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## Nonlinear Response of the Equatorial Current Jet to External Action and Its Influence on Electromagnetic Waves of the Whistle Range in the Magnetosphere

The nonlinear response of the equatorial current jet to external actions is considered, as well as

some geophysical effects produced by it. Irradiating the current jet by shortwave electromagnetic radiation

with amplitude modulation in ranges of VLF emission and geomagnetic pulsations, one can provide for con

ditions when a nonlinear antenna is realized in the current jet region. Estimations have shown that under the

current jet on the ground surface electromagnetic signals on modulation frequencies can be two orders of

magnitude larger than at middle latitudes due to modulated electron temperature and density. The effect of

signals from the modulated equatorial current jet on the modes of operation of the plasma magnetospheric

maser in VLF waveband is considered. The resonance modification of the spectra of natural electromagnetic

waves of VLF range in the magnetosphere is shown to be possible.

In quiet low-latitude Earth's ionosphere, a rather developed current system that is responsible for the S_{q} magnetic-field variations is formed in quiet sunny days under the action of tidal streams. The density of the corresponding currents is maximal at the equatorial latitudes in the midday hours, where the so-called equatorial current jet is formed. In this work, we discuss the nature of the equatorial current jet. The original part of this paper is dedicated to the study of the value of its response to external effects. First of all, it is related to estimating the possibility of using the equatorial current jet for generating the low-frequency electromagnetic signals during periodic heating of the ionosphere by the heating-facility radiation. The equatorial current jet can also produce electrodynamic response to the natural atmospheric processes, e.g., an acoustic-gravitational wave.

The article is aimed to clarify the contradictory nature of the urban atmosphere phenomenon by defining its’ nuances and the genesis of its’ appearance in social sciences. Such approach will help to conceptualize the phenomenon and will lead to the creation of the future urban atmosphere model suitable for further operationalization.

The research is represented by the theoretical analysis of works interested in urban atmosphere phenomenon in the field of sociology, phenomenology, management, literature, cultural geography.

The work can be divided into two parts. The first part describes the differences between urban atmosphere nuances, namely ambiance and atmosphere, and define them. Then the second part provide us with the information about ambiance and atmosphere origin and the process of its’ development from ancient times to this day. In the end of the article the necessity of taking into account the urban atmosphere shades, when dealing with model creation, is argued.

According to the analysis the atmosphere is invisible but is characterized by magnetic properties making the urban space attractive for living bodies. The ambience is produced by the atmosphere, but have the more pronounced qualitative properties which characterize the urban space. The ambience influence on our lifetime by mediating the relations between living bodies.

The consideration of the urban atmosphere genesis in different research fields showed that the atmosphere has been studied mainly within natural science and literature as descriptive quantitative phenomenon aimed to define the space of existence for living bodies. Whereas the ambiance, full of qualitative and tangible characteristics, has been appeared later and has been borrowed by a number of research disciplines (such as sociology, psychology, economics, management) as possible to be analyzed and slightly applied in practice.

According to the analysis the author reaches the conclusion that the urban atmosphere is the highly constructed phenomenon consisting of either atmosphere, or ambience. The second one is the qualitative continuation of the first one and the characteristics of both shouldn’t be overlooked when conceptualizing the phenomenon. The analysis also showed that the functioning principles of physical atmosphere and ambiance can be applied in the model creation. It is connected with the absence of explanation of urban atmosphere and ambience functioning by social scientists. The application of these principles from physics will provide the full scheme of urban atmosphere components interrelation and interaction.

Using the linear theory of waves in a compressible atmosphere located in a gravitational field, we found a family of sound speed profiles for which the wavefield can be represented by a traveling wave with no reflection. The vertical flux of wave energy on these nonreflected profiles is retained, which proves that the energy transfer may occur over long distances.

A method based on the spectral analysis of thermowave oscillations formed under the effect of radiation of lasers operated in a periodic pulsed mode is developed for investigating the state of the interface of multilayered systems. The method is based on high sensitivity of the shape of the oscillating component of the pyrometric signal to adhesion characteristics of the phase interface. The shape of the signal is quantitatively estimated using the correlation coefficient (for a film–interface system) and the transfer function (for multilayered specimens).

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.