Volume 235, Nº 2 (2018)
- Ano: 2018
- Artigos: 8
- URL: https://journals.rcsi.science/1072-3374/issue/view/14971
Article
Initial-Boundary Value Problem for the Nonstationary Radiative Transfer Equation with Diffuse Reflection and Refraction Conditions
Resumo
We consider the initial-boundary value problem for the nonstationary radiative transfer equation in a system of semitransparent bodies with the conditions of diffuse reflection and refraction of radiation. We establish the unique solvability of the problem with boundary and initial data in the complete scale of Lebesgue spaces. We obtain estimates for solutions.
Modified Steklov Functions and Numerical Differentiation Formulas
Resumo
We consider an approximation method based on Steklov functions of the first and second order. We obtain estimates for the norms in the space C of continuous periodic functions and clarify how they connect with numerical differentiation formulas.
Smoothness in the Dini Space of a Single Layer Potential for a Parabolic System in the Plane
Resumo
We prove estimates in the Dini space for the second order spatial derivative of a vector parabolic single layer potential. We obtain estimates for higher order derivatives of solutions to initial-boundary-value problems for one-dimensional parabolic systems with Dini-continuous coefficients in a curvilinear domain with nonsmooth lateral boundary.
Criteria for the Best Approximation by Simple Partial Fractions on Semi-Axis and Axis
Resumo
We study uniform approximation of real-valued functions f, f(∞) = 0, on ℝ+ and ℝ by real-valued simple partial fractions (the logarithmic derivatives of polynomials). We obtain a criterion for the best approximation on ℝ+ and ℝ in terms of the Chebyshev alternance. This criterion is similar to the known criterion on finite segments. For the problem of approximating odd functions on ℝ we construct an alternance criterion with a weakened condition on the poles of fractions. We present a criterion for the best approximation by simple partial fractions on ℝ+ and ℝ in terms of Kolmogorov. We prove analogs of the de la Vallee-Poussin alternation theorem.
On Eigenfunctions of the Fourier Transform
Resumo
A nontrivial example of an eigenfunction in the sense of the theory of distributions for the planar Fourier transform was described by the authors in their previous work. In this paper, a method for obtaining other eigenfunctions is proposed. Positive homogeneous distributions in ℝn of order −n/2 are considered, and it is shown that F(ω)|x|−n/2, |ω| = 1, is an eigenfunction in the sense of the theory of distributions of the Fourier transform if and only if F(ω) is an eigenfunction of a certain singular integral operator on the unit sphere of ℝn. Since \( {Y}_{m,n}^{(k)}\left(\omega \right){\left|\mathbf{x}\right|}^{-n/2} \), where \( {Y}_{m,n}^{(k)} \) denote the spherical functions of order m in ℝn, are eigenfunctions of the Fourier transform, it follows that \( {Y}_{m,n}^{(k)} \) are eigenfunctions of the above-mentioned singular integral operator. In the planar case, all eigenfunctions of the Fourier transform of the form F(ω)|x|−1 are described by means of the Fourier coefficients of F(ω).
Integrable Systems with Dissipation and Two and Three Degrees of Freedom
Resumo
We establish the integrability for some classes of dynamic systems on the tangent bundles of two– and three-dimensional manifolds (systems with two and three degrees of freedom). The force fields possess the so-called variable dissipation and generalize those considered in the previous publications of the author.