A model of the self-similar process of relaxation is given, and a method of derivation of the kinetic equations for the total polarization based on the ideas of fractional kinetics is suggested. The derived kinetic equations contain integro-differential operators having non-integer order. They...

It is proved that kinetic equations containing non-integer integrals and derivatives appear in the result of reduction of a set of micromotions to some averaged collective motion in the mesoscale region. In other words, it means that after a proper statistical average the microscopic dynamics is...

A “universal” fitting function has been recognized that makes use of the eigen-coordinates method (Physica A 285 (2000) 547) to accurately describe the distribution of ordered amplitudes within random sequences (taken from a diversity of sources). It is shown that sequences with a discrete...

For a given level of digitization, a number of relative frequencies presented by a histogram constructed for a short sample (defined as a segment of a random series), related in a certain way to both the length of the sampling (L) and the number of decompositions (K), may form a set of some...

For detecting weak signals (when their amplitude is comparable with the amplitude of the noise track) a new class of transformations of random series to a straight line has been suggested. It has been shown that these transformations are quasi-linear and can be defined as a signal-to-staircase...

Nonextensive statistical distributions suggested by Tsallis are studied in the framework of the so-called eigencoordinates (ECs) method which allows to recognize them with high level of authenticity. At first, the possibilities of the ECs method have been demonstrated on model files to exhibit...

A simple difference equation for one type of correlators has been obtained by the method of direct calculation of the correlation functions (CF). It is correct for the Ising model of an arbitrary dimension with the exactness O(1z) (z-number of particles covered by the interaction potential). The...