Contents

Doklady Mathematics

Vol. 97, No. 1, 2018

A simultaneous English language translation of this journal is available from Pleiades Publishing, Ltd.
Distributed worldwide by Springer. Doklady Mathematics ISSN 1064-5624.

Mathematics

The Liouville Foliation of Nonconvex Topological Billiards

V. V. Vedyushkina p. 1  abstract

New Monte Carlo Algorithms for Estimating Probability Moments of Criticality Parameters for a Scattering Process with Multiplication in Stochastic Media

Corresponding Member of the RAS G. A. Mikhailov and G. Z. Lotova p. 6  abstract

On Heyde’s Theorem for Probability Distributions on a Discrete Abelian Group

G. M. Feldman p. 11  abstract

Multiple Complete Rational Arithmetic Sums of Polynomial Values

V. N. Chubarikov p. 15  abstract

Sawyer Duality Principle in Grand Lebesgue Spaces

P. Jain, A. P. Singh, M. Singh and Corresponding Member of the RAS V. D. Stepanov p. 18  abstract

Besov Classes on a Space with a Gaussian Measure

E. D. Kosov p. 20  abstract

The Niltriangular Subalgebra of the Chevalley Algebra: the Enveloping Algebra, Ideals, and Automorphisms

V. M. Levchuk p. 23  abstract

Topology of Maximally Writhed Real Algebraic Knots

G. B. Mikhalkin and S. Yu. Orevkov p. 28  abstract

The Kato Conjecture for Elliptic Differential-Difference Operators with Degeneration in a Cylinder

A. L. Skubachevskii p. 32  abstract

Instability Degree and Singular Subspaces of Integral Isotropic Cones of Linear Systems of Differential Equations

N. V. Denisova p. 35  abstract

Study of the Solvability of Some Volterra-Type Integral and Integro-Differential Equations of Third Kind

A. I. Kozhanov p. 38  abstract

Many-Sheeted Versions of the Pólya–Bernstein and Borel Theorems for Entire Functions of Order ρ ≠ 1 and Their Applications

L. S. Maergoiz p. 42  abstract

On a Bound in Extremal Combinatorics

A. M. Raigorodskii and A. A. Sagdeev p. 47  abstract

Monotonicity Formula for a Problem with Hysteresis

D. E. Apushkinskaya and N. N. Uraltseva p. 49  abstract

Continual Version of the Perron Effect of Change in Values of Characteristic Exponents

N. A. Izobov and Corresponding Member of the RAS A. V. Il’in p. 52  abstract

Finite Difference Scheme for Barotropic Gas Equations

F. B. Imranov, G. M. Kobel’kov and A. G. Sokolov p. 58  abstract

One-Point Commuting Difference Operators of Rank One and Their Relation with Finite-Gap Schrödinger Operators

G. S. Mauleshova and Corresponding Member of the RAS A. E. Mironov p. 62  abstract

On the Regularity of a Boundary Point for the p(x)-Laplacian

Yu. A. Alkhutov and M. D. Surnachev p. 65  abstract

Partial Decomposition of a Domain Containing Thin Tubes for Solving the Heat Equation

A. A. Amosov and G. P. Panasenko p. 69  abstract

Area of Some Hölder Surfaces on Carnot–Carathéodory Spaces

M. B. Karmanova p. 73  abstract

On the Construction of Combined Finite-Difference Schemes of High Accuracy

O. A. Kovyrkina and V. V. Ostapenko p. 77  abstract

Cut Locus in the Sub-Riemannian Problem on Engel Group

A. A. Ardentov and Yu. L. Sachkov p. 82  abstract

Investigation of the Spectrum of the Problem of Normal Waves in a Closed Regular Inhomogeneous Dielectric Waveguide of Arbitrary Cross Section

Yu. G. Smirnov and E. Yu. Smolkin p. 86  abstract

Optimized Symmetric Bicompact Scheme of the Sixth Order of Approximation with Low Dispersion for Hyperbolic Equations

A. V. Chikitkin and B. V. Rogov p. 90  abstract

Маthematical Physics

Statistical Problems for the Generalized Burgers Equation: High-Intensity Noise in Waveguide Systems

O. V. Rudenko and S. N. Gurbatov p. 95  abstract

On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification

N. N. Nefedov and Academician of the RAS O. V. Rudenko p. 99  abstract

Computer Science

Approximation of the Effective Hull of a Nonconvex Multidimensional Set Given by a Nonlinear Mapping

G. K. Kamenev and A. V. Lotov p. 104  abstract