This is the inaugural volume of a new book series published under the auspices of the St. Petersburg Mathematical Society. The book contains contributions by some of the leading mathematicians in St. Petersburg. Ranging over a wide array of topics, these papers testify to the diverse interests and productive mathematical life of the St. Petersburg Mathematical Society.

Contains articles on analysis, probability, partial differential operators, frames, and other areas of mathematics. This volume also contains a comprehensive article about the classification of pseudo-regular convex polyhedra. It is suitable for a broad group of graduate students and researchers interested in the topics presented here.

The articles in this collection present new results in partial differential equations, numerical analysis, probability theory, and geometry. The results, ideas, and methods given in the book will be of interest to a broad range of specialists.

Translations of articles on mathematics appearing in various Russian mathematical serials.

Books in this series highlight some of the most interesting works presented at symposia sponsored by the St. Petersburg Mathematical Society. Aimed at researchers in number theory, field theory, and algebraic geometry, the present volume deals primarily with aspects of the theory of higher local fields and other types of complete discretely valuated fields. Most of the papers require background in local class field theory and algebraic $K$-theory; however, two of them, ``Unit Fractions'' and ``Collections of Multiple Sums'', would be accessible to undergraduates.

This collection presents new results in algebra, functional analysis, and mathematical physics. In particular, evolution and spectral problems related to small motions of viscoelastic fluid are considered. Specific areas covered in the book include functional equations and functional operator equations from the point of view of the $C*$-algebraic approach, the existence of an isomorphism between certain ideals regarded as Galois modules, spectral problems in singularly perturbed domains, scattering theory, the existence of bounded solutions to the equation $\operatorname{div} u = f$ in a plane domain, and a compactification of a locally compact group. Also given is an historic overview of the mathematical seminars held at St. Petersburg State University. The results, ideas, and methods given in the book will be of interest to a broad range of specialists.

This volume contains 10 papers with new results on problems in mathematical physics, differential equations, and probability. Included also is an article on the dramatic history of mathematics in Leningrad in the 1930s.