Table of contents

In this paper the author establishes the correct order (the asymptotics of the logarithm) of the number of terms in the Hilbert-Kamke problem.

Bibliography: 24 titles.

In this paper the author obtains high-frequency asymptotics of the trace of the product of a pair of spectral projections of elliptic operators in a bounded domain and of a number of similar expressions. Applications are given to the asymptotics' of the joint spectrum of a pair of commuting operators, to reducibility, and to quasiclassical asymptotics of the spectrum of an elliptic operator.

Bibliography: 11 titles.

Analogues of fundamental solutions and corresponding transition functions of Markov processes are constructed for parabolic equations with unbounded discontinuous coefficients satisfying certain dissipation conditions. In particular, an analytic construction of a Markov process of a stochastic model of quantum mechanics is obtained.

Bibliography: 40 titles.

It is proved that the quotient V/G, where G is a finite group generated by pseudoreflections in a finite-dimensional real space V, is homeomorphic to V.

Bibliography: 12 titles.

In this paper the author defines and studies a suspension sequence in the theory of links that generalizes the classical suspension sequence of knot theory (i.e. one-component links).

Bibliography: 9 titles.

This paper contains a construction of time evolution for linear boson models of quantum statistical mechanics. The main result is a theorem on convergence to a quasifree moment functional in the course of linear time evolution. A connection between linear evolution of the moment functional and evolution of the corresponding state of an infinite quantum system is discussed.

Bibliography: 30 titles.

In this paper the author establishes, under natural conditions, the local polyhedrality of the closed cone of curves of a three-dimensional algebraic variety in the part that is negative with respect to the canonical class. In particular, it is shown that there always exists an extremal ray giving a contraction. The results can be used in three-dimensional birational geometry.

Bibliography: 10 titles.