Fullerite C60 optical constants in the C 1s NEXAFS region

Using data on the absorption cross sections the refraction coefficient spectral dependence n(E) and the spectra of the remaining optical coefficients (reflection coefficient, phase shift, and atomic form factor) in the fullerite C60 C 1s near edge X-ray absorption fine structure (NEXAFS) region (280–350 eV) were determined. For the n(E) calculations the Kramers-Kronig integral relations (KKRs) were used. The KKR computations were performed using data on atomic carbon absorption cross sections in the 10–30000 eV range and on solid and gaseous C60 – in the 0–120 eV. Absorption cross section spectrum in the fullerite C60 C 1s NEXAFS region were measured.

Problem with data on the characteristics for a loaded system of hyperbolic equations

We consider a problem with data on the characteristics for a loaded system of hyperbolic equations of the second order on a rectangular domain. The questions of the existence and uniqueness of the classical solution of the considered problem, as well as the continuity dependence of the solution on the initial data, are investigated. We propose a new approach to solving the problem with data on the characteristics for the loaded system of hyperbolic equations second order based on the introduction new functions. By introducing new unknown functions the problem is reduced to an equivalent family of Cauchy problems for a loaded system of differential with a parameters and integral relations. An algorithm for finding an approximate solution to the equivalent problem is proposed and its convergence is proved. Conditions for the unique solvability of the problem with data on the characteristics for the loaded system of hyperbolic equations of the second order are established in the terms of coefficient's system.

Temperature State of the Electrical Insulation Layer of a Superconducting DC Cable with Double-Sided Cooling

For the reliable operation of a high-voltage DC cable with high-temperature superconducting current-carrying conductors with a sufficiently high difference in electrical potentials, it is necessary to maintain a fixed temperature state not only of the conductors but also of other cable elements, including the electrical insulation layer. In this layer, despite the high electrical resistivity of its material, which can be polymer dielectrics, Joule heat is released. The purpose of this study was to build a mathematical model that describes the temperature state of an electrical insulation layer made in the form of a long hollow circular cylinder, on the surfaces of which a constant potential difference of the electric field is set. Within the study, we consider an alternative design of a cable with central and external annular channels for cooling liquid nitrogen. Using a mathematical model, we obtained integral relations that connect the parameters of the temperature state of this layer, the conditions of heat transfer on its surfaces, and the temperature-dependent coefficient of thermal conductivity and electrical resistivity of an electrical insulating material with a given difference in electrical potentials. A quantitative analysis of integral relations is carried out as applied to the layer of electrical insulation of the superconducting cable. The results of the analysis make it possible to assess the possibilities of using specific electrical insulating materials in cooled high-voltage DC cables under design, including superconducting cables cooled with liquid nitrogen

Some Applications of the Wright Function in Continuum Physics: A Survey

The Wright function is a generalization of the exponential function and the Bessel functions. Integral relations between the Mittag–Leffler functions and the Wright function are presented. The applications of the Wright function and the Mainardi function to description of diffusion, heat conduction, thermal and diffusive stresses, and nonlocal elasticity in the framework of fractional calculus are discussed.

On Relations Between the Relative Entropy and χ2-Divergence, Generalizations and Applications

The relative entropy and the chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these relations, their information-theoretic applications, and some generalizations pertaining to the rich class of f-divergences. Applications that are studied in this paper refer to lossless compression, the method of types and large deviations, strong data–processing inequalities, bounds on contraction coefficients and maximal correlation, and the convergence rate to stationarity of a type of discrete-time Markov chains.

Explicit solution of the scattering problem involving a vertical flexible membrane

<p>The problem of normally incident water wave scattering by a flexible membrane is completely solved. The physical problem in a half-plane is reduced to a couple of equivalent quarter-plane problems by allowing incident waves from either direction of the membrane. In the same way, quarter-plane boundary value problems are posed for solid wave potentials that are solutions of the scattering problem involving a rigid structure of the same geometric configuration. Then, two novel integral relations are introduced to establish a link between the required solution wave potentials and few resolvable solid wave potentials. Explicit expressions for the scattering quantities such as the reflection and the transmission wave amplitudes are obtained. Also, the deflection of the flexible vertical membrane and the solution potentials are determined analytically. Numerical results for the scattering quantities and the membrane deflection are presented.</p>