Vestnik St. Petersburg University, Mathematics
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Formulation and Solution of a Generalized Chebyshev Problem: Second Part
Vestnik St. Petersburg University, Mathematics - - 2020
Bases of singular solutions in problems of mechanics of cracks
Vestnik St. Petersburg University, Mathematics - Tập 41 - Trang 303-314 - 2009
The mechanics of cracks serves as a remarkable example of a consistent application of the general results of the theory of elliptic boundary value problems to domains with piecewise smooth boundaries (see key papers [1–3] and also monographs [4, 5]). In the first place, this applies to the analysis of the behavior of stress-strain state in the vicinity of the crack tip and to operations involving ......
Constructive Description of Hölder Classes on Some Multidimensional Compact Sets
Vestnik St. Petersburg University, Mathematics - Tập 54 Số 3 - Trang 245-253 - 2021
Optimization of the quasi-Monte Carlo algorithm for solving systems of linear algebraic equations
Vestnik St. Petersburg University, Mathematics - Tập 41 Số 1 - Trang 60-64 - 2008
Power Series of One Variable with Condition of Logarithmical Convexity
Vestnik St. Petersburg University, Mathematics - Tập 53 - Trang 20-28 - 2020
We obtain a new version of the Hardy theorem about power series reciprocal to the power series with positive coefficients in this work. We prove that, if the sequence {an}, n ≥ K is logarithmically convex, then the reciprocal power series has only negative coefficients bn, n > 0 for any K if the first coefficient a0 is sufficiently large. The classical Hardy theorem corresponds to the case K = 0. ......
On the Asymptotic Power of a Method for Testing Hypotheses on the Equality of Distributions
Vestnik St. Petersburg University, Mathematics - - 2023
An improved nonlinear Reynolds equation for a thin flow of a viscous incompressible fluid
Vestnik St. Petersburg University, Mathematics - Tập 41 - Trang 171-175 - 2008
A scalar nonlinear second-order equation describing a fluid flow between two closely spaced rigid walls is constructed on the basis of an asymptotic analysis of the Navier-Stokes equations. This equation takes into account the convective term and the surface curvature; it improves the Reynolds equation and provides a two-term asymptotics for the solution to the initial problem. Integral and pointw......
On some problems of guaranteed search on graphs
Vestnik St. Petersburg University, Mathematics - Tập 43 - Trang 68-73 - 2010
Pursuit-evasion differential games on graphs with no information on the evader are considered. Special attention is given to the following ɛ-search problem posed by Golovach. A topological graph embedded in three-dimensional Euclidean space is considered. For simplicity, its edges are assumed to be polygonal, only simple motions of the pursuers and the evader are allowed, and the graph is a phase ......
Initial supercritical behavior of buckled transversely isotropic elastic medium
Vestnik St. Petersburg University, Mathematics - Tập 44 - Trang 44-50 - 2011
The paper is concerned with a transversely isotropic homogeneous elastic medium subjected to uniform compression in the isotropy plane. The medium becomes unstable in the sense of Hadamard [1] at a definite level of initial strain. The critical strain is established to be uniquely determinate from the system of equations of bifurcation of equilibrium; however, there are many modes of buckling corr......
Hilbert pairing on Lorentz formal groups
Vestnik St. Petersburg University, Mathematics - Tập 50 - Trang 117-121 - 2017
In this paper, we construct an explicit pairing in Cartier series for formal Lorentz groups of the form (X + Y + XY)/(1 + c
2
XY), where c is a unit of the ring of integers of the local field. We prove the basic properties of this pairing, namely, bilinearity and invariance, which make it possible to explicitly construct the generaliz......
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