An application of approximate transformation groups to study dynamics a system with distinct time scales is discussed. The utilization the Krylov-Bogoliubov-Mitropolsky method averaging find solutions Lie equations considered. Physical illustrations from plasma kinetic theory demonstrate potentialities suggested approach. Several examples invariant for Vlasov-Maxwell two-component (electron-ion...

1 P. YU ET AL. KB AND GALERKIN METHODS 2 SUMMARY The objective of this paper is to consider the dynamic motions of second order, weakly nonlinear, discrete systems. The main attention is focused on a comparison, for such systems, of the method of Krylov-Bogoliubov (KB) and an enhanced Galerkin (EG) method which produce seemingly diierent solutions. Despite the apparent diierences, the two metho...

In this short paper, we establish a variational expression of the Tsallis relative entropy. In addition, we derive a generalized thermodynamic inequality and a generalized Peierls-Bogoliubov inequality. Finally we give a generalized Golden-Thompson inequality.

Combinatorial harmonic analysis techniques are used to develop new functional analysis methods based on Bogoliubov functionals. Concrete applications of the methods are presented, namely the study of a non-equilibrium stochastic dynamics of continuous systems.

Some logarithmic trace inequalities involving the notions of relative entropy are reobtained from a log-majorization result. The thermodynamic inequality is generalized and a chain of equivalent statements involving this inequality and the Peierls-Bogoliubov inequality is obtained.

We consider the fractional generalizations of the phase volume, volume element, and Poisson brackets. These generalizations lead us to the fractional analog of the phase space. We consider systems on this fractional phase space and fractional analogs of the Hamilton equations. The fractional generalization of the average value is suggested. The fractional analogs of the Bogoliubov hierarchy equ...

The oscillator representation is used for the non-perturbative description of vacuum particle creation in a strong time-dependent electric field in the framework of scalar QED. It is shown that the method can be more effective for the derivation of the quantum kinetic equation (KE) in comparison with the Bogoliubov method of time-dependent canonical transformations. This KE is used for the inve...