On the deficiency index of a certain class of differential operators

This paper studies problems on the behavior of solutions for a certain class of differential equations of the form l _n y = λy as x → +0, where l _n is a scalar, formally self-adjoint, quasidifferential expression of an arbitrary order with complex coefficients. The results obtained allow us to find the defficiency index of the operator generated by the expression l _n . __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 36, Suzdal Conference-2004, Part 2, 2005.     

Mössbauer study of layered iron hydroxysulfides: Tochilinite and valleriite

Natural and synthetic layered iron hydroxysulfides: tochilinite and valleriite, have been investigated by Mössbauer spectroscopy. Tochilinite, magnetite, troilite, and pyrite phases were found in the products of tochilinite synthesis under different conditions. The relative contents of the phases found are determined as functions of the relative magnesium content in the initial mixture. Crystallochemical identification of the ⁵⁷Fe subspectra of valleriite has been performed.     

Effect of optical blooming of a nanocrystal monolayer and the interface between two media

It is shown that several parameters of the near-field interaction of particles effectively control the reflectance of the interface between vacuum and a semi-infinite medium in a structured monolayer of nanoparticles, changing it from 0 to 1. The formulas derived for the electric field amplitudes inside and outside the nanostructural layer take into account the periodic arrangement of nanoparticles. The ideal blooming condition of the boundary of the underlying medium is derived, under which the reflectance of the interface tends to zero in a wide range of wavelengths in the visible optical range.     

Synthesis and structure of O-(arylcarbamoyl)butyrhydroximoyl chlorides

The O-(arylcarbamoyl)butyrhydroximoyl chlorides were synthesized, and the x-ray structural analysis (XSA) of one of them — O-(o-tolylcarbamoyl)butyrhydroximoyl chloride — was performed. It was established from the data of the XSA and the PMR spectra that all synthesized compounds are the Z isomers.Institute of Physiologically Active Substances, Russian Academy of Sciences, 142432 Chernogolovka. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 2, pp. 315–319, February, 1992.     

Patterns in parabolic problems with nonlinear boundary conditions

We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of eigenvalues and eigenfunctions of the Laplace operator in such domains. This information is used to show that the asymptotic dynamics of the heat equation in this domain is equivalent to the asymptotic dynamics of a system of two ordinary differential equations diffusively (weakly) coupled. The main tools employed are the invariant manifold theory and a uniform trace theorem.     

On the role of mechanical effects during dynamic fatigue of PbTiO3 single crystals

The details of the mechanical effects (twinning and microcracking) are clarified at various stages of dynamic fatigue of PbTiO₃ crystals using a polarization microscope and selective etching.     

Possibility of observing chiral-symmetry effects in ferromagnetic nanoparticles

The statistics of left-and right-handed vortical magnetization states in a system of submicron-sized ferromagnetic disks is studied experimentally. Lattices of elliptic cobalt particles with a planar size of 750 × 450 nm and a thickness of 25 nm were formed using high-resolution electronic lithography. To visualize the magnetization distributions in the disks, magnetic force microscopy was used. The experimental results indicate the conservation of magnetic chiral symmetry in cobalt ferromagnetic particles of the above size and shape.