Absolute Continuity of Spectra of Two-Dimensional Periodic Schrodinger Operators with Strongly Subordinate Magnetic Potentials

A two-dimensional periodic magnetic Schrodinger operator with a variable metric is considered. It is shown that under the condition of strong subordination of the magnetic potential, the spectrum of the operator is absolutely continuous. A similar result concerning the Schrodinger operator in a simply connected periodic waveguide is also formulated. Bibliography: 23 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 303, 2003, pp. 279–320.     

Asymptotic expansion of the integrated density of states of a two-dimensional periodic Schrödinger operator

We prove the complete asymptotic expansion of the integrated density of states of a two-dimensional Schrödinger operator with a smooth periodic potential.     

Stereoselective Formation of Fully Substituted Ketone Enolates

The application of stereochemically defined acyclic fully substituted enolates of ketones to the enantioselective synthesis of quaternary carbon stereocenters would be highly valuable. Herein, we describe an approach leading to the formation of several new stereogenic centers through a combined metalation–addition of a carbonyl–carbamoyl transfer to reveal in situ stereodefined α,α‐disubstituted enolates of ketone as a single stereoisomer. This approach could produce a series of aldol and Mannich products from enol carbamate with excellent diastereomeric ratios.     

On the inverse resonance problemfor Jacobi operators—uniqueness and stability

We estimate the difference of the coefficients of two Jacobi operators (from a certain class) from knowledge about their eigenvalues and resonances. More specifically, we prove that if eigenvalues and resonances of the two operators in a sufficiently large disk are respectively close, then the coefficients are close too. A uniqueness result for the inverse resonance problem follows as a corollary.     

Self-assembled calix[6]pyrrole capsules: solid-state encapsulation of different guests in preorganized calix[6]pyrrole capsules

meso-hexamethyl-meso-hexaphenyl calix[6]pyrrole assembles into well-defined dimeric capsules in the crystalline state; the preorganized capsule serves as an efficient host for different organic guests as well as for solvent molecules.     

Addition of polyhaloalkanes to 1-vinylsilatrane

Conclusions Polyhaloalkanes react readily with 1-vinylsilatrane upon photoinitiation or in the presence of peroxides with almost quantitative formation of the products of the regiospecific addition of the perhaloalkyl radical to the terminal carbon atom of the vinyl group.Deceased.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 204–205, January, 1987.