Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials

We give a complete description of the set of spectral data (eigenvalues and specially introduced norming constants) for Sturm--Liouville operators on the interval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$ and suggest an algorithm reconstructing the potential from the spectral data that is based on Krein's accelerant method.Comment: 39 pages, uses iopart.cls, iopams.sty and setstack.sty by IO

Random matrices, non-backtracking walks, and orthogonal polynomials

Several well-known results from the random matrix theory, such as Wigner's law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the limiting spectral measure play a role in this approach.Comment: (more) minor change

Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result extends the celebrated two-spectrum uniqueness theorem of Borg and Marchenko to the case where there is also a continuous spectru

Explicit solutions to the Korteweg-de Vries equation on the half line

Certain explicit solutions to the Korteweg-de Vries equation in the first quadrant of the $xt$-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schr\"odinger equation. In the reflectionless case such solutions reduce to pure $N$-soliton solutions. An illustrative example is provided.Comment: 17 pages, no figure

Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators

We investigate the eigenvalues of perturbed spherical Schr\"odinger operators under the assumption that the perturbation $q(x)$ satisfies $x q(x) \in L^1(0,1)$. We show that the square roots of eigenvalues are given by the square roots of the unperturbed eigenvalues up to an decaying error depending on the behavior of $q(x)$ near $x=0$. Furthermore, we provide sets of spectral data which uniquely determine $q(x)$.Comment: 14 page

Information Warfare Narratives: Yesterday and Today

The article deals with the historical and legal aspects of the development of the means of informa- tion struggle in the world, changes in the activities of state and military administration bodies in the information and communication environment are traced, the issues of organizing information coun- teract to modern attempts to falsify the main events of the Great Patriotic War and the post-war stage of development of the Russian state are examined.The authors of the article demonstrate the use of narratives as ways of organizing the information space, trace and analyze examples of information confrontation between the past and the present, including, using the cases of modern armed conflicts between Russia and Georgia in South Ossetia and the military-political confrontation in eastern Ukraine, draw conclusions about the need to increase and update the content of the state information policy, taking into account new militarypolitical threats and dangers

Ab-initio density functional studies of stepped TaC surfaces

We report on density functional total energy calculations of the step formation and interaction energies for vicinal TaC(001) surfaces. Our calculations show that double and triple-height steps are favored over single-height steps for a given vicinal orientation, which is in agreement with recent experimental observations. We provide a description of steps in terms of atomic displacements and charge localization and predict an experimentally observable rumpled structure of the step-edges, where the Ta atoms undergo larger displacements compared to the C atoms.Comment: 4 pages, 4 figure

Проблемы финансирования малого бизнеса в Украине

В статті досліджено можливі джерела фінансування малих підприємств, особливості банківського кредитування та системи державної підтримки малого бізнесу, проблеми залучення різних джерел фінансування.This article is considered of possible sources of funding for small businesses, specificity of bank lending and government support of small business, problems of involving different funding sources.В статье рассмотрены возможные источники финансирования малых предприятий, особенности банковской и системы государственной поддержки малого бизнеса, проблемы привлечения разных источников финансирования