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.
Signal denoising is directly related to sample estimation of received signals, either by estimating the equation parameters for the target reflections or the surrounding noise and clutter accompanying the data of interest. Radar signals recorded using analogue or digital devices are not immune to noise. Random or white noise with no coherency is mainly produced in the form of random electrons, and caused by heat, environment, and stray circuitry loses. These factors influence the output signal voltage, thus creating detectable noise. Differential Evolution (DE) is an effectual, competent, and robust optimisation method used to solve different problems in the engineering and scientific domains, such as in signal processing. This paper looks
... Show MoreIn the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.
In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations nonhomogeneous of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) 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 (LFFIDEs) by the assistance of Matlab10.
Nitrogen (N) and phosphorus (P) are the most important nutrients for crop production. The N contributes to the structural component, generic, and metabolic compounds in a plant cell. N is mainly an essential part of chlorophyll, the compound in the plants that is responsible for photosynthesis process. The plant can get its available nitrogen from the soil by mineralizing organic materials, fixed-N by bacteria, and nitrogen can be released from plant as residue decay. Soil minerals do not release an enough amount of nitrogen to support plant; therefore, fertilizing is necessary for high production. Phosphorous contributes in the complex of the nucleic acid structure of plants. The nucleic acid is essential in protein synthesis regulation; t
... Show MoreStudy of determining the optimal future field development has been done in a sector of South Rumaila oil field/ main pay. The aspects of net present value (economic evaluation) as objective function have been adopted in the present study.
Many different future prediction cases have been studied to determine the optimal production future scenario. The first future scenario was without water injection and the second and third with 7500 surface bbls/day and 15000 surface bbls/day water injection per well, respectively. At the beginning, the runs have been made to 2028 years, the results showed that the optimal future scenario is continuing without water in
Background: Breast cancer is the most common malignancy affecting the Iraqi population and the leading cause of cancer related mortality among Iraqi women. It has been well documented that prognosis of patients depends largely upon the hormone receptor contents and HER-2 over expression of their neoplasm. Recent studies suggest that Triple Positive (TP) tumors, bearing the three markers, tend to exhibit a relatively favorable clinical behavior in which overtreatment is not recommended. Aim: To document the different frequencies of ER/PR/HER2 breast cancer molecular subtypes focusing on the Triple Positive pattern; correlating those with the corresponding clinico-pathological characteristics among a sample of Iraqi patients diagnosed with th
... Show MoreThis work describes two efficient and useful methods for solving fractional pantograph delay equations (FPDEs) with initial and boundary conditions. These two methods depend mainly on orthogonal polynomials, which are the method of the operational matrix of fractional derivative that depends on Bernstein polynomials and the operational matrix of the fractional derivative with Shifted Legendre polynomials. The basic procedure of this method is to convert the pantograph delay equation to a system of linear equations and by using, the operational matrices we get rid of the integration and differentiation operations, which makes solving the problem easier. The concept of Caputo has been used to describe fractional derivatives. Finally, some
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