Regioselective synthesis of functional tellanes from tellurium tetrahalides and 1-octene

Proceeding from TeCl₄ and 1-octene a regioselective method was developed of the synthesis of trichloro(2-chlorooctyl)tellane. At adding methanol to this compound chlorine was easily replaced at room temperature by a methoxy group affording trichloro(2-methoxyoctyl)tellane. The reaction of TeBr₄ with 1-octene in methanol resulted in tribromo(2-methoxyoctyl)tellane. A reduction of trichloro- and tribromo(2-methoxyoctyl)tellanes occurs the most selectively in the system NaBH4–water–THF giving 1,2-bis(2-methoxyoctyl)ditellane. The reactions are characterized by a high selectivity and quantitative yields of the products.     

Estimates for a spectral parameter in elliptic boundary value problems with discontinuous nonlinearities

Under study are the two classes of elliptic spectral problems with homogeneous Dirichlet conditions and discontinuous nonlinearities (the parameter occurs in the nonlinearity multiplicatively). In the former case the nonlinearity is nonnegative and vanishes for the values of the phase variable not exceeding some positive number c; it has linear growth at infinity in the phase variable u and the only discontinuity at u = c. We prove that for every spectral parameter greater than the minimal eigenvalue of the differential part of the equation with the homogeneous Dirichlet condition, the corresponding boundary value problem has a nontrivial strong solution. The corresponding free boundary in this case is of zero measure. A lower estimate for the spectral parameter is established as well. In the latter case the differential part of the equation is formally selfadjoint and the nonlinearity has sublinear growth at infinity. Some upper estimate for the spectral parameter is given in this case.     

Generation mechanism of bed wave in a sand-bed channel

The previously proposed theory of bed load motion by fluid flow is developed. A plane system of equations for bed perturbations is obtained using a formula for the sediment transport rate which takes into account the effect of free-surface perturbations on sediment transport and is extended to the two-dimensional case. Dependences of the lengths and velocities of longitudinal and transverse waves with the most rapidly increasing amplitude on Froude number are determined. The effect of macroturbulent viscosity and surface waves on the generation of bed waves is determined.     

Functions of normal operators under perturbations

In Peller (1980) [27], Peller (1985) [28], Aleksandrov and Peller (2009) [2], Aleksandrov and Peller (2010) [3], and Aleksandrov and Peller (2010) [4] sharp estimates for f(A)−f(B) were obtained for self-adjoint operators A and B and for various classes of functions f on the real line R. In this paper we extend those results to the case of functions of normal operators. We show that if a function f belongs to the Hölder class Λα(R²), 0<α<1, of functions of two variables, and N₁ and N₂ are normal operators, then ‖f(N₁)−f(N₂)‖?const‖fΛα_‖‖N₁−N₂α^‖. We obtain a more general result for functions in the space for an arbitrary modulus of continuity ω. We prove that if f belongs to the Besov class , then it is operator Lipschitz, i.e., . We also study properties of f(N₁)−f(N₂) in the case when f∈Λα(R²) and N₁−N₂ belongs to the Schatten–von Neumann class Sp.     

Effects of the interaction of electron paramagnetic resonance transitions of copper and gadolinium centers in lead germanate single crystals

This paper reports on the results of investigations into the temperature and orientation dependences of the electron paramagnetic resonance spectrum in the vicinity of accidental coincidence of the spectral lines attributed to the signals (homogeneously broadened or with an antisymmetric arrangement of the spin packets) from Cu²⁺ and Gd³⁺ impurity centers in the ferroelectric lead germanate Pb₅Ge₃O₁₁. The parameters of the broadening and coupling of the spectral components are determined using computer simulation of the electron paramagnetic resonance spectra involving coupling (exchanging) components.     

Influence of interacting resonances on the electron paramagnetic resonance spectrum of Gd<Superscript>3+</Superscript> dipole centers in fluorites

This paper discusses the possibility of detecting the selective averaging of spin packets in the vicinity of coincidence of the electron paramagnetic resonance signals associated with transitions of Gd³⁺ dipole centers due to orientational relaxation.     

Dielectric Properties of Low-Polarity Substances and Their Description Taking into Account Intermolecular Interactions

Optical and dielectric properties of low-polarity liquids (benzene, xylene, toluene, carbon tetrachloride, carbon disulfide) are considered. A generalized equation of dielectric polarization is suggested to describe these properties; its specific feature is the correction for the kind and intensity of intermolecular interaction. This correction is determined on the basis of the model of the molecular electronic shell expanding owing to cross self-polarization of molecules. A material equation improving the agreement of the calculated quantities with the experiment is obtained.