In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.

This paper proposes improving the structure of the neural controller based on the identification model for nonlinear systems. The goal of this work is to employ the structure of the Modified Elman Neural Network (MENN) model into the NARMA-L2 structure instead of Multi-Layer Perceptron (MLP) model in order to construct a new hybrid neural structure that can be used as an identifier model and a nonlinear controller for the SISO linear or nonlinear systems. Two learning algorithms are used to adjust the parameters weight of the hybrid neural structure with its serial-parallel configuration; the first one is supervised learning algorithm based Back Propagation Algorithm (BPA) and the second one is an intelligent algorithm n

Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

Chloroacetamide derivatives (2a-g) have been prepared through reaction of chloroacetyl chloride(1) (which prepared by the reaction of chloroacetic acid with thionyl chloride) with primary aromatic amines and sulfa compounds to afford compounds (2a-g) which then reacted with p-hydroxy benzaldehyde via Williamson reaction to obtaine the new compounds 2-(4-formyl phenoxy)-N-aryl acetamide (3a-g). Finally , compounds (3a-g) will be use as a good synthon to prepare the Schiff bases represented by compounds 2-(4-aryliminophenoxy)-N-arylacetamide (4a-g). through , reaction with some primary aromatic amine. All the prepared compounds were investigated by the available physical and spectroscopic methods.

      Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.

         Allopurinol derivative were prepared by reacting the (1-chloroacetyl)-2-Hydropyrazolo{3,4-d}pyrimidine-4-oneiwith 5- methoxy- 2-aminoibenzothiazoleiunder certain conditions to obtain new compound  ( N- (2-aminoacetyl (5-methoxy) benzothiazole -2yl) (A₄), Reaction of 5-(P-dimethyl amine benzene)-2-amino-1,3,4- oxadiazole in the presence of potassium carbonate anhydrous to yield new  compound (N-(2- aminoacetyl-5-(P-dimethyl amine benzene )-1,3,4-oxadiazoles-2-yl)(A₃₀) and Azo compound (N-(5-(Azo-2-hydroxy-5-amino benzene)-1,3-Diazol-2yl)Allopurinol(A₄₆). The structure of prepared compounds were confirmed by (FT-IR)