In this paper, we discuss some question related to the nature and manifestation of the equatorial electrojet. We study the equatorial electrojet as nonlinear antenna for generating ultra-low-frequency electromagnetic signals during periodic heating of the ionosphere by the short-wave heating-facility radiation. It is shown that for modulation at the frequency corresponding to the ULF band the generation of electromagnetic signals can be the considerable intensified. This effect is especially important for day-time magnetosphere where in same frequency band there are eigen-frequencies of plasma magnetospheric maser in the electron radiation belts. This can lead to modification of VLF emissions in the subauroral magnetosphere.
Peculiarities of acoustic-gravity wave near the solar atmosphere transition region are analysed. An investigation is based on an original characteristic relation of waves in a two layers model with a temperature jump. Special attention is paid to an analysis of the properties of the surface waves, generated by the source of mass, which crosses the solar atmosphere transition region. An exact analytical solution of this problem, which involves several modes propagating along the boundary, is found. It is shown on the basis of the obtained results that the wave front from the local instantaneous source moves in radial directions with acceleration. The obtained results are important for explanation of observed properties of wave perturbations near the solar atmosphere transition region, whose appearance correlates with coronas mass injection.
The possibility that vertical acoustic waves with frequencies lower than the cutoff frequency corresponding to the temperature minimum pass this minimum is investigated. It is shown that the averaged temperature profile in the solar atmosphere can be approximated by several so-called reflectionless profiles on which the acoustic waves propagate without internal reflection. The possibility of the penetration of vertical acoustic waves, including low-frequency ones, into the solar corona is explained in this way.
Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov , we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.
I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables