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.

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.

Asymptotics of the Solution of Parabolic Problems with Multipoint Stationary Phase

Asan ÖMÜRALİEV | Ella ABILAYEVA

The aim of this paper is to construct regularized asymptotics of the solution of a singularly perturbed parabolic problem when the limit operator has not range and with rapidly oscillating free term, its derivative of the phase vanishes at finite points. The vanishing of the first derivative of the phase of the free term induces transition layers. It is shown that the asymptotic solution of the problem contains parabolic, inner, corner and rapidly oscillating boundary-layer functions. Corner boundary-layer functions have two components: the first component is described by the product of parabo ...Daha fazlası

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.

Solutions of the Rational Difference Equations xn+1 = xn-11/1+xn-2xn-5xn-8

Dağıstan ŞİMŞEK | Burak OĞUL

In this paper a solution of the following difference equation xn+1=xn-111+xn-2xn-5xn-8 was investigated, where x-11, x-10, ..., x-2, x-1, x0 ∈ (0, ∞).

Topology of Soft Cone Metric Spaces

Dağıstan ŞİMŞEK

In Simsek's paper it was introduced a concept of soft cone metric space via soft elements and some fixed point theorems in soft cone metric space were provided. In this work, we examine topological structures such as open ball, soft neighbourhood and soft open set in soft metric spaces and their some properties, and prove that every soft cone metric space under some condition is a soft topological space according to elementary operations on soft sets.

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.