Browsing by Author "Popov, I. I."

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Citation - WoS: 1
Citation - Scopus: 1
Application of the Linear Principle for the Strongly-Correlated Variables: Calculations of Differences Between Spectra
(Elsevier Science Bv, 2011) Popov, I. I.; Baleanu, D.; Dinc, E.; Solak, A. O.; Eksi, H.; Guzel, R.; Nigmatullin, R. R.
In this paper the authors suggest a new method of detection of possible differences between similar near infrared (NIR) spectra based on the self-similar (fractal) property. This property is a general characteristic that belongs to a wide class of the strongly-correlated systems. As an example we take a set of NIR spectra measured for three systems: (1) glassy carbon (GC) electrodes, (2) GC electrodes affected by azobenzene (AB) substance and finally (3) films (AB-FILM). Besides the physical model that should describe the intrinsic properties of these substances we found the fitting function that follow from the linear principle for the strongly-correlated variables. This function expressed in the form of linear combination of 4 power-law functions describes with the high accuracy the integrated curves that were obtained from the averaged values of the initially measured spectra. The nine fitting parameters can be considered as the quantitative "finger prints" for detection of the differences between similar spectra. Besides this result we established the self-similar behavior of the remnant functions. In other words, the difference between the initially integrated function and its fitting function can be expressed in the form of linear combinations of periodical functions having a set of frequencies following to relationship omega(k) = omega(0)xi(k), where the initial frequency omega(0) and scaling factor xi are determined by the eigen-coordinates method. This behavior in the NIR spectra was discovered in the first time and physical reasons of such behavior merit an additional research. (C) 2011 Published by Elsevier B.V.
Citation - WoS: 7
Predictions Based on the Cumulative Curves: Basic Principles and Nontrivial Example
(Elsevier, 2011) Popov, I. I.; Baleanu, D.; Nigmatullin, R. R.
In this paper the new prediction method based on analysis of the integrated (cumulative) curves is suggested. This method includes the procedure of the optimal linear smoothing (POLS) for the finding of optimal trends, independent "reading" of relative fluctuations in terms of beta-distribution function that are formed after subtraction of the calculated trend and the recognition of the proper fitting hypothesis for the integrated optimal trends by the eigen-coordinates method. The combined noninvasive approach was applied to analysis of temperature data obtained from the site http://data.giss.nasa.gov/gistemp/ related to the global warming (GW) phenomenon. These data are considered as nontrivial examples of verification of new forecasting method. The available data were combined into six files covering the mean/anomalous temperature 1546 month's points covering the period from the January of 1880 up to October of 2008. Besides the global registered points the combined files included in themselves the north/south data points measured independently for both the Earth's hemispheres. The combined new method (preliminary verified on mimic data) applied to these files predicts the changing of the GW period by the global cooling (GC) period that will happen during the years 2038-2136. Besides this important result a new method helps to discover the influence of a small but stable oscillating process with a set of self-similar periods Omega(n) = Omega(0)xi(n), n = 0, +/- 1, +/- 2, +/- 3, +/- 4 with mean period < T > = 12.55 year. This fact should present interest for ecologists and meteorologists working in this field. (C) 2010 Elsevier B.V. All rights reserved.