Results 1 - 10 of 1458
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[en] The spectrum of a selfadjoint operator which is a one-dimensional perturbation of the second derivative operator on a finite interval is analysed. It is shown that all the components of the one-dimensional perturbation can be recovered from two spectra up to complex conjugation. Bibliography: 13 titles.
[en] A boundary-value problem for a second order parabolic equation on a half-line is considered. A uniform asymptotic approximation to a solution to within any power of t-1 is constructed and substantiated. Bibliography: 8 titles.
[en] We improve the Frankl-Rödl estimate for the product of the numbers of edges in uniform hypergraphs with forbidden cardinalities of the intersection of edges. By using this estimate, we obtain explicit bounds for the chromatic number of a space with forbidden monochromatic equilateral triangles. Bibliography: 31 titles
[en] We discuss the construction of coverings of the unit ball of a finite dimensional Banach space. There is a well-known technique based on comparing volumes which gives upper and lower bounds on covering numbers. However, this technique does not provide a method for constructing good coverings. Here we study incoherent systems and apply them to construct good coverings. We use the following strategy. First, we build a good covering using balls with a radius close to one. Second, we iterate this construction to obtain a good covering for any radius. We shall concentrate mainly on the first step of this strategy. Bibliography: 14 titles
[en] All the Fomenko-Zieschang invariants are calculated for the Kovalevskaya-Yehia problem, for all noncritical values of the parameters g and λ, by constructing admissible systems of coordinates and determining the mutual disposition of the basis cycles. The family of Kovalevskaya-Yehia systems contains 29 pairwise Liouville non-equivalent foliations. These foliations include those that are equivalent to previously known foliations, which arose in the integrable cases of Kovalevskaya and of Kovalevskaya-Yehia for g = 0, in the Zhukovskiı case, and in the Goryachev-Chaplygin-Sretenskiı case. Eleven new foliations are included in the 29 foliations, new in the sense that they are not Liouville equivalent to any foliations discovered earlier which arose in the known integrable cases of the rigid body. The topological type of the Liouville foliation for the family of Kovalevskaya-Yehia systems stabilizes at large values of the energy H, and this 'high-energy' system is roughly Liouville equivalent, at one of the energy levels, to the Goryachev-Chaplygin-Sretenskiı integrable case, which is already known. Bibliography: 29 titles
[en] In the paper, a new description of the generalized Lions-Peetre method of means is found, which enables one to evaluate the interpolation orbits of spaces constructed by this method. The list of these spaces includes all Lorentz spaces with functional parameters, Orlicz spaces, and spaces close to them. This leads in turn to new optimal embedding theorems for Sobolev spaces produced using the Lions-Peetre construction in rearrangement invariant spaces. It turns out that the optimal space of the embedding is also a generalized Lions-Peetre space whose parameters are explicitly evaluated. Bibliography: 18 titles
[en] In this paper, we study distributions on compact homogeneous spaces, including invariant distributions and also distributions admitting a sub-Riemannian structure. We first consider distributions of dimension 1 and 2 on compact homogeneous spaces. After this, we study the cases of compact homogeneous spaces of dimension 2, 3, and 4 in detail. Invariant distributions on simply connected compact homogeneous spaces are also treated. Bibliography: 18 titles
[en] The paper is concerned with a nonlinear system of partial differential equations with parameters which describes the two-layer quasi- solenoidal Lorenz model for a baroclinic atmosphere on a rotating two- dimensional sphere. The right-hand side of the system is perturbed by white noise. A unique stationary measure for the Markov semigroup defined by the solutions of the Cauchy problem for this problem is considered. An estimate for the rate of convergence of the distributions of all solutions in a certain class of this system to the unique stationary measure as is proposed. A similar result is obtained for the equation of a barotropic atmosphere and the two-dimensional Navier-Stokes equation. A comparative analysis with some of the available related results is given for the latter. Bibliography: 39 titles. (paper)
[en] Let be a Cauchy transform of a possibly complex-valued Borel measure and a system of orthonormal polynomials with respect to a measure , where . An th Frobenius-Padé approximant to is a rational function , , , such that the first Fourier coefficients of the remainder function vanish when the form is developed into a series with respect to the polynomials . We investigate the convergence of the Frobenius-Padé approximants to along ray sequences , , when and are supported on intervals of the real line and their Radon-Nikodym derivatives with respect to the arcsine distribution of the corresponding interval are holomorphic functions. Bibliography: 30 titles. (paper)
[en] This paper is concerned with the existence of semiregular solutions to the Dirichlet problem for an equation of elliptic type with discontinuous nonlinearity and when the differential operator is not assumed to be formally self-adjoint. Theorems on the existence of semiregular (positive and negative) solutions for the problem under consideration are given, and a principle of upper and lower solutions giving the existence of semiregular solutions is established. For positive values of the spectral parameter, elliptic spectral problems with discontinuous nonlinearities are shown to have nontrivial semiregular (positive and negative) solutions. Bibliography: 32 titles