Doklady Mathematics最新文献

Homogeneous Markov chains with continuous time are considered. A new approach is proposed that makes it possible to obtain accurate perturbation bounds for such chains with respect to perturbations of infinitesimal characteristics. It is shown how the results can be applied to stationary queuing systems of several classes and to some nonstationary systems.

This work examines basic categorial grammars and categorial grammars with the unique type assignment condition. For the first formalism, it is proven that determining for an arbitrary context-free language (L) whether it is generated by some grammar from this class is algorithmically undecidable. It is also proven that, for any two grammars of this class, the problem of determining the emptiness of the intersection of the languages generated by these grammars is algorithmically undecidable. For the second formalism, it is proven that, for any two categorial grammars with unique type assignment, the problem of determining language inclusion is algorithmically undecidable.

Consider the set (mathcal{E}(G,k)) of all sizes (numbers of edges) of induced subgraphs of size k in a given graph (G) on (n) vertices. For the binomial random graph (G = G(n,p)), we prove that, for each (alpha > 0) and (varepsilon ) small enough, the set (mathcal{E}(G,k)) with high probability contains a long interval for all k such that ({{(ln n)}^{{1 + alpha }}} < k < varepsilon n). We also find the asymptotic length of this interval.

Differential equations describing the behavior of continuous media with creep involve integral type operators, in accordance with Volterra’s linear theory, which is applicable to a wide range of materials with amorphous and heterogeneous structures. In these equations, the kernel of the integral operator is represented as a sum of exponentials or as a weakly singular kernel (Rabotnov function). Obtaining an analytical solution for the equations in question is problematic in some cases, so it is necessary to develop a numerical method and algorithm, taking into account the memory of the considered medium. In this paper, the equations are solved using the grid-characteristic method and dimensional splitting (for multidimensional problems). The approximation and stability of the proposed method are numerically investigated.

The three-dimensional exterior Neumann problem for the Helmholtz equation is considered. Using the potential method, we reduce it to a weakly singular boundary Fredholm integral equation of the second kind, which is solved numerically. To improve the accuracy of the numerical solution algorithm and to reduce its computational complexity, we average the kernel of the integral operator and localize its singular part during discretization by applying simple analytical expressions. Examples of using this approach in the numerical solution of the original problem are given.

In this paper, we propose a modification of the discontinuous Galerkin method using time-dependent basis functions. The use of such basis functions allows one to naturally and stably calculate strong discontinuities.

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.