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## Грубые диффеоморфизмы с базисными множествами коразмерности один

The contribution of electron–phonon scattering to conductivity of a quantum cylinder in a lon-gitudinal magnetic field has been studied. It has been shown that the conductivity of the nanotube undergoes Aharonov–Bohm oscillations with variations in the magnetic flux through the nanotube cross section. The formulas describing the temperature dependence of the resistance of the nanostructure both in the case of an isotropic phonon spectrum and with allowance for the effects of phonon confinement have been obtained in the analytical form.

The method of elasstic recoils detection of deutrons and protons (ERDA) was used for the study of the accumulation and redistribution of hydrogen and deuterium atoms under the action of high-temperature deuterium plasma using of the "Plasma Focus" (PF-4) in an assembly of two Ni, Ti and Zr foils of high purity. It was found that when exposed to pulsed high-temperature plasma is a redistribution of the implanted deuterium and hydrogen gas impurities to great depths in the assemblies of the studied foils, considerably exceeding the ranges of deuterium ions (at their maximum speeds of up to 108 cm /s).

As in earlier studies, the observed phenomenon can be explained by: a) removal of the implanted hydrogen under the influence of powerful shock waves formed in the metal foil by pulsed deuterium plasma, and (or) the acceleration of the diffusion of hydrogen atoms under the influence of compression-dilatation waves in the front of a shock wave to the redistribution of hydrogen to great depths. A similar behavior is found in assemblies of two or three or more foils of nickel, vanadium, niobium, tantalum, different thicknesses, including assembly and foils of different materials, which have been well studied.

Assemblies of Ta|CD2| Ta|Ta |CD2|Ta|Ta and Nb|CD2|Nb foils were irradiated 30th pulses of high-argon plasma on the "Plasma Focus" (PF-4). After irradiation, all samples foils were investigated by the elastic scattering of the recoil nuclei of hydrogen and deuterium (ERDA) on both sides. It found redistribution of hydrogen and deuterium in stacks of foils. Experimental results for lung penetration ultradeep gaseous impurities: hydrogen and deuterium are explained based on the effects of shock waves on the foils and accelerated diffusion induced by an external force.

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.

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.

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.