Mathematical Appendix
41
Mathematical Appendix
Used for treatment of meteo-data
42
Logic scheme for L5 (part 1)
SS – |
What is SS- |
equation? |
scenario? |
|
|
Uncont. factors
Envlp( )- power-law
Fit. F-n S(z)
MC-
Programs
Algorithm? 
Convention 
al Laws
H-analysis
Feder-Frctls
Fitting
Data function
Price of Au
Meteo data
Data, no more!
Complex
Systems
Rg( ) / Stdev( )
H
Eqn S(z),
MW-f-n C(t)
ECs method
Results and
Discussion
Some References
[1]B. Mandelbrot, Fractal Geometry of Nature, Freeman, San-Francisco, 1982.
[2]Fractals in Physics, Essays in honour of B. Mandelbrot, Editors: A. Aharony, J. Feder, North- Holland, Amsterdam, 1989.
[3]S. G. Samko, A.A. Kilbas and O. I. Marichev. Integrals and derivatives of the fractional order and their some applications. "Nauka and Tekhnika" Publishing House, 1987 P. 688. (in Russian).
[4]J.A.T. Machado, V. Kiryakova, F. Mainardi. Recent history of fractional calculus.
Communications in Nonlinear Science and Numerical Simulation. 16 (2011) pp.1140-1153.
[5]R.R. Nigmatullin, J.A.T. Machado, R. Menezes. Self-Similarity principle: the reduced description of randomness. Central European J. of Physics, (2013). (Accepted for publication).
[6]R. R. Nigmatullin. Journal of Applied Nonlinear Dynamics, 1, (2012) 207.
[7]J. Kwapien, S. Drozdz. Physics Reports, 515, (2012) 115.
[8]R. R. Nigmatullin. Physics of Wave Phenomena, 16, (2008) 119.
[9]Osborne M.R. and Smyth G.K. A modifiied Prony algorithm for fiitting functions defiined by difference equations, SIAM Journal of Scientifiic and Statistical Computing, 12, (1991) 362.
[10]Kahn M., Mackisack M.S., Osborne M.R. and Smyth G.K. On the consistency of Prony’s method and related algorithms, Journal of Computational and Graphical Statistics, 1, (1992) 329.
[11]Osborne M.R. and Smyth G.K. A modifiied Prony algorithm for fiitting sums of exponential functions, SIAM Journal of Scientifiic and Statistical Computing, 16, (1995) 119.
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Some References
[12]R.R. Nigmatullin: The statistics of the fractional moments: Is there any chance to read “quantitatively” any randomness? J. Signal Process. 86, (2006) 2529–2547.
[13]R.R. Nigmatullin: Universal distribution function for the strongly-correlated flluctuations: general way for description of random sequences. Commun. Nonlinear Sci. Numer. Simul. 15, (2010) 637–647.
[14]R.R. Nigmatullin, C. Ionescu, D. Baleanu. NIMRAD: novel technique for respiratory data treatment. J. of Signal and Video Processing, (2013) DOI 10.1007/s11760-012-0386-1.
[15]Ciurea, M.L., Lozanu, S., Stavaracher, I., Lepadatu, A.-M., Iancu, V., Mitroi, M.R., Nigmatullin, R.R., Baleanu, C.M.: Stressed induced traps in multilayed structures. J. Appl. Phys. 109, (2011) 013717.
[16]S.M.Pershin, A.F.Bunkin, V.A. Lukyanchenko, R.R.Nigmatullin. "Detection of the OH band fine structure in a liquid water by means of new treatment procedure based on the statistics of the fractional moments." Lazer Phys.Lett. 4 (11) (2007) 809.
[17]S.M.Pershin, A.F.Bunkin, V.A. Lukyanchenko. Evolution of the spectral components of ice in the OH band of water at temperatures 13-99 C. Quantum Electronics 40(12) (2010) 1146.
[18]Raoul R. Nigmatullin, José Tenreiro Machado, Rui Menezes. Self-similarity principle: the reduced description of randomness. Central European Journal of Physics. 11(6) (2013) P 724- 739. (DOI: 10.2478/s11534-013-0181-9).
[19]R.R. Nigmatullin, A.A. Khamzin and J. T. Machado, Detection of quasi-periodic processes in complex systems: how do we quantitatively describe their properties?
Physica Scripta 89 (2014) 015201 (11pp).
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