Volume 14, Issue 3

This issue is dedicated to the memory of Academician
Aleksandr D. Aleksandrov (4.08.1912 - 27.07.1999).

Signposts of the Life
of Aleksandr D. Aleksandrov

The great russian geometer of the twentieth century
Kutateladze S. S.

This is a short overview of the life and contribution of Aleksandr Danilovich Alexandrov (1912-1999). Most attention is paid to his general outlook and ethical principles.

Article (rus.) - [pdf] [zip-pdf]

Minimal absolutely representing systems
of exponential functions in spaces of analytic functions with given boundary smoothness
Abanin A. V., Petrov S. V.

We consider spaces of functions holomorphic in a convex domain which are infinitely differentiable up to the boundary and have certain estimates of all derivatives. Some necessary and sufficient conditions are obtained for a minimal system of exponential functions to be an absolutely representing system in the spaces which are generated by a single weight. Relying on these results, we prove that absolutely representing systems of exponentials do not have the stability property under the passage to the limit over domains.

Article (rus.) - [pdf] [zip-pdf]

The inverse coefficient problem for dissipative operators and identification of the properties
of viscoelastic materials
Bogachev I. V. and Vatulyan A. O.

We give some general formulation and the variational equation of the inverse problem of identifying the inhomogeneous characteristics of three-dimensional viscoelastic body. Under consideration is the problem of reconstruction of the functional coefficients of dissipative operators arising in solving several problems of identification of the properties of layered inhomogeneous viscoelastic structures in the analysis of spectral characteristics. We suggest a method for constructing an iterative process and present the results of recovering functions of different types.

Article (rus.) - [pdf] [zip-pdf]

Matrices comparable by columns and proportional by columns over lattices
Zhuklina A. V.

Matrices over a lattice (L, ≤)   comparable by columns are studied. (A matrix is comparable by columns iff its columns form a linearly ordered set with the partial order induced from L .) Some properties of the matrices are obtained. Solvability of matrix equations in this class of matrices is studied. The set of matrices proportional by columns is the subset of the set of matrices comparable by columns. Some properties as well as solvability of matrix equations are also studied for suth matrices.

Article (rus.) - [pdf] [zip-pdf]

Structure of lie derivations on algebras of measurable operators
Juraev I. M.

We prove that every Lie derivation on algebras of measurable operators is of standard form, that is, it can be uniquely decomposed into the sum of a derivation and a center-valued trace.

Article (rus.) - [pdf] [zip-pdf]

The Riemann-Hilbert boundary value problem for generalized analytic functions in Smirnov classes
Klimentov S. B.

Under study is the Riemann-Hilbert boundary value problem for generalized analytic functions of a Smirnov class in a bounded simply connected domain whose boundary is a Lyapunov curve or a Radon curve without cusps. The coefficient of the boundary value condition is assumed continuous and perturbed by a bounded measurable function or continuous and perturbed by a bounded variation function. The paper uses the special representation for generalized analytic functions of Smirnov classes from the author's paper [16], which reduces the problem to that for holomorphic functions. The problem for the holomorphic functions was under study in the author's papers [1, 2].

Article (rus.) - [pdf] [zip-pdf]

J. W. Fickett's problem for isosceles triangles
Rasskazova N. V.

Two congruent overlapping isosceles triangles with the least angle between lateral sides are considered in the Euclidean plane. J. W. Fickett offered a bilateral estimation for the relation of the length of the part of the first triangle's boundary in the second triangle to the length of the part of the second triangle's the boundary in the first triangle. The paper shows that J. W. Fickett's supposition is not true in general. An analog of J. W. Fickett's estimation is proved for the isosceles triangles with the least angle between lateral sides.

Article (rus.) - [pdf] [zip-pdf]