Spectral asymptotics of Pauli operators and orthogonal polynomials in complex domains

We consider the spectrum of a two-dimensional Pauli operator with a compactly supported electric potential and a variable magnetic field with a positive mean value. The rate of accumulation of eigenvalues to zero is described in terms of the logarithmic capacity of the support of the electric potential. A connection between these eigenvalues and orthogonal polynomials in complex domains is established.Comment: 16 page

Method for loading cargo trucks using two-dimensional packing algorithms

The paper describes the method for optimization of loading cargo trucks using two-dimensional packing algorithms. The point of this method is to reduce loading cargo problem to two-dimensional packing problem. This problem can be solved by using of various algorithms. There is analysis of several algorithms that are most often used in practical calculations of objects distribution in 2D space in this paper. The object of this study is transport of the metal processing company and its products (cargo). PHP programming language, MySQL database, and Apache web server are used to create client application. The interface developed using HTML5, CSS and javascript. © 2019 IOP Publishing Ltd. All rights reserved.The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0006

Production of Welding Fluxes Using Waste Slag Formed in Silicomanganese Smelting

The possibility in principle of using slag, which is formed in the silicon-manganese smelting process, in producing welding fluxes is shown. The composition of and technology used for a new fused flux has been designed. A comparative evaluation of the new flux and the widely used AN-348 type flux was done. It has been proved that the new flux has high strength properties

Absence of bound states for waveguides in 2D periodic structures

We study a Helmholtz-type spectral problem in a two-dimensional medium consisting of a fully periodic background structure and a perturbation in form of a line defect. The defect is aligned along one of the coordinate axes, periodic in that direction (with the same periodicity as the background), and bounded in the other direction. This setting models a so-called "soft-wall" waveguide problem. We show that there are no bound states, i.e., the spectrum of the operator under study contains no point spectrum.Comment: This is an updated version of our paper (in slightly different form in Journal of Mathematical Physics). An anonymous reviewer kindly made us aware that ref. 10 is not applicable in our situation. An application of the theorem in ref. 10 would have proved the absence of singular continuous spectrum also. Our result on the absence of point spectrum is not affected by thi

Hyperbolic transmission-line metamaterials

We demonstrate how to realize an indefinite media with hyperbolic isofrequency surfaces in wavevector space by employing two-dimensional metamaterial transmission lines. We classify different types of such media, and visualize the peculiar character of wave propagation by study of the cross-like emission pattern of a current source placed in the lattice center. Our results are supported by a solution of the Kirchhoff equations, an analytical theory, and experimental data.The authors acknowledge a support from the Ministry of Education and Science of the Russian Federation, Russian. Foundation for Basic Research, Dynasty Foundation (Russia), the Engineering and Physical Sciences Research Council (UK), and the Australian Research Council (Australia)

Effects of bipolarons on oxidation states, and the electronic and optical properties of W18O49

W18O49 has been studied by means of ab initio techniques in the framework of the density functional theory using the onsite Hubbard-U correction applied to the W-d states as well as using the hybrid potential. The existence of bipolarons is found to be an intrinsic feature of this oxide resulting in the presence of different oxidation states of W atoms (W6+ and W5+) and in the co-existence of localized and delocalized electrons. We also discuss possible switching from the W6+ to W5+ and from the W5+ to W4+ oxidation states in the presence of an O vacancy. It appears that O vacancy formation does not cause any additional charge localization at W sites but solely contributes to delocalized electrons. The calculated absorption and reflection coefficients manifest a transparency window in the visible region. At the same time, sizable absorption, occurring due to the presence of free carriers, is detected in the far and mid infrared regions. Additionally, in the near infrared region we confirm and explain an experimentally observed shielding effect originating from transitions involving the localized bipolaronic states

Acid-Base Properties Of Glass Substrate And SiO[2]-Bi[2]O[3]Thin-Film Systems Obtained On It

The article describes an experimental research as a result of which SiO[2]–Bi[2]O[3] films have been synthesized of film-forming solutions based on tetraethoxysilane and bismuth nitrate (III). Acid-base properties of a glass substrate and SiO[2]–Bi[2]O[3] films obtained on it have been studied. The dependency of physical and chemical properties of SiO[2]–Bi[2]O[3] composites on their percentage composition have been revealed