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On the analysis of data emerging in non-linear and complex systems comparison of two x-ray prony spectra

dc.contributor.authorNigmatullin, Raoul R.
dc.contributor.authorKhramov, A. S.
dc.contributor.authorKiyamov, A. G.
dc.contributor.authorFatkhullin, B. F.
dc.contributor.authorMachado, J. A. Tenreiro
dc.contributor.authorBaleanu, Dumitru
dc.date.accessioned2017-04-24T07:43:51Z
dc.date.available2017-04-24T07:43:51Z
dc.date.issued2015
dc.departmentÇankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümüen_US
dc.description.abstractNew arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the "best fit" model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A-("cheap') and B-("expensive') that are used after their proper calibration for the measuring of the same substance (corundum a-Al20). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) -X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to "ideal" experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the I M in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal "filling") are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposesen_US
dc.description.publishedMonth12
dc.identifier.citationNigmatullin, R.R...et al. (2015). On the analysis of data emerging in non-linear and complex systems comparison of two x-ray prony spectra. Revista De Chimie, 66(12), 1929-1937.en_US
dc.identifier.endpage1937en_US
dc.identifier.issn0034-7752
dc.identifier.issue12en_US
dc.identifier.startpage1929en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12416/1566
dc.identifier.volume66en_US
dc.language.isoenen_US
dc.publisherChiminform Data SAen_US
dc.relation.ispartofRevista De Chimieen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectComplex Systemsen_US
dc.subjectX-Ray Diffractometeren_US
dc.subjectFourier And Prony's Decompositionsen_US
dc.subjectDataen_US
dc.subjectTreatment Analysisen_US
dc.subjectIdeal Experimenten_US
dc.subjectIntermediate Modelen_US
dc.subjectCorundumen_US
dc.titleOn the analysis of data emerging in non-linear and complex systems comparison of two x-ray prony spectratr_TR
dc.titleOn the Analysis of Data Emerging in Non-Linear and Complex Systems Comparison of Two X-Ray Prony Spectraen_US
dc.typeArticleen_US
dspace.entity.typePublication

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