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 $A$ and $V$ be bounded self-adjoint operators. Assume that the spectrum of $A$ consists of two disjoint parts $\sigma$ and $\Sigma$ such that $d=\text{dist}(\sigma, \Sigma)>0$. We show that the norm of the difference of the spectral projections \EE_A(\sigma) and \EE_{A+V}\big (\{\lambda | \dist(\lambda, \sigma) $<d/2\}\big)$ for $A$ and $A+V$ is less then one whenever either (i) $\|V\|<\frac{2}{2+\pi}d$ or (ii) $\|V\|<{1/2}d$ and certain assumptions on the mutual disposition of the sets $\sigma$ and $\Sigma$ 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 $L^2[0,1]$ 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

Halide-Perovskite Resonant Nanophotonics

Halide perovskites have emerged recently as promising materials for many applications in photovoltaics and optoelectronics. Recent studies of their optical properties suggest many novel opportunities for a design of advanced nanophotonic devices due to low-cost fabrication, high values of the refractive index, existence of excitons at room temperatures, broadband bandgap tunability, high optical gain and nonlinear response, as well as simplicity of their integration with other types of structures. This paper provides an overview of the recent progress in the study of optical effects originating from nanostructured perovskites, including their potential applications.Comment: revie