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On the property of equal ratios in the problem of boundary vector control of elastic vibrations described by Fredholm integro-differential equations = О равных отношениях в задаче граничного векторного управления упругими колебаниями, описываемыми фредгольмовыми интегро-дифференциальными уравнениями

Elmira ABDILDAYEVA

В статье исследуется нелинейная задача оптимального управления упругими колебаниями, описываемыми фредгольмовыми интегро-дифференциальными уравнениями в случае, когда управление осуществляется граничными источниками. В исследовании использовано понятие обобщенного решения краевой задачи управляемого процесса. На основе принципа максимума для систем с распределенными параметрами получены условия оптимальности в виде систем равенств и неравенств. Обнаружено, что условия оптимальности в виде равенств обладают свойством равных отношений. Это обстоятельство позволило упростить процедуру построения ...More

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Optimal distributed control for the processes of oscillation described by Fredholm integro-differential equations

Elmira ABDILDAYEVA

In this paper we investigate the problem of distributed optimal control for the oscillation processes described by Fredholm integro-differential equations with partial derivatives when the function of the external source depends nonlinearly on the control parameters. We have developed an algorithm for finding approximate solutions of nonlinear optimization problems with arbitrary precision. The developed method of solving nonlinear optimization problems is constructive and can be used in applications. - Keywords and phrases: boundary value problem, generalized solution, approximate solutions, ...More

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A class linear integral equations of Fredholm-Stilties of the first kind = Об одном классе линейных интегральных уравнений Фредгольма-Стилтьеса первого рода

Avıt ASANOV

In this article the line.r integral equation of Fredgolm-Stilties of the first kind is given. Using the method proposed in A. Asanov, estimates and stability built on M.M.Lavrentev regularizing operator for solving singularly perturbed integral equations of the first kind. The questions of uniqueness of solution of the integral equation and prove a theorem about the sustainability assessment solutions in the classroom L-2.

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Approximating the Stieltjes integral by using the generalized trapezoid rule

Avıt ASANOV | Mustafa Haluk ÇELİK

Accurate approximations for the Stieltjes integral by the generalized trapezoid rule. The generalized trapezoid rule is established on the basis of the derivative of function with respect to strictly increasing function, defined in [9].

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Approximating the Stieltjes Integral Using the Generalized Midpoint Rule

Avıt ASANOV | Mustafa Haluk ÇELİK

Accurate approximations for the Stieltjes integral by the generalized midpoint rule. The generalized midpoint rule is established on the notion of the derivative of function with respect to the strictly increasing function defined in [9]. Keywords: Stieltjes integral; generalired midpoint rule; the derivative of the function with respect to the strictly increasing function; generalized formula of Taylor. 2010 Mathematics Subject Classification 26D15; 26A42.

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