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Vol 228, No 6 (2018)
- Year: 2018
- Articles: 10
- URL: https://journals.rcsi.science/1072-3374/issue/view/14883
Article
A Remark on Denoising of Greyscale Images Using Energy Densities with Varying Growth Rates
Abstract
We prove the solvability in Sobolev spaces for a class of variational problems related to the TV-model proposed by Rudin, Osher and Fatemi for the denoising of greyscale images. In contrast to their approach, we discuss energy densities with variable growth rates depending on |∇u| in a rather general form including functionals of (1, p)-growth.
705-722
The Case of Integrable Systems with Dissipation on the Tangent Bundle of a Multidimensional Sphere
Abstract
We establish the integrability of dynamical systems of some classes arising in multidimensional dynamics. The force fields under consideration possess the so-called variable dissipation with zero mean and generalize the studied earlier ones.
723-730
Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations
Abstract
We establish the existence in the sense of sequences of stationary solutions for some reaction-diffusion type equations in appropriate H2 spaces. It is shown that, under reasonable technical conditions, the convergence in L1 of the integral kernels implies the existence and convergence in H2 of solutions. The nonlocal elliptic equations involve second order differential operators with and without the Fredholm property. Bibliography: 21 titles.
601-632
The Hurwitz Product, p-Adic Topology on ℤ, and Fundamental Solution to Linear Differential Equation in the Ring ℤ[[x]]
Abstract
We study the linear inhomogeneous first order differential equation by′ + f(x) = y in the ring of formal power series with integer coefficients. Using the p-adic topology on the ring of integers, we construct a counterpart of the Hurwitz product of the Euler series and an arbitrary formal power series with integer coefficients. It is shown that the Euler series can be interpreted as the fundamental solution to the equation under consideration. Bibliography: 8 titles.
633-638
Integer Realization of Spline-Wavelet Decomposition
Abstract
We consider integer spline-wavelet algorithms for processing digital flows. We obtain integer variants of the decomposition and reconstruction formulas and give an example demonstrating the practical realizability of the proposed algorithms.
639-654
Trace Theorem and Applications
Abstract
We characterize three-dimensional vector fields on the basis of the trace of a certain combination of normal derivatives, curl, and divergence. We clarify an unconditional connection between the values of a vector-valued function and the values of gradient, curl, and divergence on the boundary, which makes it possible to consider boundary value problems with boundary conditions that involve the basic first order differential operations of field theory.
655-661
662-671
On Solutions to the Schwarz Problem in a Disk in the Three-Dimensional Case
Abstract
We consider the Schwarz problem for first order elliptic systems in the plane. We obtain the conditions on three– and two-dimensional matrices J admitting nondiagonal Jordan form under which a solution to the Schwarz problem in an arbitrary disk exists and is unique in Hölder classes. We describe an algorithm for constructing the solution. Bibliography: 5 titles.
672-683
The Range of the Berezin Transform
Abstract
We give a description of all functions of the form \( \sum \limits_{i=1}^N{f}_i{\overline{g}}_i \) in the range of the Berezin transform, where fi and gi, 1 ≤ i ≤ N, are holomorphic functions on the unit disk ????, which generalizes the corresponding result of Ahern. We also give a very simple proof of the results of Ahern and the results due to Čučković and Li who deal with the special case N = 2 and g2 = zn.
684-694
695-704