Vol 18, No 6 (2012)

Articles

THE SPACES THAT CONTAIN MULTIPLICATIVE ETA-FUNCTIONS

Voskresenskaya G.

Abstract

In the article westudythestructureofthespacesofmodularformsthat containthemultiplicativeeta-functions.We find dimensionsandbasises.Wealso studythebehaviorofthefunctionsincusps.
Vestnik of Samara University. Natural Science Series. 2012;18(6):5-12
pages 5-12 views

THE CALCULATING OF MEANINGS OF EIGEN FUNCTIONS OF DISCRETE SEMIBOUNDED FROM BELOW OPERATORS VIA METHOD OF REGULARIZED TRACES

Kadchenko S., Kakushkin S.

Abstract

The numerical method of finding of meanings of eigenfunctions of discrete semibounded from below operator is developed. Estimates of residuals of sums of series of Reley–Schrodinger of the ”weighed” corrections of the perturbation theory are gained. Approbation of the method on the example of Laplace operator with perturbed function of complex variable is produced.
Vestnik of Samara University. Natural Science Series. 2012;18(6):13-21
pages 13-21 views

ABOUT THE BOUNDARY BEHAVIOR OF A CLASS OF POWER SERIES

Korotkov A.

Abstract

In the paper we prove the algebraic values of the radial derivatives at point z = 1 for a class of power series.
Vestnik of Samara University. Natural Science Series. 2012;18(6):22-26
pages 22-26 views

ABOUT A TRANSFORMATION OF SCHWARZ PROBLEM

Nikolaev V.

Abstract

We consider the Schwarz problem for vector-valued functions analytic according to Douglis. We prove that under certain conditions on the matrix this problem is reduced to the Dirichlet problem for some equivalent system of second-order PDEs. The reversebility of transformations is proved, and on that ground the theorem of uniqueness is established. A special case when reduction is impossible is also viewed. The examples are given.
Vestnik of Samara University. Natural Science Series. 2012;18(6):27-34
pages 27-34 views

ON REGULIRATION MULTIPLE EIGENVALUE BY REDUCTION PSEUDOPERTURBATION METHODS

Rakhimov D.

Abstract

On the base of the bifurcation theory methods it is considered the problem of the retaining multiple eigenvalues and relevant eigenvectors and roots elements. An approch is suggested which allows reduce algebraic multiple to unit, that is reduce the problem of the retaining multiple eigenvalues to simple. For construction iterated process applied pseudoperturbation methods.
Vestnik of Samara University. Natural Science Series. 2012;18(6):35-41
pages 35-41 views

NECESSARY AND SUFFICIENT CONDITIONS FOR PRIME PARSEVAL FRAMES

Ryabtsov I.

Abstract

In the article we consider two disjoint classes of frames, prime and composite Parseval frames, the union of which forms a set of Parseval frames. The main goal is to obtain a description of these two classes. In this article we prove necessary and sufficient conditions for the frame to be a prime Parseval frame.
Vestnik of Samara University. Natural Science Series. 2012;18(6):42-48
pages 42-48 views

SLOW INTEGRAL MANIFOLDS WITH A CHANGE OF STABILITY

Simonova T.

Abstract

The paper is devoted to the investigation of slow integral manifolds with a change of stability in the case of vector fast variable. The existence conditions of the gluing function are given. The problem of construction of the integral manifold with a change of stability for systems with vector fast and slow variables is solved.
Vestnik of Samara University. Natural Science Series. 2012;18(6):49-57
pages 49-57 views

UNIFORM EXHAUSTIVITY CRITERIA OF A FAMILY OF VECTOR OUTER MEASURES

Sribnaya T.

Abstract

The uniform exhaustivity criteria are proved for a sequence of exhaustive outer measures defined on the non-sigma-complete class of sets and taking values in an Abelian topological group.
Vestnik of Samara University. Natural Science Series. 2012;18(6):58-65
pages 58-65 views

PARAMETERIZATION OF SLOW INVARIANT MANIFOLDS IN THE MODEL OF THE SPREAD OF MALARIA

Tropkina E.

Abstract

In the paper the Ross Macdonald model of the distribution of malaria is considered. The order reduction of this model on the basis of parametric slow invariant manifolds is realized. As a result a simplified model which describes with a high accuracy the behavior of the solution of the original system is obtained.
Vestnik of Samara University. Natural Science Series. 2012;18(6):66-74
pages 66-74 views

EXPLICIT SOLUTION OF THE MIXED PROBLEM IN ANISOTROPIC SEMISPACE WITH BRIGHTLY EXPRESSED VERTICAL PERMEABILITY FOR BARENBLATT–ZHELTOV–KOCHINA EQUATION

Umarov K.

Abstract

For Barenblatt–Zheltov–Kochina model presentation of filtering of liquids in fissured-porous rocks the explicit solution of the mixed problem in anisotropic semispace with brightly expressed vertical permeability is found by reduction of the considered problem of filtering to the solution of the abstract initial boundary-value problem in Banach space.
Vestnik of Samara University. Natural Science Series. 2012;18(6):75-99
pages 75-99 views

THE THEOREM OF AVERAGING FOR THE ALMOST-PERIODIC FUNCTIONS

Filatov O.

Abstract

It is proved that the limit of maximal mean is an independent variable of initial conditions if a vector exists from the convex hull of a compact set out of a finite-dimensional space and the components of vector are independent variables with respect to the spectrum of almost-periodic function. The compact set is the right hand of differential inclusion. The limit of maximal mean is taken over all solutions of the Couchy problem for the differential inclusion.
Vestnik of Samara University. Natural Science Series. 2012;18(6):100-112
pages 100-112 views

SPATIALLY MODULATED STRUCTURES IN NEMATIC LIQUID CRYSTAL UNDER OSCILLATORY COUETTE FLOW AT ULTRALOW FREQUENCIES

Kozhevnikov E., Samoilova Y.

Abstract

The distortion of homeotropic structure of nematic liquid crystal under the influence of periodic shear at ultralow frequencies is theoretically described. It is shown that periodic shear action results in spatially modulated structure in NLC layer. Threshold shear amplitude and spacial periodicity of new molecular orientational structure are found on the base of nonlinear nematic liquid crystal hydrodynamic equations using Galerkin method. Theoretical analysis shows that at low frequencies threshold shear amplitude does not depend on frequency and the spatial period of the order of NLC layer thickness. Theoretical results are compared with experimental data.
Vestnik of Samara University. Natural Science Series. 2012;18(6):113-123
pages 113-123 views

COMPELLED AXYSIMMETRIC FLEXURAL FLUCTUATIONS OF THICK ROUND RIGID PIEZOCERAMIC PLATE

Shlyakhin D.

Abstract

New closed solution of axisymmetric nonstationary problem of the theory of electroelasticity for thick round piezoceramic 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, the stress-strain state of the testing element, and also the potential and intensity of the induced electric field.
Vestnik of Samara University. Natural Science Series. 2012;18(6):124-135
pages 124-135 views

NONLINEAR RESONANCE IN OSCILLATORY CIRCUIT WITH FRACTAL CAPACITY

Zaitsev V., Karlov A.

Abstract

A model of oscillation circuit containing a nonlinear fractal component of capacity is proposed. The differential equation of motion of fractional order for forced oscillations under the action of an external signal is obtained. An approximate analytical solution of the equation of motion is conducted by methods of equivalent linearization and slowly varying amplitudes. The amplitude-frequency and phase response of fractional oscillator with cubic nonlinearity are analyzed.
Vestnik of Samara University. Natural Science Series. 2012;18(6):136-142
pages 136-142 views

MATHEMATICAL MODELLING OF OPTIMUM CULTIVATION OF BIOLOGICAL CULTURE

Razzhevaikin V., Yusufov A.

Abstract

Questions of optimum control over the process of organization of cultivation of biological culture in the conditions of two-regime cultivates are studied. Ways of acceptance of optimum decisions concerning conveyance of production made in the conditions of one of the ways in the conditions of the second, based on estimations of observable variables are specified.
Vestnik of Samara University. Natural Science Series. 2012;18(6):143-158
pages 143-158 views

SYNTHESIS OF ADAMANTILOXYTRINITROMETHYL-1,3,5-TRIAZINES

Gidaspov A., Burkov S., Kuleschowa I., Bakharev V.

Abstract

The interaction of silver salt of 2-hydroxy-4,6-bistrinitromethyl-1,3,5-triazine with 1- and 2-bromadamantans was studied. The relative 2-adamantyloxy-4,6-bistrinitromethyl-1,3,5-triazines was synthesized for the first time. It was shown that one of trinitromethyl group in 2-adamantyloxy-4,6-bis(trinitromethyl)-1,3,5-triazines could be substituted selectively under the action of various nucleophiles.
Vestnik of Samara University. Natural Science Series. 2012;18(6):159-166
pages 159-166 views

THE EFFECTS OF GASTRIN-RELEASING PEPTIDE MICROINJECTIONS INTO THE PRE-BOTZINGER COMPLEX ON THE RESPIRATORY PARAMETERS OF RATS

Aliev A., Inyushkin A.

Abstract

In the article, the results of investigation of the respiratory effects of gastrinreleasing peptide microjections into the pre-Botzinger complex are presented. It was found that microinjections of neuropeptide induced an increase in respiratory rate, tidal volume, amplitude of diaphragm and external intercostal muscles bursting activity. The statistically significant respiratory responses observed when 10^-5 M of GRP was used, while 10^-8 M of GRP appeared to be sub-threshold and didn’t alter the breathing pattern and activity of inspiratory muscles. The suggested mechanisms of action of GRP at the level of pre-Botzinger complex are discussed.
Vestnik of Samara University. Natural Science Series. 2012;18(6):167-173
pages 167-173 views

INFLUENCE OF STARK SHIFT ON ENTANGLEMNT OF TWO ATOMS WITH DEGENERATE TWO-PHOTON TRANSITIONS

Bashkirov E., Nikiforova Y.

Abstract

The influence of dynamical Stark shift on the entanglement between two atoms prepared in initial W-like states in Tavis — Cummings model with degenerate two-photon transitions has been investigated. The results show that effect of sudden death of entanglement the effect can be weakened for some initial states with taking into account the Stark shift.
Vestnik of Samara University. Natural Science Series. 2012;18(6):174-178
pages 174-178 views

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