# Vol 21, No 3 (2015)

**Year:**2015**Articles:**17**URL:**https://journals.ssau.ru/est/issue/view/219

## Статьи

### Problem on vibration of a bar with nonlinearsecond-order boundary damping

#### Abstract

In this paper, we study the initial-boundary problem with nonlinear dynam- ical boundary condition for the pseudohyperbolic equation. This problem repre- sents a mathematical model of longitudinal vibration in a thick short bar with dynamic nonlinear second-order boundary damping. The existence and unique- ness of a generalized solution are proved. The proof is based on a priori estimates and Galerkin procedure. This approach allows to construct approximation in the suitable for practical application form.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):9-20

9-20

### On almost nilpotent varieties in theclass of commutative metabelian algebras

#### Abstract

A well founded way of researching the linear algebra is the study of it using the identities, consequences of which is the identity of nilpotent. We know the Nagata-Higman’s theorem that says that associative algebra with nil condition of limited index over a ﬁeld of zero characteristic is nilpotent. It is well known the result of E.I.Zel’manov about nilpotent algebra with Engel identity. A set of linear algebras where a ﬁxed set of identities takes place, following A.I. Maltsev, is called a variety. The variety is called almost nilpotent if it is not nilpotent, but each its own subvariety is nilpotent. Here in the case of the main ﬁeld with zero characteristic, we proved that for any positive integer m there exist commutative metabelian almost nilpotent variety of exponent is equal to m.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):21-28

21-28

### On the solvability of spatial nonlocal boundary value problemsfor one-dimensional pseudoparabolic and pseudohyperbolic equations

#### Abstract

In the present work we study the solvability of spatial nonlocal boundary value problems for linear one-dimensional pseudoparabolic and pseudohyperbolic equations with constant coeﬃcients, but with general nonlocal boundary conditions by A.A. Samarsky and integral conditions with variables coeﬃcients. The proof of the theorems of existence and uniqueness of regular solutions is carried out by the method of Fourier. The study of solvability in the classes of regular solutions leads to the study of a system of integral equations of Volterra of the second kind. In particular cases nongeneracy conditions of the obtained systems of integral equations in explicit form are given.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):29-43

29-43

### On one problem with dynamic nonlocal condition for ahyperbolic equation

#### Abstract

In this article, boundary value problem for hyperbolic partial diﬀerential equation with nonlocal data in an integral of the second kind form is considered. The emergence of dynamic conditions may be due to the presence of a damping device. Existence and uniqueness of generalized solution is proved in a given cylindrical ﬁeld. There is some limitation on the input data. The uniqueness of generalized solution is proved by apriori estimates. The existence is proved by Galerkin’s method and embedding theorems.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):44-52

44-52

### Keldysh problem for Pulkin’s equation in a rectangular domain

#### Abstract

In this article for the mixed type equation with a singular coeﬃcient Keldysh problem of incomplete boundary conditions is studied. On the basis of property of completeness of the system of own functions of one-dimensional spectral prob- lem the criterion of uniqueness is established. The solution is constructed as the summary of Fourier-Bessel row. At the foundation of the uniform convergence of a row there is a problem of small denominators.Under some restrictions on these tasks evaluation of separation from zero of a small denominator with the corresponding asymptotics was found, which helped to prove the uniform con- vergence and its derivatives up to the second order inclusive, and the existence theorem in the class of regular solutions.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):53-63

53-63

### Global theorem of existence and uniqueness of the ﬁrstboundary value problem for nonlinear integrodiﬀerential equations ofparabolic type

#### Abstract

Global theorem of existence and uniqueness of solution of the ﬁrst boundary value problem for nonlinear integrodiﬀerential equation of parabolic type is proved. If the right-hand side of the equation is integrally bounded, then we have estimate of the norm of the diﬀerence of two solutions, which implies continuous dependence of solution on the initial function and uniqueness of so- lution of the ﬁrst boundary value problem. The problem under consideration generalizes the real model for measuring the level of incompressible ﬂuid in the fuel tanks missiles. Therefore, such problem have a current application.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):64-72

64-72

### Digital image processing in interference-optical methodsof solid mechanics

#### Abstract

In the paper the detailed review and comparison of modern methods of digital object processing in present-day interference optical techniques (namely, photomechanics) are given. The methods of fringe thinnig, fringe clustering, fringe tracing are discussed. Applications of methods to digital photomechanics and fracture mechanics parameter determination are considered. The example of cracked semidisc for compression is analyzed.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):73-87

73-87

### Models for measuring the liquid level in thetank of rocket carrier

#### Abstract

The models for measuring the level of a viscous incompressible ﬂuid in the tank by liquid level in the measuring tube are considered. The tank is in the gravitational ﬁeld and the level of liquid inside varies according to some law. The base model is the ﬁrst boundary value problem for nonlinear integro-diﬀerential equation of parabolic type. The empirical model is Cauchy problem for nonlinear ordinary second order diﬀerential equation. It is numerically founded that for linear time-decreasing level of ﬂuid tank ﬂuid level in the measuring tube oscillates about level in the tank with damping amplitude.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):88-96

88-96

### Modeling the motion of a spherical drop into a laminarboundary layer using Ansys Fluent

#### Abstract

The article provides a formulation to the problem of spherical drop motion into laminar boundary layer over a ﬂat semi-inﬁnite plate (Blasius problem). The paper presents the solution in the package Ansys Fluent without taking into account deformation and rotation of drops. The article describes building of geometric area, construction of the grid models, boundary and initial conditions statement, methods of solution, course of computation. The article describes the examples of problem solving for various initial conditions of a drop, compares the results obtained using diﬀerent methods. There is good agreement between the results. A combination of diﬀerent methods for solving similar problems is the guarantee of a successful solution.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):97-105

97-105

### Incremental analysis of the twoaxial loading of the platewith central circular hole: shakedown (accomodation), alternating plasticity,ratcheting

#### Abstract

In the article the results of ﬁnite element calculations for the determination of stress-strain state of elasto-plastic plate with central circular hole which is under the action of cycle loading are presented. Incremental and direct methods of deﬁning asymptotic behaviour of the structure: adaptability, alternating plas- ticility and progressive plastic ﬂow are presented. In the package Simulia Abaqus incremental cyclic loading of samples with stress concentrators is performed.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):106-124

106-124

### On the nonlinear eigenvalue problems arising in fracturemechanics

#### Abstract

In the article the stress-strain state near a Mode II crack tip under plane stress conditions in power-law materials is considered. It is noted that nowadays the whole eigenspectrum and orders of stress singularity at the crack tip for a power-law medium are of prevailing interest. Additional eigenvalues for the stress ﬁeld at a static mode II crack under plane stress condition are numerically obtained for diﬀerent values of the exponent n via the Runge-Kutta method in conjunction with the shooting method. However, in this case the shooting method is multi-parameter since it is necessary to select two parameters and, consequently, the results obtained require further veriﬁcation and justiﬁcation. For this purpose the technique developed in perturbation theory for study of nonlinear eigenvalue problems is oﬀered and applied for eigenvalue problems arising from fracture mechanics analysis.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):125-139

125-139

### Connection of diﬀerent parametrizations of theproton electromagnetic current operator in discrete symmetries violation case

#### Abstract

In this paper ﬁeld and canonical parameterizations of matrix elements of proton electromagnetic current operator in discrete symmetries violation case were reviewed. The main principles of ﬁeld and canonical operator parameteri- zations were described. The connection between proton form-factors in ﬁeld and canonical parametrization has been constructed. Physical interpretation of the proton electromagnetic current odd part formfactors in canonical parametriza- tion has been obtained. Opportunity of using obtained results for solving the actual problems of proton electromagnetic structure theory - the non-rosenbluth ep-scattering problem and the proton radius puzzle - was discussed.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):140-152

140-152

### Research of chromatographic spectra of retention oflight components of headspace of medicinal herbs ”Lavandula Spica”, ”Menthapiperita L.”, ”Artemisia dracunculus L.”

#### Abstract

On the example of research of chromatographic spectra of retention of light components of headspace of medicinal herbs of lavender (Lavandula Spica), peppermint (Mentha piperita L.) and estragon (tarragon herb, Artemisia dracunculus L.), the possibility of express estimate of their authenticity per totality of retention index of light components in the mode of linear programming of temperature on capillary column with polydimethylsiloxane stationary phase with the use of present in the laboratories available gas chromatographic equipment with ﬂame ionization detector is shown.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):153-163

153-163

### Analysis ofmulticomponent mixture on the example of the drug ”Pentalgin” bythe methods of TLC and IR-Fourier spectrometry

#### Abstract

The deﬁnition of a qualitative composition of multicomponent drugs ”Pen- talgin” and ”Pentalgin ICN” by TLC and IR-spectrometry is carried out. It is shown that using just TLC or just FT-IR spectrometry does not allow us to identify all the major components. It has been proposed an authentication scheme, which includes the steps of isolating of the test components, their sep- aration by TLC, followed by extraction of components and deﬁnition by FTIR spectrometry. The combination of these two techniques allows to separate and identify almost all the most important components of the mixture.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):164-173

164-173

### Diﬀerentiation of the four-reciprocal system Li, Na // F, Br, NO3 using innovative methodology

#### Abstract

Systems with participation of nitrates and halogenides of alkaline metals ﬁnd more and more broad practical application.The four-component mutual system Li, Na // F, Br, NO3 is for the ﬁrst time described and studied. With the use of innovative methodology of research for the system Li, Na // F, Br, NO3 the model of a tree of phases conﬁrmed experimentally with the DTA method is constructed. The power-intensive three- fold eutectic structure of LiF-LiNO3-NaBr with a temperature of melting of 220,8 ◦C for application as the medium temperature heataccumulator is revealed.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):174-180

174-180

### Morphological variability of generative shoots of Nepeta grandiﬂora M. Bieb. in natural conditions andat introduction

#### Abstract

Interpopulation variability of Nepeta grandiﬂora M. Bieb. in the nature and in the conditions of an introduction based on complex of morphological fea- tures of generative shoots was studied. Assessment of investigational traits of generative shoot of N. grandiﬂora showed reducing the size of annual shoots altitude of growth in natural conditions, and introduction. The reproductive ef- fort and leaf-bearing have not always in positive correlative communication with productivity of shoots. It was detected that the weight traits of shoots have a high level of variability in all populations under various conditions of growth. The data obtained are of interest for understanding the mechanisms of adaptive reactions of introduced plants and may be used for introduction forecasting.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):181-188

181-188

### Mycobiota of the snow cover of the territory of Samaracity

#### Abstract

The article presents a characterization of mycobiota of the formed snow cover in Samara in 2013 and 2014. In the snow cover of suburb, uncontaminated areas of coastal parks Strukovsky and Zagorodnyi micromycetes were detected in the form of single colonies, or were not detected at all. Increase of microscopic fungi in the snow cover of the city (42 CFU/ml) was observed on the territories bordering highways, streams of people, that is due to the horizontal transfer of air masses. The composition of dominant micromycetes of the snow cover (a measure of occurrence was greater than 60 %) in 2013 and 2014 varied considerably and depended on the climatic conditions of the previous warm period of the year and the strength of the current winter frosts. Subdominant (incidence below 11 %), of the snow cover in winter periods studied were similar and were the fungi of the genus Alternaria, constantly prevailing in mycobiota air environment of the city in the summer-autumn period.

**Vestnik of Samara University. Natural Science Series**. 2015;21(3):189-197

189-197