Mathematics

Almost Periodic at Infinity Functions Relative to the Subspace of Functions Integrally Decrease at Infinity

Authors: Trishina I. A.

In the paper we introduce and study a new class of almost periodic at infinity functions, which is defined by means of a subspace of  integrally decreasing at infinity functions. It is wider than the class of almost periodic at infinity functions introduced in the papers of A.G.Baskakov (with respect to the subspace of functions vanishing at infinity). It suffices to turn to the approximation theory for a new class of functions, where the Fourier coefficients are slowly varying at infinity functions with respect to the subspace of functions that decrease integrally at infinity.

Adjustment of Functions and Lagrange Interpolation Based on the Nodes Close to the Legendre Nodes

Authors: Novikov V. V.

It is well known that the Lagrange interpolation of a continuous function based on the Chebyshev nodes may be divergent everywhere (for arbitrary nodes, almost everywhere) like the Fourier series of a summable function. On the other hand any measurable almost everywhere finite function can be “adjusted” in a set of arbitrarily small measure such that its Fourier series will be uniformly convergent. The question arises: does the class of continuous functions have a similar property with respect to any interpolation process?

Connections of Nonzero Curvature on Three-dimensional Non-reductive Spaces

Authors: Mozhey N. P.

When a homogeneous space admits an invariant affine connection? If there exists at least one invariant connection then the space is isotropy-faithful, but the isotropy-faithfulness is not sufficient for the space in order to have invariantconnections. If a homogeneousspace is reductive, then the space admits an invariant connection.Thepurposeoftheworkisadescriptionofthree-dimensionalnon-reductivehomogeneousspaces, admitting invariant affine connections of nonzero curvature only, and the affine connections, curvature and torsion tensors.

Approximation of Control for Singularly Perturbed System with Delay with Integral Quadratic Constraints

Authors: Grebennikova I. V., Kremlev A. G.

The purpose of the work is the development and theoretical substantiation of analytical approximate or asymptotic methods for solving optimal control problems for singularly perturbed systems with constant delay in phase variables under conditions of uncertainty with respect to the initial data. For achievement of a goal the control problem for the singularly perturbed system with delay with indeterminate initial conditions and integral quadratic constraints on the control resources according to the minimax criterion is considered.