"Vestnik St. Petersburg University. Mathematics"

Series "Mathematics, Mechanics, Astronomy", Issue 2, 2007

CONTENTS
Dedicated to the 150th anniversary of the birth of A. M. Lyapunov
Pliss V.A. The life and work of Aleksandr Mikhailovich Lyapunov 3
Andreev A.F., Andreeva I.A. Local research of any family of plane cubic systems 11
Bodunov N.A. Local parametric identifiability of linear stationary systems via a single-time observation of solutions 17
Vasilyeva E.V. Stable periodic points of two-dimensional C1 diffeomorphisms 20
Kryzhevich S.G. Symmetrization method and limit cycles of vibro-impact systems 27
Petrov N.N. Stability problems of fixed points for polynomial maps in some compact rings 32
Kholshevnikov K.V. On the Lyapunov theory of equilibrium figures of celestial bodies 39
Mathematics
Bugaychenko D.Yu., Soloviev I.P. Logical formalism for specification of real-time multi-agent systems 49
Źīrkmasov F. Ģ. On the approximation of continuous functions of two variables 58
Zhenji Tian. The lattice of regular subsemigroups of a regular semigroup 73
Shpilev P.V. L-optimal designs in trigonometric regression model on the full circle 80
Mechanics
Antipov K.A. On the influence of geomagnetic potential octupole components on the process of a spacecraft electrodynamic stabilization 90
Gasratova N.A., Shamina V.A. On a certain approach for solving the axi-symmetric problem of linear elasticity theory 101
Kolesnikov E.K., Manuilov A.S., Matveev M.S. The influence of time dependence of the radius of a relativistic electronic beam on the development of resistive hose instability 107
Landman I.M. On the rotating cylindrical shell vibrating with the frequencies close to the accumulation point 113
Lushchenko I.V., Ryabinin A.N. Experimental investigation of cylinder vibrations in the air flow 120
Mironov A.N. The contact between a spherical shell and an absolutely rigid ring 124
Mikheev A.V. Analysis of local stability of shallow orthotropic shells on the elastic base 128
Nezderov A.A. The turning movement of a front-driven car 134
Pronina Yu.G. Centres of compression and dilatation in an elastic half-plane 140
Filippov S.B., Naumova N.V., Ivanov D.N. Vibration of three-layered cylindrical shells 150
Yufereva L.M., Lavrov Yu.A., Kot P.N. Comparison of amendments to the lowest natural frequencies of the cylindrical acoustic resonator 157
Chronicle
N.N. Polyakhov (dedicated to the 100th anniversary of his birth) 164
Papers 167

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