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## On heteroclinic separators of magnetic fields in electrically conducting fluids

It has been shown that both RF plasma and plasma-jet treatments lead to electron traps formation in the bulk of SiO2 films. As a result it is possible to increase breackdown voltage of MOS structure when breakdown probability is being decreased significantly.

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.

The behaviour and erosion of tungsten, copper and W-Cu composition under irradiation by high intensive hydrogen plasma have been investigated. The erosion coefficients of these materials have been determined. The importance of copper redepositions in the mechanism of sputtering and erosion of W-Cu composition has been emphasised.

The sputtering of a number of materials due to an intense polyenergetic flux of hydrogen particles has been investigated. The irradiation of pure tungsten, copper, aluminium, titanium, aluminium-lithium alloys, stainless steel and tungsten-copper composition has been carried out at particle flux densities of 1017-1018 cm~2 s~' and at fluences of 1020-1022 cm~2. Furthermore, W-Cu composition has been subjected to the effect of high-current plasma pulses for simulating the disruption heat loads in a thermonuclear reactor.

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.

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.

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.