Vestnik KRAUNTS. Fiziko-matematicheskie nauki

9-27

Authors: S.Yu. Belov

Monitoring of the earth’s surface by remote sensing in the short-wave band can provide quick identification of some characteristics of natural systems. This band range allows one to diagnose subsurface aspects of the earth, as the scattering parameter is affected by irregularities in the dielectric permittivity of subsurface structures. The new method is suggested. This method based on the organization of the monitoring probe may detect changes in these environments, for example, to assess seismic hazard, hazardous natural phenomena, changes ecosystems, as well as some man-made hazards and etc. The problem of measuring and accounting for the scattering power of the earth’s surface in the short-range of radio waves is important for a number of purposes, such as diagnosing properties of the medium, which is of interest for geological, environmental studies. In this paper, we propose a new method for estimating the parameters of incoherent signal/noise ratio. The paper presents the results of comparison of the measurement method from the point of view of their admissible relative analytical errors. A comparative analysis and shows that the analytical (relative) accuracy of the determination of this parameter new method on the order exceeds the widely-used standard method. Analysis of admissible relative analytical error of estimation of this parameter allowed to recommend new method instead of standard method

35-42

Authors: V. G. Margaryan

The regularities of the space-temporal distribution of the radiation balance of the underlying surface for the conditions of the mountainous territory of the Republic of Armenia were discussed and analyzed.

51-56

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

One of the important applications of lidar technologies is the study of the thermal regime of the atmosphere. Such studies in the monitoring mode at the Institute of Atmospheric Optics of the SB RAS have been launched since 1994 and are continuing at the present time. Particular attention is paid to the study of the manifestation of sudden disturbances in the middle stratosphere caused by winter stratospheric warming (SW). The results obtained on this topic can be found in [1]-[7]. In this paper, studies of the vertical temperature distribution over Tomsk in the disturbed and calm periods of 2016 are presented.

64-75

Authors: P.M. Nagorskiy, T.A. Zenchenko, K.N. Pustovalov, M.S. Cherepnev, G.A. Yakovlev, V.S. Yakovleva

The detail analysis of results of simultaneous monitoring of the same electrophysical, meteorological and radiation quantities inside and outside of buildings with the aim of revealing of technosphere influence on behavior of these quantities is presented. It was obtained that all controlled quantities could be divided into three groups for which: 1) presence of building does not change spectral and temporal variation pattern of quantity (magnetic field, atmospheric pressure); 2) presence of building partially changes spectral and temporal variation pattern of quantity (γ-background, temperature); 3) presence of building fully changes spectral and temporal variation pattern (relative air humidity, characteristics of turbulence and wind, electric field intensity, the number of light ions of both sighs, α- and β-background). It is necessary to take into account obtained results when investigate the influence of heliophysical parameters and radioactivity on biological objects and systems.

83-90

Authors: M. A. Mishchenko, I. A. Larionov, L. M. Bogomolov, V. N. Sychev

The results of complex geodeformation observations in Kamchatka are presented. A laser strainmeter-interferometer (developed at IKIR FEB RAS) and a three-component piezoelectrical seismometer, constructed by ZAO “Geoakustica” and provided by IMGiG FEB RAS within a joint research, were used as the registering systems. Signals, received simultaneously by different registration systems, were analyzed. Seismic signals from earthquakes, pulses with the frequency up to 100 Hz and higher-frequency geoacoustic signals, which had been registered by a system of spaced hydrophones at IKIR FEB RAS before, were detected.

101-108

Authors: S. E. Cherny, A. N. Efremenko, I. D. Kanarsky, A. S. Podchassky

We propose an approach to solving the problem of operational control of seismic situation on the basis of automation of process of monitoring of seismotectonic deformation in real time.

5-9

Authors: R. Z. Berezgova

In this paper we consider a nonlocal boundary value problem with an integral condition for the McKendrick von Foerster loaded equation with the Caputo operator. The existence and uniqueness theorem for the solution of the problem is proved.

20-24

Authors: A. M. Shkhagapsoev

We consider the boundary-value problem for a third-order equation of parabolic type with the fractional derivative of Caputo. By the method of energy inequalities an a priori estimate of the solution of the analogue of the second boundary value problem for an equation with multiple characteristics.

50-60

Authors: G. A. Pyukke

The question of the coincidence of estimates of reliability parameters with their true values is considered, when planning maintenance and determining estimates of the reliability parameters of operated systems. The main attention is paid to the problem of constructing models that simulate the behavior of systems during operation in the future. Establishing such a connection consists in using the Bayesian approach and estimating the parameters of the reliability model, covering systems with partially known reliability parameters, which are specified by a priori distributions.

70-77

Authors: Z. M. Shibzukhov

We propose a new clustering method for partitioning of finite sets from Rn, which is based on the application of averaging aggregating functions and an iterative re-weighing method for searching cluster centers.

90-99

Authors: V.V. Kuznetsov

Climate variation during the last 700 – 800 kyr is known to reveal some periods of the temperature fluctuation. It is during about 100 kyr when temperature is slowly lowering, glaciation, and then it quickly raises resulting in ice melting. Some short period temperature fluctuations usually interpreted by Milancovich theory [1] are argued here to be a well known flicker noise. This approach allows a new insight into climate mechanism and prognosis of its variation.

7-19

Authors: K. T. Karimov

The eigenvalues and eigenfunctions of two boundary value problems for three-dimensional equations of elliptic types with singular coefficients with lower terms are found.

41-52

Authors: M. Nadjafikhah, S. R. Hejazi

Lie group method is applicable to both linear and non-linear partial differential equations, which leads to find new solutions for partial differential equations. Lie symmetry group method is applied to study Newtonian incompressible fluid’s equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra such as Levi decomposition, radical subalgebra, solvability and simplicity of symmetries is given.

59-64

Authors: S.V. Myshkin

The model integro-differential Bernlulli equation is considered in the paper. This equation was reduced to a differential equation with derivatives of fractional orders and solved numerically with the help of Newton’s iteration method. Depending on the values of the control parameters, calculated curves were constructed.

76-80

Authors: A. S. Valchuk

The paper proposes and implements, in the form of a mathematical model and software package, the concept of using value coefficients, for ranging answers in universal hybrid question-answer systems, which will improve the efficiency of their work.

89-98

Authors: F.V. Korolev

A web interface was developed to visualize the calculation of the spatial distribution of correlation links between the whistler flux intensity and planetary thunderstorm activity.

111-116

Authors: M. M. Esonov

The paper deals with the problem of constructing a straight line perpendicular to a given line, and on constructing a line perpendicular to a given plane, as a rule, reduce to constructing the height of some triangle. In the general case this problem is a metric problem.

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.