Vicinal N,C-difluorination of secondary polynitroalkylamine Mannich bases

The direct fluorination of Mannich bases containing nitro groups in one or two alkyl substituants in the position relative to the amine nitrogen gives previously unreported vicinal N,C-difluorides.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1692–1693, July, 1991.     

Polynitro-substitutedN-alkylalkaneimidoyl chlorides

The reaction of -fluorosubstituted polynitroalkylaldimines with HCl results in replacement of the fluorine atom by a chlorine atom. The hitherto unknown -chlorosubstituted polynitroalkylaldimines have been obtained, and their X-ray structural investigation has been performed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 440–443, March, 1994.     

The Fisher-Hartwig Formula and Entanglement Entropy

Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use the Fisher-Hartwig formula, as well as the recent results concerning the asymptotics of the block Toeplitz determinants, to calculate entanglement entropy of large block of spins in the ground state of XY spin chain.     

The mass spectrum and theS matrix of the massive Thirring model in the repulsive case

The repulsive case of the quantum version of the massive Thirring model is considered. It is shown that there is a rich particle spectrum in the theory. TheS matrix of fermions proves to be a discontinuous function of the coupling constant. These effects are the result of the qualitative change of the physical vacuum in the limit of the strong repulsiong →?π.     

Completely integrable models in quasicrystals

The general method of construction of integrable dynamical models in quasicrystals is presented in the paper. It is illustrated on the example of the model of interacting spins for Penrose nonperiodic tiling of the plane. Another example constructed is the three dimensional model of interacting spins for icosahedral tiling of the three dimensional space. The bulk free energy is calculated for these models.     

N-Substituted tetrahydro-1,3-oxazines and oxazolidines. 1. A new version of the Mannich reaction involving amino alcohols

A new version of the Mannich reaction involving amino alcohols (3-aminopropan-1-ol and aminoethanol) was developed. These compounds react with formaldehyde and CH or NH acids to give N-substituted tetrahydro-1,3-oxazines or oxazolidines.     

Temperature correlators of the impenetrable Bose gas as an integrable system

It is shown that the temperature equal-time correlators of impenetrable bosons in one space dimension are described by a classical integrable system. Partial differential equations for two-point as well as for multipoint correlators are obtained. The short-distance and low-density expansions are constructed.