A Guide to the Russian Academy of Sciences - University of Texas ...

9. Laboratory of Statistical Methods: Staff: I. A. Ibragimov, (Head of Laboratory),
A. N. Borodin, A. Iurii Zaitsev, M. S. Nikulin, V. N. Solev, V. N. Udakov, A.
V. Teplyaev, L. A. Khalfin, and N. M. Khalfina. New methods of investigation of
the limiting behavior of statistical parameter estimates in the asymptotic estimation
theory were suggested, which led to the final solution of the old problem about the
asymptotic efficiency of maximum likelihood estimates. Methods of solution of
nonparametric estimation problems were developed.
The approximation of the distribution of sums of independent random variables by infinite
divisible distributions was studied. In particular an old A. N. Kolmogorov's
problem about the order of accuracy of such approximation in the Levy metric was
solved.
Methods of investigation of asymptotic behavior of the distribution of functionals defined
on random walks were suggested, which proved for the first time, the appropriate
limit theorems under natural conditions.
Researches were carried out in the theory of Gaussian processes, spectral theory and in
statistics of stationary processes and homogeneous fields.
10. Laboratory of Algorithmic Methods: Staff: D. Iurii Grigor'ev, (Head of
Laboratory), A. Iurii Volkov, N. N. Vorob'ev, L. Iurii Kolotilina, T. Ya.
Kon'kova, V. N. Kublanovskaia (aya), N. B. Lebedinskaia (aya), M. M.
Lebedinskii, and V. N. Simonova. For theories of the first order of algebraically
closed, as well as real closed, fields, algorithms of solutions were constructed with
subexponential complexity under a bounded number of changes of quantors in the
theory formula.
An algorithm of solution of systems of polynomial inequalities over a real closed field in a
subexponential time, an algorithm of elimination in the first order theory of ordinary
differentially closed fields with an elementary estimate of complexity and an
algorithm of polynomial complexity for finding the greatest common divisor of a
family of linear ordinary differential operators were suggested.
A new approach to the construction of algorithms of the solution of spectral problems for
bundles of matrices, as well as for polynomial and rational matrices of general type
(both regular and singular), based on the minimal (non cancelable) factorization of
the rational matrix was suggested.
11. Laboratory of Mathematical Problems of Geophysics: Staff: V. M. Babich,
(Head of Laboratory), A. I. Bobenko, B. V. Budaev, N. S. Zabavnikova, A. P
Kachalov, N. Ya. Kirpichnikova, L. A. Krauklis, P. V. Krauklis, Ya. V. Kurylev,
E. M. Ledovskaia (aya), L. A. Molotkov, S. M. Novoselova, G. I. Petrashen',
Iurii A. Surkova, T. N. Surkova, V. B. Filippov, and Z. A. Yanson.
Exact solutions of wave problems from the point of view of applications of these solutions
to the numeric calculation of wave phenomena of different nature were studied.
Asymptotic methods of solution of wave problems, i.e. the space-time ray method, the
method of Gaussian bundles, were developed, which can be used for representation
of a wave field both in the area of regularity of the ray and in the caustics.
On the basis of the developed exact and asymptotic methods of solution of wave problems
computer programs for numeric solution of these problems were constructed and
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