Response from M.A. Chuev

A response is given to critical and erroneous comments on my results reported in Pis’ma Zh. Éksp. Teor. Fiz. 85, 744 (2007) [JETP Lett. 85, 611 (2007)]. A more accurate magnetic dynamic model has been proposed for the calculation of the magnetization curves of an ensemble of single-domain particles. The preliminary calculations confirm that the asymptotic behavior in weak magnetic fields differs from the Langevin limit.     

A new proof of M. Herman's theorem

A new proof of the M. Herman theorem on the smooth conjugacy of a circle map is presented here. It is based on the thermodynamic representation of dynamical systems and the study of the ergodic properties for the corresponding radom variables.Dedicated to Walter Thirring on his 60^th birthday     

A note on the intensities of N.M.R. absorption lines

A proof is given of the proposition that the intensity of the N.M.R. absorption line from a group of n equivalent protons is proportional to n. To do this, it has been necessary to satisfy the Pauli exclusion principle by classifying states according to the irreducible representations of the symmetric group. As far as spin is concerned, this classification is equivalent to one according to the value of I, the total spin. Degeneracy with respect to I, which would otherwise occur, is prohibited by the exclusion principle, and a correlation (not one-to-one) is established between I and the symmetries of the rotational states.     

Acousto-Optical Spectrometers for broadband millimeter radioastronomy at I.R.A.M.

The Observatoire de Paris, in collaboration with the Institute of Millimeter Radio Astronomy (I.R.A.M.), has designed and built a 500 MHz bandwidth, 1 MHz resolution Acousto-Optical Spectrometer for the 30 m radiotelescope in Granada (Spain). The main characteristics of the device are shortly described. A dedicated Bragg cell was designed and built in order to achieve high efficiency and wide band. The performances obtained as well in lab as on site, and extensively measured by comparison with those of reference filterbanks, show that the AOS is fully qualified for high sensitivity, broadband millimeter radioastronomy. Albeit its limitation in frequency resolution, for which other technics as digital autocorrelation are more appropriate, the main advantages of such an AOS are wide band, compactness, and low cost. Its high reliability is evidenced by two years of uninterrupted operations on site.     

A unified approach to classical and quantum K.M.S. theory

We study a generalized K.M.S. condition which includes the classical and quantum mechanical K.M.S. conditions as special cases. We consider also a generalized centre of the von Neumann algebra and prove that with respect to the above K.M.S. condition it has properties analogous to the properties of the centre with respect to the quantum mechanical K.M.S. condition.