Contents
Doklady Mathematics

Vol. 77, No. 3, 2008

English language translation of the journal is available from Pleiades Publishing, Ltd.
Distributed worldwide by Springer. Doklady Mathematics ISSN 1064–5624.

Translated from Doklady Akademii Nauk, Volume 420, Nos. 1–6, 2008

Volume 77, May–June.

Mathematics

Nonpower Asymptotic Forms of Solutions to a System of Ordinary Differential Equations

A. D. Bruno p. 325  abstract

The “Pontryagin Derivative” in Optimal Control

R. V. Gamkrelidze p. 329  abstract

Local Holomorphic Cauchy Problem for Soliton Equations of Parabolic Type

A. V. Domrin p. 332  abstract

The Independence of Optimal Boundary Controls of String Oscillations
from the Choice of a Point of Compatibility of the Initial and Final Conditions

V. A. Il’in p. 336  abstract

A Rigidity Condition for the Boundary of a Submanifold in a Riemannian Manifold

A. P. Kopylov p. 340  abstract

Weighted Monte Carlo Algorithms with Branching Corresponding Member of the RAS

G. A. Mikhailov p. 342  abstract

Feynman and Feynman–Kac Formulas for Evolution Equations with Vladimirov Operator

O. G. Smolyanov and N. N. Shamarov p. 345  abstract

Properties of Solutions of Parabolic Equations with Unknown Right-Hand Side
and Adjoint Problems

N. L. Gol’dman p. 350  abstract

On the Stability of Pseudorelativistic Systems of Identical Particles
with Permutation Symmetry

G. M. Zhislin p. 356  abstract

The Canonical Schur Form of a Matrix with Simple Eigenvalues

Kh. D. Ikramov p. 359  abstract

Uniqueness Theorems for Generalized Solutions to Four Mixed Problems
for the Wave Equation with Nonlocal Boundary Conditions

V. A. Il’in p. 361  abstract

Generalization of the Dunkl Operator on the Space of Entire Functions

V. E. Kim and V. V. Napalkov p. 365  abstract

Additional Gradings in the Khovanov Complex for Thickened Surfaces

V. O. Manturov p. 368  abstract

Optimal Control of Cavitation

V. N. Monakhov ^† and E. V. Gubkina p. 371  abstract

The Bessel and Hilbert Properties for Root Functions of Second-Order
Ordinary Differential Operators with the Carleman Condition Violated

A. S. Tsareva p. 375  abstract

Antisymmetric Solutions of Poincaré–Steklov Integral Equations

A. B. Bogatyrev p. 378  abstract

On Passage to the Limit in Nonlinear Elliptic Equations

V. V. Zhikov p. 383  abstract

The Condition of the Coneigenvalues of Conjugate-Normal Matrices

Kh. D. Ikramov p. 388  abstract

An Analytic Form of an Optimal Boundary Control by Displacement at One End
of a String under a Model Nonlocal Boundary Condition of One of Four Types

V. A. Il’in p. 391  abstract

Banach–Saks Index in Spaces with Symmetric Basis

A. I. Novikova, E. M. Semenov, and F. A. Sukochev p. 396  abstract

On the Theory of Antiprior Estimates in the Sense of V.A. Il’in

M. A. Sadybekov and A. M. Sarsenbi p. 398  abstract

The Nonuniqueness of Solutions to Elliptic Equations for Probability Measures

S. V. Shaposhnikov p. 401  abstract

On Cross Approximation of Multi-Index Arrays

S. A. Goreinov p. 404  abstract

Optimization of an Optimal Boundary Control by an Elastic Force at One End
of a String under a Model Nonlocal Boundary Condition of One of Four Types

V. A. Il’in p. 407  abstract

Gyroscopic Stabilization of Degenerate Equilibria and the Topology
of Real Algebraic Varieties

V. V. Kozlov p. 412  abstract

Gravity-Driven Nonlinear Flow in Areas with Impermeable Inclusions

V. N. Monakhov ^† and E. V. Gubkina p. 416  abstract

Quasi-Invariance of Poisson Distributions with Respect to Transformations of Configurations

O. V. Pugachev p. 420  abstract

Parametrix, Kernel Asymptotics, and Regularized Trace for the Diffusion Semigroup

S. A. Stepin p. 424  abstract

Direct Numerical Method for Solving Optimal Control Problems

V. V. Ternovskii and M. M. Khapaev p. 428  abstract

Sharp Bounds for Geometric Rigidity of Isometries on Heisenberg Groups

S. K. Vodop’yanov and D. V. Isangulova p. 432  abstract

On Two Problems of Turing Complexity for Strongly Minimal Theories

S. S. Goncharov p. 438  abstract

On the Index of Nonlocal Elliptic Operators

V. E. Nazaikinskii, A. Yu. Savin, and B. Yu. Sternin p. 441  abstract

Majorants of Functions with Zero Integrals over Balls of Fixed Radius

O. A. Ochakovskaya p. 446  abstract

Trajectories with the Longest Lifetime

V. G. Boltyanski p. 449  abstract

Correctness Criteria for Algebraic Closures of the Estimate-Calculating Algorithm Model

A. G. D’yakonov p. 453  abstract

A Method for Distorting the Frequency of Character Occurrence in the Simple Substitution Cipher

M. P. Mineev and V. N. Chubarikov p. 457  abstract

Mathematical Physics

Spectral Theory of Root Transfer Matrices and Its Application to Statistical Models
on a Triangular Lattice

V. V. Katrakhov and Yu. N. Kharchenko p. 460  abstract

Development of Landau Turbulence in the Multiplier–Accelerator Model

A. Yu. Kolesov, A. N. Kulikov, and N. Kh. Rozov p. 463  abstract

Blowing up Solutions of the Novikov–Veselov Equation

I. A. Taimanov and S. P. Tsarev p. 467  abstract

Control Theory

Transcendental Numbers and Fractal Functions in Problems of Finite Control
of Distributed Systems

A. N. Agadzhanov and A. G. Butkovskii p. 469  abstract

Paraglider: Mathematical Model and Control

P. V. Zaitsev and A. M. Formal’skii p. 472  abstract

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