Том 213, № 6 (2016)
- Год: 2016
- Статей: 12
- URL: https://journals.rcsi.science/1072-3374/issue/view/14723
Article
Estimation of the Number of Cells via the Number of Randomly Occupied Cells
Аннотация
We consider a scheme of series where the growth of the distribution support is asymptoticially proportional to the growth of the sample size. It is assumed that the values of sample elements are inaccessible, whereas the number of different elements is known. Based on this statistic, we construct a consistent and asymptotically normal estimate for the parameter expressing the limiting ratio of the sample size to the number of support elements. Bibliography: 5 titles.
Solitary Waves in Two-Layer Shallow Water
Аннотация
Propagation of nonlinear waves in a two-layer fluid in the shallow water approximation is considered. In a horizontal channel with a free surface and under lid, the large amplitude subsurface solitary waves describing the wave with “trapped core” are investigated. The flow regime diagram for solitary waves is constructed in the plane of governing parameters. Bibliography: 17 titles. Illustrations: 3 figures.
Estimates for Solutions of One Class of Nonlinear Neutral Type Systems with Several Delays
Аннотация
We consider a class of systems of nonlinear differential equations of neutral type with several delays. We obtain conditions of exponential stability of the zero solution and establish estimates characterizing the exponential decay rate of solutions at infinity. Bibliography: 14 titles.
Harmonic Analysis of Nonquasianalytic Operators in a Real Banach Space
Аннотация
In a real Banach space, we consider linear bounded invertible operators such that the norms of their powers are nonquasianalytic. We obtain the condition of the existence of a nontrivial invariant subspace and the condition of decomposability (in the sense of Foia¸s) of such operators. Bibliography: 14 titles.
Error Estimate for the Stationary Galerkin Method Applied to a Semilinear Parabolic Equation with Alternating Time Direction
Аннотация
We prove the existence and uniqueness of a solution in the space W22,1(Q) to the first boundary value problem for a semilinear parabolic equation in a cylindrical domain Q ⊆ Rn+1. We obtain an error estimate in the W21,0(Q)-norm in terms of eigenvalues of the selfadjoint spectral problem for a second order elliptic equation. Bibliography: 5 titles.
Identification and Discretization of Linear Differential Equations with Constant Coefficients
Аннотация
We consider the variational problem of approximation and identification of finite sequences. Using the identification problem, we study discretization of the corresponding differential equations. We obtain necessary and sufficient conditions for the uniqueness of discretization and identification problems. Under these conditions, the proposed variational discretization and the known analytic discretization lead to the same result. Bibliography: 14 titles.
Single-Valued q-Differentials on a Variable Finite Riemann Surface
Аннотация
We consider single-valued meromorphic functions and differentials on finite Riemann surfaces. We construct elementary q-differentials of all types. We find the dimension of two important quotient spaces of Abelian q-differentials, in particular, the first holomorphic de Rham cohomology group of 1-differentials. For these quotient spaces we construct bases that locally holomorphically depend on the moduli of the Riemann surfaces. Bibliography: 6 titles.
Spectral Analysis of a Differential Operator with Involution
Аннотация
We consider the differential operator L with involution defined by the differential expression l(y) = y′(x) − q(x)y(ω − x), q ∈ L2[0, ω], and boundary condition y(0) = y(ω). We study spectral properties of the operator L by using the method of similar operators. Bibliography: 6 titles.
The Gellerstedt Equation with Integral Perturbation in the Cauchy Data
Аннотация
We establish the well-posedness of the problem for a degenerate hyperbolic equation of the first kind in the characteristic triangle with integral perturbation in the Cauchy data along the degeneracy line. Bibliography: 16 titles.