In this paper the characteristic problem for the wave equation loaded with a special
shift. A theorem on the uniqueness of the solution of the Goursat problem and find
necessary conditions for its solvability.
We studied a models of loaded equation of mixed hyperbolic-parabolic type with characteristicly and not characteristicly modifying line. For the proposed equation models boundary value problem is considered and solutions is written out.
We study a spectral problem for an ordinary differential equation with composition of fractional order differentiation operators in Riemann-Liouville and Caputo senses with
different origins. We prove that for the problem under study there exist infinite sequences of eigenvalues and eigenfunctions. All of the eigenvalues are real and positive, and the eigenfunctions form an orthogonal basis in L2(0;1).
We describe the large-scale model geodynamo, which based on indirect data of inhomogeneities in the density of the Earth’s core. Convection structure is associated with spherical harmonic Y24 , which defines the basic poloidal component of velocity. Coriolis drift of this mode determines the toroidal component of velocity. Thus, 6 convective cells are formed. 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. The velocity of convection and the dipole component of the magnetic field are close to the observed ones.
In the paper investigates the question of the possibility of a reversal in the framework of
low-mode model, αΩ-dinamo. The parameters of the MHD system in which the possible
reversal of the magnetic field in the relative constancy of the velocity field are defined. There are results of numerical solution of the assumption of various type of α-effect amplitude dependence from the radius.
One approximation of magnetohydrodynamics equations, which describe the cosmic object’s magnetic field, is considered. The analytic properties of a nonlinear system are investigated by Painlev´e test. Values of the coefficients in a simplified magnetohydrodynamics system are calculated for the necessary condition of Painlev´e property.
The question of preservation of the third adiabatic invariant motion of charged particles
vII = 0 (equatorial plane) in the flow and the canonical form in magnetic fields having a
weak asymmetry. Go to rotating with the angular velocity of the drift coordinate system
allows us to reduce the problem to have been solved, namely, the task of saving the third adiabatic invariant in the axially symmetric, but the time-varying magnetic field.
The approach of geoacoustic emission signals denoising from native and technogenic noises based on sparse approximation method is offered in this paper. The use of this means made it possible to clear geoacoustic emission pulses from technogenic parasitical component
This is the description of the whistlers automatic detection algorithm, based on the nonlinear transformation of the spectrogram VLF signal. In the converted spectrogram the whistler graphic is presented by a straight line, detection of which is algorithmically simple task. The testing of the program implementation of the algorithm showed that a detection can be managed in the real-time mode.
The paper proposed a new mathematical model of the variation of the charge cloud drops in storm clouds. The model takes into account the fractal properties of storm clouds, and the solution was obtained using the apparatus of fractional calculus
The paper considers a nonlinear fractal oscillatory Duffing system with friction. The numerical analysis of this system by a finite-difference scheme was carried out. Phase portraits and system solutions were constructed depending on fractional parameters
According to the developing model, the nonpotential part of the geomagnetic field is due to the vertical current associated with positive charge transfer by water vapour during plant and water surface evaporation in the same direction and with negative rain current in the opposite direction. These two processes are quite irregular both in space and in time, but the total charge transfered upwards to the clouds is almost equal to the charge transfered downwards to the Earth surface. Nevertheless, these processes result in the accumulation of positive charge in the lower ionosphere at the height of about 90 km.
The model, which hit a mountain (technogenic earthquakes) — is presented as a way out of the shock wave at the inner wall of the shaft. This raises the unloading wave, stretching, moving backward (deep wall) direction. Shock wave accompanied by the movement of the medium in the propagation direction of the shock waves at a speed considerably less than that of the wave. The totality of phenomena occurring on the inner surface of the mine, leads to the release of coal dust and methane dissolved in the coal, which is the cause of the explosion.
Complex monitoring of acoustic emission (AE) in the sound frequency range has been
carried out in the Kamchatka peninsular since 1999. In the course of the investigation, the existence of acoustic emission effect in sedimentary rocks was detected. It consists in the increase of geoacoustic radiation intensity in the frequency range from hundreds of hertz to the first tens of kilohertz during the growth of rock mass deformation rate. This effect was stably observed at several spaced stations and appears the most vividly at the final stage of earthquake preparation. During the acoustic emission effect, clear anisotropy of geoacoustic radiation directivity occurs which is determined by the source orientation of acoustic oscillations in the stress field of near surface sedimentary rocks.
The results of calibration of α-, β- and γ-radiation detectors mounted into borehole at depths of 0.5 and 1 m, which are destined for soil radon monitoring, are represented and analyzed. The radon isotopes radiometer RTM 2200 (SARAD GmbH, Germany) was used for the calibration aim.
The results of monitoring of meteorological and radiation parameters in Tomsk Observatory of Radioactivity and Ionizing Radiation are presented and analyzed in this work. The advantages of new radiation monitoring technology including the investigation of radiation parameters vertical profiles are presented. The verification of existing soil and atmosphere radon isotopes transport models were conducted for urban environment with help of analysis results of radiation monitoring data