Shirokov, M. E. Holevo, A. S.
Published in
Lobachevskii Journal of Mathematics

In the developing theory of infinite-dimensional quantum channels the relevance of the energy-constrained diamond norms was recently corroborated both from physical and information-theoretic points of view. In this paper we study necessary and sufficient conditions for differentiability with respect to these norms of the strongly continuous semigro...

Volkov, B. O.
Published in
Lobachevskii Journal of Mathematics

A covariant definition of the Levy Laplacian on an infinite dimensional manifold is introduced. It is shown that a time-depended connection in a finite dimensional vector bundle is a solution of the Yang—Mills heat equations if and only if the associated flow of the parallel transports is a solution of the heat equation for the covariant Levy Lapla...

Shakhverdiev, A. Kh. Shestopalov, Yu. V.
Published in
Lobachevskii Journal of Mathematics

The behavior and properties of solutions of two-dimensional quadratic polynomial dynamical system on the phase plane of variables and time are considered. A complete qualitative theory is constructed which includes the analysis of all singular points and the features of solutions depending on all parameters of the problem. A main result is that, wi...

Harutyunyan, T. N.
Published in
Lobachevskii Journal of Mathematics

We introduce new supplementary data to the set of the eigenvalues, to determine uniquely potential matrix in the inverse problem for Dirac canonical operator. Besides, we obtain others uniqueness theorems in inverse problems, which are the analogues of well-known Borg, Marchenko and McLaughlin-Rundell theorems in inverse Sturm-Liouville problems.

Abgaryan, G. V. Pleshchinskii, N. B.
Published in
Lobachevskii Journal of Mathematics

The rectangular waveguide is attached to a hole in a wall of rectangular resonator and the corresponding to the hole part of the waveguide boundary is cross-section of the waveguide. The problem of excitation of the resonator by an eigen wave of the waveguide is investigated. The condition on a hole is obtained from the condition defining the wave ...

Efremova, L. S. Grekhneva, A. D. Sakbaev, V. Zh.
Published in
Lobachevskii Journal of Mathematics

We consider the transformation of the initial data space for the Schrödinger equation. The transformation is generated by nonlinear Schrödinger operator on the segment [−π, π] satisfying the homogeneous Dirichlet conditions on the boundary of the segment. The potential here has the type ξ(u)=(1+∣u∣2)p2u\documentclass[12pt]{minimal} \usepackage{amsm...

Amosov, G. G. Mokeev, A. S.
Published in
Lobachevskii Journal of Mathematics

We continue the study of non-commutative operator graphs generated by resolutions of identity covariant with respect to unitary actions of the circle group and the Heisenber-Weyl group as well. It is shown that the graphs generated by the circle group has the system of unitary generators fulfilling permutations of basis vectors. For the graph gener...

Evstigneev, R. O. Medvedik, M. Yu.
Published in
Lobachevskii Journal of Mathematics

In this paper a scalar inverse problem on a hemisphere is considered. The incident field is radiated by point source located outside the body. We are looking for a solution of the inverse problem using the measurements of the field outside the body. We suggest an original approach to solve the problem. The various numerical results of solving the p...

Avanesov, A. S. Man’ko, V. I.
Published in
Lobachevskii Journal of Mathematics

Using the known possibility to associate the completely positive maps with density matrices and recent results on expressing the density matrices with sets of classical probability distributions of dichotomic random variables we construct the probability representation of the completely positive maps. In this representation, any completely positive...

Amosov, G. G. Korennoy, Ya. A.
Published in
Lobachevskii Journal of Mathematics

We obtain sufficient conditions on kernels of quantum states under which Wigner functions, optical quantum tomograms and linking their formulas are correctly defined. Our approach is based upon the Sobolev Embedding theorem. The transition probability formula and the fractional Fourier transform are discussed in this framework.