# Vol 17, No 8 (2011)

**Year:**2011**Articles:**25**URL:**https://journals.ssau.ru/est/issue/view/232

## Articles

5-20

### SMOOTH APPROXIMATION FOR THE SOLUTIONS OF ELLIPTIC SYSTEMS

#### Abstract

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.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):21-28

21-28

29-36

### THE SYSTEM OF SHIFTS OF FUNCTIONS

#### Abstract

The system of shift of functions in L^{2} (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 L^{2} (R).

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):37-44

37-44

45-49

### FOURIER VECTOR TRANSFORMATION WITH DISCONTINUOUS COEFFICIENTS IN THE THEORY OF ELASTICITY

#### Abstract

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.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):50-58

50-58

### L-STABLE (4,2)-METHOD OF THE FOURTH ORDER FOR SOLVING STIFF PROBLEMS

#### Abstract

(M,k)-methods for solving stiff problems, in which on each step two times the right-hand side of the system of differential equations is calculated are investigated. It is shown that the maximum order of accuracy of the L-stable (m,2)-method is equal to four. (4,2)-method of maximal order is built.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):59-68

59-68

### LIMIT THEOREM FOR INDEPENDENCE TRANSFORMATIONS COPULAS OF STUDENT'S t-DISTRIBUTION

#### Abstract

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.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):69-85

69-85

86-94

95-101

### A PROBLEM WITH DISPLACEMENTS IN THE BOUNDARY CONDITIONS

#### Abstract

A problem with conditions relating to the values of an unknown function on the opposite sides of a rectangular characteristiс domain D for a linear hyperbolic equations is considered. This problem is reduced to the system of Fredholm equations of the second kind. The proof of solvability is based on the a priori estimates of additional conditions on the coefficients of the equation.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):102-107

102-107

### NONLOCAL PROBLEMS FOR THE EQUATION OF THE MIXED PARABOLIC-HYPERBOLIC TYPE

#### Abstract

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.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):108-117

108-117

### MODELING OF DOUBLY PERIODIC SYSTEM OF PRODUCING WELLS. 2. PRODUCTIVITY INDEX

#### Abstract

The question of productivity of doubly periodic systems of production wells is considered. Using the idealized production regime with a constant flow rate the analytical representation for the productivity index (PI) of the well was obtained and values depending on the drainage shapes were analyzed. Also an analytic representation for the Dietz's shape factor, which agrees with numerical calculations by the method of imaginary producing wells was obtained.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):118-127

118-127

### A RECTANGULAR PLATE ON A TWO-PARAMETER ELASTIC BASE: THE ANALYTICAL SOLUTION

#### Abstract

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.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):128-133

128-133

134-141

### THE COMPELLED AXISYMMETRIC BENDING FLUCTUATIONS OF THICK ROUND RIGID PLATE

#### Abstract

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.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):142-152

142-152

### THE INFLUENCE OF DIPOLE-DIPOLE INTERACTION ON THE ENTANGLEMENT FOR MANY-PHOTON TAVIS — CUMMINGS MODEL

#### Abstract

The influence of dipole-dipole interaction on the entanglement between two atoms and field in many-photon Tavis — Cummings with coherent cavity mode has been investigated. The results show that in the case of one-photon model the dipole-dipole interaction leads to the stabilization of atom-field entanglement.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):153-156

153-156

### DENS-PHORESIS — A RATIONAL WAY OF USING MEDICAL MUD IN THE TREATMENT OF OSTEOARTHRITIS OF THE KNEE JOINT

#### Abstract

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.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):157-162

157-162

### METHODS OF OBTAINING STRONTIUM AZIDE

#### Abstract

In this paper all the ordinary ways of obtaining strontium azide are discussed. A new and more appropriate method of obtaining strontium azide from sodium azide is introduced. The most effective conditions of this method are described.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):163-166

163-166

### PHARMACOLOGICAL ACTIVITY OF A PYRIMIDINE DERIVATIVES

#### Abstract

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.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):167-172

167-172

### HEAVY METALS IN SOIL COVER OF ULIANOVSK CITY CHILDREN PARK

#### Abstract

The features of heavy metals content and lateral distribution of heavy metals in soil cover of Ulianovsk city children park are described in the article. The possible sources of polymetallic territory pollution are discussed.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):173-178

173-178

### INFLUENCE OF DEFICIENCY OF CALCIUM AND MAGNESIUM ON MAINTENANCE OF PEPTIDE CONNECTIONS IN HUMAN ERYTHROCYTES AT THE INCUBATION IN VITRO

#### Abstract

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.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):179-182

179-182

### SOME MATERIALS ABOUT FEATURES OF STRUCTURE OF BIOLOGICAL GROUPS OF PLANTS IN THE AFFORESTATIONS SERVING AS HABITATS OF CONVALLARIA MAJALIS L

#### Abstract

The floristic structure of the investigated afforestations with participation of Convallaria majalis L. is considered. The rare species of plants growing together with Convallaria majalis L. are established. Potential stocks of medicinal raw materials of cenopopulations of Convallaria majalis L. in various afforestations are defined.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):183-195

183-195

### ANATOMO-HISTOLOGICAL RESEARCH OF LEAFLETS OF DIFFICULT SHEET HEDYSARUM GRANDIFLORUM PALL

#### Abstract

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.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):196-201

196-201

### LIVER FAT DYNAMICS OF AMUR SLEEPER PERCCOTTUS GLENII DYBOWSKI, 1877

#### Abstract

According to the materials received in 2007 and 2009 years, the data on liver fat reserve dynamics of Amur sleeper in concordance with their age, sex and maturity stage throughout the vegetation period is given.

**Vestnik of Samara University. Natural Science Series**. 2011;17(8):202-205

202-205