Doklady Mathematics最新文献

A mixed problem for a B-hyperbolic equation in Euclidean domains with different locations relative to singular coordinate hyperplanes is considered. In each of these domains, energy integrals with respect to the Lebesgue–Kipriyanov integral measure with weak and strong singularities are introduced. It is proved that there is no energy flow through the singular coordinate hyperplanes, which are the internal boundary of mirror-symmetric domains in Euclidean space. If solutions to these problems exist, their uniqueness is proved.

We consider weighted modules of entire functions that are dual to general spaces of (Omega )-ultradifferentiable functions. We explore the local description problem for primary submodules in these modules. It is shown that there exist primary submodules that are not weakly localizable. Nontrivial conditions are obtained under which a local description is possible. All assertions can be reformulated as equivalent dual ones concerning the spectral synthesis problem for differentiation-invariant subspaces of (Omega )-ultradifferentiable functions.

The paper proposes four parameters to measure the efficiency of investments and their inflation. These parameters were calculated individually for 49 relatively large countries with a fairly advanced level of economic development, for the rest of the world within three international economic associations (OECD, Old EU countries, and New EU countries), and for the world (as a whole) in two time ranges: (1996–2008) and (2009–2023). Based on the calculated parameters, ratings of the efficiency of investments and broad money supply (M3 aggregate) and their inflation are constructed for these 53 subjects, which include all countries of the world. The necessary conditions for ensuring GDP growth in modern Russia above the global average while maintaining macroeconomic stability are shown.

We consider the problem of characterizing the set of extreme points of the unit ball in a Hardy–Lorentz space (H(Lambda (varphi ))), posed by E.M. Semenov in 1978. New necessary and sufficient conditions under which a normalized function f in (H(Lambda (varphi ))) belongs to this set are found. The most complete results are obtained in the case when f is the product of an outer analytic function and a Blaschke factor.

The existence and uniqueness of a strong solution for an inhomogeneous incompressible Kelvin–Voigt fluid motion model is proved. It is not assumed that the initial value of the fluid density is separated from zero. To prove the existence of a solution, an approximation problem is considered, its solvability is proved, and strong a priori estimates independent of the approximation parameter are established for its solutions. After that, passing to the limit as the approximation parameter tends to zero, we show that the solutions of the approximation problem converge to a strong solution of the original problem as the approximation parameter tends to zero. The uniqueness of the solution is established using the Gronwall–Bellman inequality.

We investigate a nonlinear Schrödinger equation of general form in which the chromatic dispersion and the potential are given by two arbitrary functions. The equation is a natural generalization of a wide class of related nonlinear partial differential equations that are often encountered in various fields of theoretical physics and mechanics, including nonlinear optics and plasma physics. For several general nonlinear Schrödinger equations, new exact solutions in implicit form are found, which are expressed in terms of elementary and arbitrary functions. One-dimensional reductions are described, which reduce the considered partial differential equation to simpler ordinary differential equations or systems of such equations.

The paper describes a new method for constructing triangle-free graphs with an arbitrarily large chromatic number. The method is substantiated using properties of various types of ultrafilter extensions of functions and predicates.

The unique DipolarCalc software system is presented, which makes it possible to calculate the polarization of biomolecules through the total dipole moment of chemical bonds of “functional topological atoms” (FTA). The program implements a user-friendly interface that provides intuitive data entry and visualization of calculation results, as well as it uses analytical expressions that allow accurate calculations to be performed in real time. The presented software package is aimed at use in computational biology and provides a convenient tool for modeling intra- and intermolecular interactions of biological molecular structures.

Given a compact metric space with Carathéodory measure, we consider ergodic transformations of the space that are measure-preserving, but not necessarily invertible. The behavior of the Birkhoff sums for integrable and almost everywhere bounded functions with zero mean value in terms of the Carathéodory measure is studied. It is shown that for almost all points of the metric space there is an infinite sequence of “time instants” along which the Birkhoff sums tend to zero and the trajectory points at the these instants approach their initial position as close as possible (as in the Poincaré recurrence theorem). As an example, we consider the transformation (x mapsto 2x) (bmod 1) of the unit interval (0,leqslant ,x,leqslant ,1) closely related to Bernoulli trials.

We consider an even-order ordinary differential operator with a spectral parameter and integral conditions. An a priori estimate of solutions to the problem is obtained for sufficiently large values of the spectral parameter. The discreteness and the sectoral structure of the spectrum of the corresponding operators are proved.