NAFASS in action: How to control randomness?

Communications in Nonlinear Science and Numerical Simulation, Volume 18, Issue 3, March 2013, Pages 547-558.
R.R. Nigmatullin, Wei Zhang

 

Institute of Physics, Theoretical Physics Department, Kazan (Volga Region) Federal University, Kremlevskaya Str. 18, Kazan, 420008 Tatarstan, Russia and

Jinan University, College of Information Science and Technology, JNU-KFU Joint-Lab. of Information Technology and Processing of Signals, Department of Electronic Engineering, Guangzhou, Guangdong Province, China

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Abstract

 

In this paper the original method of transformation of one random function to another one is suggested. The problem of transformation of one random function to another one is based on the NAFASS approach suggested previously by one of the authors (RRN) in paper [1]. The problem can be formulated as follows: is it possible to transform one random function to another one (the functional forms of the both functions are notknown) during the fixed segment of time t₁? The solution of this problem shown in this paper gives a chance to manage with random functions that describe many complex systems, where the adequate model pretending on their functional or analytical description is not known. This transformation based on the successful solution of the Prony’s problem gives unique chances to manage with some chemical processes, technological processes and understand better the general behavior of the different complex systems which cannot be managed by the human being. Besides this solution another solution of this problem related to control of detrended random sequences is considered also.

 

 

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Professor R.R. Nigmatullin contact:

Institute of Physics, Theoretical Physics Department, Kazan (Volga Region) Federal University, Kremlevskaya Str. 18, Kazan, 420008 Tatarstan, Russia.

Email: [email protected]