617 research outputs found
Perturbation of spectra and spectral subspaces
We consider the problem of variation of spectral subspaces for linear
self-adjoint operators under off-diagonal perturbations. We prove a number of
new optimal results on the shift of the spectrum and obtain (sharp) estimates
on the norm of the difference of two spectral projections
On a Subspace Perturbation Problem
We discuss the problem of perturbation of spectral subspaces for linear
self-adjoint operators on a separable Hilbert space. Let and be bounded
self-adjoint operators. Assume that the spectrum of consists of two
disjoint parts and such that . We show that the norm of the difference of the spectral projections
\EE_A(\sigma) and \EE_{A+V}\big (\{\lambda | \dist(\lambda, \sigma)
for and is less then one whenever either (i)
or (ii) and certain assumptions on the
mutual disposition of the sets and are satisfied
Towards all-dielectric metamaterials and nanophotonics
We review a new, rapidly developing field of all-dielectric nanophotonics
which allows to control both magnetic and electric response of structured
matter by engineering the Mie resonances in high-index dielectric
nanoparticles. We discuss optical properties of such dielectric nanoparticles,
methods of their fabrication, and also recent advances in all-dielectric
metadevices including couple-resonator dielectric waveguides, nanoantennas, and
metasurfaces
A restricted shift completeness problem
We solve a problem about the orthogonal complement of the space spanned by
restricted shifts of functions in posed by M.Carlsson and
C.Sundberg.Comment: 7 page
Radiation-Induced Degradation of Organic Compounds and Radiation Technologies for Purification of Aqueous Systems
Environmental application of radiation technologies is an important part of radiation processing. Radiation treatment of aqueous systems contaminated with organic compounds is a promising method of water and wastewater purification and corresponding technologies are being developed. In this chapter, the following aspects of radiation treatment process are considered: sources of contamination and major contaminants of water and wastewater; primary processes in aqueous systems initiated by ionizing radiation; principal ways of contaminant conversion as consequences of primary processes (complete mineralization of organic compounds, partial decomposition of organic molecules resulted in detoxification, decolorization, disinfection of polluted water, and improvement in biological degradation of contaminant, polymerization of monomers’ contaminants, oxidation-reduction processes, and coagulation of colloids); sources of ionizing radiation; and main equipment applied in radiation technologies of aqueous system purification
- …