Fifty years of the Siberian Division of the Russian Academy of Sciences

This is a write-up on the foundation of the Sobolev Institute of Mathematics in 1957.     

Approximate Toeplitz Matrix Problem Using Semidefinite Programming

Given a data matrix, we find its nearest symmetric positive-semidefinite Toeplitz matrix. In this paper, we formulate the problem as an optimization problem with a quadratic objective function and semidefinite constraints. In particular, instead of solving the so-called normal equations, our algorithm eliminates the linear feasibility equations from the start to maintain exact primal and dual feasibility during the course of the algorithm. Subsequently, the search direction is found using an inexact Gauss-Newton method rather than a Newton method on a symmetrized system and is computed using a diagonal preconditioned conjugate-gradient-type method. Computational results illustrate the robustness of the algorithm.     

The Knizhnik-Zamolodchikov equations associated with the root system <Emphasis Type="Italic">G</Emphasis><Subscript>2</Subscript>

At the end of the twentieth century, in mathematical physics, the Knizhnik-Zamolodchikov equations for the root systems A _n and their generalizations for the root systems of types B _n , C _n , and D were constructed. For the root system of type G ₂, the vector version of the Knizhnik-Zamolodchikov equations was obtained by M. P. Zamakhovskii and V. P. Leksin. However, the tensor version of these equations has remained unstudied. In this paper, the Knizhnik-Zamolodchikov equations associated with the root system of type G ₂ are considered. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal Conference-2004, Part 3, 2006.     

Output-feedback control robust stabilization of nonlinear pulse systems

A nonlinear pulse systems with a time-variant continuous linear part is considered. A method for synthesizing an output-feedback robust stabilizing control is suggested.     

Stress monitoring in a Guinness 10-day scuba dive

Nowadays, there is high demand for sensitive gas sensors both for human and environmental monitoring. This paper deals with a high-resolution (0.2 ppb) laser-based photoacoustic spectroscopic system realized at ENEA Frascati, Italy, applied for monitoring stress in scuba divers during sustained immersion by analyzing breath samples. Blood tests and psychometric tests for scuba divers were performed at Catholic University in Rome. Results will be reported and discussed.     

Conditions of stability of magnetic sublattices at exchange mixing of states with different spins

The conditions of compatibility of the magnetic sublattice hypothesis with the requirements of quantum theory have been derived. These conditions imply the presence of (even weak) magnetic anisotropy and a macroscopic number of spins in the sublattice.