Self-adjoint local boundary problems on compact surfaces. I. Spectral flow

The paper deals with first order self-adjoint elliptic differential operators on a smooth compact oriented surface with non-empty boundary. We consider such operators with self-adjoint local boundary conditions. The paper is focused on paths in the space of such operators connecting two operators conjugated by a unitary automorphism. The first result is the computation of the spectral flow for such paths in terms of the topological data over the boundary. The second result is the universality of the spectral flow: we show that the spectral flow is a universal additive invariant for such paths, if the vanishing on paths of invertible operators is required. In the next paper of the series we generalize these results to families of such operators parametrized by points of an arbitrary compact space instead of an interval. The integer-valued spectral flow is replaced then by the family index taking values in the $K^1$-group of the base space

Indication for the coexistence of closed orbit and quantum interferometer with the same cross section in the organic metal (ET)4(H3O)[Fe(C2O4)3].C6H4Cl2: Persistence of SdH oscillations above 30 K

Shubnikov-de Haas (SdH) and de Haas-van Alphen (dHvA) oscillations spectra of the quasi-two dimensional charge transfer salt $\beta$"-(ET)$_4$(H$_3$O)[Fe(C$_2$O$_4$)$_3$]$\cdot$C$_6$H$_4$Cl$_2$ have been investigated in pulsed magnetic fields up to 54 T. The data reveal three basic frequencies F$_a$, F$_b$ and F$_{b - a}$, which can be interpreted on the basis of three compensated closed orbits at low temperature. However a very weak thermal damping of the Fourier component F$_b$, with the highest amplitude, is evidenced for SdH spectra above about 6 K. As a result, magnetoresistance oscillations are observed at temperatures higher than 30 K. This feature, which is not observed for dHvA oscillations, is in line with quantum interference, pointing to a Fermi surface reconstruction in this compound.Comment: published in Eur. Phys. J. B 71 203 (2009

Peculiarities of sub-barrier fusion with quantum diffusion approach

With the quantum diffusion approach the unexpected behavior of fusion cross section, angular momentum, and astrophysical S-factor at sub-barrier energies has been revealed. Out of the region of short-range nuclear interaction and action of friction at turning point the decrease rate of the cross section under the barrier becomes smaller. The calculated results for the reactions with spherical nuclei are in a good agreement with the existing experimental data.Comment: 11 pages, 5 figure

Reduction Operators of Linear Second-Order Parabolic Equations

The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1+1)-dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary differential ones are exhaustively described. This problem proves to be equivalent, in some sense, to solving the initial equations. The ``no-go'' result is extended to the investigation of point transformations (admissible transformations, equivalence transformations, Lie symmetries) and Lie reductions of the determining equations for the nonclassical symmetries. Transformations linearizing the determining equations are obtained in the general case and under different additional constraints. A nontrivial example illustrating applications of reduction operators to finding exact solutions of equations from the class under consideration is presented. An observed connection between reduction operators and Darboux transformations is discussed.Comment: 31 pages, minor misprints are correcte

Personality description and evaluation by colour similes in Russian, English and French

The author classifies different types of content created by colour similes in Russian, English and French contexts and explains the analogical connection between the features of human appearance and the objects chosen for colour representation. A new content appears due to cognitive interaction between two concepts: the object of comparison (OC) and the colour representative (CR)

Development trends of diversified agro-industrial enterprises in the context of international integration of economic relations

Globalization and growing competition have exacerbated the problems of analysis and diagnosing the level of economic development sustainability and the possibilities of economic entity market potential use at the global level. The development of a complete, reliable and up-to-date information base on the current financial, economic and technical level of an industrial enterprise development, its strategic development opportunities, making informed effective decisions on the directions of diversification or agro-industrial production restructuring is extremely important today from the standpoint of state policy development regarding the support for the key sectors of the Russian agro-industrial complex.In modern conditions, characterized by the intensification of economic relation integration in international markets

Institutional foundations of digital transformation of business in economic sectors

The article examines the external prerequisites for the digital transformation of business in the Russian economy. The object of research is the institutional infrastructure of the digital economy. The subject of the study is the state digital ecosystem. The main problem of the study is the insufficient digital maturity of the business with limited availability of technologies. The purpose of the study is to determine the technological limitations of the institutional environment for the systemic transformation of Russian business in accordance with global trends in the development of digital technologies. The methodology of the research is based on the analysis of the development of the digital ecosystem of the Russian economy for the formation of cross-industry business cooperation based on Internet technologies. The indicative method and comparative analysis of the e-government rating based on the e-government development index were used as an analysis tool. As a result, an assessment of the formation of the public sector of electronic services for business is given, a set of indicators is defined to assess the development of the technological basis of the institutional state ecosystem of digital business transformation

The Role of Education in the Political Socialization of Youth

Рассматривается роль институтов образования и воспитания в различных парадигмах политической социализации молодежи ХХ–ХХI вв. Обосновывается идея, что образование является мощным ресурсом и инструментом формирования гражданственности, патриотизма и служения Родине. Определяются шаги, реализуемые на государственном уровне, по формированию новой модели политической социализации молодых людей в рамках образовательной политики современного российского государства.The role of institutions of education and upbringing in various paradigms of political socialization of youth of the 20th–21st centuries is considered. The idea is substantiated that education is a powerful resource and tool for the formation of citizenship, patriotism and service to the motherland. The steps implemented at the state level are determined to form a new model of political socialization of young people within the framework of the educational policy of the modern Russian state