Contents
Doklady Mathematics

Vol. 82, No. 1, 2010

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

Translated from Doklady Akademii Nauk, Volume 433, Nos. 1–6, 2010

Volume 82, July–August.

Mathematics

On the Singular Spectrum of Powers and Products of Random Matrices

N. V. Alexeev, F. Götze, and A. N. Tikhomirov p. 505  abstract

Homoclinic Orbits to 1-Elliptic Points and KAM-Curves and Scattering

L. M. Lerman and A. P. Markova p. 508  abstract

Decomposition of Homologically Trivial Knots in F I

S. V. Matveev p. 511  abstract

Mean-Square Optimization for Global Monte Carlo Algorithms

G. A. Mikhailov and I. N. Medvedev p. 514  abstract

On the Index of Nonlocal Elliptic Operators for the Group of Dilations

A. Yu. Savin and B. Yu. Sternin p. 519  abstract

D’Alembert-Type Formula for Vibrations of an Infinite Rod Consisting
of Two Segments with Different Densities Described by the Telegraph Equation

I. N. Smirnov p. 523  abstract

Autostable Atomic-Ideal Enrichments of Computable Boolean Algebras

P. E. Alaev p. 528  abstract

A New Local-Global Principle for Quadratic Functional Fields

V. V. Benyash-Krivets and V. P. Platonov p. 531  abstract

Computation of the Genetic Code

N. N. Kozlov p. 535  abstract

Algorithm for Constructing Counterexamples to the Kalman Problem

G. A. Leonov, V. O. Bragin, and N. V. Kuznetsov p. 540  abstract

A Semipolynomial Parameterization of Fourth-Order Spinor Groups

N. G. Marchuk p. 543  abstract

A Generalization of a Theorem of Fischer

V. V. Napalkov p. 546  abstract

Factors of Minimal Models for Saddle Singularities of Integrable Hamiltonian Systems

A. A. Oshemkov p. 549  abstract

To the Theory of Regular Boundary Value Problems for Ordinary Linear Differential
Operators in the Space Lp,n

A. I. Vagabov p. 554  abstract

On the Asymptotic Properties of Solutions of Ordinary Differential Systems
on a Logarithmic Scale of Growth

O. V. Druzhinina and A. A. Shestakov p.558  abstract

Constructive Sufficient Conditions for the Existence of a Unitary Similarity Transformation
that Converts a Given Complex Matrix into a Real One

Kh. D. Ikramov p. 563  abstract

Generalization of the Schwarz–Jensen Formula

I. I. Bavrin p. 566  abstract

Embedding Constants and Embedding Functions for Sobolev-Like Spaces on the Unit Sphere

V. L. Vaskevich p. 568  abstract

Uniqueness Classes in Inverse Problems for Parabolic Equations
with Several Unknown Coefficients

N. L. Gol’dman p. 573  abstract

Necessary and Sufficient Stabilization Conditions for the Solution of the Cauchy Problem
for a Parabolic Equation with Nonzero Lower Order Coefficients

V. N. Denisov p. 578  abstract

Analogues of the Problem of Analytic Continuation from Circles
for Some Differential Equations

O. A. Ochakovskaya p. 581  abstract

Basis Properties of the Root Functions of an Eigenvalue Problem
with a Spectral Parameter in the Boundary Conditions

Z. S. Aliev p. 583  abstract

The Structure of Multidimensional Diophantine Approximations

A. D. Bruno p. 587  abstract

On the Compensated Compactness Principle

V. V. Zhikov and S. E. Pastukhova p. 590  abstract

Asymptotics of the Spectrum of the Sturm–Liouville Operator with Local Interaction

R. S. Ismagilov and A. G. Kostyuchenko† p. 596  abstract

On the Convergence of Shock-Capturing Difference Schemes

O. A. Kovyrkina and V. V. Ostapenko p. 599  abstract

Strongly Regular Graph with Parameters (486, 112, 36, 66) Does not Exist

A. A. Makhnev and A. A. Makhnev, Jr. p. 604  abstract

Graphs in Which the Neighborhoods of Vertices Are Pseudogeometric Graphs for GQ(3, 3)

A. K. Gutnova and A. A. Makhnev p. 609  abstract

Characterization of General Radon Integrals

V. K. Zakharov, A. V. Mikhalev, and T. V. Rodionov p. 613  abstract

Properties of Root Vector Functions for the One-Dimensional Dirac Operator

V. M. Kurbanov and A. I. Ismailova p. 617  abstract

Solvability of Some Nonlocal Boundary Value Problems
for the Helmholtz Equation in a Half-Disk

E. I. Moiseev and V. E. Ambartsumyan p. 621  abstract

Mathematical Physics

Differential Identities Relating the Modulus and Direction of a Vector Field
and Euler’s Hydrodynamic Equations

A. G. Megrabov p. 625  abstract

Dynamics of a Quantum Particle with Discontinuous Position-Dependent Mass

V. G. Sakbaev and O. G. Smolyanov p.630  abstract

One-Dimensional Quasilinear Eigenvalue Problem

D. P. Kostomarov p. 634  abstract

Some Differential Identities and Their Applications to the Eikonal Equation

A. G. Megrabov p. 638  abstract

Computer Science

Bidirectional Resource Networks: A New Flow Model

O. P. Kuznetsov and L. Yu. Zhilyakova p. 643  abstract

Decomposition for Solutions of Large-Scale Multicriteria Problems

Ya. I. Rabinovich p. 647  abstract

Control Theory

Frequency-Domain Estimates for the Oscillation Periods of Nonlinear Discrete Systems

G. A. Leonov and A. A. Fyodorov p. 651  abstract

Yet Another Strong Equilibrium for Game Problems

E. R. Smol’yakov p. 655  abstract

On Possible Scenarios of the Transition to Turbulence in Rayleigh–Bénard Convection

N. M. Evstigneev and N. A. Magnitskii p. 659  abstract

Algorithm for Localizing Chua Attractors Based on the Harmonic Linearization Method

G. A. Leonov, V. I. Vagaitsev, and N. V. Kuznetsov p. 663  abstract

Adaptive Regulators for the Control of an Uncertain Linear Discrete-Time System
with a Reference Model

E. Yu. Nebos’ko, A. V. Proskurnikov, and V. A. Yakubovich p. 667  abstract

Necessary and Sufficient Conditions of Nanorobot Synthesis

M. B. Ignatyev p. 671  abstract

Algebra of Sets of Dynamic Processes with Differential Realizations in a Hilbert Space

V. A. Rusanov p.676

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