Vestnik KRAUNTS. Fiziko-matematicheskie nauki

8-16

Authors: Yu. B. Bashkuev, V. R. Advokatov, D. G. Buyanova, M. G. Pushkarev, M. G. Dembelov

An analysis of the amplitude and additional phase ϕadd of the additional field of the VLF ADN RNS RSDN-20 field during strong magnetic storms and solar flares from September 1-12, 2017 was carried out. Paths of the latitudinal strike were inves-tigated: 1 “Novosibirsk — Ulan-Ude”, length — 1580 km; 2 “Komsomolsk-on-Amur — Ulan-Ude”, length — 2080 km. Daily variations of the median amplitude of radio signals of 11.9 and 14.88 kHz on tracks 1 and 2, obtained after decimation and transmission of the measurement array through the digital smoothing polynomial Savitsky – Golay filter, are considered. The field calculations in the Earth-ionosphere waveguide are presented. Analysis of the propagation conditions of radio waves during magnetic storms and solar flares revealed significant differences in the spatial amplitude-phase phenomena in normal and anomalous geomagnetic conditions at frequencies of 11.9 and 14.88 kHz when propagating along spatially separated paths of latitudinal strike. The main factor influencing the parameters of the VLF signal in the Earth-ionosphere waveguide during heliogeophysical disturbances is the increase in the electron concentration in the D layer of the ionosphere and the associated change in the waveguide geometry.

24-33

Authors: V. N. Marichev, D. A. Bochkovsky

This article presents a study of the vertical temperature distribution over Tomsk, carried out in disturbed and calm periods of the year for 2012-2015. Based on the accumulated experimental material, a number of features of the intra-annual dynamics of the stratospheric thermal regime were established. So, winter stratospheric warming occurs annually. During this period, two strong (major) warmings of the winters of 2009/10 and 2012/13 were recorded, during which the transfer of air masses from the western to the eastern in the upper atmosphere, and four weak (minor) airflows, were winters 2011/10, 2012 /11, 2014/13 and 2015/14 Over many years of observations, it has been shown that for the region of Western Siberia for a long period of the year April-November, in the overwhelming majority of cases, the vertical temperature distribution is in good agreement with the model CIRA-86 distribution.

42-54

Authors: G. G. Petrova, I. N. Panchishkina, A. I. Petrov, O. G. Chkhetiani, E. V. Egorov, V. A. Boldyreva

The atmospheric-electrical measurements results obtained from 2012 to 2017 at the Laboratory of Geophysical Research of the Department of Physics of the Southern Federal University are discussed. Long-term studies allow us to typify the observed atmospheric electrical profiles. According to measurements of the potential gradient in the surface layer, the form of electric field vertical profiles indicates the presence of negative space charge layers in the lower atmosphere. A possible interpretation of their appearance is based on the fact that the volumetric charges of light ions near the earth are adsorbed by aerosols. Charge accumulation on aerosols promotes the long-term presence of charged layers in the surface atmosphere, which affect the spatial distribution of the electric field and its magnitude. Measurement of aerosols concentration of submicron and micron ranges in expeditions after 2012 supplemented the measuring complex. The results of regression and dispersion analysis of the potential gradient connection with the content of aerosols in the surface atmosphere are presented. The role of humidity in the aerosol formation and the possible indirect influence of this factor on the atmospheric electric field variations are considered.

62-73

Authors: P. V. Muratov, O. P. Rulenko, Yu. V. Marapulets, A. A. Solodchuk

For the first time, a joint electrical and acoustic response of near-surface sedimentary rocks to deformation during the eartquake seismic waves passage was detected. The results of the time-frequency analysis of this response of four earthquakes of South Kamchatka with magnitude 4.9–7.2 at the epicentral distance of 100–200 km were presented. The dependence of the responce on the earthquake magnitude was found.

83-98

Authors: A. S. Zakupin, E. P. Semenova

the seismic regime of southern Sakhalin before the Krillon earthquake on April 23, 2017 (Mw=5.0) was Investigated. Seismic hazard calculations were carried out within the framework of the LURR (load-unload response ratio) method. According to the catalog of the local network of field stations, the precursor of earthquake preparation at the end of 2015 was determined. The process of relaxation in the focal zone was studied according to the data of aftershock activity during 2017.

115-129

Authors: V. N. Uvarov, I. A. Larionov, E. I. Malkin

The geological environment of the earth’s crust is considered as a non-equilibrium active open system. It is shown that the rock is a favorable medium for the occurrence of seismic-acoustic oscillations and unfavorable for the occurrence of electromagnetic oscillations in the low-frequency region. It is shown that the analysis of known mechano-electromagnetic mechanisms, explaining the existence of electromagnetic radiation accompanying earthquakes, is deformation-induced dipole radiation, the intensity of which is determined by both the nature of the movements and the electrophysical properties of the rock. An analysis of two-dimensional histograms of crustal deformations and natural electromagnetic radiation made it possible to identify several clusters corresponding to stable conditions of mechano-electromagnetic transformations, which can be explained by the nature of mechano-electromagnetic properties of the rock in the deformation sites. A joint analysis of the catalog of earthquakes and electromagnetic radiation signals made it possible to isolate electromagnetic signals of lithospheric origin.

10-18

Authors: S. Z. Dzhamalov

In the present work, the problems of correctness of inverse problem for the multidimensional equation mixed type of the first kind of the second order with periodic conditions are considered. For this problem, the theorems on existence and uniqueness of the solution are proved in a certain class by «e-regularization»; a priori estimations and of successive approximations methods.

29-39

Authors: M. Mamajonov

In this paper, one boundary task for the equation of the fourth order of a parabolo-hyperbolic holotype look ∂/∂y(a2 ∂/∂x +b2 ∂/∂y) (Lu) = 0 is put and investigated in pentagonal area. Unequivocal resolvability of this put task is proved by methods of creation of the decision, the integrated and differential equations

50-53

Authors: О. Kh. Masaeva

The uniqueness theorem for the solution of the Dirichlet problem for a multidimensional partial differential equation of fractional order in an unbounded domain is proved. The equation under study is an equation of the second order elliptic type when the orders of fractional derivatives are integer.

61-65

Authors: L. M. Eneeva

In the paper, we investigate solvability of the Neumann problem for an equation with fractional derivatives with different starting points. An estimate for the first nonzero eigenvalue is found.

90-96

Authors: G. M. Vodinchar, A. S. Perezhogin

A model of high stress zone in the medium with point sources in the form of double forces is presented. Linear and nonlinear dilatancy criteria is calculated on data from the seismic Havard CMT catalog. Using the example of a visco-elastic model, power laws are constructed for the promotion of deformations under constant stress in a medium. A computational scheme is presented on the basis of finding the fractional degree of the operator of a system of algebraic linear equations.

109-116

Authors: V. Ch. Kudaev, A. K. Buzdov

The methods of modeling and optimization of long pipelines built into the urban water supply network, based on engineering practice, are presented.

127-132

Authors: L. I. Serbina

In the framework of the development of search methods for effective approximate analytical methods for solving a generalized nonlinear partial differential equation of second order of parabolic type, which is the basis for solving long-term forecast problems of groundwater regime, a method of its reduction to linear differential equations of mixed type with associated boundary integral conditions.

148-157

Authors: M. A. Bagov

This paper presents optimization algorithms and methods for Steiner flow network problem employing optimal rank dynamic mode decomposition.

166-177

Authors: F. A. Karova

Solution of boundary value problems for the Haller equation in differential and difference settings are studied. By the method energy inequalities, a priori estimates are obtained for the solution of the differential problems.

186-196

Authors: V. Yu. Osipov, A. I. Vodyaho, A. B. Tristanov, N. A. Zhukova, O. O. Lukovenkova

The problems of model synthesis according to data received by monitoring object state are considered in this article. The current state of the object and its state at different time intervals are of interest. Known models and methods of linking information elements are analyzed. Approach to the synthesis of models using relatively finite automata is proposed.

208-212

Authors: A. M. Shkhagapsoev

The boundary value problems for the third-order equation of parabolic type with fractional derivative of Caputo are considered. The uniqueness and existence of a generalized solution of the boundary value problem with a non-local Samara condition for the equation with multiple characteristics with a spectral parameter is proved by the method of energy inequalities.

226-234

Authors: Yu., V. Shevchenko

The regional network of seismic stations in Kamchatka provides continuous observations of the seismicity of the Kamchatka region and the fulfillment of tasks within the framework of the Emergency Seismic Reporting Service, Tsunami Warning Service and seismic monitoring of volcanoes in order to predict eruptions and monitor their condition. A brief description of calibration methods and organization of the metrology data structure at seismic stations in Kamchatka are presented.

14-18

Authors: A. Kh. Attaev

In this paper, we consider the Goursat problem for a loaded hyperbolic equation with the wave operator in the principal part. We prove the uniqueness and existence of solution for the problem under study, and give the solution in the closed form.

27-35

Authors: M.R. Golava

We study rate of approximation of Valle Poussin means of Fourier series in generalized Holder spaces.

42-47

Authors: F. T. Bogatyreva

We discussed the problem of solvability of initial value problem for one model ordinary differential equation of fractional order. It is shown that the dimension of the kernel depends on the distribution parameters of Dzhrbashyan-Nersesyan operators and also can be trivial.

57-66

Authors: L. L. Karasheva

We construct a representation of the solution for higher order parabolic equation with time fractional derivative in the half-strip and prove uniqueness theorem in the class of fast-growing functions.

76-82

Authors: M. O. Mamchuev

For a system of first-order equations with partial derivatives of fractional order in the Riemann-Liouville sense, we give a correct statement of the Cauchy problem in the case when the matrix coefficient in the main part has only positive eigenvalues.

91-97

Authors: R. A. Pshibikhova

In this paper we prove a theorem of existence and uniqueness of solutions of the Darboux problem for the generalized telegraph equation of fractional order with Riemann-Liouville derivatives.

106-115

Authors: E. A. Korchagina

The methods of statistical modeling are used to define the tendencies of climate elements dynamics. Degree of stability completeness of the tendencies was estimated by means of coefficient of ranks correlation of Ch. Spearmen. It is received that in dynamics of the average annual and seasonal sums of an atmospheric precipitation and air temperature in mountain zone KChR the tendency of increase in summer temperature during 1959-2017 and also summer and annual air temperature during 1976-2017 are statistically significant. Degree of stability completeness is moderate.

124-130

Authors: F. M. Losanova, R. O. Kenetova

In this paper, we consider a mathematical model describing population dynamics in view of the sexual structure. We obtain a nonlinear convolution equation for determining the density of family pairs, and discuss approaches to its solution.

140-147

Authors: A. A. Sokurov

In the current paper we consider a small liquid drop resting on a horizontal smooth surface with the effect of gravity and wich is in thermodynamic equilibrium with its own vapor. Taking into account the size dependence of the surface tension systems of nonlinear firstorder differential equations describing the droplet profile are obtained . The relation between the coordinates of an arbitrary point on the surface of the drop and the volume is found. All obtained equations and formulas go over to the earlier known if the parameter responsible for the size effect equals zero.

158-167

Authors: B. A. Ashabokov, I. D. Taisaev, M. Kh. Shkhanukov-Lafishev

This paper considers a locally one-dimensional scheme for a parabolic equation of general form in a p-dimensional parallelepiped.To describe coagulation processes in the cloud, the equation under study involves a non-local source of a specific type [1]. An a priori estimate for the solution to the locally one-dimensional scheme is obtained and its convergence is proved. Sign definiteness for the operator in the principal part of the equation is not assumed.

180-183

Authors: R. A. Zhilov

The solution of the classification problem is becoming more urgent due to the development of technology and the growth of the processed data volumes. The use of neural networks is mandatory when solving classification problems, because Neural networks have the ability to identify significant features and hidden patterns. The advantages of a logical neural network are: higher classification accuracy, higher learning and retraining.

190-194

Authors: E.V. Shmatova

In this paper, we propose a method of applying continuous logic to identify data ejections in order to eliminate noise and erroneous values.

8-19

Authors: R. I. Parovik

In the training course of the theory of differential equations, there exists a section on the investigation of the stability of systems of differential equations. If the system of differential equations consists of differential equations of integer order, then the stability theory of Lyapunov is usually used to study the stability of their rest points. However, in the case when the system of differential equations consists of differential equations of non-integer order, then it is necessary to use other methods of investigating the stability of such systems. Therefore, this article is devoted to the method of investigating the rest points of systems of differential equations of fractional order. In this paper we will investigate the stability of the rest points of the hereditary dynamical systems by the example of some fractal oscillators. Moreover, we will consider two types of hereditary dynamical systems: commensurable and incommensurate, for which the corresponding stability theorems for rest points are valid. Next, examples of applying these stability theorems to a fractal linear oscillator, the Duffing fractal oscillator, are considered. The results of the study of the stability of the rest points of the hereditary dynamical systems were confirmed by constructing phase trajectories for the fractal oscillators under consideration. This article can be useful in the study of a fairly new section in the theory of differential equations-fractional calculus.

28-32

Authors: A. A. Nabokin

This article describes the problem of creating scientific services based on web technologies. The implementation of the software complex of processing of atmospheric phenomena data at different heights is presented. The software package uses the method of elastic light scattering, atmospheric model NRLMSISE-00 and fork of this model, to get a ratio of scattering at heights from 0 to 150 kilometers.

45-52

Authors: M. I. Garapov

In this article, the problem of using distributed computing systems for solving global projects of simulation simulation and mathematical calculations is considered. Also, in the historical example, the use of BOINC distributed computing in practice is considered. The problems of practical implementation of distributed computing projects and ways to solve them are identified. A distributed computing server and a test task to it have been created. Implemented a system of network services and interaction of project users with the database.

71-84

Authors: Y. I. Senkevich, M. I. Gapeev

We present a technology of creation of visual application design environment for hardwaresoftware complexes (VDE HSC) aimed at acoustic and electromagnetic emission signal processing and analysis. The technology includes the operations of block visual design method with auto-negotiation of interblock connection, method of modeling and design tools integration by connection devices of known and self-developed instrumentation means and algorithms of inner-established blocks. The obtained effect from application of the created environment will allow the researches of laboratories to avoid the necessity of obtaining new special knowledge not referring to their experience and to simplify significantly application of functional modules and electronic libraries of universal design environments built in the developed program interface wrapper, on one side, and to create acting experimental units ready for operation when its structural scheme has been drawn, on the other side. The results of the investigations on implementation and extending the capabilities of experiment software environment receive practical approval at the Laboratory of Acoustic Research of the Institute of Cosmophysical Research and Radio Wave Propagation (IKIR FEB RAS).

100-111

Authors: V.V. Kuznetsov

The author in recent years is developing a shock-wave model of the earthquake. The shock wave (SW) at the time of the earthquake is formed when the structural phase transition is realized in the hypocentre region, it comes to the surface of the Earth and is reflected. In this case, a reflected wave of expansion (discharge) appears, directed opposite to the shock wave. The interaction of these waves leads to strong movements: surface ruptures, decompaction of the ground, its vibrational movements, and so on. It is known that earthquakes and volcanic eruptions are «related phenomena». They occur on Earth, as a rule, in the same place (for example, on the coast of the Pacific Ocean). Analyzing the seismic wave pattern under the source of volcanoes, one can see that in most cases the magmatic source does not have roots that go into the mantle to the outer core of the Earth. The question arises, how is an magma chamber isolated from the outside world created, and how does magma preheat it? As you know, there is no sound answer. In this work, a fundamentally new model of the volcano is proposed, according to which the origin of the magma chamber and its regular «feeding»by energy occur due to shock waves exactly the same as those that cause earthquakes. The shock wave, which leads to an earthquake, spreads in an elastic medium and comes to the Earth’s surface with practically no loss of energy and when it leaves the earth’s surface it destroys it. If the hydrocarbon meets in its path an inelastic (eg porous or liquid) medium in which an unloading wave occurs, then the shock wave dissipates with heating of the medium and the formation of a magmatic source. It is obvious that on the surface of the Earth in this case the SW leaves a completely different «trace and this will already be a volcano.

128-144

Authors: T.P. Yakovleva

In the article the control work on the discipline «Theory and technology of development of mathematical representations in children»is presented. It covers: 25 options; methodical recommendations on writing, execution and execution of the test work.

6-20

Authors: Ю.П. Апаков

Для параболо-гиперболического уравнения исследуются трехмерный аналог задачи Трикоми с нехарактеристическими параллельными плоскостями изменения типов уравнения. Единственность решения задачи доказана методом априорных оценок, а существование решения задачи сведено к существованию решения системы интегральных уравнений Вольтерра второго рода.

32-47

Authors: Anvar Hasanov, Maged G. Bin Saad, Ainur Ryskan

Horn [1931, Hypergeometrische Funktionen zweier Veranderlichen, Math. Ann.,105(1), 381-407], (corrections in Borngasser [1933, Uber hypergeometrische funkionen zweier Veranderlichen, Dissertation, Darmstadt], defined and investigated ten second order hypergeometric series of two variables). In the course of further investigation of Horn’s series, we noticed the existence of hypergeometric double series H*2 analogous to Horn’s double series H*2. The principal object of this paper is to present a natural further step toward the mathematical properties and presentations concerning the analogous hypergeometric double series H*2 Indeed, motivated by the important role of the Horn’s functions in several diverse fields of physics and the contributions toward the unification and generalization of the hyper-geometric functions, we establish a system of partial differential equations, integral representations, expansions, analytic continuation, transformation formulas and generating relations. Also, we discuss the links for the various results, which are presented in this paper, with known results.

64-77

Authors: R. F. Shamoyan, A. N. Shipka

We prove new projection theorems for new Herz type spaces in various domains in Cn in the unit disk, unit ball, bounded pseudoconvex domains and based on these results we provide sharp estimates for distances in such type spaces under one condition on Bergman kernel. Similar type result in such type spaces in tubular domains over symmetric cones will be also provided.

93-116

Authors: Р. И. Паровик

В статье рассмотрена задача Коши для широкого класса фрактальных осцилляторов и проведено ее численное исследование с помощи теории конечно-разностных схем. Фрактальные осцилляторы характеризуют колебательные процессы со степенной памятью или в общем случае с эредитарностью и описываются с помощью интегро-дифференциальных уравнений с разностными ядрами – функциями памяти. Выбирая функции памяти степенными, интегро-дифференциальные уравнения приводятся к уравнениям с производными дробных порядков. В работе, с помощью аппроксимации дробных производных Герасимова-Капуто, была разработана нелокальная явная конечно-разностная схема, обоснованы ее устойчивость и сходимость, приведены оценки вычислительной точности численного метода. Приведены примеры работы предложенной явной-конечной схемы. Показано, что порядок вычислительной точности стремиться к единице при увеличении количества расчетных узлов сетки и совпадает с порядком аппроксимации явной конечно-разностной схемы.