Optical spectroscopy and electronic structure of the GdCux compounds (x = 1, 2, 5)

Optical properties of the GdCu, GdCu2, and GdCu5 compounds with various crystal lattices have been investigated using ellipsometry in a spectral range of 0. 22-16 μm. Theoretical calculations of the electronic structure of these intermetallic compounds have been performed in the approximation of local electron density with the correction for strong electron correlations in a 4f shell of gadolinium ions. Based on the results of calculations, the interpretation of experimental spectra of interband optical conductivity has been proposed. The plasma and relaxation frequencies of conduction electrons have been determined. © 2013 Pleiades Publishing, Ltd

Construction of Solutions to Control Problems for Fractional- Order Linear Systems Based on Approximation Models

We consider an optimal control problem for a dynamical system whose motion is described by a linear differential equation with the Caputo fractional derivative of order α ∈ (0, 1). The time interval of the control process is fixed and finite. The control actions are subject to geometric constraints. The aim of the control is to minimize a given terminal-integral quality index. In order to construct a solution, we develop the following approach. First, from the considered problem, we turn to an auxiliary optimal control problem for a first-order linear system with lumped delays, which approximates the original system. After that, the auxiliary problem is reduced to an optimal control problem for an ordinary differential system. Based on this, we propose a closed-loop scheme of optimal control of the original system that uses the approximating system as a guide. In this scheme, the control in the approximating system is formed with the help of an optimal positional control strategy from the reduced problem. The effectiveness of the developed approach is illustrated by a problem in which the quality index is the norm of the terminal state of the system. © 2020 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.This work was supported by RSF (project no. 19-11-00105)

Traversing Target Points Under Lack of Information: A Game-Theoretical Approach

A dynamical object controlled under conditions of unknown disturbances or counteractions is considered. The goal is to bring the object to given target points at given times regardless of the disturbance actions. To solve this problem, the quality index is introduced that evaluates the distance between the object and target points at the indicated times, and a zero-sum differential game is considered in which the control actions minimize this quality index while the disturbance actions maximize it. The initial problem is reduced to calculating the game value and constructing a saddle point of the game. The corresponding resolving procedure is proposed that is based on the upper convex hulls method. An example is considered. Results of numerical simulations are presented. © 2018Russian Academy of SciencesThis work is supported by the Program of the Presidium of the Russian Academy of Sciences No. 1 `Fundamental Mathematics and its Applications’ under grant PRAS-18-01

Effect of electronic correlations on the electronic structure, magnetic and optical properties of the ternary RCuGe compounds with R = Tb, Dy, Ho, Er

In this study, the ab initio and experimental results for RCuGe ternary intermetallics were reported for R = Tb, Dy, Ho, Er. Our theoretical calculations of the electronic structure, employing local spin density approximation accounting for electron-electron correlations in the 4f shell of Tb, Dy, Ho, Er ions were carried in DFT+U method. The optical properties of the RCuGe ternary compounds were studied at a broad range of wavelengths. The spectral and electronic characteristics were obtained. The theoretical electron densities of states were taken to interpret the experimental energy dependencies of the experimental optical conductivity in the interband light-absorption region. From the band calculations, the 4f shell of the rare-earth ions was shown to provide the major contribution to the electronic structure, magnetic and optical properties of the RCuGe intermetallics. The accounting for electron-electron correlations in Tb, Dy, Ho, Er resulted in a good agreement between the calculated and experimental magnetic and optical characteristics. © 2020 by the authors.Russian Science Foundation, RSF: 18-72-10098Ministry of Science and Higher Education of the Russian Federation: AAAA-A18-118020190098-5, DST/INT/RFBR/IDIR/P-01/2016The theoretical studies are supported by the Russian Science Foundation, project grant No. 18-72-10098. The optical studies are supported by Ministry of Science and Higher Education of the Russian Federation (theme "Electron" No. AAAA-A18-118020190098-5). K.G.S. acknowledges financial support through Indo-Russian project: DST/INT/RFBR/IDIR/P-01/2016

Path-Dependent Hamilton–Jacobi Equations: The Minimax Solutions Revised

Motivated by optimal control problems and differential games for functional differential equations of retarded type, the paper deals with a Cauchy problem for a path-dependent Hamilton–Jacobi equation with a right-end boundary condition. Minimax solutions of this problem are studied. The existence and uniqueness result is obtained under assumptions that are weaker than those considered earlier. In contrast to previous works, on the one hand, we do not require any properties concerning positive homogeneity of the Hamiltonian in the impulse variable, and on the other hand, we suppose that the Hamiltonian satisfies a Lipshitz continuity condition with respect to the path variable in the uniform (supremum) norm. The progress is related to the fact that a suitable Lyapunov–Krasovskii functional is built that allows to prove a comparison principle. This functional is in some sense equivalent to the square of the uniform norm of the path variable and, at the same time, it possesses appropriate smoothness properties. In addition, the paper provides non-local and infinitesimal criteria of minimax solutions, their stability with respect to perturbations of the Hamiltonian and the boundary functional, as well as consistency of the approach with the non-path-dependent case. Connection of the problem statement under consideration with some other possible statements (regarding the choice of path spaces and derivatives used) known in the theory of path-dependent Hamilton–Jacobi equations is discussed. Some remarks concerning viscosity solutions of the studied Cauchy problem are given. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature

RESONANT PHOTOEMISSION OF INTERMETALLIC COMPOUNDS RMn2Si2

The compounds RMn2Si2 (R = La, Sm, Tb) with tetragonal ThCr2Si2 – type structure were studied. Experiments on resonant photoemission were performed and the partial densities of La 5d, 4f, Sm 4f, Tb 4f, and Mn 3d states, which form a valence band in the RMn2Si2, were found.Работа выполнена при финансовой поддержке Российского фонда фундаментальных исследований (проект 20-02-00541 А)

Incommensurate-commensurate magnetic phase transitions in Tb1-xErxNi5 compounds

Spontaneous and magnetic field induced incommensurate - commensurate magnetic phase transitions have been studied in Tb1-xErxNi5 compounds near the critical concentration x c = 0.125. Compounds crystallize in the hexagonal CaCu5 type phase (P6/mmm space group). In compounds with x ≥ x c the magnetic order is a commensurate ferromagnetic one. The samples with x < x c have an incommensurate structure that is a fan like magnetic structure and described by two propagation vectors. An incommensurate - "lock in" magnetic transition takes place at 10 K at cooling regime. © Published under licence by IOP Publishing Ltd.3.6121.2017/8.9, 02.This research was carried out at Neutron Science Division of KAERI and IMP Neutron Material Science Complex within the state assignment of FASO of Russia (theme “Flux” No. ААА-А18-118020190112-8) and supported in part by the State contract (No. 3.6121.2017/8.9), Act 211 Government of RF (contract No. 02.A03.21.0006)