# Vol 20, No 7 (2014)

**Year:**2014**Articles:**21**URL:**https://journals.ssau.ru/est/issue/view/222

## Статьи

### PROPERTIES OF DUAL MODULES OVER STEENROD ALGEBRA

#### Abstract

Properties of annulators and modules generated by annulators, including dual modules over Steenrod algebra are studied. Properties of Kroneker pairing are proved using general properties of Steenrod algebra and dual algebra as graded connected Hopf algebras. Isomorphisms between modules generated by annulators and dual modules over dual Stennrod algebra are proved. It is shown that these modules are Hopf comodules induced by coproduct in dual Steenrod algebra. All generators of these modules are found. The method of ﬁnding basis of module of indecomposable elements, viewed as vector space over cyclic ﬁeld for some of the studied modules

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):9-16

9-16

### ON THE UNCERTAINTY CONSTANTS FOR LINEAR COMBINATION OF SOME SUBSYSTEMS OF COHERENT STATES

#### Abstract

Uncertainty constants for coherent states obtain irreduciable value. But problems of interpolation and orthogonalization requires the original system of functions to move to linear combinations. Localization of linear combinations of coherent states subsystems which have been set on a rectangular lattice are studied. Formulas for uncertainty constants of these combinations in general case and at additional assumptions on coeﬃcients are received. Formulas for uncertainty constants of linear combinations of uniform shifts of Gauss function in general case and at additional assumptions on coeﬃcients are received. Results of numerical calculations are given for the interpolating scaling functions constructed for uniform shifts of Gauss function

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):17-31

17-31

### STABILIZATION OF HAMILTONIAN SYSTEMS WITH A GUARANTEED ESTIMATE OF QUALITY OF MANAGEMENT

#### Abstract

Stabilization problem with guaranteed estimate of quality of management of zero solution of nonautonomous Hamiltonian system was solved. It arises from the problem of optimal stabilization by reducing functional requirements for a estimate: instead of minimizing it is only necessary that it excelled to a pre-assessment. The solution is obtained by means of synthesis of active program control, acting to the system, and stabilizing control of feedback. The problem is solved analytically by the direct method of Lyapunov's stability theory with Lyapunov's function with constant sign derivatives. As examples, problems of synthesis and stabilization of program motions of homogeneous rod of variable length and variable-length pendulum in a rotating plane are solved.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):32-44

32-44

### NECESSARY NON-LOCAL CONDITIONS FOR A DIFFUSION-WAVE EQUATION

#### Abstract

In this article, diﬀusion-wave equation with fractional derivative in Rieman- n-Liouville sense is investigated. Integral operators with the Write function in the kernel associated with the investigational equation are introduced. In terms of these operators necessary non-local conditions binding traces of solution and its derivatives on the boundary of a rectangular domain are found. Necessary non-local conditions for the wave are obtained by using the limiting properties of Write function. By using the integral operator’s properties the theorem of existence and uniqueness of solution of the problem with integral Samarski’s condition for the diﬀusion-wave equation is proved. The solution is obtained in explicit form.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):45-59

45-59

### INTEGRABLE SYSTEMS ON TANGENT BUNDLE OF MULTI-DIMENSIONAL SPHERE

#### Abstract

The systems which have ﬁnite-dimensional spheres as the space of positions, are arising in many problems of multi-dimensional dynamics. Accordingly, tan- gent bundles of those spheres become phase spaces of such systems. In the article activity of inductive transition in the system on tangent bundle of low-dimen- sional sphere under increase of its dimension and absence of force ﬁeld is ana- lyzed. At that, nonconservative ﬁelds of forces are presented with the presence of which the systems possess the complete choice of ﬁrst integrals expressing in terms of ﬁnite combination of elementary functions and are, in general, the transcendental functions of its variables.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):60-69

60-69

### ON VARIETIES OF ASSOCIATIVE ALGEBRAS WITH WEAK GROWTH

#### Abstract

We prove that any variety of associative algebras with weak growth of the sequence {c_n(V)}_{n\geq 1} satisﬁes the identity [x_1, x_2][x_3, x_4] . . . [x_2_{s-1}, x_{2s}] = 0 for some s. As a consequence, the exponent of an arbitrary associative variety with weak growth exists and is an integer and if the characteristic of the ground ﬁeld is distinct from 2 then there exists no varieties of associative algebras whose growth is intermediate between polynomial and exponential.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):70-74

70-74

### METHOD OF SEQUENTIAL CHANGINGOF STATIONARY STATES FOR ONE-DIMENSIONAL FILTRATION PROBLEM WITH LIMITING GRADIENT OF PRESSURE

#### Abstract

Taking into account nonlinear eﬀects observed in experiments with low-per- meability layers, at low pressure gradients (e.g., about 105 Pa/m), reﬁnement of Darcy law is proposed. On the basis of this model, by means of method of sequential change of stationary states and the problem of one-dimensional ﬁlter- ing is numerically solved. It is established that approximate solutions received by the method of sequential change of stationary states, for the description of distribution of pressure in layer and a well production, will be agreed with the numerical solution of the equation of a ﬁltration in full statement. The analysis of inﬂuence of pressure gradient q and limiting exponent deﬁning the rate of yield of the nonlinear ﬁltration law to the linear Darcy’s law with increasing pressure gradient γ, on the features of hydrodynamic ﬁelds and well production is carried out.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):75-84

75-84

### QUASISTATIC STATIONARY GROWTH OF ELASTOPLASTICAL CRACK

#### Abstract

The boundary value problem with relations to the theory of ﬂow with non- linear hardening in derivatives stress and strain tensors in the parameter loading is formulated to estimate local mechanical properties in the vicinity of crack tip of mode of loading for plane strain of elastic-plastic material at the stage of quasi-static growth. Complete solutions are obtained by the method of asymp- totic decompositions. The redistribution of stress and strain ﬁelds in the plastic region at quasi-static growing crack for the intermediate structure is investigat- ed. The form of plastic zones was found in the evolution of fracture process of material. We also obtained direct estimates of errors and diameters of con- vergence when dropping residues of series.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):85-95

85-95

### THIN-WALLED STRUCTURES DESTRUCTION AND LOCATION STRAIN ON CHART RIGID-CURRENT

#### Abstract

In this article the model of fracture of thin plates with cracks, which is a con- tinuation and generalization of rocket fuel components model (Leonov-Panasyuk- Dugdale) and based on the idea of plastic zone at the crack tip as the areas in which deformations occur on a rigid scheme of Prager ﬂow.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):96-103

96-103

### VAN DER POL AND RAYLEIGH OSCILLATORS IN DISCRETE TIME

#### Abstract

New discrete displays of classical self-oscillatory systems - Van der Paul and Rayleigh’s oscillators are oﬀered. Displays with the kept temporary characteristics of response of linear system on external inﬂuence are received on the basis of combination of methods of parametrical synthesis and invariancy of pulse char- acteristics of dynamic systems. Examples of generation of regular and chaotic self-oscillations in discrete time are given. For the analysis of self-oscillations in the received discrete systems the method of slowly changing amplitudes is used. The eﬀect of substitution of frequencies in a range of self-oscillations with use of the improved ﬁrst approach is considered.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):104-114

104-114

### ENTANGLEMENT OF ATOMS SUCCESIVELY PASSING A CAVITY TAKING INTO ACCOUNT THE STARK SHIFT

#### Abstract

In the article we consider the influence of dynamical Stark shift on entanglement degree of two atoms with degenerate two-photon transitions successively passing an ideal one-mode cavity. We suppose that the field be prepared in vacuum state and the atoms be prepared in coherent superposition of excited and ground states. Thus it was also supposed that atoms fly by the cavity for identical time. On the basis of exact expression of evolution operator we carried out atom-atom entanglement for different values of two-atom coherence parameters and different values of cavity flight time. It is shown that Stark shift of energy levels can be used for effective control on a degree of atomic entanglement.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):115-124

115-124

### SCENARIO STUDY OF HIGGS BOSON IN THE FRAMEWORK NMSSM

#### Abstract

The questions of implementation in the theory of few Higgs bosons is consid- ered in this article. The corresponding hypothesis, which are the consequences of interpretation of results of LHC-experiments are experienced. Arguments in fa- vor of supersymmetric models are presented. Within the frameworks of NMSSM, estimates for the areas of variation of free parameters of the model are made, masses of Higgs bosons and neutralino, which is a candidate for dark matter particles are calculated. The values of these physical quantities collected in a speciﬁc set can be combined in the so-called scenario study of Higgs boson. Four scenarios in which there is an explanation of existing hypotheses are revealed.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):125-133

125-133

### EXPERIMENTAL INVESTIGATION OF LABORATORY PROTOTYPE OF SPACECRAFT OPTICAL TELESCOPE ASSEMBLY IN LABORATORY CONDITIONS

#### Abstract

In this paper the speciﬁcations of precision system of ensuring thermal regime of spacecraft optical telescope assembly designed for Earth remote sensing are considered. The laboratory model of thermal control system is designed for ex- perimental investigations in the vacuum chamber. Experimental investigations of laboratory model of thermal regime under conditions of simulating space enviroment (low space temperature, direct and reﬂected from the Earth solar ﬂux, Earth heat ﬂux) is carried out. High temperature stability and low power consumption of the system is shown.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):134-144

134-144

### ASSOCIATES OF DOT DEFECTS OF VARIOUS NATURE IN SiC-PHASE OF SEMICONDUCTOR HETEROSTRUCTURE OF SiC//Si, RECEIVEDBY ENDOTAKSIYA METHOD

#### Abstract

One of the main ways of increasing of reliability of sensors of physical quantities on the basis of high-temperature and radiation-hardened heterostructure of β-SiC/Si is the analysis of technological aspects of its forming (endotaksiya) regarding concentration distribution of dot defects of various nature, their probable models of association with participation of foreign impurity. Besides, the analysis of reversible processes of association opens ways of optimization of kinetics of diﬀusive mass transfer at phase transformation of substrate of silicon into a ﬁlm of carbide of silicon. In the article dependences of concentration of neutral defects on factors of supersaturation of gas phase on conditional atomic concentration of carbon, from concentration of foreign impurity are given in a gas phase, from concentration of own defects of various nature having potential of formation of deep levels in the forbidden zone and potential of association. The analysis of the given dependences is made and recommendations about carrying out technological process of formation of diﬃcult heterostructures of diﬀerent function are made.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):145-162

145-162

### METHOD OF REGENERATION OF AZIDE ION

#### Abstract

In this article the results of research devoted to the development of methods of disposal and regeneration of azide ion contained in the liquid wastes are stated. As a rule, all existing methods of disposal of azide ion in the liquid wastes based on its destruction, which is not only economically impractical because it is irretrievably lost, but also dangerous, as this forms an extremely explosive and toxic hydrazoic acid, which signiﬁcantly increases the risk of the process of disposal of liquid wastes. Researches carried out by the authors allowed for the ﬁrst time to suggest an eﬀective method of disposal of azide ion at producing organic azides that consists in deletion of azide ion from reaction mass in the form of azide of quaternary ammonium which is highly active azidating agent and can be eﬀectively used in the processes of getting organic azides. In this case at getting organic azides before its ﬁnishing quaternary amonium chloride is added to the reaction mass.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):163-167

163-167

### PRODUCTION WASTES OF TNT AS AN EFFICIENT RAW MATERIAL FOR GETTING FOAM GLASS

#### Abstract

In the given article results of studies on experimental estimate of possibility of waste recycling of production of TNT in foam glass are presented. Authors for the ﬁrst time demonstrated experimentally that there is a real possibility of using wastes as a feedstock to produce silicate foam glass, which in turn is used for the manufacture of silicate glass foam - one of the most eﬀective and eco- friendly modern heat-insulating materials. Initial raw charge used for producing silicate glass comprises a third waste, which signiﬁcantly reduces the cost of resulting foam glass. For puriﬁcation of gaseous discharges formed from the manufacture of original silicate glass from nitrogen oxides, an eﬃcient thermal method for neutralizing them on the basis of active carbons is ﬁrst suggested. It is shown by experiments that the highest possible degree of cleaning (≈ 98 %) in the present process can be achieved at 580-600 ◦C.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):168-176

168-176

### ASSESSMENT OF QUALITY OF RENDERING PALLIATIVE CARE TO THE ONCOLOGY PATIENTS

#### Abstract

The analysis of prevalence of cancer in the world, in Russia and on the territory of the Samara Region. The results of analysis of neglect of oncological diseases in the Samara region; the results of regression analysis of growth of oncological diseases are presented. The organization of rendering palliative care in the Samara Region is studied and assessment of provision of palliative patients with berths is carried out. The estimate of provision of patients with malignant neoplasms with drugs for pain management. Factors that reduce the quality of rendering of medical assistance to the oncology patients are revealed. Directions of improving the quality of pharmaceutical care of patients with cancer are suggested.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):177-187

177-187

### SOME ADDITIONS CONCERNING SCHIVERECKIA PODOLICA (BESS.) ANDRZ. EX DC. IN THE SOROCHINSKIE HILLS OF THE SAMARA REGION

#### Abstract

The data on two new populations of Schivereckia podolica on the Sorochenskie Hills along the rocky foot of Barsuk limestone massive are given in the article. High-altitude limits of Schivereckia podolica dispersion are revealed for two independent populations on Barsuk mountain (46-103 and 55-104 meters correspondingly) also as the total high-altitude diapason of Schivereckia podolica dispersion in Sorochinsky mountains (46-104 meters). The origin of two new found populations is presumably connected with the known before Schivereckia podolica population disposing on the high salient slope of Barsuk mountain from where the seeds can be drive by wind and water. Flower-bud formation and early ﬂowering of Schivereckia podolica on the Sorochinskie Hills dates from the middle of April, mass ﬂowering takes place at the end of April - beginning of May, ﬂowering ﬁnishes in the middle of May. In the summer of 2013 the most of plants formed fruits in the last ten days of May and dispersed seeds from the last ten days of June up to the beginning of July. We revealed the eﬀects of autumn ﬂower-bud formation and reﬂorescence from 28.10.2013 to 22.11.2013.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):188-196

188-196

### ASSESSMENT OF RELATIVE LIFE CONDITION OF PLANTATIONS OF DROOPING BIRCH (BETULAPENDULA ROTH.) AND BALSAM POPLAR (POPULUS BALSAMIFERA L.) IN INDUSTRIAL AND RESIDENTIAL AREAS OF STERLITAMAK INDUSTRIAL CENTER

#### Abstract

Determination of relative life condition of tree plantations allows to evaluate the suitability of certain trees and plants to the eﬀects of technogenic environmental factors. Plantations of drooping birch and balsam poplar in the industrial and residential areas of Sterlitamak industrial center are investigated. At collection and processing of factual material conventional methods of study of tree plantations are used. Instrumental (diameter, height, age) and visual determination (crown density, degree of leaf damage, presence of dead branches) of diagnostic parameters are carried out. An assessment of relative life condition is carried out.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):197-206

197-206

### TWO-CLASSIFICATION ARTIFICIAL IMMUNE SYSTEM

#### Abstract

In the article the practical aspect of application of principles of biological immune system for solving the problem of analysis and classiﬁcation of email is viewed. In the capacity of analyzed emails ordinary emails (electronic mail) and mails from closed systems (electronic document ﬂow or business management systems) were taken. In the article two-classiﬁcation artiﬁcial immune system was developed with further comparison of eﬀectiveness of their usage with naive Bayesian classiﬁcation algorithm. Practical realization of the developed system with the application in the system of analysis of emails of the commercial structure is carried out.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):207-220

207-220

### METHOD FOR ESTIMATION OF VITALITY OF ALLOCATED INFORMATION SYSTEMS

#### Abstract

The method refers to the information security domain of information networks and can be used at a comparative estimation of information networks structures in order to determine their stability to the failures, caused by the impact of random or deliberate interferences. The destination is to improve results reliability of comparative estimation of information networks structures. To achieve technical result the dynamics of impact of random or deliberate interferences on information network nodes and also possibilities on communication recovery between transit nodes of information network are consider. For this purpose values of indexes of availability of information network nodes, time of achievement of critical ratio of "dangerous"and "safe"nodes for each variant of connection of subscribers, and also connectivity of adjacent "dangerous"nodes forming chains, eliminating exchange between subscribers are calculated.

**Vestnik of Samara University. Natural Science Series**. 2014;20(7):221-232

221-232