On the R -compactification of uniform spaces

As it is well known, there are various constructions of the R-compactification (Hewitt real compactification) of a uniform space [13], [15]. In this work we propose a new construction of the R-compactification (Hewitt real compactification) of a uniform space. Keyword: A0-boundedness; R-compactification; R-completeness.; R-extension

On the Solvability of a Boundary Value Problem for Nonlinear Optimization of Oscillatory Processes

Elmira ABDILDAYEVA

The paper investigates the solvability of a boundary value problem in the control of an oscillatory process described by control in partial derivatives of the first order. It has been established that there are an infinite set of controls, as solutions to the system of nonlinear Fredholm integral equations of the first kind, each of which transfers the controlled process from the initial state to the final specified state in a specified time. Sufficient conditions for the existence of a nonlinear optimization solution are found.

On Solvability of Optimization Problem for Elastic Oscillations with Multipoint Sources of Control

Elmira ABDILDAYEVA

In the paper we investigate the optimal control problem for elastic oscillation under multipoint influences of external forces when oscillation process is described by Fredholm integro-differential equation. Sufficient conditions for unique solvability of nonlinear optimization problem were found and the algorithm for constructing complete solution to this problem was developed.

Numerical Analysis of Convergence Rate of Approximation Solutions to Boundary Value Problem for Oscillation Processes

Elmira ABDILDAYEVA

In this paper, the dynamics of convergence rate is investigated for the approximations depending on the changes of the stiffness coefficient of the elastic fixation. The results of the numerical analysis show that with increasing of stiffness coefficient (parameter alpha) of the elastic fixation the radius of convergence of Neumann series increases, and the convergence rate of the approximations to the exact solution accelerates.

Peculiarities of Constructing an Optimal Vector Distributed Control with Nonlinear Optimization of Oscillation Processes

Elmira ABDILDAYEVA

Nonlinear optimization problem is investigated for oscillation processes described by Fredholm integro-differential equations in partial derivatives when the function of the external source nonlinearly depends on vector distributed control. It is established that, the optimal control procedure is greatly simplified with vector control. Algorithm is developed for constructing a complete solution of the nonlinear optimization problem.

On the solvability of nonlinear integral equations

Elmira ABDILDAYEVA

The article explores general nonlinear equations with a parameter. Sufficient conditions for the existence of a solution of nonlinear integral equations in the form of the sum of two functions for the individual values of the parameter are found.

On numerical solution of the second-order linear Fredholm-Stieltjes integral equation

Avıt ASANOV

In this framework, the necessary and sufficient conditions for the existence and uniqueness of the second-order linear Fredholm-Stieltjes-integral equations, u(x) = lambda integral(b)(a) K(x, y) u(y) dg(y) + f(x), x is an element of[a, b], are thoroughly derived. Moreover, instead of approximating the integral equation by different numbers of partition n, the optimal number n for the given error tolerance is established. The system of equations is implemented in MAPLE for the Runge method. An efficient scheme is proposed for second-order integral equations. The solution has been compared with ...More