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.