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.

Formulas for solution of Riccati's equationle

Avıt ASANOV

In this paper we obtained the formula for the common solution of Riccati equations. Here Riccati equations was solved for common cases. Results obtained have been compared with the conventional ones and a comment has been made on them.

Uniformities for Wallman compactifications and realcompactifications

Asılbek ÇEKEEV

The natural methods of uniform topology for construction of Wallman compactifications and Wallman realcompactifications are developed. Results on partial order and relations of dimensions in the lattice of compactifications are presented. The construction of the maximal compactification among compactifications of X with fixed realcompactification is given. - MSC 54E15; 54D35; 54D60; 54F45 . - Keywords: Uniformity; (Wallman, β-like) compactification; (Wallman) realcompactification; Normal base; Dimension

Method of spherical harmonic series in the problem of minimization of atmosphere pollution by fractions of harmful admixtures

Ramiz RAFATOV

The problem of minimization of atmosphere pollution by fractions of harmful admixtures is studied. It is supposed that a controlled object is described by non-stationary integral–differential transfer equation with special boundary conditions and control parameters, which are included in the right part of equation as delta-functions. Minimized integral quadratic functional characterizes energy expenditure for control and depends on the average squared deflection of fraction concentration from the desired final state. Optimal conditions are obtained with the help of Pontryagin’s maximum princip ...Более

Ultrafilter-completeness on zero-sets of uniformly continuous functions

Asılbek ÇEKEEV

The various types of ultrafilter-completeness on zero-sets of uniformly continuous functions are introduced, their properties are studied and characterizations in the category are given.

R-Compact Uniform Spaces in the Category ZUnif

Asılbek ÇEKEEV

A number of basic properties of R-compact spaces in the category Tych of Tychonoff spaces and their continuous mappings are extended to the category ZUnif of uniform spaces with the special normal bases and their coz-mappings.

Direct Integration of Systems of Linear Differential and Difference Equations

Anarkül URDALETOVA

Traditionally the Euler method is used for solving systems of linear differential equations. The method is based on the use of eigenvalues of a system's coefficients matrix. Another method to solve those systems is the D'Alembert integrable combination method. In this paper, we present a new method for solving systems of linear differential and difference equations. The main idea of the method is using the coefficients matrix eigenvalues to find integrable combinations of system variables. This method is particularly advantageous when nonhomogeneous systems are considered.

About Uniqueness of Solutions of Fredholm Linear Integral Equations of the First Kind in the Axis

Avıt ASANOV

In this work, we apply the method of integral transformation to prove uniqueness theorems for the new class of Fredholm linear integral equations of the first kind in the axis.

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.