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In this manuscript we demonstrate the possibilities of a new spectroscopy that has controllable errors and enables to decompose any smoothed strongly-correlated signal into a linear combination of the trigonometric functions. These possibilities are illustrated on analysis of the FTIR spectra related to Zn with addition of a small concentration of dopant Mn at different temperatures. The Prony's distribution of frequencies can contain information about possible fractal structure of the signal analyzed. The informative-significant band of frequencies that is obtained after the application of the Prony's decomposition can open new possibilities in analysis of different smoothed signals. © 2013 IFAC.

Many specialists working in the field of the fractional calculus and its applications simply replace the integer differentiation and integration operators by their non-integer generalizations and do not give any serious justifications for this replacement. What kind of "Physics" lies in this mathematical replacement? Is it possible to justify this replacement or not for the given type of fractal and find the proper physical meaning? These or other similar questions are not discussed properly in the current papers related to this subject. In this paper new approach that relates to the procedure of the averaging of smooth functions on a fractal set with fractional integrals is suggested. This approach contains the previous one as a partial case and gives new solutions when the microscopic function entering into the structural-factor does not have finite value at N ≫ 1 (N is number of self-similar objects). The approach was tested on the spatial Cantor set having M bars with different symmetry. There are cases when the averaging procedure leads to the power-law exponent that does not coincide with the fractal dimension of the self-similar object averaged. These new results will help researches to understand more clearly the meaning of the fractional integral. The limits of applicability of this approach and class of fractal are specified. © 2013 Versita Warsaw and Springer-Verlag Wien.

In this study a chromatographic separation of active ingredients for four drugs namely Combivir, Kaletra, Valcyte and Viramune was performed on thin layer chromatography (TLC). Their spectra were analyzed for acquired immunodeficiency syndrome by using the Fourier transform infrared spectroscopy spectra combined with the new procedure of the optimal linear smoothing. Fourier transform of the second type was applied as the Fitting function based on some significant set of frequencies for the smoothed signals. The obtained results show that the proposed method is efficient and easy to apply in extracting of a hidden information from signals corresponding to the four investigated drugs.

A model of the self-similar process of relaxation is given, and a method of derivation of the kinetic equations for the total polarization based on the ideas of fractional kinetics is suggested. The derived kinetic equations contain integro-differential operators having non-integer order. They lead to the Cole-Cole expression for the complex dielectric permittivity. It is shown rigorously that the power-law exponent α in the Cole-Cole expression coincides with the dimension of the mixed space-temporal fractal ensemble. If the discrete scale invariance for the temporal-space structure of the dielectric medium considered becomes important, then the expression for the complex dielectric permittivity contains log-periodic corrections (oscillations) and, hence, it generalizes the conventional Cole-Cole expression. The corrections obtained in this model suggest another way of interpretation and analysis of dielectric spectra for different complex materials. © 2012 Elsevier B.V. All rights reserved.

Detonation nanodiamonds (NDs) have shown to be promising agents in several industries, ranging from electronic to biomedical applications. These NDs are characterized by small particle size ranging from 3 to 6 nm, while having a reactive surface and a stable inert core. Nanodiamonds can exhibit novel intrinsic properties such as fluorescence, high refractive index, and unique Raman signal making them very attractive imaging agents. In this work, we used several nanodiamond preparations for Raman spectroscopic studies. We exposed these nanodiamonds to increasing temperature treatments at constant heating rates (425-575°C) aiding graphite release. We wanted to correlate changes in the nanodiamond surface and properties with Raman signal which could be used as a detection marker. These observations would hold potential utility in biomedical imaging applications. First, the procedure of optimal linear smoothing was applied successfully to eliminate the high-frequency fluctuations and to extract the smoothed Raman spectra. After that we applied the secondary Fourier transform as the fitting function based on some significant set of frequencies. The remnant noise was described in terms of the beta-distribution function. We expect this data treatment to provide better results in biomolecule tracking using nanodiamond base Raman labeling. © 2013 Raoul R. Nigmatullin et al.

In this paper the original method of transformation of one random function to another one is suggested. The problem of transformation of one random function to another one is based on the NAFASS approach suggested previously by one of the authors (RRN) in paper [1]. The problem can be formulated as follows: is it possible to transform one random function to another one (the functional forms of the both functions are not known) during the fixed segment of time t 1? The solution of this problem shown in this paper gives a chance to manage with random functions that describe many complex systems, where the adequate model pretending on their functional or analytical description is not known. This transformation based on the successful solution of the Prony's problem gives unique chances to manage with some chemical processes, technological processes and understand better the general behavior of the different complex systems which cannot be managed by the human being. Besides this solution another solution of this problem related to control of detrended random sequences is considered also. © 2012 Elsevier B.V.

In the frame of fractional-kinetic approach, the model of the structural α-relaxation in the presence of the secondary β-relaxation processes is suggested. The model is based on the rigorous bond between β-processes with α-process and leads to the generalized and justified expression for the complex dielectric permittivity (CDP). It allows to form a new sight on the problem of the fitting of multi-peak structure of the dielectric loss spectra in glass-forming materials. The consistency of the CDP expressions obtained is based on a good fit of experimental data for binary methanol-water mixtures. © 2013 AIP Publishing LLC.

The micro/mesoscopic theory of dielectric relaxation has been developed. Based on the fractional kinetics it gives a possibility to obtain the desired expression for the complex dielectric permittivity (CDP) and describe the asymmetric peaks that are created presumably by the so-called "excess wing" located in high-frequency region. The well-known empirical Cole-Davidson expression and its generalization for the CDP were obtained from this theory. This theory is based on self-similar phenomenon and multi-channel organization of relaxation process in disordered dielectrics. The relaxation parameters are connected with the structural parameters of the medium considered. © 2013 Versita Warsaw and Springer-Verlag Wien.

The generalized functional equations describing a wide class of different self-similar processes are derived. These equations follow from the observation that microscopic function describing an initial self-similar process increases monotonically or even cannot have a certain value. The last case implies the behavior of trigonometric functions cos(zn), sin(zn) at > 1 and n >> 1 that can enter to the microscopic function and when the limits of the initial scaling region are increasing and becoming large. The idea to obtain the desired functional equations is based on the approximate decoupling procedure reducing the increasing microscopic function to the linear combination of the same microscopic functions but having smaller scales. Based on this idea the new solutions for the well-known Weierstrass- Mandelbrot function were obtained. The generalized functional equations derived in this paper will help to increase the limits of applicability in description of a wide class of self-similar processes that exist in nature. The procedure that is presented in this paper allows to understand deeper the relationship between the procedure of the averaging of the smoothed functions on discrete self-similar structures and continuous fractional integrals. © 2012 Diogenes Co., Sofia.

International audience

We suggest a model that allows to describe the β-relaxation and Excess Wing phenomena from the unified positions based on the hypothesis related to the self-similar (fractal) character of dielectric relaxation. It has been shown that these phenomena have similar nature but with different organization of relaxation channels. Additional arguments proving that additive combination of the well-known empirical functions forming an expression for the complex dielectric permittivity in frequency domain is not suitable for description of experimental data are given. In the frame of the model suggested we derive new functions for the complex dielectric permittivity that describe well the experimental data where two phenomena mentioned above (β-relaxation and Excess Wing) take place. © 2012 Elsevier B.V. All rights reserved.

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.

Based on a self-similar spatial-temporal structure of the relaxation process, we construct a microscopic model for a non-Debye (nonexponential) dielectric relaxation in complex systems. In this model, we derive the Cole-Cole expression for the complex dielectric permittivity and show that the exponent α involved in that expression is equal to the fractal dimension of the spatial-temporal self-similar ensemble characterizing the structure of the medium and the relaxation process occurring in it. We find a relation between the macroscopic relaxation time and the micro- and mesoparameters of the system. We obtain a generalized Cole-Cole expression for the complex dielectric permittivity involving log-periodic corrections that occur because of a discrete scaling invariance of the fractal structure generating the relaxation process on the mesoscopic scale. The found expression for the dielectric permittivity can be used to interpret dielectric spectra in disordered dielectrics. © 2012 Pleiades Publishing, Ltd.

International audience

The generalized Jonschers law for complex conductivity (derived earlier) is tested on available experimental data. We suggest some criteria, which are used for verification of the analytical expression describing the data related to complex conductivity. It is shown that the generalized Jonschers law is suitable for description of the electrode polarization phenomenon. © 2012 American Institute of Physics.

The self-similar model of spin-system of the Ising type is formulated. The thermodynamic properties of this model are considered. Analytically and numerically the specific heat of this system is calculated in the nearest neighbor approximation (only the influence of two neighboring spins was taken into account). It is shown that in temperature dependence of the specific heat the log-periodic oscillations are appeared. These oscillations are imposed on the expected power-law dependence.

In the frame of Mori-Zwanzig formalism the empirical Navriliak-Negami expression for the complex dielectric permittivity has been derived. The derivation is based on construction of kinetic equations for relaxation and memory functions accordingly. They contain integro-differential operators of non-integer order.

© 2012, Springer-Verlag London. 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.

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the framework of the static fluctuation approximation method. This method based only on a single and controllable approximation allows obtaining the so-called far-distance equations. These equations connecting the quantum states of a Fermi particle with variables of the local field operator contain all necessary information related to the calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system. The basic expressions for the mean energy and heat capacity for the electron gas at low temperatures in the high-density limit were obtained. All expressions are given in the units of r s, where r s determines the ratio of a mean distance between electrons to the Bohr radius a 0. In these expressions, we calculate terms of the respective order r s and r 2 s It is also shown that the static fluctuation approximation allows finding the terms related to higher orders of the decomposition with respect to the parameter r s. © Pleiades Publishing, Inc., 2012.

The theoretical generalization of the Jonscher's relationship for the complex conductivity of carriers moving in self-similar medium is derived. It is shown that the correction derived enters to more general expression, which, in turn, we define as the generalized Jonscher's relationship. The basic idea which was used for the derivation of the relationship is based on the supposition that disordered medium has self-similar property. The derived relationship is confirmed on dielectric spectroscopy data related to sodium nitrite embedded to porous glasses. Based on new relationship there is a possibility to extract additional information about relaxation processes of a system of dipoles from the processes related to conductivity. It is important in the cases when the contribution to relaxation peaks is small and unnoticeable on the background of essential domination of processes related to conductivity. © 2011 Elsevier B.V. All rights reserved.

In this paper we describe novel results of the application of the non-orthogonal amplitude-frequency analysis of the smoothed signals (NAFASS) approach [1] for the analysis of the dielectric response of some complex materials. Our goal is to convince experimentalists that the NAFASS approach can serve as a useful tool in the cases when an underlying physical model is absent or in cases when it is necessary to calibrate the equipment with uncertain quantitative characteristics. The parameters obtained in the frame of the NAFASS approach can be used as metrological parameters for comparison of electromagnetic responses associated with properties of different dielectric materials. © 1994-2012 IEEE.

In this paper we presented a new method (Eigen-Coordinates (ECs)) that can be used for calculations of the critical points (CPs) energy of the interband-transition edges of the heterostructures. This new method is more accurate and complete in comparison with conventional ones and has a wide range of application for the calculation of the fitting parameters related to nontrivial functions that initially have nonlinear fitting parameters that are difficult to evaluate. The new method was applied to determine the CPs energies from the dielectric functions of the MBE grown GaAs1-xPx ternary alloys obtained using spectroscopic ellipsometry (SE) measurements at room temperature in the 0.5-5 eV photon energy region. The obtained results are in good agreement with the results of the other methods. © 2010 Versita Warsaw and Springer-Verlag Berlin Heidelberg.

We obtain an expression for the NMR line at low temperatures for a system of nuclear spins described by a Hamiltonian with equal spin-spin coupling constants. We show that in the case of "easy axis" anisotropy, the line has a logarithmic low-frequency singularity and an exponentially decreasing high-frequency asymptotic behavior at the temperature of an anomalous peak of heat capacity. In the case of "easy plane" anisotropy, the line has the traditional Gaussian form. We discuss the possibility of using NMR data to discover specific thermodynamic and magnetic properties of the considered model system. © 2011 MAIK/Nauka.

In this paper we demonstrate new approach that can help in calculation of electrostatic potential of a fractal (self-similar) cluster that is created by a system of charged particles. For this purpose we used the simplified model of a plane dendrite cluster [1] that is generated by a system of the concentric charged rings located in some horizontal plane (see Fig. 2). The radiuses and charges of the system of concentric rings satisfy correspondingly to relationships: rn=r0ξn and en=e0bn, where n determines the number of a current ring. The self-similar structure of the system considered allows to reduce the problem to consideration of the functional equation that similar to the conventional scaling equation. Its solution represents itself the sum of power-low terms of integer order and non-integer power-law term multiplied to a log-periodic function [5,6]. The appearance of this term was confirmed numerically for internal region of the self-similar cluster (r0≪r≪rN-1), where r0, rN-1 determine the smallest and the largest radiuses of the limiting rings correspondingly. The results were obtained for homogeneously (b>0) and heterogeneously (b

In this paper we proposed a new approach to modify the Langmuir model by considering nonlinear effects such as diffusion of water molecules in/out of an adsorbing film for humidity adsorption and desorption kinetics. The model was tested on the humidity adsorption and desorption data of a spin coated 50. nm thick Ruthenium polypridyl complex (Ru-PC K314) film, measured under relative humidity between 11% and 97% using by Quartz Crystal Microbalance (QCM) technique. © 2011 Elsevier B.V.

The trap parameters of defects in Si/CaF 2 multilayered structures were determined from the analysis of optical charging spectroscopy measurements. Two kinds of maxima were observed. Some of them were rather broad, corresponding to "normal" traps, while the others, very sharp, were attributed to stress-induced traps. A procedure of optimal linear smoothing the noisy experimental data has been developed and applied. This procedure is based on finding the minimal value of the relative error with respect to the value of the smoothing window. In order to obtain a better accuracy for the description of the trapping-detrapping process, a Gaussian temperature dependence of the capture cross-sections characterizing the stress-induced traps was introduced. Both the normal and the stress-induced traps have been characterized, including some previously considered as only noise features. ©2011 American Institute of Physics.

NMR line shape of isolated spin clusters in moving nanocontainers with self-similar correlation law was calculated. It was shown that taking into account self-similarity in stochastic dynamics of pores leads to new shapes of NMR lines which differ from traditional shapes of Gauss and Lorentz types. Fractal dimension of spatial-temporal ensemble can serve as convenient fitting parameter for experimental data interpretation.

Description of random sequences in strongly-correlated systems with the help of β - distribution has been considered. This new method was applied to analysis of CCD-matrix noises recorded at different temperatures. Every noise sequence was "read" in terms of fitting parameters of the β - distribution. Relative fitting error does not exceed the value of 2.2% with the value of Pearson correlation coefficient close to 1. The fitting parameters are rather stable to a difference in treatment procedures. In first treatment method the procedure was applied to the mean values of the noise sequence, while in the second - to each separate sampling with subsequent averaging in the end. For the first method the relative error is located in the vicinity of 1%, while for the second approach this value is about 2.2%. This simple comparison confirms that the self-averaging phenomenon occurs as a result of repetition of the same measurement. With the help of the ECs method we recognized a hypothesis for temperature behavior of the mean values that were calculated for each sampling. This hypothesis represents itself in a linear combination of two exponential functions. One can judge about the temperature stability of the CCD device analyzing the fitting parameters with respect to the temperature. The method has potential application in device calibration or in determination its readiness to a normal work. © 2011 SPIE.

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 β-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 1546month'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 Ω n=Ω 0ξ n, n=0, ±1, ±2, ±3, ±4 with mean period 〈T〉=12.55year. This fact should present interest for ecologists and meteorologists working in this field. © 2010 Elsevier B.V.

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.

In this paper we suggest a new discrete spectroscopy for analysis of random signals and fluctuations. This discrete spectroscopy is based on successful solution of the modified Prony's problem for the strongly-correlated random sequences. As opposed to the general Prony's problem where the set of frequencies is supposed to be unknown in the new approach suggested the distribution of the unknown frequencies can be found for the strongly-correlated random sequences. Preliminary information about the frequency distribution facilitates the calculations and attaches an additional stability in the presence of a noise. This spectroscopy uses only the informative-significant frequency band that helps to fit the given signal with high accuracy. It means that any random signal measured in t-domain can be "read" in terms of its amplitude-frequency response (AFR) without model assumptions related to the behavior of this signal in the frequency region. The method overcomes some essential drawbacks of the conventional Prony's method and can be determined as the non-orthogonal amplitude frequency analysis of the smoothed sequences (NAFASS). In this paper we outline the basic principles of the NAFASS procedure and show its high potential possibilities based on analysis of some actual NIR data. The AFR obtained serves as a specific fingerprint and contains all necessary information which is sufficient for calibration and classification of the informative-significant band frequencies that the complex or nanoscopic system studied might have. © 2011 Elsevier Ltd. All rights reserved.

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 ω(k)=ω0ξk, where the initial frequency ω0 and scaling factor ξ 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. © 2011.

Titanium dioxide thin films were obtained by RF magnetron sputtering system with different Ar and O atmospheres. Chemical bonding structures of the thin films were investigated using the Fourier transform infrared spectroscopy (FTIR) in the range of 400-7500 cm - 1 for as-deposited and conventionally thermal annealed films at different temperature in air. These structural characterizations of the films were carried out by describing the low-frequency fluctuations of the FTIR spectra using the noninvasive (i.e. error controllable) procedure of the optimal linear smoothing. This approach is based on the criterion of the minimal relative error in selection of the proper smoothing window. It allows the receiving an optimal separation of a possible trend from the high-frequency fluctuations, defined as a random sequence of the relative fluctuations possessing zero trends. Thus, the noise can be read and extra information about the structures was then obtained by comparing with the experimental results. In the film annealed at 900 °C, the rutile phase was the dominant crystalline phase as revealed by infrared spectroscopy. At the annealing temperatures lower than 900 °C, both the anatase and the rutile phases were coexisting. In addition, symmetric and asymmetric Si-O-Si vibrations modes were observed at around 1000 cm - 1 and 800 cm - 1, respectively. These peaks suggest that a thin SiO 2 film was formed at the TiO 2/Si interface during the growth and the annealing of the TiO 2 films. It was also observed that the reactivity between TiO 2 film and Si substrate is increased with the increasing annealing temperature. © 2011 Elsevier B.V. All rights reserved.

In the present paper, we have introduced the generalized Newtonian law and fractional Langevin equation. We have derived potentials corresponding to different kinds of forces involving both the right and the left fractional derivatives. Illustrative examples have worked out to explain the formalism. © Versita Warsaw and Springer-Verlag Berlin Heidelberg.

In this study we analyzed the Newtonian equation with memory. One physical model possessing memory effect is analyzed in detail. The fractional generalization of this model is investigated and the exact solutions within Caputo and Riemann-Liouville fractional derivatives are reported. © Springer Science+Business Media B.V. 2009.

The glassy dynamics have been investigated using electric capacitance measurements for thin films of poly(2-chlorostyrene). The observed relaxation behavior of the electric capacitance has been analyzed using a new smoothing procedure for the noisy curves and the eigen-coordinates method for the fitting trends obtained in the results of the smoothing procedure. Such analysis has given us a fascinating relaxation function related to the glassy dynamics. New aging curve will give us a chance to understand a proper physical mechanism (related to a possible formation of dynamical self-similar interacting clusters) that can describe this interesting phenomenon. Physical consequences for the recognized relaxation function are discussed. © 2009 Elsevier B.V. All rights reserved.

A simple model is proposed for describing magnetic properties of magnetoactive nanoclusters, which permits exact analytic solution. Exact expressions are obtained for thermodynamic characteristics of the model, which hold in the entire range of temperatures, magnetic fields, and interaction parameters. It is found that in the case of easy-axis anisotropy, the field dependence of magnetization of a nanocluster consisting of N particles with a spin of 1/2 has [N/2] fractional plateaus ([⋯] is the integer part) corresponding to polarized phases with ruptures singlet pairs. A nonmonotonic behavior observed for the magnetic susceptibility of an easy-plane cluster is typical of gap magnets. The spin gap between the ground state and excited states is proportional to the anisotropy parameter. © 2010 Pleiades Publishing, Ltd.

Based on a new approach presented in detail in this paper one can find new evidences of existence of the fractional kinetics not only in the frequency range. One can find rather general principles of detection of different collective motions in temperature region. These principles can be expressed in terms of an algorithm (defined in the paper as an approach). This approach includes some steps that help to separate a couple of the neighboring collective motions (expressed in the frequency range as a linear combination of two power-law exponents) from each other and establish the temperature evolution of the extreme point that follows to the generalized Vogel-Fulcher-Tamman (VFT)-equation. This experimentally confirmed fact gives new evidences for supporting of the theory of dielectric relaxation based on the fractional kinetics on the frequency/temperature domain. As an example for verification of this new approach the ibuprofen complex permittivity data measured in the wide frequency/temperature range were chosen. The reason of such selection was the following. It helps to compare the conventional study of this complex substance recently published in [1] and use possibilities of the developed approach that can add some new features to the picture obtained in the frame of the conventional treatment. We suppose that possibilities presented by new approach will be extremely useful for detection of different collective motions in other substances studied by the method of broadband dielectric spectroscopy (BDS). © 2009 Elsevier B.V. All rights reserved.

The main aim of this study is to characterize the nanosurface of the mercaptophenyl diazonium modified gold (Au) surface by a new statistical approach. In this study the gold electrode surfaces were self-assembled in ethyl alcohol by 1.0 mM mercaptophenyl diazonium. FT-IR spectra of the surface modifier molecules in both solid and nanofilm of mercaptophenyl diazonium (MCP-Au) forms were recorded in the spectral range of 600-4,000 cm-1. The FT-IR spectra of solid mercaptophenyl diazonium tetrafluoroborate salt were obtained by using KBr pellets. The above FT-IR spectra of both bare Au and its nanofilm of mercaptophenyl diazonium were processed by new statistical approach to reach optimal smoothing trend for the characterization of the modified electrode surface consisting of the nanofilm of gold-mercaptophenyl diazonium. In the frame of new statistical approach all measured spectra have been 'read' in terms of a set of universal statistical parameters. These new parameters help to establish the statistical proximity of the smoothed spectra compared and give a possibility to classify the measured spectra in accordance with new set of statistical and robust quantitative values. Besides, there is a possibility to receive the relative fluctuations and the smoothed spectra of the second order. So, thanks to new approach we do not loose any measured information: the smoothed spectra and accompanied them noise (relative fluctuations) can be analyzed separately for detection of possible influence of predominant external factors that can be essential for this type of measurements. Copyright © 2010 American Scientific Publishers All rights reserved.

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. © Springer Science+Business Media, LLC 2010.

It has been proved that for the strongly-correlated fluctuations there is a universal distribution function for the relative fluctuations (UDFRF). The analytical form of this function follows from the solution of some types of the functional equations. For obtaining the UDFRF a procedure of the optimal linear smoothing (POLS) has been developed. This procedure based on criterion of the minimal relative error helps to separate correctly a possible trend (the "low-frequency" curve, defined as the generalized mean value curve or trend) from the "high-frequency" (HF) fluctuations, defined as a random sequence of relative fluctuations with zero trend. A universal treatment procedure outlined in this paper helps to find an optimal trend, separate it from the relative HF fluctuations and read them quantitatively. The statistics of the fractional moments outlined in this paper helps "to read" the found trends and express them in terms of the fitting parameters if the model for their description is absent. These new possibilities can be applied for description of different noises (quantum fluctuations, for example) that always present on the scale (10-6 ÷ 10-9 m). Quantitative reading of these noises with their subsequent classification is important for every developing nanotechnology that it has a possibility to be applied in this range of scales. © 2009 Elsevier B.V. All rights reserved.