# Vol 20, No 10 (2014)

**Year:**2014**Articles:**18**URL:**https://journals.ssau.ru/est/issue/view/221

## Статьи

### EXISTENCE OF POSITIVE SOLUTION OF TWO-POINT BOUNDARY PROBLEM FOR ONE NONLINEAR ODE OF THE FOURTH ORDER

#### Abstract

In the work suﬃcient conditions for existence at least one positive solution of two-point boundary problem for one class of strongly nonlinear diﬀerential equations of the fourth order are received. The problem is considered on a segment [0,1] (more general case of segment[0, a] is reduced to considered). On the ends of a segment the solution of y and its second derivative of y′′ areequal to zero. Right part of an equation f (x, y) isn’t negative at x\geq 0 andat all y. Performance of suﬃcient conditions is easily checked. Performance ofthese conditions is easily checked. In the proof of existence the theory of conesin banach space is used. Also apriori estimates of positive solution, which ispossible to use further at numerical construction of the solution are obtained.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):9-16

9-16

### WELL-POSEDNESS OF POINCARE PROBLEM IN THE CYLINDRICAL DOMAIN FOR A CLASS OF MULTI-DIMENSIONAL ELLIPTIC EQUATIONS

#### Abstract

The boundary value problems for second order elliptic equations in domains with edges are well studied. For elliptic equations, boundary-value problems on the plane were shown to be well posed by using methods from the theory of analytic functions of complex variable. When the number of independent variables is greater than two, diﬃculties of fundamental nature arise. Highly attractive and convenient method of singular integral equations can hardly be applied, because the theory of multidimensional singular integral equations is still incomplete. In this paper with the help of the method suggested by the author, the unique solvability is shown and explicit form of classical solution of Poincare problem in a cylindrical domain for a one class of multidimensional elliptic equations is received.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):17-25

17-25

### NONLOCAL PROBLEM WITH INTEGRAL CONDITION FOR A FOURTH ORDER EQUATION

#### Abstract

In this paper, we consider a nonlocal problem with integral condition with respect to spacial variable for a forth order partial diﬀerential equation. The conditions on the data for unique solvability of the problem in Sobolev space are determined. Proving of uniqueness of generalized solution is based on acquired apriori estimates. To prove the solvability we use a following scheme: sequence of approximate solutions using Galerkin procedure is built, apriory estimates that allow to extract from it a convergent subsequence are received, on the ﬁnal stage it is shown that the limit of subsequence is the required generalized solution.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):26-37

26-37

### ON SPACES OF MODULAR FORMS OF EVEN WEIGHT

#### Abstract

In the article we study the structure of space of cusp forms of an even weight and a level N with the help of cusp forms of minimal weight of the same level. The exact cutting is studied when each cusp form is a product of ﬁxed function and a modular form of a smaller weight. Except the levels 17 and19 the cutting function is a multiplicative eta - product. In the common case the space f(z) M _{k-l}(Γ_{0}(N)) is not equal to the space S_{k} (Γ_{0}(N)), the structure of additional space is competely studied. The result is depended on the value of the level modulo 12. Dimensions of spaces are calculated by the Cohen - Oesterle formula, the orders in cusps are calculated by the Biagioli formula.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):38-47

38-47

### ON THE SUBMODULARITY OF THE PROFIT FUNCTION IN A PROBLEM OF TRANSPORT PLANNING

#### Abstract

In this paper the possibility of using the method of successive calculations to solve the transportation problem on the maximum proﬁt is investigated. The feature of this problem is that a set of consumers isn’t deﬁned and gets out from wider set of possible consumers by the criterion of a maximum of proﬁt. Proﬁt is calculated on the basis of consumer demand and prices, which are determined by the contract between the consumer and the company carrying out transportation. It is shown that this problem is reduced to maximization of the proﬁt function deﬁned on the set of all subsets of consumers. The submodularity of proﬁt function is proved, that justiﬁed application of method of successive calculations to solve this problem.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):48-54

48-54

### METRIC AND TOPOLOGICAL FREEDOM FOR SEQUENTIAL OPERATOR SPACES

#### Abstract

In 2002 Anselm Lambert in his PhD thesis [1] introduced the deﬁnition of sequential operator space and managed to establish a considerable amount of analogs of corresponding results in operator space theory. Informally speaking, the category of sequential operator spaces is situated ”between” the categories of normed and operator spaces. This article aims to describe free and cofree objects for diﬀerent versions of sequential operator space homology. First of all, we will show that duality theory in above-mentioned category is in many respects analogous to that in the category of normed spaces. Then, based on those results, we will give a full characterization of both metric and topological free and cofree objects.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):55-67

55-67

### LINEARLY ORDERED SPACE WHOSE SQUARE AND HIGHER POWERS CANNOT BE CONDENSED ONTO A NORMAL SPACE

#### Abstract

One of the central tasks in the theory of condensations is to describe topological properties that can be improved by condensation (i.e. a continuous one-to-one mapping). Most of the known counterexamples in the ﬁeld deal with non-hereditary properties. We construct a countably compact linearly ordered (hence, monotonically normal, thus ” very strongly” hereditarily normal) topological space whose square and higher powers cannot be condensed onto a normal space. The constructed space is necessarily pseudocompact in all the powers, which complements a known result on condensations of non-pseudocompact spaces.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):68-73

68-73

### DIFFERENCE-DIFFERENTIAL GAME OF CONVERGENCE - EVASION IN HILBERT SPACE, II

#### Abstract

For conﬂict operated diﬀerential system with delay studying of dynamic game of convergence - evasion relatively functional goal set, now regarding evasion and solution of a problem of existence of alternative in the case under consideration is continued. In the work realization of condition of saddle point relatively to the right part of operated system is not supposed. Earlier similar tasks were set and solved for ﬁnite-dimensional space at scientiﬁc school of the academicianN.N. Krasovsky. For a case of inﬁnite-dimensional space of continuous functions similar tasks were considered by the author. In the suggested work at theorem proving about convergence - evasion, the norm of Hilbert space is used.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):74-83

74-83

### CONDITION OF FINITENESS OF COLENGTH OF VARIETY OF LEIBNITZ ALGEBRAS

#### Abstract

This paper is devoted to the varieties of Leibnitz algebras over a ﬁeld of zero characteristic. All information about the variety in case of zero characteristic of the base ﬁeld is contained in the space of multilinear elements of its relatively free algebra. Multilinear component of variety is considered as a module of symmetric group and splits into a direct sum of irreducible submodules, the sum of multiplicities of which is called colength of variety. This paper investigates the identities that are performed in varieties with ﬁnite colength and also the relationship of this varieties with known varieties of Lie and Leibnitz algebras with this property. We prove necessary and suﬃcient condition for a ﬁniteness of colength of variety of Leibnitz algebras.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):84-90

84-90

### DIRICHLET PROBLEM FOR PULKIN’S EQUATION IN A RECTANGULAR DOMAIN

#### Abstract

In the given article for the mixed-type equation with a singular coeﬃcient the ﬁrst boundary value problem is studied. On the basis of property of completeness of the system of own functions of one-dimensional spectral problem the criterion of uniqueness is established. The solution the problem is constructed as the sum of series of Fourier - Bessel. At justiﬁcation of convergence of a row there is a problem of small denominators. In connection with that the assessment about apartness of small denominator from zero with the corresponding asymptotic which allows to prove the convergence of the series constructed in a class of regular solutions under some restrictions is given.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):91-101

91-101

### ON A SUPERCLASS OF A-GRAMMARS

#### Abstract

In this paper we consider a superclass of automaton grammars that can be represented in terms of paths on graphs. With this approach, we assume that vertices of graph are labeled by symbols of ﬁnite alphabet A . We will call such grammars graph-generated grammars or G-grammars. In contrast to the graph grammars that are used to describe graph structure transformations, G-grammars using a graphs as a means of representing formal languages. We will give an algorithm for constructing G-grammar which generate the language recognized by deterministic ﬁnite automaton. Moreover, we will show that the class of languages generated by G-grammars is a proper superset of regular languages.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):102-108

102-108

### MATHEMATICAL MODELING OF A MEDIUM INTERACTION ONTO RIGID BODY AND NEW TWO-PARAMETRIC FAMILY OF PHASE PATTERNS

#### Abstract

Mathematical model of a medium interaction onto a rigid body with the part of its interior surface as the cone is considered. The complete system of body motion equations which consists of dynamic and kinematic parts is presented. The dynamic part is formed by the independent three-order subsystem. New family of phase patterns on phase cylinder of quasi-velocities is found. This family consists of inﬁnite set of topologically non-equivalent phase patterns. Furthermore, under the transition from one pattern type to another one, the reconstruction of topological type occurs by the degenerate way. Also the problem of key regime stability, i.e., rectilinear translational deceleration, is discussed.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):109-115

109-115

### WATERFLOODING FRONT MOVING TASK IN DUAL PERIODICAL AREA: PISTON-LIKE DISPLACEMENT CASE

#### Abstract

Water-oil contact moving task has a high signiﬁcance in a waterﬂooding the- ory: it’s possible to improve oil recovering characteristics due to prediction of ﬂow features for both liquids - oil and water displaced it. There is the simplest mathematical pattern for conjoint oil-water ﬂow presenting: it is called ”versi- color” liquids model and it suggests making oil and water physically identical to simplify solving process for water-oil contact moving task. However, another pattern was used in research described in this paper: it is called pistonlike dis- placement model and it supposes that oil and water physical characteristics, for example, viscosities, may be diﬀerent. As for the oil-keeping reservoir pattern used in this research it was presented as homogeneous and inﬁnity, with ﬁxed thickness: furthermore its surface was covered by dual periodical lattice included production and injection wells in its cells.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):116-129

116-129

### TIME DEPENDENCE OF THE POINT SPREAD FUNCTION OF A FOUR-WAVE CONVERTER IN A WAVEGUIDE WITH THERMAL NONLINEARITY

#### Abstract

The time dependence of a quality of wave-front reversal has been analyzed at four-wave interaction in a waveguide with thermal nonlinearity. The inﬂuence of waveguide parameters and mode structure of pumping waves on time dependence character has been investigated. It has been shown, that increases of number of single-mode pumping waves lead to decreases of diﬀerence in point spread function width in steady state and initial state.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):130-139

130-139

### CONCERNING THE SPACE EXPERIMENT WITH SCIENTIFIC GEAR MRT ON SPACECRAFT ”FOTON-M” № 4

#### Abstract

The short description of scientiﬁc equipment of МРТ (multichannel recorder of temperatures) is resulted and experimental results about current temperatures in local zones of containers of the scientiﬁc equipment, received in 42 daily ﬂight of a space vehicle ”FOTON-M” № 4 are presented. It is shown, that the most essential factors deﬁning a thermal mode in containers of scientiﬁc equipment, their position on the external surface of the spacecraft, focused almost during all ﬂight by panels of solar batteries on the Sun and conditions on coils or, that’s the same, current deviation of a normal to a plane of orbit spacecraft from a direction on the Sun. Thus time numbers of data about values of temperatures have strongly pronounced oscillatory character with the orbital period of movement of spacecraft and with high level of correlation between them, and also dependence values of temperatures from the position of a plane of orbit of a spacecraft concerning the Sun.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):140-152

140-152

### CHROMATOGRAPHIC SPECTRA RETENTION OF VOLATILE COMPONENTS IN THE EQUILIBRIUM VAPOR PHASE OF MEDICINAL PLANTS ”EUCALYPTUS VIMINALISE LABILL”, ”MELISSA OFFICINALIS L.”, ”SOPHORA JAPONICAL L.”

#### Abstract

Gas chromatographic investigation of headspace of starting materials of herbal origin of Melissa (Melissa oﬃcinalis L.), manna gum (Eucalyptus viminalise Labill) and Chinese scholar tree (Sophora Japonical L.) is carriediout. For light constituents retention indices I

_{i}^{T}on capillary column withpolydimethylsiloxane stationary phase in the mode of linear programming oftemperature and relative areas of peaks A_{i;отн}are determined. It is establishedithat gas chromatographic spectrum (complex of values I_{i}^{T}and A_{i;отн}) oflight constituents of headspace has a speciﬁc character and may serve as acharacteristics of authenticity of starting materials of herbal origin.**Vestnik of Samara University. Natural Science Series**. 2014;20(10):153-165

153-165

### ANALYSIS OF NUMBER AND DISTRIBUTION OF SOME TYPES OF MARTEN FAMILY IN THE KINELSKY REGION OF THE SAMARA REGION

#### Abstract

The article provides data on the distribution in the Kinelsky District of the Samara Region of some members of the Mustelidae family (American mink, pine marten, forest polecat and steppe polecat) in three biotopes (lime-oak deciduous forest, fallow lands and ﬁelds, riparian areas of the ﬂoodplain in Samara River valley). It is noted that the traces of American mink were found only in riparian areas near the thawed patches and ﬁshing holes where animals foraging. European pine marten occurs in all biotopes avoiding unforested sites, but the greatest number of traces was observed in the forest. Polecat traces were mostly recorded in the open areas. In the forest, they were observed every year, but in smaller quantities. The work also presents data on the population dynamics of mustelids in the Kinelsky District of the Samara Region in the winter period of 2005-2011.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):166-173

166-173

### TO THE DISTRIBUTION OF ETHMIA DISCREPITELLA (REBEL, 1901) (LEPIDOPTERA, ETHMIIDAE)

#### Abstract

New data of the distribution of little known species - Ethmia discrepitella (Rebel, 1901) are given. The species Ethmia discrepitella (Rebel, 1901), previously known only from Orenburg, Saratov and Altai Area, is found in Samara, Chelyabinsk, and Krasnodar Area. The new data extend the understanding of the distribution of this little-known species. Images of this species ”in nature” are given for the ﬁrst time.

**Vestnik of Samara University. Natural Science Series**. 2014;20(10):174-177

174-177