"Vestnik St. Petersburg University. Mathematics"

Series "Mathematics, Mechanics, Astronomy", Issue 1, 2008

CONTENTS
Dedicated to the centenary of D.K.Faddeev’s birth
Yakovlev A.V. D. K. Faddeev and St.Petersburg algebraic school 3
Vavilov N. A., Stepanov A. V. The standard commutator formula 9
Volkov Yu. V. The classes of stable equivalence of selfinjective algebras of the tree class Dn 15
Vostokov S. V., Orlova K. Yu. A generalization and an application of the Eisenstein recip-rocity law 22
Mathematics
Kosovskaya Ò. Ì. Level descriptions of classes for decreasing of step number of solving of a pattern recognition problem described by propositional formulas 29
Krivulin N. K. On evaluation of the growth rate of state vector in a second-order general-ized linear stochastic system 38
Matveev A. S. A study of a termination control for a nonlinear discrete-time system 49
Nazarov S. A., Taskinen J. On the spectrum of the Steklov problem in a domain with a peak 56
Ponomarenko A. K. Some invariant cubature formulae of the eleventh degree containing Laplasian operator 66
Rukavishnikova A. I. Optimization of the Quasi Monte-Carlo algorithm for solving lin-ear algebraic equations 73
Sulimov M. G. On localization of the complex nulls of a certain quasi-polynomial 78
Mechanics
Abushik G. V. The stress-strain state of a composite spherical soft shell previously loaded with interior pressure 85
Grekov M. A. A slightly curved crack near the interface in dissimilar materials 93
Kolesnikov E. K., Manuilov A. S., Matveev M. S. On the question of influence of an ex-ternal longitudinal magnetic field on dynamics of resistive hose instability of a relativistic electron beam 101
Pavlovsky V. A. The tensor form of additional masses coefficients 109
Platonov V. V. The stability of a nanocorrugated plat 118
Smirnov V. I. Application peculiarities of the structural criterion of brittle fracture 126
Astronomy
Baluyev R. V. Exploration of the exoplanetary statistics by means of the continuous wavelet analysis 135
Brief scientific reports
Kabardov M. M. On the Laplace transform inversion based on the Fourier-Legendre ex-pansion of the original function 144
Leonov G. A. The conjecture for prediction of multiparameter markets 149
Ryabov V. M. Finding the point of jump and the value of jump of determining function by using its Laplace transform 151
Papers 156
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