Homogeneous spaces and invariant tensors

In the present survey a method is presented for the construction of invariant tensors (with respect to a given representation) called the inclusion principle and the possibility of applying the cited method to various problems of algebra, topology, geometry, and analysis.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 18, pp. 105–142, 1986.     

Analyticity properties of the surface free energy of the Ising model

For an Ising ferromagnet with nearest-neighbour interactions of strengthK and surface magnetic fieldh, the surface free energy in the presence of a positively (or negatively) magnetized zero-field bulk phase is shown to be analytic inh for Reh<K–/, where =2.96 ... and is the inverse temperature. This puts the lower boundK–/ on the values ofh at which wetting and layering transitions can take place.     

Wave propagation in quasi-one-dimensional quantum plasma in a magnetic field

A cold electron gas fills the lowest Landau level for high enough magnetic fields and for low enough densities. Such a situation is expected to occur for the Malmberg-O'Neil experiment and also for pulsar crusts and atmospheres. Such plasmas behave as a quasi-one-dimensional system and exhibit some peculiarities in their wave structure. We study the dispersion and damping of the low frequencies, i.e., the whistler mode, and the extraordinary mode for zero temperature. The behavior of the whistler mode depends critically on the filling number _Fc=_F/ , where _F is the Fermi energy and is the cyclotron frequency. The one-dimensional character of the system affects the pair excitation spectrum and thus the decay of modes. We find that, in contrast to the three-dimensional situation, the plasma mode and the extraordinary mode remain undamped, while the whistler mode is undamped for all but very highk values.     

Complementary influence of electric and magnetic fields on the sample voltage oscillations ofP-type ultrapure germanium

We report on a previously not observed behaviour of oscillations of the voltage over a hyperpure germanium sample, when increasing the sample current from 0.05 to 13 A, for a number of transverse magnetic fields ranging from 697 to 1746 gauss. The sample temperature was 7.54 K±0.02 K. For each magnetic field the first observed peaks in the frequency spectrum of the sample voltage go to chaos by the period-doubling route and simultaneously shift to lower frequencies (first scenario). Superimposed upon this chaotic spectrum a new peak emerges, which again shifts to lower frequencies with increasing sample current (second scenario). A complementary effect of the sample current and the magnetic field is detected for four properties: firstly, the sudden onset of high resistance in the current versus voltage diagram, secondly, the transition between the two frequency scenarios described above, thirdly the presence of certain frequencies in the sample voltage spectra and fourthly the occurrence of an amplitude maximum for the principal frequency of the first scenario. It is shown that the first two transitions are interrelated.     

Synthesis and pyrolysis of (cyclobutylmethyl)trimethylsilane

Russian Chemical Bulletin -