Vestnik KRAUNTS. Fiziko-matematicheskie nauki

7-13

Authors: S. Z. Djamalov

In the present work the problems of correctness of a linear inverse problem for the mixed type equation of the second kind of the second order in three-dimensional space are considered. For this problem, the theorems on existence and uniqueness of the solution are proved in certain class by «ε-regularization», Galerkin’s and of successive approximations methods.

22-32

Authors: B. I. Islomov, N. K. Ochilova

The existence and the uniqueness of solution of local problem for degenerating mixed type equation is investigated. Considering parabolic-hyperbolic equation involve the Caputo fractional derivative. The uniqueness of solution is proved using the method of the extremume principle and integral energy, the existence is proved by the method of integral equations.

44-53

Authors: D. A. Tvyordyj

We consider the Riccati differential equation with a fractional derivative of variable order. The introduction of a derivative of a fractional variable order into the initial equation determines the property of the medium — the memory effect or the heredity, which consists in the dependence of the current state of the dynamic system on its previous states.

68-81

Authors: O. V. Kudrinskaya

The article discusses methods for solving optimization problems with the use of table processor tools — «Solution search»and «Script manager». Solutions of several examples of linear and integer optimization are presented. The tasks of optimization are widely used in science, economics, engineering and are used when it is necessary to obtain the best results under certain conditions.

9-14

Authors: A. Kh. Attaev

For equations of the form ux + uy = λux(x;0) + µuy(0;y) the investigation on the correctness of the number of initial value problems in bounded and unbounded domains.

21-26

Authors: F. T. Bogatyreva

In this paper we construct an explicit representation of the solution of the Cauchy problem for ordinary differential equation of fractional order with Dzhrbashyan-Nersesyan operators.

32-37

Authors: L. L. Karasheva

In this paper we derived an estimate for the fundamental solution of high order parabolic equation with time fractional derivative.

45-49

Authors: R. Kh. Makaova

First boundary value problem is investigated for the Hallaire inhomogeneous equation. With the help of the Fourier method we have found an explicit representation of a regular solution.

56-65

Authors: K. U. Khubiev

The solution to the Goursat problem is written out explicitly for a hyperbolic secondorder loaded equation, proposed as a mathematical model of Aller equation under certain conditions.

72-79

Authors: B. I. Efendiev

In this work we build a fundamental solution to a regular continuous differential equation of second order with regularized derivatives of segment order and find an explicit solution to Cauchy problem in terms of fundamental solution.

85-92

Authors: M. A. Bagov, V. Ch. Kudaev

The optimization method for the Steiner pipeline network based on dynamic decomposition.

101-106

Authors: R. A. Zhilov

A method of constructing an optimal cognitive maps consists in optimizing the input data and the dimension data structure of a cognitive map. Pro-optimization problem occurs when large amounts of input data. Optimization of time-dimension data is clustering the input data and as a method of polarization-clusters using hierarchical agglomerative method. Cluster analysis allows to divide the data set into a finite number of homogeneous groups. Optimization of the structurery cognitive map is automatically tuning the balance of influence on each other concepts of machine learning methods, particularly the method of training the neural network.

112-125

Authors: Z. M. Shibzukhov, M. A. Kazakov

The paper proposes a new scheme for the gradient solution to minimize losses averaged problem. It is an analog circuit used in the SAG algorithm in the case when the risk is calculated using the arithmetic mean. An illustrative example of the construction of robust classification based on the maximization of the surrogate median indentation.

7-11

Authors: R. Z. Berezgova

In this paper, we study the boundary value problem for loaded differential equations of fractional order with the Barrett operator in the main part.

17-23

Authors: G. M. Vodinchar, A. N. Godomskaya, O.V. Sheremetyeva

We describe a low-mode dynamo model. This model implements the various known regimes of cosmic dynamo systems, in particular, the various regimes of reversals. The source of regular reversals in the model is its internal dynamics. Violation of this cyclicality, transition to the chaotic regime of reversals are caused by fluctuations of the parameters, that are interpreted as the result of spontaneous coherent addition of the higher modes. The simplicity of the model allows you to easily modify it for various celestial bodies.

30-35

Authors: R. I. Parovik

The work was a mathematical model that describes the effect of the sliding attachment (stick-slip), taking into account hereditarity. explicit finite-difference scheme for the corresponding. Cauchy problem was constructed. Built on the basis of its waveform and phase trajectories.

43-48

Authors: E. A. Malysh, G. M. Vodinchar, N.V. Cherneva

The whistlers pattern recognition algorithm in the spectrogram of VLF-radiation and algorithm of the filtering of pulse signals in the spectrograms are proposed.

56-62

Authors: V.V. Bogdanov, A.V. Kaysin, A. A. Romanov

The paper presents the results of investigation of cyclone impact on ionosphere parameters. Ionosphere state was observed by the automatic sounding equipment applying low-orbital navigational spacecrafts in the conditions of low seismicity.

74-79

Authors: Yu.V. Marapulets, A. A. Solodchuk, A. O. Shcherbina

To investigate high frequency geoacoustic emission, a receiving system based on a compound vector receiver was installed in Kamchatka. It allows the authors to determine the direction of sound wave arrival. In the result of the data analysis for the period from August 2008 to January 2016, it was determined that geoacoustic emission directivity anomalies occur during the majority of the earthquakes with Ks >9.0 in the South of Kamchatka.

86-91

Authors: S. E. Smirnov

Statistical estimates of the effect in the electric field of the surface layer of the atmosphere parameters, such as time of the beginning, time of a maximum, its intensity and duration, were obtained. It was shown experimentally that the diurnal variation maximum of atmospheric electric field intensity is associated with air temperature height distribution. Power spectra of time variations of electric field intensity in the near ground atmosphere and of the horizontal component of geomagnetic field were under study. It was shown that there are oscillations with the periods of T _ 2, 0–2,5 hours in the power spectra of these parameters during a day. A possible mechanism of generation of these oscillations was proposed. It is associated with vortex motion of convective cells arising during the sunrise in the atmosphere exchange layer.

99-105

Authors: G. I. Druzhin, Y. B. Bashkuev, I. B. Naguslaeva, N.V. Cherneva, B. M. Shevtsov

The data obtained by the World Wide Lightning Location Network (WWLLN) in the territory of Zabaykal’e are compared with the data received by the equipment for observations of Earth’s natural pulse electromagnetic field installed in Buryatia. Diurnal and seasonal dependence of lightning strokes observed in Zabaikal’e territory were obtained. It was shown that the maxima in diurnal variation registered by the instrumentation in Buryatiya coincide with the main world lightning sources.

112-117

Authors: S.Y. Khomutov, I. N. Khomutova

The possibilities of digitization of old magnetograms to obtain new data about magnetic field variations are considered.

7-13

Authors: S. Reza Hejazi, A. Naderifard, S. Rashidi

In this study, we consider a 4-th order (1+1)-dimensional PDE called Zoomeron equation. Some conservation laws are derived based on direct method. We also derived some similarity solutions using the symmetries.

23-28

Authors: G. M. Vodinchar, L. K. Feshchenko

We describe a large-scale geodynamo model based on hypothesis about 6-jet convection in the Earth’s core. This hypothesis suggests indirect data of inhomogeneities in the density of the Earth’s core. The convection pattern is associated with a spherical harmonic Y24 which defines the basic poloidal component of velocity. The model takes into account the feedback effect of the magnetic field on convection. It was ascertained that the model contains stable regimes of field generation with reversals. The velocity of convection and the dipole component of the magnetic field are similar to the observed ones.

34-39

Authors: O.V. Mandrikova, E. A. Zhizhikina

The paper presents our software system for estimation the degree of disturbance of the geomagnetic field. The system automatically classifies registered geomagnetic data and determines the state of the geomagnetic field for the current day. The results of approbation of the system showed the prospect of its application in problems of estimation and prediction of space weather. The system allows us to allocate weak disturbances of the geomagnetic field, which may occur before strong magnetic storms.

47-52

Authors: M. A. Mishchenko

Statistics of occurrence of anomalous disturbances in high-frequency geoacoutic emis-sion of the near surface sedimentary rocks and in atmospheric electric field by the ground surface before earthquakes is presented. Long-term continuous series of measure-ments of geoacoustic emission for the period of 2003-2012 at «Mikizha» site and the data of measurements of atmospheric electric field obtained for the summer-autumn periods of 2006-2008 at «Mikizha» site and for 2009-2012 at «Karymshina» site were used in the analysis. Anomalous disturbances of the emission and of the field were compared with the earthquake catalogue of Kamchatka Branch of Geophysical Service RAS.

72-78

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

The possibility of joint perturbation of geoacoustic, emanation and atmospheric electric fields by the earth’s crust — atmosphere boundary before an earthquake is considered.

85-90

Authors: I. A. Larionov, Yu. A. Nepomnyashchiy

The results of investigations of the deformation process in the near surface sedimentary rocks, which has been carried out in a seismically active region of Kamchatka peninsular since 2007,are presented. The peculiarity of the experiments on the registration of geodeformations is the application of a laser deformograph-interferometer constructed according to the Michelson interferometer scheme.

98-102

Authors: S.Y. Khomutov, S. E. Smirnov, S.V. Butin, I.Y. Babakhanov

The results of continuous measuring of vertical gradient of AEF potential by CS110 during a few months are presented. The comparison of CS110 and ”Pole-2” are performed.

7-11

Authors: L. Kh. Gadzova

The asymptotics of the fundamental solution of the linear ordinary differential equation of fractional order with constant coefficients, for large values of spectral parameter λ is found.

18-23

Authors: A. Kh. Kodzokov, Z. O. Beslaneev, A. L. Nagorov, M. B. Tkhamokov

The paper discusses ways to solve linear Diophantine equations in the particular case of two unknowns, and, in general, with a few unknowns. The main result is contained in Theorem 1, which provides a general method for solving any Diophantine equation, based on a comparison of the relevant module.

28-33

Authors: Z. S. Madrakhimova

This paper deals with the formulation and study of boundary value Gellerstedt type problem for parabolic-hyperbolic equation with degeneration of the type and order within the area which equivalently reduced to integral equations.

43-49

Authors: I.V. Drobysheva

The paper presents a mathematical model hereditarity Duffing oscillator with friction, which is a generalization of previously known classical model of Duffing oscillator. This generalization is replaced in the model equation integral derivative on derivatives of fractional order in the sense of Riemann-Liouville. Built explicit finite difference scheme for calculating approximate solutions, as well as the phase trajectories for different values of the control parameters.

55-61

Authors: D.V. Makarov

The paper presents a mathematical model that generalizes the famous Kondratiev cycles model (model Dubovskiy) used to predict economic crises. This generalization is to integrate the memory effect, which occurs frequently in the economic system. With the help of numerical methods, to receive a generalized model, according to which the phase paths have been built.

68-72

Authors: M. B. Tkhamokov, A. L. Nagorov, Z. O. Beslaneev, A. Kh. Kodzokov

This article attempts to estimate the entropy Karachay-Balkar printed texts. As of the object were taken by famous national writers, as well as the texts of periodicals. With this program, written by the authors calculated the frequency of the letters, different combinations and phrases modeled on the basis of the results obtained. When calculating performance used known standard techniques. An entropy to the twenty-fifth day of the order and the value of the redundancy of the language. The results of studies of domestic and foreign authors in the field of counting entropy. A comparative analysis of the different orders of the entropy for European languages.

79-89

Authors: O. K. Zhdanova

This article presents the materials of the seminar held for mathematics teachers and all those interested in similar problems in Vitus Bering Kamchatka State University. The seminar was devoted to solving problems with parameters and the high level problems of the Unified State Exam.