Some quantum mechanical problems in Lobachevsky space

Quantum mechanical problems are considered for potentials satisfying Bertrand's problem in Lobachevsky space. The self-adjointness of the corresponding Schrödinger operators is proved. The energy levels are calculated both from the Schrödinger equation and by means of the Bohr-Sommerfeld method. The effect of the quantum binding of classically infinite motion was discovered and is presented for the first time. It is shown that the quasi-classical limit is equivalent, in a sense, to the Euclidean limit.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 395–405, December, 1996.     

On the moment characteristics of distributions

We study different moment characteristics of (mostly discrete) distributions: general, central, binomial, and factorial moments, and also ordinary and factorial semi-invariants. We establish the relations that connect various kinds of “moments” of arbitrary order, and we derive recursion formulas. Translated fromMetody Matematicheskogo Modelirovaniya, pp. 34–41, 1998.     

Lyapunov’s direct method in estimates of topological entropy

An upper estimate for the topological entropy of a dynamical system defined by a system of ODE is obtained. The estimate involves the Lyapunov functions and Losinskii’s logarithmic norm. The proof uses the known fact that the topological entropy of a mapping acting in a compact space K can be estimated via the fractal dimension of K. Bibliography: 28 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 62–75. Translated by V. A. Boichenko and G. A. Leonov.     

A note on the line-distinguishing chromatic number and the chromatic index of a graph

Let λ(G) be the line-distinguishing chromatic number and x′(G) the chromatic index of a graph G. We prove the relation λ(G) ≥ x′(G), conjectured by Harary and Plantholt. © 1993 John Wiley & Sons, Inc.     

On removable singularities of solutions to first order elliptic systems with irregular coefficients

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 1, pp. 65–69, January–February, 1993.     

Critical behavior of the wave functions of icosahedral quasicrystals

The character of the localization of the wave functions of an icosahedral quasicrystal is investigated in the tight-binding approximation. It is found that the wave functions exhibit “critical behavior”: they are neither localized, as in the case of Anderson localization, nor delocalized, as in the case of Bloch states. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 559–563 (25 October 1996)