Browsing by Author "Nigmatullin, R. R."

Now showing 1 - 6 of 6

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: 33
Citation - Scopus: 35
Is It Possible To Derive Newtonian Equations of Motion With Memory
(Springer/plenum Publishers, 2010) Baleanu, D.; Nigmatullin, R. R.
In this paper for a given example we proved that the Riemann-Liouville fractional integral term appears naturally and relates the external force with acceleration within the fractional Newtonian equation. The consideration of some self-similar process that leads to the fractional integral as well as some possible generalizations of the proposed model was discussed.
Citation - WoS: 11
Citation - Scopus: 15
Nimrad: Novel Technique for Respiratory Data Treatment
(Springer London Ltd, 2014) Nigmatullin, R. R.; Ionescu, C.; Baleanu, D.
This paper illustrates the efficiency and simplicity of a new technique which is determined in this paper as NIMRAD (the non-invasive methods of the reduced analysis of data) for describing information extracted from biological signals. As a specific example, we consider the respiratory data. The NIMRAD can be applied for quantitative description of data recorded for complex systems in cases where the adequate model is absent and the treatment procedure should not contain any uncontrollable error. The theoretical developments are applied to signals measured from the respiratory system by means of the forced oscillation technique based on non-invasive lung function test. In order to verify the feasibility of the proposed algorithm for developing new diagnosis tools, we apply NIMRAD on two different respiratory data sets, namely from a healthy subject and from a patient diagnosed with asthma. The results are promising and suggest that NIMRAD could be further tailored and used for specific clinical applications.
Citation - WoS: 8
Citation - Scopus: 10
Non-Invasive Methods Applied for Complex Signals
(Editura Acad Romane, 2012) Nigmatullin, R. R.; Baleanu, Dumitru; Ionescu, C. M.; Osokin, S. I.; Baleanu, D.; Toboev, V. A.; Matematik
This paper presents the application of a novel algorithm on virtually generated data from patients during anesthesia. Realistic artefacts are simulated in order to validate the usefulness of the proposed methods in separating the signal components: biological trend and artefacts. The results show that the proposed new algorithm can be successfully employed on biological signals to dynamically extract information and distil useful parameters for clinical evaluation.
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.
Citation - WoS: 3
Citation - Scopus: 2
Unification and Extension of the Factorization Method for Constructing Exactly and Conditionally-Exactly Solvable Potentials. the Case of a Single Potential Generating Function
(Elsevier, 2022) Nigmatullin, R. R.; Khamzin, A. A.; Baleanu, D.
The article proposes a new algorithm for applying the factorization method to the problem of calculating the spectrum of exactly and conditionally exactly solvable potentials. The proposed algorithm allows us to unify and extend the capabilities of the factorization method to construct exactly solvable potentials. The new approach is demonstrated by calculating the eigenvalues of exactly solvable potentials constructed using a single function in the form of the Laurent-type polynomial. The algorithm makes it possible to significantly simplify the scheme for calculating the spectrum, parameters of the superpotential, as well as the constrain conditions for the parameters of the potential, in the case of conditionally exactly solvable potentials. It is shown that the shape of the spectrum is determined only by the differential equation, which is satisfied by the potential generating function.