In this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.

In this paper we present a new method for solving fully fuzzy multi-objective linear programming problems and find the fuzzy optimal solution of it. Numerical examples are provided to illustrate the method.

This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.

           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

In the image processing’s field and computer vision it’s important to represent the image by its information. Image information comes from the image’s features that extracted from it using feature detection/extraction techniques and features description. Features in computer vision define informative data. For human eye its perfect to extract information from raw image, but computer cannot recognize image information. This is why various feature extraction techniques have been presented and progressed rapidly. This paper presents a general overview of the feature extraction categories for image.

An experimental study is made here to investigate the discharge coefficient for contracted rectangular Sharp crested weirs. Three Models are used, each with different weir width to flume width ratios (0.333, 0.5, and 0.666). The experimental work is conducted in a standard flume with high-precision head and flow measuring devices. Results are used to find a dimensionless equation for the discharge coefficient variation with geometrical, flow, and fluid properties. These are the ratio of the total head to the weir height, the ratio of the contracted weir width to the flume width, the ratio of the total head to the contracted width, and Reynolds and Weber numbers. Results show that the relationship between the discharge co

     This article contains a new generalizations of Ϻ-hyponormal operators which is namely (Ϻ,θ)-hyponormal operator define on Hilbert space H.  Furthermore, we investigate some properties of this concept such as the product and sum of two (Ϻ, θ)-hyponormal operators, At the end the operator equation  where  ,  has been used for getting several characterization of (Ϻ,θ)-hyponormal operators.  

    This work is concerned with studying the solvability for optimal classical continuous control quaternary vector problem that controls by quaternary linear hyperbolic boundary value problem. The existence of the unique quaternary state vector solution for the quaternary linear hyperbolic boundary value problem  is studied and demonstrated by employing the method of Galerkin, where the classical continuous control quaternary vector  is Known. Also, the existence theorem of an optimal classical continuous control quaternary vector related to the quaternary linear hyperbolic boundary value problem is demonstrated. The existence of a unique solution to the adjoint quaternary linear hyperbolic boundary value problem a

Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

Many fuzzy clustering are based on within-cluster scatter with a compactness measure , but in this paper explaining new fuzzy clustering method which depend on within-cluster scatter with a compactness measure and between-cluster scatter with a separation measure called the fuzzy compactness and separation (FCS). The fuzzy linear discriminant analysis (FLDA) based on within-cluster scatter matrix and between-cluster scatter matrix . Then two fuzzy scattering matrices in the objective function assure the compactness between data elements and cluster centers .To test the optimal number of clusters using validation clustering method is discuss .After that an illustrate example are applied.