Strongly correlated variables and existence of a universal distribution function for relative fluctuations

R. R. Nigmatullin and G. Smith, “Fluctuation-Noise Spectroscopy and a “Universal” Fitting Function of Amplitudes of Random Sequences,” Physica A. 320, 291 (2003).

J. Feder, Fractals (Plenum Press, N.Y., 1988).

D. J. Hudson, Statistics (Lectures on Elementary Statistics and Probability) (CERN, Geneva, 1964).

M. G. Kendall and A. Stuart, The Advanced Theory of Statistics. Vol. 1 (Ch. Griffin & Co. LTD, N.Y., London, Sydney, Toronto, 1962).

C. Tsallis, “Nonextensive Statistics: Theoretical, Experimental and Computational Evidences and Connections,” Brazil. J. Phys. 29(1), 1 (1999).

V. V. Uchaikin, “Self-Similar Anomalous Diffusion and Levy-Stable Laws,” Phys. Usp. 46, 821 (2003).

R. R. Nigmatullin, “’Fractional’ Kinetic Equations and ‘Universal’ Decoupling of a Memory Function in Mesoscale Region,” Physica A. 363(2), 282 (2006).

R. R. Nigmatullin, “The Quantified Histograms: Detection of the Hidden Unsteadiness,” Physica A. 309(1–2), 214 (2002).

A. Mehaute, R. R. Nigmatullin, and L. Nivanen, Fleches du Temps et Geometrie Fractale (Hermez, Paris, 1998).

R. R. Nigmatullin and A. Le Mehaute, “Is There Geometrical/Physical Meaning of the Fractional integer with Complex Exponent?,” J. Non-Cryst. Solids. 351, 2888 (2005).

R. R. Nigmatullin, “Recognition of Nonextensive Statistical Distributions by the Eigencoordinates Method,” Physica A. 285(3–4), 547 (2000).

M. M. A.-G. Jafar and R. R. Nigmatullin, “Identification of a New Function Model for the AC-Impedance of Thermally Evaporated Undoped Selenium Films Using the Eigen-Coordinates Method,” Thin Solid Films. 396(1), 282 (2001).

R. R. Nigmatullin, M. M. A.-G. Jafar, N. Shinyashiki, S. Sudo, and S. Yagihara, “Recognition of a New Permittivity Function for Glycerol by the Use of the Eigen-Coordinates Method,” J. Non-Cryst. Solids. 305, 96 (2002).

J. Aczel and J. Dhombres, Functional Equations in Several Variables (Cambridge University Press, Cambridge, N.Y., New Rochelle, Melbourne, Sydney, 1989).

A. Renyi, Probability Theory (North-Holland Publ. Co., Amsterdam, 1970).

D. Eisenberg and W. Kauzmann, The Structure and Properties of Water (Oxford Univ. Press, Oxford, 1969).

S. A. Akhmanov and N. I. Koroteev, Methods of Nonlinear Optics in Light Scattering Spectroscopy (Nauka, Moscow, 1981) [in Russian].

A. F. Bunkin, D. V. Vlasov, A. S. Galumyan, and K. O. Sursky, Opt. Spectrosc. 58(3), 481 (1985); S. M. Pershin, “Raman Spectroscopy of the OH Group Vibrations in Structural Complexes of Liquid Wate,” Opt. Spectrosc. 98(4), 543 (2005).

S. M. Pershin, A. F. Bunkin, V. A. Lukyanchenko, and R. R. Nigmatullin, “Detection of the OH Band Fine Structure in Liquid Water by Means of New Treatment Procedure Based on the Statistics of the Fractional Moments,” Laser Phys. [in print].

Yi. Liu and J. P. Dilger, “Opening Rate of Acetylcholine Receptor Channels,” Biophys. J. 60, 424 (1991).

P. C. Molenaar and B. S. Oen, “Analysis of Quantal Acetylcholine Noise at End-Plates of Frog Muscle During Rapid Transmitter Secretion,” J. Physiol. 400, 335 (1988).

D. Wray, “Prolonged Exposure to Acetylcholine: Noise Analysis and Channel Inactivation in Cat Tenuissimus Muscle,” J. Physiol. 310, 37 (1981).

A. A. Potapov and V. A. German, “Detection of Artificial Objects with Fractal Signatures,” Pattern Recognition and Image Analysis. 8(2), 226 (1998).

R. R. Nigmatullin, “The Statistics of the Fractional Moments: Is There Any Chance to “Read Quantitatively” Any Randomness?,” Signal Processing. 86(10), 2529 (2006).

R. R. Nigmatullin, A. Moroz, and G. Smith, “Application of the Generalized Mean Value Function to the Statistical Detection of Water in Decane by Near-Infrared Spectroscopy,” Physica A. 352(2–4), 379 (2005).

R. R. Nigmatullin and G. Smith, “The Generalized Mean Value Function Approach: a New Stastistical Tool for the Detection of Weak Signals in Spectroscopy,” J. Phys. D: Appl. Phys. 38(2), 328 (2005).