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Number 4, August 2001
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A A Bolibrukh
P V Gapeev
A A Gerko
A Yu Golubkov
M M Grinenko
A V Grishin
V M Manuilov and K Thomsen
D V Millionshchikov
S M Natanzon
D A Shakin
V N Silaev
Yu N Subbotin and Sergei A Telyakovskii
O Ya Viro and Stepan Yu Orevkov
V A Zorich
W W Zudilin
B A Amosov, M Sh Birman and M I Vishik
S S Demidov, A N Parshin and S S Petrova
L A Basalygo and M L Blank
S I Adian
I M Gelfand and M I Graev
A function on is assigned to any non-singular complex matrix , where and are arbitrary positive integers. A relationship is established between these functions and the solutions of general hypergeometric systems of differential equations and their generalizations, the so-called GG-systems. It is natural to treat the functions as regularizations of solutions of these systems. Conversely, from any function one can recover the set of solutions of the corresponding GG-system. Also considered are analogues of GG-systems and related functions obtained by replacing the differentiation operators by operators of more general form, in particular, by q-differentiation operators.
A G Pinus
The notion of program-computable function on a universal algebra is formalized through the notion of conditional term. This leads to a somewhat new approach to the study of traditional algebraic problems related to both universal classes and specific finite algebras, and also enables one to pose and investigate the problem of the computation resources of universal algebras.
T M Suidan
The surprising connection between a one-dimensional gravitationally interacting gas of sticky particles and the convex minorant process generated by Brownian motion on [0,1] is studied. A study is made of the dynamics of this 1-D gas system by identifying three distinct clustering regimes and the time scales at which they occur. At the critical moment of time the mass distribution of the gas can be computed in terms of functionals of the convex minorant process.
S B Shlosman
Geometric solutions are presented for some variational problems of statistical mechanics and combinatorics, and the Wulff construction predicting crystal shapes is discussed along with a construction determining the shape of a typical Young diagram and a typical skyscraper.
A V Arutyunov, N S Bakhvalov and M E Bogovskii
