Regularized extremal shift in problems of stable control

We discuss a technical approach, based on the method of regularized extremal shift (RES), intended to help solve problems of stable control of uncertain dynamical systems. Our goal is to demonstrate the essence and abilities of the RES technique; for this purpose we construct feedback controller for approximate tracking a prescribed trajectory of an inaccurately observed system described by a parabolic equation. The controller is "resource-saving" in a sense that control resource spent for approximate tracking do not exceed those needed for tracking in an "ideal" situation where the current values of the input disturbance are fully observable. © 2013 IFIP International Federation for Information Processing.German Sci. Found. (DFG) Eur. Sci. Found. (ESF);Natl. Inst. Res. Comput. Sci. Control France (INRIA);DFG Research Center MATHEON;Weierstrass Institute for Applied Analysis and Stochastics (WIAS);European Patent Offic

Bosonic Spectral Function and The Electron-Phonon Interaction in HTSC Cuprates

In Part I we discuss accumulating experimental evidence related to the structure and origin of the bosonic spectral function in high-temperature superconducting (HTSC) cuprates at and near optimal doping. Some global properties of the spectral function, such as number and positions of peaks, are extracted by combining optics, neutron scattering, ARPES and tunnelling measurements. These methods give convincing evidence for strong electron-phonon interaction (EPI) with the coupling constant between 1-3 in cuprates near optimal doping. Here we clarify how these results are in favor of the Eliashberg-like theory for HTSC cuprates near optimal doping. In Part II we discuss some theoretical ingredients - such as strong EPI, strong correlations - which are necessary to explain the experimental results related to the mechanism of d-wave pairing in optimally doped cuprates. These comprise the Migdal-Eliashberg theory for EPI in strongly correlated systems which give rise to the forward scattering peak. The latter is further supported by the weakly screened Madelung interaction in the ionic-metallic structure of layered cuprates. In this approach EPI is responsible for the strength of pairing while the residual Coulomb interaction (by including spin fluctuations) triggers the d-wave pairing.Comment: 59 pages, 38 figures, review articl

On the theory of magnetic field dependence of heat conductivity in dielectric in isotropic model

Phonon polarization in a magnetic field is analyzed in isotropic model. It is shown, that at presence of spin-phonon interaction phonon possess circular polari-zation which causes the appearance of heat flux component perpendicular both to temperature gradient and magnetic field.Comment: 5 pages, 0 figure

On an algorithm for dynamic reconstruction of the input

We consider the problem of dynamic reconstruction of the input in a system described by a vector differential equation and nonlinear in the state variable. We indicate an algorithm that is stable under information noises and computational errors and is aimed at infinite system operation time. The algorithm is based on the dynamic regularization method. © 2013 Pleiades Publishing, Ltd