Crystallographic report: Crystal structure of 1‐bromo‐1′‐[(2S)‐N‐(1‐hydroxy‐3‐methylbutane‐2‐yl)]‐ferroceneamide

For the unsymmetrical title compound, 1‐bromo‐1′‐[(2S)‐N‐(1‐hydroxy‐3‐methylbutane‐2‐yl)]‐ferroceneamide, two independent molecules were found in the asymmetric unit. Copyright © 2003 John Wiley & Sons, Ltd.     

Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation

This paper is a direct continuation of [1] where we began the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators ${\bf Q}_{\pm}(\lambda)$ which act in the highest weight Virasoro module and commute for different values of the parameter λ. These operators appear to be the CFT analogs of the Q - matrix of Baxter [2], in particular they satisfy Baxter's famous T- Q equation. We also show that under natural assumptions about analytic properties of the operators as the functions of λ the Baxter's relation allows one to derive the nonlinear integral equations of Destri-de Vega (DDV) [3] for the eigenvalues of the Q-operators. We then use the DDV equation to obtain the asymptotic expansions of the Q - operators at large λ; it is remarkable that unlike the expansions of the T operators of [1], the asymptotic series for Q(λ) contains the “dual” nonlocal Integrals of Motion along with the local ones. We also discuss an intriguing relation between the vacuum eigenvalues of the Q - operators and the stationary transport properties in the boundary sine-Gordon model. On this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum Hall system. Received: 2 December 1996 / Accepted: 11 March 1997     

Nonhomogeneous Rankin convolutions

The properties of the Rankin convolutions of two eigenfunctions of different parities from the discrete part of the spectrum of the Laplace operator are studied. Analytical continuability of these convolutions into the left half-plane is proved and a functional equation of Riemann type is obtained. Applications to arithmetical convolutions are given. In particular the asymptotics of such convolutions is obtained by using the nonhomogeneous Rankin convolutions. Bibliography: 4 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 37–51.     

Field evaporation and field desorption from HTSC single-crystal surfaces

The problems of field evaporation (FE) and field desorption (FD) from surface of oxide high-temperature superconductors (HTSC) of 123, 2212 and 2223 type are discussed. Wide-angle atom probe, usual time-of-flight atom probe and field ionization magnet mass-spectrometer have been used in these experiments. The main purpose of the investigation was to search for effects connected with phase transition. Therefore, the experiments were carried out over a wide range of temperatures: from T of solid nitrogen to room T.

Composition of pure, contaminated and deep corroded surface and typical species of FE and FD spectra have been studied. The bond energies between some atoms (or clusters) and the surface have been estimated on the basis of experimental results and FE theory. From these estimations, and from discovering of correlated ion pairs, it was concluded that the redistribution of local bonds should be taken into consideration in this case. The increase of FE rate was observed at cryogenic temperatures. Various versions are discussed to explain these effects. Some of them are connected with phase transition.

A detailed study of FD of water protonized clusters is performed and the catalytic activity of HTSC crystal surfaces is discussed.     

A generalized square of the zeta function. Spectral decompositions

The spectral decomposition for the square of the classical Riemann zeta function ζ²(s) is generalized to the case of the product of two such functions ζ(s₁) · ζ(s₂) of different arguments. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 17–44.