Mathematics

The Solution of the Problem of Determining the Density of Heat Sources in a Rod

Authors: Khromov A. A., Khromova G. V.

We give a solution of a problem of determining the density of heat sources in the bav, which is set to a fixed temperature, if the temperature is given approximately. Mathematically it is the problem of finding uniform approximations to the right-hand side of the ordinary differential equation when uniform approximations to the solution and values of error are known.

Approximation of Functions of Bounded p-variation by Euler Means

Authors: Tyuleneva A. A.

In this paper we study the Euler means
eqn(f)(x) =∑k=0n(nk)qn−k(1 + q)−nSk(f)(x), q > 0, n ∈ Z+,

Gluing Rule for Bernstein Polynomials on the Symmetric Interval

Authors: Tikhonov I. V., Sherstyukov V. B., Petrosova M. A.

We study special laws that arise in a sequence of the Bernstein polynomials on a symmetric interval. In particular, we set the exact rule of regular pairwise coincidence (gluing rule) which is acting for the Bernstein polynomials of a piecewise linear generating function with rational abscissas of break points. The accuracy of this rule for convex piecewise linear generating functions is shown. The possibility of “random” gluing for the Bernstein polynomials in a non-convex case is noted. We give also some examples and
illustrations.

On Accuracy of Estimation of the Number of Steps for the Algorithm for Construction of Scaling Function on Local Fields

Authors: Kruss Y. S.

In this paper we discuss a problem of accuracy of estimation of the number of steps for the algorithm for construction of orthogonal scaling function which generates multiresolution analisys on local fields of positive characteristic. The resulting function is a step function with a compact support. The number of steps in the algorithm is closely related to the support of the Fourier transformation of the scaling function. Thus the estimate for number of steps is not only of computational interest. The upper estimate for this number was already known.

On Functional Stability of the Solution for the Problem of Convex Body Best Approximating by a Ball with Fixed Radius

Authors: Dudov S. I., Osipcev M. A.

A finite-dimensional problem of finding a uniform estimate (approximation in the Hausdorff metric) of a convex body by a fixed-radius ball in an arbitrary norm is considered. It is known that this problem can be reduced to a linear programming problem in the case, when the convex body and the norm ball are polytops. Therefore, we prove the functional stability of the optimal value of the objective function with respect to accuracy of the given convex body and accuracy of the unit ball for the norm used. The stability rating is derived.

Homogenization of the Acoustics Mathematical Model

Authors: Gerus A. A., Gritsenko S. A.

We consider a mathematical model of acoustics in heterogeneous medium with two different components with the common boundary. One of these is a bounded liquid domain and the other is a poroelastic medium. Poroelastic medium is perforated by pores. A pore space is filled with a viscous liquid. The motion of the liquid and the joint motion of the poroelastic media with porous space are governed by the differential equations based on the continuum mechanics laws. These equations contain rapidly oscillating terms, depending on the small parameter.

Almost Contact Metric Spaces with N-connection

Authors: Galaev S. V.

On a manifold with an almost contact metric structure (ϕ, ~ξ, η, g,X,D) and an endomorphism N : D → D, a notion of the N-connection is introduced. The conditions under which an N-connection is compatible with an almost contact metric structure ∇Nη = ∇Ng = ∇N~ξ = 0 are found. The relations between the Levi – Civita connection, the Schouten – van-Kampen connection and the N-connection are investigated. Using the N-connection the conditions under which an almost contact metric structure is an almost contact Kahlerian structure are investigated.

Several Questions of Approximation by Polynomials with Respect to Multiplicative Systems in Weighted Lp Spaces

Authors: Volosivets S. S., Likhacheva T. V.

In this paper we study approximation by Vilenkin polynomials in weighted Lp spaces. We prove the Butzer – Scherer type result on equivalence between the rate of best approximation of a function f and the growth of generalized derivatives and approximating properties of the best approximation polynomial tn(f). Some applications to the approximation by linear means of the Fourier – Vilenkin series are given.

To Chang Theorem

Authors: Antonov S. Y., Antonova A. V.

Multilinear polynomials H (¯x, ¯y) and R(¯x, ¯y), the sum of which is the Chang polynomial F(¯x, ¯y) have been introduced in this paper. It has been proved by mathematical induction method that each of them is a consequence of the standard polynomial S−(¯x). In particular it has been shown that the double Capelli polynomial of add degree C2m−1(¯x, ¯y) is also a consequence of the polynomial S−m(¯x, ¯y). The minimal degree of the polynomial C2m−1(¯x, ¯y) in which it is a polynomial identity of matrix algebraMn(F) has been also found in the paper.