# Vol 19, No 6 (2013)

**Year:**2013**Articles:**22**URL:**https://journals.ssau.ru/est/issue/view/225

## Статьи

### THE STRUCTURE OF MODULAR FORM: THE PHENOMEN OF THE SECTION

#### Abstract

In the article we study the structure of spaces of modular forms S

_{k}(Г_{0}(N),х) and M_{k}(Г_{0}(N ),х) for the levels N such that for a value k_{0}S_{k0}(Г_{0}(N),х) is a one-dimensional space generated by a multiplicative n-product.**Vestnik of Samara University. Natural Science Series**. 2013;19(6):5-12

5-12

13-22

### NUMERICAL METHOD FOR THE SOLUTION OF INVERSE PROBLEMS GENERATED BY PERTURBATIONS OF SELF-ADJOINT OPERATORS BY METHOD OF REGULARIZED TRACES

#### Abstract

In the article a new method for the solution of inverse problems generated by perturbations of self-adjoint operators on their spectral characteristics is developed. The method was tested on inverse problems for Sturm-Liouville problems. The results of numerous calculations showed the computational efficiency of the method.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):23-30

23-30

31-39

### DIRICHLET PROBLEM FOR LOADED DEGENERATING EQUATION OF THE MIXED TYPE IN THE RECTANGULAR AREA

#### Abstract

In this work necessary and sufficient conditions for uniqueness of a solution to the first boundary problem for Lavrentiev-Bitsadze equation in rectangular domain are established. The solution to the problem is constructed as a sum of series with respect of eigenfunctions of a corresponding one-dimensional Stour-m-Liouviele problem. The stability is shown.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):40-53

40-53

### ON THE UNIFORM CONVERGENCE OF THE APPROXIMATE SOLUTION OF SINGULAR INTEGRO-DIFFERENTIAL EQUATION OF THE FIRST KIND

#### Abstract

The article presents the study of the boundary problem for singular inte-gro-differential equation of the first kind with Cauchy kernel. The authors introduce the pair of weight spaces to prove the correctness of the stated problem. The article states the sufficient conditions for the convergence of the general direct method, the method of orthogonal polynomials, and as a result uniform estimates for errors of approximate solution.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):54-60

54-60

61-73

### ON CHARACTERISTIC PROBLEMS FOR ONE HYPERBOLIC SYSTEM IN THREE-DIMENSIONAL SPACE

#### Abstract

We consider characteristic problems for a hyperbolic system with three independent variables. Using the Riemann method and theory of integral equations we obtain conditions of one-valued solvability for this problems.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):74-84

74-84

### NUMERICAL METHOD OF CONSTRUCTION OF EIGEN VALUE SPECTRUM OF A NON LINEAR PROBLEM ARISING FROM ONE PROBLEM OF MIXED DEFORMATION OF PLATE WITH CRACK

#### Abstract

In the work a method of numerical finding of eigen values of class of non linear problems on eigen values arising from the problem of defining stress-edly-deformed state near the apex of crack in the materials with exponential determining equations in conditions of compound deforming in full range of mixed forms of deformation from normal fracture up to simple shear is suggested. With the help of suggested approach new eigen values of the problem, different from the known eigen value, that corresponds to the classical solution of Hutchison-Rice-Rosengren are obtained.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):85-99

85-99

### INVARIANT INTEGRALS IN EQUILIBRIUM PROBLEM FOR A TIMOSHENKO TYPE PLATE WITH THE SIGNORINI TYPE CONDITION ON THE CRACK

#### Abstract

The equilibrium problem for the elastic Timoshenko type plate with a crack is considered. On the crack faces, the non-penetration conditions of inequality type (Signorini type conditions) are given. It is proved that there exist invariant integrals that are equal to the derivative of the energy functional with respect to perturbation parameter.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):100-115

100-115

### ON THE THEORY OF MIGRATION OF METHANE BUBBLES IN THE CONDITION OF HYDRATE FORMATION

#### Abstract

The paper a theoretical model and migration of methane bubbles in the hydrate formation conditions in the upward flow of water in a vertical channel is suggested and built. We obtain critical values of mass flow rates of gas and water, providing the necessary conditions for the full transition to the reactor, the gas in the gas hydrate. It is found out that at migration of gas bubbles in the reactor, two possible modes of the process of hydrate depending on the initial mass flow rate of water: gas bubbles or completely converted into hydrated state as separate inclusions or partially, forming bubbles with a hydrated shell. Analysis of influence of size of gas bubbles on the process of hydrate formation).

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):116-125

116-125

### ON THE THEORY OF THE BULK FOAM-FORMATION OF GAS-SATURATED LIQUID DURING THE DEPRESSURIZING OF CONTAINER

#### Abstract

The problem of depressurizing in the gas-saturated liquid is considered. It is found out that the smaller is the initial radius of original germ of gas, the more pressure drops as compared with equilibrium pressure. The solution of the system that describes the transition from the metastable state to the equilibrium two-phase state is found. It is found that the characteristic time of exit from the metastable state depends on the initial number of gas germ.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):126-132

126-132

### NON-STATIONARY AXISYMMETRIC PROBLEM OF INVERSE PIEZOEFFECT FOR CIRCULAR BIMORPHOUS PLATE OF STEPPED VARIABLE THICKNESS AND RIGIDITY

#### Abstract

Non-stationary axisymmetric problem for a thin circular bimorphous plate under the action on the end surfaces of electric potential, which is an arbitrary function of time is viewed. On the basis of the theory of Tymoshenko by method of finite integral transformation a new closed solution for the viewed electricity and elastic system of stepped variable rigidity and thickness is built. The obtained calculated correlations allow to explore the frequency characteristics and stress-deformed state of bimorphous elements.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):133-140

133-140

### DYNAMICS OF SELF-OSCILLATIONS IN A TWO-STAGE VAN DER POL OSCILLATOR

#### Abstract

The results of numerical simulation of self-oscillations in a two-stage ring oscillator with active cells of Van der Pol are presented. It is shown that for large exceedances of generation threshold in a system with identical cells, non-uniform spatial distribution of amplitudes of self-oscillations is observed.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):141-146

141-146

### THE MODELLING OF PARAMETRS OF MOTION OF CENTRE OF MASS OF SPACE VEHICLE AND METHODS OF PROCESSING

#### Abstract

A mathematical model of motion of centre of mass of space vehicle is suggested and methods of processing of parameters based on the usage of Kalman filter and combined wavelet filter are also suggested. The results of numerical experiments of defining parameters are presented.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):147-152

147-152

### NEUTRALIZATION, UTILIZATION AND WASTE PROCESSING OF PRODUCTION OF TNT

#### Abstract

In the given article the results of perennial studies on the development of ways of utilization and waste processing of production of TNT are presented. The efficient ways of utilization of wastes at production of clayite, gypsum, water glass and silicious glass are suggested.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):153-166

153-166

### EPHEDRINE AND VERAPAMYLE DENSITOMETRIC ANALYSIS IN JUDICIAL-CHEMICAL EXAMINATION

#### Abstract

In this article the analytical characteristics of method of analysis of ephedrine and verapamyle with application of thin-layer chromatography and densitometry is considered. Detection limit of ephedrine and verapamyle is 10,0 /tg/ml in a sample. The possibility of ephedrine and verapamyle quantitative determination in model samples in the range of 10,0-250,0 /tg/ml concentration is indicated.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):167-174

167-174

175-181

### THE EFFECT OF BIOLOGICALLY ACTIVE COMPONENTS OF HEMOLIMPH OF LARVAE GALLERIA MELLONELLA ON THE ACTIVITY OF ALKALINE

#### Abstract

The effect of low concentrations of peptide compounds of hemolymph of wax moth larvae on the kinetic characteristics of alkaline phosphatase of E.coli is studied. Activating effect of one of the components of chromatographic fractions of hemolymph on the rate of phosphatase reaction after 2-4 minutes after the addition of substrate is disclosed. It is assumed that peptide compounds in small doses can have a regulatory effect on the activity of enzymes of E.coli.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):182-187

182-187

### SEASONAL DYNAMICS OF MICOBIOTA'S LEAF AREA OF TREES IN URBAN TERRITORY

#### Abstract

This article deals with seasonal dynamics of micobiota's leaf area of Acer platanoides and Tilia cordata in Samara Park "Zagorodny". The correlations of seasonal dynamics of micobiota's of leaf area of trees with urban aeromicoflora and physiological characteristics of plants were considered in the article.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):188-195

188-195

### MODULATION OF RESPIRATORY REACTIONS AT ELECTRICAL STIMULATION OF MAGNUS RAPHE NUCLEUS OF MIDDLE SEAM BEFORE AND AFTER MICROINJECTION OF GABAZIN

#### Abstract

In the article the inhibitory effects on respiratory parameters during electrical or chemical stimulation of the magnus raphe nucleus are induced mainly by the participation of GABA. To elucidate the involvement of GABA

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):196-200

196-200

### ON SOME PROBLEMS FOR A LOADED PARABOLIC-HYPERBOLIC EQUATION

#### Abstract

Some problems with various boundary conditions for the loaded mixed type equation in rectangular area are studied. The criterion of uniqueness is established and theorems of an existence of solutions to the problems are proved. The solutions are constructed as Fourier series with respect to eigenfunctions of a corresponding one-dimensional problem.

**Vestnik of Samara University. Natural Science Series**. 2013;19(6):201-204

201-204