Theoretical investigation of TbNi_{5-x}Cu_x optical properties

In this paper we present theoretical investigation of optical conductivity for intermetallic TbNi_{5-x}Cu_x series. In the frame of LSDA+U calculations electronic structure for x=0,1,2 and on top of that optical conductivities were calculated. Disorder effects of Ni for Cu substitution on a level of LSDA+U densities of states (DOS) were taken into account via averaging over all possible Cu ion positions for given doping level x. Gradual suppression and loosing of structure of optical conductivity at 2 eV together with simultaneous intensity growth at 4 eV correspond to increase of Cu and decrease of Ni content. As reported before [Knyazev et al., Optics and Spectroscopy 104, 360 (2008)] plasma frequency has non monotonic doping behaviour with maximum at x=1. This behaviour is explained as competition between lowering of total density of states on the Fermi level N(E_F) and growing of number of carriers. Our theoretical results agree well with variety of recent experiments.Comment: 4 pages, 3 figure

Bounds on changes in Ritz values for a perturbed invariant subspace of a Hermitian matrix

The Rayleigh-Ritz method is widely used for eigenvalue approximation. Given a matrix $X$ with columns that form an orthonormal basis for a subspace \X, and a Hermitian matrix $A$, the eigenvalues of $X^HAX$ are called Ritz values of $A$ with respect to \X. If the subspace \X is $A$-invariant then the Ritz values are some of the eigenvalues of $A$. If the $A$-invariant subspace \X is perturbed to give rise to another subspace \Y, then the vector of absolute values of changes in Ritz values of $A$ represents the absolute eigenvalue approximation error using \Y. We bound the error in terms of principal angles between \X and \Y. We capitalize on ideas from a recent paper [DOI: 10.1137/060649070] by A. Knyazev and M. Argentati, where the vector of absolute values of differences between Ritz values for subspaces \X and \Y was weakly (sub-)majorized by a constant times the sine of the vector of principal angles between \X and \Y, the constant being the spread of the spectrum of $A$. In that result no assumption was made on either subspace being $A$-invariant. It was conjectured there that if one of the trial subspaces is $A$-invariant then an analogous weak majorization bound should only involve terms of the order of sine squared. Here we confirm this conjecture. Specifically we prove that the absolute eigenvalue error is weakly majorized by a constant times the sine squared of the vector of principal angles between the subspaces \X and \Y, where the constant is proportional to the spread of the spectrum of $A$. For many practical cases we show that the proportionality factor is simply one, and that this bound is sharp. For the general case we can only prove the result with a slightly larger constant, which we believe is artificial.Comment: 12 pages. Accepted to SIAM Journal on Matrix Analysis and Applications (SIMAX

Разработка технологий получения топливных присадок из техногенных отходов производств капролактама

Currently the issues of alternative use of chemical wastes, which have significan

Method of variational calculation of influence of the propulsion plants of forestry machines upon the frozen and thawing soil grounds

The forests, which grow in the conditions of complete expansion of the perpetually frozen ground, are unique forests in accordance with their taxational characteristics, quality indicators of the felled timber, and the ecological functions, which these forests perform in the nature. They are characterised by the low biological productivity, as well as by the high vulnerability due to climatological changes and human economic activities. It is fair to say that conservation of the permafrost is one of the main functions of the forests, which grow within the cryolithozone. Because of this, it is necessary to ensure special regimes for the forestry management and forest exploitation within the forests of the cryolithozone. We formulated the variational problem in order to determine influence of the changeability of the physical and mechanical properties of the thawing soil ground at the boundary with the permafrost ground. © 2019 SERSC

Bounds for the Rayleigh quotient and the spectrum of self-adjoint operators

The absolute change in the Rayleigh quotient (RQ) is bounded in this paper in terms of the norm of the residual and the change in the vector. If $x$ is an eigenvector of a self-adjoint bounded operator $A$ in a Hilbert space, then the RQ of the vector $x$, denoted by $\rho(x)$, is an exact eigenvalue of $A$. In this case, the absolute change of the RQ $|\rho(x)-\rho(y)|$ becomes the absolute error in an eigenvalue $\rho(x)$ of $A$ approximated by the RQ $\rho(y)$ on a given vector $y.$ There are three traditional kinds of bounds of the eigenvalue error: a priori bounds via the angle between vectors $x$ and $y$; a posteriori bounds via the norm of the residual $Ay-\rho(y)y$ of vector $y$; mixed type bounds using both the angle and the norm of the residual. We propose a unifying approach to prove known bounds of the spectrum, analyze their sharpness, and derive new sharper bounds. The proof approach is based on novel RQ vector perturbation identities.Comment: 13 page

Renormalization of hole-hole interaction at decreasing Drude conductivity

The diffusion contribution of the hole-hole interaction to the conductivity is analyzed in gated GaAs/In$_x$Ga$_{1-x}$As/GaAs heterostructures. We show that the change of the interaction correction to the conductivity with the decreasing Drude conductivity results both from the compensation of the singlet and triplet channels and from the arising prefactor $\alpha_i<1$ in the conventional expression for the interaction correction.Comment: 6 pages, 5 figure

Metal-Insulator Transition in 2D: Experimental Test of the Two-Parameter Scaling

We report a detailed scaling analysis of resistivity \rho(T,n) measured for several high-mobility 2D electron systems in the vicinity of the 2D metal-insulator transition. We analyzed the data using the two parameter scaling approach and general scaling ideas. This enables us to determine the critical electron density, two critical indices, and temperature dependence for the separatrix in the self-consistent manner. In addition, we reconstruct the empirical scaling function describing a two-parameter surface which fits well the \rho(T,n) data.Comment: 4 pages, 4 figures, 1 tabl