Frequency spectra of short-period variations of cosmic ray

Frequency spectra for different periods of solar activity were calculated by 5-minutes data of a neutron super-monitor, (altitude 3340 m, cutoff rigidity is 6, 7 GV, counting rate is about 4.5.10 per hour). It was shown that shifting of the spectrum power from low-frequency range to high-frequency range takes place from minimum to maximum of the solar activity. It was reliably distinguished the peak with 160-minutes period coincided with the period of the Sun's atmosphere oscillation and some types of geomagnetic pulsation by the method of accumulation of the frequency spectra. It was conducted the comparison of cosmic ray spectra with spectra of geomagnetic field for the same point of the registration and at the same period

The influence of nonstationarity of the solar activity and general solar field on modulation of cosmic rays

A numerical model of the propagation of galactic cosmic rays in interplanetary space was constructed for the case when the modulation depth determined by the level of solar activity changed in time. Also the contribution of particle drift in the regular field was calculated, and the agreement with experimental data concerning the ratio of protons and electrons in two solar activity minima is shown

Invariants of Lie algebras extended over commutative algebras without unit

We establish results about the second cohomology with coefficients in the trivial module, symmetric invariant bilinear forms and derivations of a Lie algebra extended over a commutative associative algebra without unit. These results provide a simple unified approach to a number of questions treated earlier in completely separated ways: periodization of semisimple Lie algebras (Anna Larsson), derivation algebras, with prescribed semisimple part, of nilpotent Lie algebras (Benoist), and presentations of affine Kac-Moody algebras.Comment: v3: added a footnote on p.10 about a wrong derivation of the correct statemen

Double extensions of Lie algebras of Kac-Moody type and applications to some hamiltonian systems

24 p. Accepté pour publication au JETP en juin 2013.We shall describe some Lie algebras of Kac-Moody type, construct their double extensions, central and by derivations; in some cases, the corresponding Lie groups will also be constructed. The case of Lie algebra of unimodular vector fields will be studied in more details. We use the linear Poisson structure on their regular duals to construct generalizations of some in finite dimensional hamiltonian systems, such as magnetohydrodynamics