[Fractal dimension and histogram method: algorithm and some preliminary results of noise-like time series analysis].

In the present work a methodological background for the histogram method of time series analysis is developed. Connection between shapes of smoothed histograms constructed on the basis of short segments of time series of fluctuations and the fractal dimension of the segments is studied. It is shown that the fractal dimension possesses all main properties of the histogram method. Based on it a further development of fractal dimension determination algorithm is proposed. This algorithm allows more precision determination of the fractal dimension by using the "all possible combination" method. The application of the method to noise-like time series analysis leads to results, which could be obtained earlier only by means of the histogram method based on human expert comparisons of histograms shapes.

[Lednev's model: theory and experiment].

The results of theoretical and experimental investigations of V.V. Lednev on interactions of weak and extremely weak magnetic fields with biosystems have been reviewed. The period since 1989, when the first version of the interference model has been suggested, until now has been considered. Some mathematical expressions, are presented, which have been published earlier in the papers that are now bibliographic rarity. The results of experimental investigations are also summarized that have been performed in this period under the supervision of V.V. Lednev in the laboratory of biophysics of intracellular regulation in the Institute of Theoretical and Experimental Biophysics of the Russian Academy of Sciences.

[Relationship between the fine structure and statistic fluctuations in measurement result distributions]. / O sootnoshenii mezhdu tonkoi strukturoi i statisticheskimi fluktuatsiiami v raspredeleniiakh rezul'tatov izmerenii.

The "near zone effect" described first in the macroscopic fluctuations researches was studied by numerical modeling. Possible mechanisms of its formation were proposed, and the lengths of portions of experimental data that retain the fine structure of histograms necessary for studying the "near zone effect" and provide the minimum level of statistical noise.