Vol 17, No 8 (2011)

The paper is devoted to the problem of piecewise-linear approximation of mapping for the elliptic system of solutions defined on triangular grids. A mapping is build to approximate the differential, and the estimate of error of approximation that does not depend on the degree of degeneracy of triangles of the grid. An analogous estimate is obtained for mappings which approximate the differential of solution of Beltrami equation.

The system of shift of functions  in L² (R) space is considered in this paper. We find conditions on real sequence g(x), which provide such properties of the system as to be a frame, Bessel system, complete sequence in the space L² (R).

The article deals with the description of the method of Fourier vector transformation with discontinuous coefficients. The dynamics of the theory of elasticity illustrates the technique of method in solving problems of mathematical physics of heterogeneous media.

In the paper we study copulas obtained as a result of independence transformation of random vectors with Student's t-distribution. For the triangular scheme of dependent r.v. connected by such IT-copulas central limit theorem is proved. In addition, it is shown that two-dimensional IT-copula of Cauchy distribution is not associated.

In this paper, we study an initial-boundary value problem with nonlocal integral condition for a hyperbolic equation. The existence and uniqueness of a generalized solution of the problem is proved.

Boundary value problems with non-local conditions for partial differential equation are considered. In these problems, non-local conditions connect the values of a required solutions on the opposite sides of a rectangular domain. Criteria of uniqueness of each of the problems are obtained. Solutions to both problems are constructed as sums of Fourier series. The stability of solutions is proved.

In the paper the approximate solution for a problem of a rectangular plate on a two-parameter elastic base is suggested. The double series of beam functions satisfying elastic support boundary conditions are constructed. The analytical expressions for series function coefficients are obtained.

The new closed solution of axially symmetric nonstationary problem of the theory of elasticity for thick round anisotropic plate with rigid of its external radial surface is constructed. Calculated relations are obtained by method of expansion in eigen vector-functions in the form of structural algorithm of finite transformations. Numerical results allow to define the natural-vibration frequency, and also the stress-strain state of the testing element.

A new method of administering pharmaceutical substances with the help of apparatuses for dynamic electroneurostimulation (DENS) was suggested. This method is available in home conditions, preventoriums, social centers for communication and health. The article sets forth the results of experimental works on electrophoresis of medical mud with the help of the DENS apparatuses in patient with deforming osteoarthritis of the knee joint. The possibility of effective reduction of pain syndrome intensity in patients with osteoarthritis of II-III degrees was shown.

The main directions of the search of biologically active compounds, pyrimi-dine derivatives are described.The synthesis of pyrimidines with anticancer, antimicrobial, antiviral activity is shown as the most frequent in recent years. The examples of compounds are given, which are already being used in medicine practice or may be good starting points for obtaining new drugs.

The maintenance of peptide connections inside red blood cells and in the incubatory environment in the conditions of presence and absence of ions of calcium and magnesium, action of 1,3-dimetilksantin and АТГ is studied. The increase in the maintenance of peptides inside erythrocytes in the conditions of blocking L-calcium of channels and АТГ and reduction of their maintenance in the incubatory environment which is not containing ions of calcium is revealed.

There were studied microscopical constitution features of the compound leaf leaflets of a large-flowered tick trefoil Hedysarum grandiflorum Pall. that was gathered in Kinel district of the Samara region, in 2,5 km to the south - east from the village of Preobrazhenka, in June, 2009. The result of the survey helped to confirm, specify and enlarge information about morphological and histological characteristics of the leaflet of a compound leaf one of the genus Hedysarum family.