Atomic absorption, F-IR, U.V-Vis. spectra, molar conductivity and magnetic susceptibility.It was found that all the complexes showed octahedral geometries.And

     The objective of this paper is, first, study a new collection of sets such as field and we discuss the properties of this collection. Second, introduce a new concepts related to the field such as measure on field, outer measure on field and we obtain some important results deals with these concepts. Third, introduce the concept of null-additive on field as a generalization of the concept of measure on field. Furthermore, we establish new concept related to - field noted by weakly null-additive on field as a generalizations of the concepts of measure on and null-additive. Finally, we introduce the restriction of a set function  on field and many of its properties and characterizations are given.

This paper deals with, Bayesian estimation of the parameters of Gamma distribution under Generalized Weighted loss function, based on Gamma and Exponential priors for the shape and scale parameters, respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation. Based on Monte Carlo simulation method, those estimators are compared in terms of the mean squared errors (MSE’s).

     In this paper, suggested formula as well a conventional method for estimating the twoparameters (shape and scale) of the Generalized Rayleigh Distribution was proposed. For different sample sizes (small, medium, and large) and assumed several contrasts for the two parameters a percentile estimator was been used. Mean Square Error was implemented as an indicator of performance and comparisons of the performance have been carried out through data analysis and computer simulation between the suggested formulas versus the studied formula according to the applied indicator. It was observed from the results that the suggested method which was performed for the first time (as far as we know), had highly advantage than t

      In this paper, the researcher suggested using the Genetic algorithm method to estimate the parameters of the Wiener degradation process,  where it is based on the Wiener process in order to estimate the reliability of high-efficiency products, due to the difficulty of estimating the reliability of them using traditional techniques that depend only on the failure times of products. Monte Carlo simulation has been applied for the purpose of proving the efficiency of the proposed method in estimating parameters; it was compared with the method of the maximum likelihood estimation. The results were that the Genetic algorithm method is the best based on the AMSE comparison criterion, then the reliab