Homogenization of the periodic magnetic Schrödinger operator with degenerate lower edge of the spectrum

Homogenization of the periodic magnetic Schrödinger operator with degenerate lower edge of the spectrum is considered. The standard problem of homogenization leads to a degenerate limiting operator. To obtain more precise information, one needs a certain modification of the problem considered. Bibliography: 10 titles.     

Tetrachlorosilane Consumption in Radio Frequency Glow Discharge

Time-resolved mass spectrometry was used for analysis of the plasma reactions in radio frequency (RF) SiCl ₄ and SiCl ₄ –O ₂ discharges as functions of starting partial pressure and electrical power. Molecular concentrations of the reactants and products from SiCl ₄ alone and with O ₂ were obtained from the mass spectra and used for plotting the kinetic curves. The SiCl ₄ and O ₂ consumption rates were calculated from the kinetic curves and compared with results of theoretical simulation of the reaction. Direct electron impact decomposition was found to be the main pathway for pure SiCl ₄ conversion. On the contrary, the consumption of SiCl ₄ in the SiCl ₄ +O ₂ mixtures was largely chemical. The experimental macrokinetics are in agreement with a model in which oxidation is caused by the atomic oxygen.     

1,3-Dioxa-6-chalcogena-2-silacyclooctanes

Conclusions Transetherification of methylvinyldialkoxyslianes by diols (HOCH₂CH₂)₂M (M=O, S, Se, and Te) gave 2-methyl-2-vinyl-1,3-dioxa-6-chalcogena-2-silacyclooctanes CH₃ (CH₂=CH)Si(OCH₂· CH₂)₂M. The IR, NMR, and mass spectra of these compounds were studied.²⁹Si NMR spectroscopy indicated that there is a transannular interaction in such heterocycles only in the case of M=Te.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1859–1861, August, 1987.     

Similarity of Some Singular Operators to Self-Adjoint Ones

The singular differential operator is studied. It is proved that if the second moment of p is finite and L has no nonreal eigenvalues, then L is similar to a self-adjoint operator. The proof is based on an integral resolvent criterion of similarity applied to a wide class of functions p(x). Bibliography: 20 titles.     

Absolute Continuity of a Two-Dimensional Magnetic Periodic Schrödinger Operator ith Potentials of the Type of Measure Derivative

A two-dimensional magnetic periodic Schrödinger operator with a variable metric is considered. An electric potential is assumed to be a distribution formally given by an expression , where d is a periodic signed measure with a locally finite variation. We also assume that the perturbation generated by the electric potential is strongly subject (in the sense of forms) to the free operator. Under this natural assumption, we prove that the spectrum of the Schrödinger operator is absolutely continuous. Bibliography: 15 titles.     

The Schrödinger operator in a periodic waveguide on a plane and quasiconformal mappings

We consider the magnetic Schrödinger operator with a variable metric in a two-dimensional simply connected periodic waveguide. All the coefficients are assumed to be periodic along the waveguide. We investigate the Dirichlet and Neumann boundary problems, as well as the boundary problem of the third type. Under wide conditions on the boundary of the waveguide providing a band structure of the spectrum, we prove the absolute continuity of the spectrum. Bibliography: 16 titles.Dedicated to Academician O. A. Ladyzhenskaya on the occasion of her jubilee__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 295, 2003, pp. 204–243.     

Addition of N,N-dichloroarylsulfamides to l-alkenylsilatranes

N,N-Dichloroarylsulf amides readily add to the double bond of 1-alkenylsilatranes. Depending on the ratio of the starting reagents, the reaction may proceed with the participation of one or both chlorine atoms of the dichloramide.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2839–2840, December, 1989.     

Complete Asymptotic Expansion of the Integrated Density of States of Multidimensional Almost-Periodic Pseudo-Differential Operators

We obtain a complete asymptotic expansion of the integrated density of states of operators of the form ${H = (-\Delta)^w+ B}$ in ${\mathbb{R}^d}$ . Here w >  0 and B belong to a wide class of almost-periodic self-adjoint pseudo-differential operators of order less than 2w. In particular, we obtain such an expansion for magnetic Schrödinger operators with either smooth periodic or generic almost-periodic coefficients.     

On the Similarity of Some Differential Operators to Self-Adjoint Ones

The paper is devoted to the study of the similarity to self-adjoint operators of operators of the form , in the space with weight . As is well known, the answer to this problem in the case is positive; it was obtained by using delicate methods of the theory of Hilbert spaces with indefinite metric. The use of a general similarity criterion in combination with methods of perturbation theory for differential operators allows us to generalize this result to a much wider class of weight functions .