Doklady Mathematics最新文献

A dynamical system with constraints in the form of linear differential inequalities is considered. It is proved that, in the general case, the motion under such constraints is impactless. The possibility of implementing such constraints by viscous friction forces is shown. An example of a nonholonomic system is given that demonstrates via numerical simulation how a system with anisotropic viscous friction transforms into a system with unilateral differential constraints as the degree of anisotropy increases.

In this paper, the first fixed-ratio approximation algorithms are proposed for a series of asymmetric settings of well-known combinatorial routing problems. Among them are the Steiner cycle problem, the prize-collecting traveling salesman problem, the minimum cost cycle cover problem by a bounded number of cycles, etc. Almost all of the proposed algorithms rely on original reductions of the considered problems to auxiliary instances of the asymmetric traveling salesman problem and employ the breakthrough approximation results for this problem obtained recently by O. Svensson, J. Tarnawski, L. Végh, V. Traub, and J. Vygen. On the other hand, approximation of the cycle cover problem was proved by applying a deeper extension of their approach.

In this paper analogues of Herbrand’s and Harrop’s theorems for the logic ({text{QHC}}) are proved.

Equations of gravitation in the form of Vlasov–Poisson relativistic equations with Lambda term are derived from the classical principle of least action. Hamilton–Jacobi consequences are used to obtain cosmological solutions. The properties of Lagrange points are investigated.

The moduli space of holomorphic differentials on curves of genus g admits a natural action of the group (G{{L}_{2}}(mathbb{R})). The study of orbits of this action and their closures has attracted the interest of a wide range of researchers in the last few decades. In the 2000s, C. McMullen described an infinite family of orbifolds that are closures of such orbits in the space of holomorphic differentials on curves of genus 2. In spaces of holomorphic differentials on curves of higher genera, well-known examples of orbifolds that are unions of (G{{L}_{2}}(mathbb{R}))-orbit closures are Prym eigenform loci. They are nonempty for surfaces of genus at most 5. This paper presents the first nontrivial calculations of the number of connected components in Prym eigenform loci for surfaces of maximum possible genus.

We consider the so-called four-equation model for dynamics of the heterogeneous compressible binary mixtures with the Noble-Abel stiffened-gas equations of state. We exploit its quasi-homogeneous form that arises after excluding the volume concentrations from the sought functions and is based on a quadratic equation for the common pressure of the components. We present new properties of this equation and a simple formula for the squared speed of sound, suggest an alternative derivation for a formula relating it to the squared Wood speed of sound and state the pressure balance equation. For the first time, we give a quasi-gasdynamic-type regularization of the heterogeneous model (in the quasi-homogeneous form), construct explicit two-level in time and symmetric three point in space finite-difference scheme without limiters to implement it in the 1D case and present numerical results.

An approach to the construction of a digital controller that stabilizes a continuous-time switched linear system with commensurate delays in control is proposed. The approach to stabilization sequentially includes the construction of a switched continuous-discrete closed system with a digital controller, the transition to its discrete model represented as a switched system with modes of various orders, and the construction of a discrete dynamic controller based on the quadratic stability condition for a closed switched discrete-time system.

In this paper, we consider the problem of constructing a numerical solution to the system of equations of an acoustic medium in a fixed domain with a boundary. Physically, it corresponds to seismic wave propagation in geological media during seismic exploration of hydrocarbon deposits. The system of first-order partial differential equations under consideration is hyperbolic. Its numerical solution is constructed by applying a grid-characteristic method on an extended spatial stencil. This approach yields a higher order approximation scheme at internal points of the computational domain, but requires a careful construction of the numerical solution near the boundaries. In this paper, an approach that preserves the increased approximation order up to the boundary is proposed. Verification numerical simulations were carried out.

Plagiarism detection in scholar assignments becomes more and more relevant nowadays. Rapidly growing popularity of online education, active expansion of online educational platforms for secondary and high school education create demand for development of an automatic reuse detection system for handwritten assignments. The existing approaches to this problem are not usable for searching for potential sources of reuse on large collections, which significantly limits their applicability. Moreover, real-life data are likely to be low-quality photographs taken with mobile devices. We propose an approach that allows detecting text reuse in handwritten documents. Each document is a picture and the search is performed on a large collection of potential sources. The proposed method consists of three stages: handwritten text recognition, candidate search and precise source retrieval. We represent experimental results for the quality and latency estimation of our system. The recall reaches 83.3% in case of better quality pictures and 77.4% in case of pictures of lower quality. The average search time is 3.2 s per document on CPU. The results show that the created system is scalable and can be used in production, where fast reuse detection for hundreds of thousands of scholar assignments on large collection of potential reuse sources is needed. All the experiments were held on HWR200 public dataset.

We study the asymptotic behavior of the solution to the diffusion equation in a planar domain, perforated by tiny sets of different shapes with a constant perimeter and a uniformly bounded diameter, when the diameter of a basic cell, (varepsilon ), goes to 0. This makes the structure of the heterogeneous domain aperiodical. On the boundary of the removed sets (or the exterior to a set of particles, as it arises in chemical engineering), we consider the dynamic unilateral Signorini boundary condition containing a large-growth parameter (beta (varepsilon )). We derive and justify the homogenized model when the problem’s parameters take the “critical values”. In that case, the homogenized problem is universal (in the sense that it does not depend on the shape of the perforations or particles) and contains a “strange term” given by a non-linear, non-local in time, monotone operator H that is defined as the solution to an obstacle problem for an ODE operator. The solution of the limit problem can take negative values even if, for any (varepsilon ), in the original problem, the solution is non-negative on the boundary of the perforations or particles.