"Vestnik St. Petersburg University. Mathematics"

Series "Mathematics, Mechanics, Astronomy", Issue 3, 2007

CONTENTS
Dedicated to the 75th birthday of Prof. N. F. Morozov
Academician of the Russian Academy of Sciences Nikita Fedorovich Morozov 3
Belyaev A.K., Muzaev A.A., Indeitzev D.A. Derivation of dynamic boundary value problem and state equations for polarized thermoelastic materials 5
Dahl Ju. M. About Kolosov expressions in the plane problem of elasticity 11
Zegzhda S.A., Sinilshchikova G.A. The propagation of a crack in a thin beam under impulse loading 15
Kuzkin V.A., Krivtsov A.M. Simple model for analytical derivation of equa-tion of state for ideal crystals 24
Petrov N.N. Stability problems of fixed points for polynomial maps in some compact rings 32
Leonov G.A. The criteria of cycles existence in two-dimensional quadratic systems 31
Osmolovskii V.G. Exact solutions of the problem of phase transitions in a one-dimensional model case 42
Tovstik P.E. On the asymptotic character of the approximate models of beams, plates and shells/font> 49
Mathematics
Alekseeva N.P. Combinatorial analysis of two basic forms of hidden periodicity in categorial sequences 55
Bugaychenko D.Y. Model checking MASL specification of distributed real-time sys-tems 65
Davydova I.M., Fedoseeva E.Y. Generalization of the Chinese Remainder Theorem 75
Kossovsky N.K., Kossovskaya T.M. About the number of steps for constructing a Boolean solution of a polynomial comparison and of a system of them 84
Krivulin N.K. Evaluation of the growth rate of the state vector in a generalized linear stochastic system 91
Gelig A.Kh., Muranov V.A. Invariant stabilization of pulse-modulated sys-tems with nonlinear continuous part 100
Nekrutkin V.V. Martingale characterization of Polya processes and sequences 111
Tovstik T.M. The algorithm of the discrepancy calculation for the finite number of points in the unit n-dimensional cube 118
Mechanics
Bauer S.M., Mironov A.N. The contact between a spherical shell and an elas-tic ring 122
Volkov I.D., Grekov M.A. Green's functions for bonded dissimilar materials with slightly curved interface 126
Mikheev A.V. Influence of the shear parameter on local stability of shallow orthotropic shells on elastic base 137
Novoselov V.S. Optimal two-impulse tangential passage with the prescribed relative velocity 144
Astronomy
Bashakov A.A., Pityev N. P. Constructing self-consistent models of stellar sys-tems by Schwarzschild's method 151
Kholshevnikov K.V. Representation of gravity potential gradient of celestial bodies by means of series in solid spherical harmonics 160
Chronicle
V.N. Fomin (dedicated to the 70th anniversary of his birth) 167
Papers 169

Editorial Board of the Complete Journal.
Editor-in-chief:   L.A.Verbitskaya.
Associate editors:   I.V.Murin, V.N.Troyan.
Editorial board:   N.A.Belyaev, S.G.Inge-Vechtomov, A.G.Morachevsky, V.T.Ryazanov, R.V.Svetlov, L.E.Smirnov, P.E.Tovstik, I.Ya.Froyanov, T.N.Peskova.
Secretary of the board: A.V.Suvorov.
Editorial Board of the Series "Mathematics, Mechanics and Astronomy".
Editor-in-chief :   P.E.Tovstik
Associate editor:   N.N.Petrov
Secretary of the board:   T.V.Voloshinova
Editorial board:   T.A.Agekyan, S.M.Ermakov, G.A.Leonov, N.F.Morozov, I.P.Mysovskikh, V.S.Novoselov, L.A.Petrosyan, V.A.Pliss, N.N.Uraltseva, B.V.Filippov, K.V.Kholshevnikov.
Address of the editorial board:  198504, Peterhof, Universitetsky pr., 28.
Translation of articles for a journal “Vestnik St. Petersburg University Mathematics” is performed by E.A.Gurmuzova.
Editor T.V.Semenova.   Technical editor A.V.Borshcheva
Phones: 328-97-84, 323-76-30, 328-21-64. E-mail: peterhof@rambler.ru