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## Ionospheric response to the acoustic gravity wave singularity

An original model of atmospheric wave propagation from the ground sources to ionosphere in the atmosphere with a realistic high-altitude temperature profile is analyzed. Shaping of a narrow domain with elevated pressure in the resonance region where the horizontal phase wave velocity is equal to the sound velocity is examined theoretically within the framework of the linearized equations. Numerical simulations for the model profiles of atmospheric temperature and viscosity confirm analytical result for the special feature of wave fields. The formation of the narrow domain with plasma irregularities in the D and low E ionospheric layers caused by the acoustic gravity wave singularity is discussed.

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.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

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.

Analytically and numerically calculations according to the original effective algorithms for largescale acoustic-gravity wave perturbations in the chromosphere from sources at the level of the photosphere are analyzed. Limitations to the energy flux of acoustic-gravity waves from the photosphere through the chromosphere are formulated. Structure of a narrow region with elevated pressure at the resonance altitude where the horizontal phase wave velocity is equal to the sound velocity is examined.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

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.