Optical and thermodynamic properties of a plastic plasma

The results of calculating the properties of an equilibrium plasma of plastic at a temperature of from 1 to 100 eV are given, according to which it is possible to model the radiation-gas-dynamic processes in the multigroup approximation. The techniques for determining the radiative absorption coefficient provided for calculating the photoionized spectra in the vacuum ultraviolet while taking into account the observed similarity in cross section, individual consideration of the contributions of numerous calculations (up to 100 per ion) of the excited states, bremsstrahlung photo-processes, negative ions, etc. The results of the calculations are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 69–73, April, 1987.The authors wish to express their gratitude to Yu. V. Boiko and A. V. Aleksandrov for their assistance in this work.     

Absolute decomposability of the group of rational numbers

We prove that the group of rational numbersQ is absolutely decomposable.     

The greedy strategy for optimizing the Perron eigenvalue

Mathematical Programming -     

Bourbaki spaces of topological groups

A study is presented of the relationship between the topological and uniformity properties of a group G and the spaces (G), (G) of all nonempty closed subsets and closed subgroups of G. A base for the neighborhood system of a closed subset X of G is formed by the sets S(X, U)={Y Y XU, X YU}, where U ranges over all neighborhoods of the identity in G. Criteria are obtained for the space (G) and some of its subspaces to be totally bounded and locally totally bounded. Some classes of groups with compact spaces (G) are described. It is proved that the spaces (G), (G) are complete in the case of projective metrizable groups G.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 542–549, April, 1990.     

Kaleidoscopical configurations

Let G be a group, and let X be a G-space with the action G × X → X, (g, x) ?gx. A subset A of X is called a kaleidoscopical configuration if there is a coloring χ : X → κ (i.e., a mapping of X onto a cardinal κ) such that the restriction χ|gA is a bijection for each g ∈ G. We survey some recent results on kaleidoscopical configurations in metric spaces considered as G-spaces with respect to the groups of their isometries and in groups considered as left regular G-spaces.     

Meyer wavelets with least uncertainty constant

In the present paper, we construct a system of Meyer wavelets with least possible uncertainty constant. The uncertainty constant minimization problem is reduced to a convex variational problem whose solution satisfies a second-order nonlinear differential equation. Solving this equation numerically, we obtain the desired system of wavelets.