Phase equilibria and glass formation in the As2S3-TlAs2S2Se2 section of the As2S3-As2Se3-TlS system

Alloys in the As₂S₃-TlAs₂S₂Se₂ section of the As₂S₃-As₂Se₃-TlS ternary system were studied and a phase diagram was constructed using physicochemical methods (differential thermal analysis, microstructural analysis, X-ray powder diffraction, also microhardness and density measurements). The diagram in the As₂S₃-TlAs₂S₂Se₂ section is a non-quasi-binary diagonal section of the As₂S₃-As₂Se₃-TlSe quasi-ternary system. It was found that all the alloys in the section under ordinary conditions are obtained in the vitreous state. At low As₂S₃ concentrations in the section, solid solutions form up to 2.5 mol %, and at low TlAs₂S₂Se₂ concentrations, their extent is 3 mol %.     

On Hill's operator with a matrix potential

In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the self‐adjoint operator generated by a system of Sturm–Liouville equations with summable coefficients and quasiperiodic boundary conditions. Then using these asymptotic formulas, we find conditions on the potential for which the number of gaps in the spectrum of the Hill's operator with matrix potential is finite. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral expansion for a nonselfadjoint periodic differential operator

In the paper, we construct the spectral expansion for the differential operator generated in L ₂(−∞, ∞) by an ordinary differential expression of arbitrary order with periodic complex-valued coefficients Lebesgue integrable on bounded intervals. Dedicated to the memory of B. M. Levitan     

Non-self-adjoint sturm-liouville operators with matrix potentials

We obtain asymptotic formulas for non-self-adjoint operators generated by the Sturm-Liouville system and quasiperiodic boundary conditions. Using these asymptotic formulas, we obtain conditions on the potential for which the system of root vectors of the operator under consideration forms a Riesz basis.     

Investigation of diene condensation of primary vinylacetylene and allylacetylene alcohols and their ethers and esters with polychlorocyclic dienes

The diene condensation of primary vinylacetylene and allylacetylene alcohols, their esters and ethers with polychlorocyclopentadienes proceeded regioselectively at the double bond of the dienophile leading to the formation of the corresponding polychlorobicyclic adducts of the endo-configuration. Kinetic parameters were determined, quantum-chemical calculations of dienes and some dienophiles were performed. Polychlorobicyclic acetylene alcohols subjected to various chemical transformations, in particular, to oxidation and acetylene-allene rearrangement, formed new functional derivatives.     

Diene Condensation of Cyclopentadiene with Dienophiles of Allylacetylene Series

Diene condensation of cyclopentadiene with 2-substituted allylacetylenes occurs nonselectively at a double and triple bonds; therewith the dienophile activity grows in parallel with the electron-withdrawing properties of the substituent. Depending on electronic character of functional groups the reaction proceeds as neutral diene synthesis. The relative activity of cyclopentadiene and 1,3-cyclohexadiene in reactions with allylacetylenes is essentially governed by the different distance between the 1,4-reactive sites in these systems.     

Spectral problems of a class of non-self-adjoint one-dimensional Schrodinger operators

In this paper we investigate the one-dimensional Schrodinger operator L(q)$L(q)$ with complex-valued periodic potential q   when q∈_L1[0,1]$q\in L_1[0,1]$ and _qn=0$q_n=0$ for n=0,−1,−2,...$n=0,-1,-2,...$, where _qn$q_n$ are the Fourier coefficients of q   with respect to the system {e^i2πnx}$\{e^{i2\pi nx}\}$. We prove that the Bloch eigenvalues are (2πn+t)²${(2\pi n+t)}^2$ for n∈Z$n\in \mathbb{Z}$, t∈C$t\in \mathbb{C}$ and find explicit formulas for the Bloch functions. Then we consider the inverse problem for this operator.