Locally nilpotent groups containing an element that commutes with only finitely many of its conjugates

We prove that a locally nilpotent group containing an element that commutes with only finitely many of its conjugates includes an abelian normal subgroup. We find some necessary conditions for the normal closure of such an element to be nilpotent.     

Observational Evidence for Energy Accumulation and Dissipation in Coronal Magnetic Loops

Using the Wigner-Ville transform, we study the dynamic spectra of low-frequency modulation of the intensity of microwave emission from several solar flares and detect the microwave bursts modulated by chirp signals (i.e., signals whose frequencies =₀± kt, where k is a constant and t is the time) with a positive chirp rate. Such a modulation corresponds to the process of energy accumulation in the corresponding coronal magnetic loop (CML). We also detect chirp modulation with a negative chirp rate corresponding to powerful dissipation of electric current in the CML during a solar flare. The chirp modulation of the intensity of microwave emission from a CML arises from the excitation of eigenoscillations of the loop as an equivalent electric circuit. In this case, the modulation frequency is proportional to the loop electric current and varies with the variation of the latter. The electric-current values found for a few events using the dynamic spectra of chirp signals lie in the range 10¹¹-10¹²A, and the rate of energy increase (decrease) is estimated to be 1.4·10²⁶-3·10²⁹ erg/sec for the characteristic time scale 10³-4·10⁴ sec. The events studied give evidence for the possibility of realizing the circuit model of solar flares under solar-corona conditions.     

On BMO-Regular Lattices of Measurable Functions. II

The main result of a previous author’s paper is refined slightly and extended to certain quasi-Banach lattices. Bibliogrhaphy: 3 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 303, 2003, pp. 161–168.     

Development of a Radioastronomical Correlation Method for Measuring Mirror-Antenna Parameters

We consider the techniques and instrumentation developed at the Radiophysical Research Institute (NIRFI) for measuring mirror-antenna parameters using signals from extraterrestrial radio sources and geostationary satellites. The results of measuring the radiation patterns of several large-scale fully-rotatory radio telescopes in a wide dynamic range and of retrieving the amplitude and phase distributions on their apertures are presented.     

On singular integrals related to the Littlewood-Paley inequality for arbitrary intervals

The proof of the inequality mentioned in the title requires the knowledge of the fact that operators of a certain class are Calderón-Zygmund singular integral operators. We slightly extend this class. Bibliography: 4 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 345, 2007, pp. 113–119.     

Letter to the editor

Radiophysics and Quantum Electronics -