quantum spectrum as a time series fluctuation measures the fluctuations in the quantum spectrum could be treated like a time series in this framework we explore the statistical self similarity in the quantum spectrum using the detrended fluctuation analysis dfa and random matrix theory rmt we calculate the hausdorff measure for the spectra of atoms and gaussian ensembles and study their self affine properties we show that dfa is equivalent to the delta3 statistics of rmt unifying two different approaches we exploit this connection to obtain theoretical estimates for the hausdorff measure

quantifying signals with power law correlations a comparative study of detrended fluctuation analysis and detrended moving average techniques detrended fluctuation analysis dfa and detrended moving average dma are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals we systematically study the performance of different variants of the dma method when applied to artificially generated long range power law correlated signals with an a priori known scaling exponent alpha 0 and compare them with the dfa method we find that the scaling results obtained from different variants of the dma method strongly depend on the type of the moving average filter further we investigate the optimal scaling regime where the dfa and dma methods accurately quantify the scaling exponent alpha 0 and how this regime depends on the correlations in the signal finally we develop a three dimensional representation to determine how the stability of the scaling curves obtained from the dfa and dma methods depends on the scale of analysis the order of detrending and the order of the moving average we use as well as on the type of correlations in the signal

observer based adaptive fuzzy decentralized control for stochastic large scale nonlinear systems with unknown dead zones this paper studies the problem of adaptive fuzzy decentralized output feedback control for a class of uncertain stochastic large scale nonlinear systems the considered systems have unknown nonlinear functions unknown dead zones unmodeled dynamics and unmeasurable state variables therefore fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy state observer is established to estimate the unmeasurable states based on the backstepping design and the supply changing function technique a robust adaptive fuzzy decentralized output feedback control approach is developed the proposed control approach can ensure the closed loop system to be input state practically stable isps in probability and accommodate the unmodeled dynamics and unknown dead zones as well the effectiveness of the proposed control approach is illustrated by a simulation example

wavelet based fractal analysis of dna sequences abstract the fractal scaling properties of dna sequences are analyzed using the wavelet transform mapping nucleotide sequences onto a dna walk produces fractal landscapes that can be studied quantitatively by applying the so called wavelet transform modulus maxima method this method provides a natural generalization of the classical box counting techniques to fractal signals the wavelets playing the role of generalized oscillating boxes from the scaling behavior of partition functions that are defined from the wavelet transform modulus maxima this method allows us to determine the singularity spectrum of the considered signal and thereby to achieve a complete multifractal analysis moreover by considering analyzing wavelets that make the wavelet transform microscope blind to patches of different nucleotide composition that are observed in genomic sequences we demonstrate and quantify the existence of long range correlations in the noncoding regions although the fluctuations in the patchy landscape of the dna walks reconstructed from both noncoding and protein coding regions are found homogeneous with gaussian statistics our wavelet based analysis allows us to discriminate unambiguously between the fluctuations of the former which behave like fractional brownian motions from those of the latter which cannot be distinguished from uncorrelated random brownian walks we discuss the robustness of these results with respect to various legitimate codings of the dna sequences finally we comment about the possible understanding of the origin of the observed long range correlations in noncoding dna sequences in terms of the nonequilibrium dynamical processes that produce the isochore structre of the genome

a class of methods based on non polynomial sextic spline functions for the solution of a special fifth order boundary value problems a family of fourth and second order accurate numerical schemes is presented for the solution of fifth order boundary value problems with two point boundary conditions the non polynomial sextic spline functions are applied to construct the numerical algorithms this approach generalizes polynomial spline algorithms and provides solution at every point of range of integration convergence of the methods is discussed through standard convergence analysis a numerical illustration is given to show the pertinent features of the technique

quartic non polynomial spline approach to the solution of a system of third order boundary value problems quartic non polynomial splines are used to develop a new numerical method for computing approximations to the solution of a system of third order boundary value problems associated with obstacle unilateral and contact problems it is shown that the new method gives approximations which are better than those produced by other collocation finite difference and spline methods convergence analysis of the method is discussed through standard procedures a numerical example is given to illustrate the applicability and efficiency of the novel method

characterizing multi scale self similar behavior and non statistical properties of fluctuations in financial time series abstract we make use of wavelet transform to study the multi scale self similar behavior and deviations thereof in the stock prices of large companies belonging to different economic sectors the stock market returns exhibit multi fractal characteristics with some of the companies showing deviations at small and large scales the fact that the wavelets belonging to the daubechies db basis enables one to isolate local polynomial trends of different degrees plays the key role in isolating fluctuations at different scales one of the primary motivations of this work is to study the emergence of the k 3 behavior x gabaix p gopikrishnan v plerou h stanley a theory of power law distributions in financial market fluctuations nature 423 2003 267 270 of the fluctuations starting with high frequency fluctuations we make use of db4 and db6 basis sets to respectively isolate local linear and quadratic trends at different scales in order to study the statistical characteristics of these financial time series the fluctuations reveal fat tail non gaussian behavior unstable periodic modulations at finer scales from which the characteristic k 3 power law behavior emerges at sufficiently large scales we further identify stable periodic behavior through the continuous morlet wavelet

globally stable adaptive backstepping fuzzy control for output feedback systems with unknown high frequency gain sign this paper addresses the problem of globally stable adaptive backstepping output feedback tracking control for a class of nonlinear systems with unknown high frequency gain sign the fuzzy systems are used as feedforward compensators to model some system functions depending on the reference signal thus the global stability of closed loop system can be guaranteed under the assumption that the unknown system functions are bounded by partly known nonlinear functions the other advantage of the proposed control scheme is that the designer can determine the approximation domain a priori via the bound of the reference signal which is very important for the choice of the centers and widths of membership functions moreover the nussbaum type function is employed to deal with the unknown high frequency gain sign two simulation examples are provided to illustrate the feasibility of control scheme presented in this paper

output feedback control of markovian jump repeated scalar nonlinear systems this paper is concerned with the induced l2 dynamic output feedback controller dofc design problem for discrete time markovian jump repeated scalar nonlinear systems by employing both the switching sequence dependent lyapunov function approach and the positive definite diagonally dominant lyapunov function technique a sufficient condition is first established which guarantees the underlying system to be stochastically stable with an induced l2 disturbance attenuation performance then the desired full or reduced order dofcs are designed by using projection approach cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem finally a numerical example is presented to show the effectiveness of the proposed methods

cubic splines method for a system of third order boundary value problems we use uniform cubic polynomial splines to develop a numerical method for computing approximations to the solution of a system of third order boundary value problem associated with odd order obstacle problems such problems arise in physical oceanography and can be studied in the framework of variational inequality theory the convergence analysis of the new method is studied and an upper bound for the error is derived a numerical example is given to illustrate the efficiency of the new method

adaptive neural control of mimo nonlinear state time varying delay systems with unknown dead zones and gain signs in this paper adaptive neural control is proposed for a class of uncertain multi input multi output mimo nonlinear state time varying delay systems in a triangular control structure with unknown nonlinear dead zones and gain signs the design is based on the principle of sliding mode control and the use of nussbaum type functions in solving the problem of the completely unknown control directions the unknown time varying delays are compensated for using appropriate lyapunov krasovskii functionals in the design the approach removes the assumption of linear functions outside the deadband as an added contribution by utilizing the integral lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead zone disturbance the closed loop control system is proved to be semi globally uniformly ultimately bounded simulation results demonstrate the effectiveness of the approach

adaptive neural tracking control for a class of nonstrict feedback stochastic nonlinear systems with unknown backlash like hysteresis this paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict feedback form with unknown backlash like hysteresis nonlinearities to overcome the design difficulty of nonstrict feedback structure variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic by combining radial basis function neural networks universal approximation capability with an adaptive backstepping technique an adaptive neural control algorithm is proposed it is shown that the proposed controller guarantees that all the signals in the closed loop system are four moment semiglobally uniformly ultimately bounded and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value simulation results further show the effectiveness of the presented control scheme

neural networks based adaptive control for nonlinear time varying delays systems with unknown control direction this paper investigates a neural network nn state observer based adaptive control for a class of time varying delays nonlinear systems with unknown control direction an adaptive neural memoryless observer in which the knowledge of time delay is not used is designed to estimate the system states furthermore by applying the property of the function tanh2 e the function can be defined at 0 and introducing a novel type appropriate lyapunov krasovskii functional an adaptive output feedback controller is constructed via backstepping method which can efficiently avoid the problem of controller singularity and compensate for the time delay it is highly proven that the closed loop systems controller designed by the nn basis function property new kind parameter adaptive law and nussbaum function in detecting the control direction is able to guarantee the semi global uniform ultimate boundedness of all signals and the tracking error can converge to a small neighborhood of zero the characteristic of the proposed approach is that it relaxes any restrictive assumptions of lipschitz condition for the unknown nonlinear continuous functions and the proposed scheme is suitable for the systems with mismatching conditions and unmeasurable states finally two simulation examples are given to illustrate the effectiveness and applicability of the proposed approach

misleading signatures of quantum chaos the main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest neighbor spacing distribution p s and the spectral rigidity given by the delta 3 l statistic it is shown that some standard unfolding procedures such as local unfolding and gaussian broadening lead to a spurious saturation of delta 3 l that spoils the relationship of this statistic with the regular or chaotic motion of the system this effect can also be misinterpreted as berry s saturation

solution of the system of fourth order boundary value problems using non polynomial spline technique non polynomial spline is used for the numerical solutions of a system of fourth order boundary value problems associated with obstacle unilateral and contact problems in addition to the boundary conditions corresponding to the second derivatives the boundary conditions corresponding to the first derivatives are also considered two examples one for each case of boundary conditions are considered for the numerical illustration of the method developed it has been observed that the method developed in this paper is better than the other collocation finite difference and spline methods

brief paper novel adaptive neural control design for nonlinear mimo time delay systems in this paper we address the problem of adaptive neural control for a class of multi input multi output mimo nonlinear time delay systems in block triangular form based on a neural network nn online approximation model a novel adaptive neural controller is obtained by constructing a novel quadratic type lyapunov krasovskii functional which not only efficiently avoids the controller singularity but also relaxes the restriction on unknown virtual control coefficients the merit of the suggested controller design scheme is that the number of online adapted parameters is independent of the number of nodes of the neural networks which reduces the number of the online adaptive learning laws considerably the proposed controller guarantees that all closed loop signals remain bounded while the output tracking error dynamics converges to a neighborhood of the origin a simulation example is given to illustrate the design procedure and performance of the proposed method

numerical solution of a system of fourth order boundary value problems using cubic non polynomial spline method abstract a cubic non polynomial spline technique is developed for the numerical solutions of a system of fourth order boundary value problems associated with obstacle unilateral and contact problems the end conditions consistent with the bvp are derived corresponding to the boundary conditions in terms of not only second derivatives but first derivatives as well the present method has less computational cost and gives better approximations than those produced by other collocation finite difference and spline methods the method developed is compared with those developed by khan et al a khan m a noor t aziz parametric quintic spline approach to the solution of a system of fourth order boundary value problems journal of optimization theory and applications 122 2 2004 309 322 al said and noor e a al said m a noor computational methods for fourth order obstacle boundary value problems communications in applied nonlinear analysis 2 1995 73 83 and siddiqi and ghazala s s siddiqi g akram solution of the system of fourth order boundary value problems using non polynomial spline technique applied mathematics and computation 185 2007 128 135 through different examples

correlation structure of the deltan statistic for chaotic quantum systems the existence of a formal analogy between quantum energy spectra and discrete time series has been recently pointed out when the energy level fluctuations are described by means of the statistic it is found that chaotic quantum systems are characterized by noise while regular systems are characterized by in order to investigate the correlation structure of the statistic we study the order height height correlation function which measures the momentum of order i e the average power of the signal change after a time delay it is shown that this function has a logarithmic behavior for the spectra of chaotic quantum systems modeled by means of random matrix theory on the other hand since the power spectrum of chaotic energy spectra considered as time series exhibit noise we investigate whether the order height height correlation function of other time series with noise exhibits the same properties a time series of this kind can be generated as a linear combination of cosine functions with arbitrary phases we find that the logarithmic behavior arises with great accuracy for time series generated with random phases

solution of fifth order boundary value problems using nonpolynomial spline technique abstract nonpolynomial spline is used for the numerical solutions of the fifth order linear special case boundary value problems end conditions for the definition of spline are taken from siddiqi and akram s s siddiqi ghazala akram sextic spline solutions of fifth order boundary value problems appl math lett submitted for publication consistent with the fifth order boundary value problem caglar et al h n caglar s h caglar e h twizell the numerical solution of fifth order boundary value problems with sixth degree b spline functions appl math lett 12 1999 25 30 presented the solution of fifth order boundary value problem using sixth degree b spline is first order convergent the method presented in this paper is observed to be a second order convergent for the numerical illustration of the method developed an example has also been considered

adaptive fuzzy output feedback control of mimo nonlinear systems with unknown dead zone inputs this paper is concerned with the problem of adaptive fuzzy tracking control for a class of multi input and multi output mimo strict feedback nonlinear systems with both unknown nonsymmetric dead zone inputs and immeasurable states in this research fuzzy logic systems are utilized to evaluate the unknown nonlinear functions and a fuzzy adaptive state observer is established to estimate the unmeasured states based on the information of the bounds of the dead zone slopes as well as treating the time varying inputs coefficients as a system uncertainty a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique it is shown that the proposed control approach can assure that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded it is also shown that the observer and tracking errors converge to a small neighborhood of the origin by selecting appropriate design parameters simulation examples are also provided to illustrate the effectiveness of the proposed approach

numerical solutions of third order system of boundary value problems we develop a two stage numerical method for computing approximate solutions of a system of third order boundary value problems associated with odd order obstacle problems such a problem arise in physical oceanography and can be studied in the framework of variational inequality theory we show that the present method is of order two and gives numerical results which are better than the other available results numerical example is presented to illustrate the applicability of the new method our results can be viewed as an important and significant refinement of the previously known results

spectral fluctuations of billiards with mixed dynamics from time series to superstatistics a statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards one with mushroomlike shape and the other from the family of the limacon billiards is presented these billiards have mixed regular chaotic dynamics but different structures in their classical phase spaces the spectrum of each billiard is represented as a time series where the level order plays the role of time two most important findings follow from the time series analysis first the spectra can be characterized by two distinct relaxation lengths this is a prerequisite for the validity of the superstatistical approach which is based on the folding of two distribution functions second the shape of the resulting probability density function of the so called superstatistical parameter is reasonably approximated by an inverse chi2 distribution this distribution is used to compute nearest neighbor spacing distributions and compare them with those of the resonance frequencies of billiards with mixed dynamics within the framework of superstatistics the obtained spacing distribution is found to present a good description of the experimental ones and is of the same or even better quality as a number of other spacing distributions including the one from berry and robnik however in contrast to other approaches toward a theoretical description of spectral properties of systems with mixed dynamics superstatistics also provides a description of properties of the eigenfunctions in terms of a superstatistical generalization of the porter thomas distribution indeed the inverse chi2 parameter distribution is found suitable for the analysis of experimental resonance strengths in the limacon billiards within the framework of superstatistics

adaptive fuzzy output feedback tracking backstepping control of strict feedback nonlinear systems with unknown dead zones in this paper an adaptive fuzzy backstepping control approach is considered for a class of nonlinear strict feedback systems with unknown functions unknown dead zones and immeasurable states fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy filters state observer is designed to estimate the immeasurable states by using the adaptive backstepping recursive design technique and constructing the dead zone inverse a new adaptive fuzzy backstepping output feedback control approach is developed it is mathematically proved that all the signals of the resulting closed loop adaptive control system are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin by appropriate choice of design parameters the proposed approach cannot only solve the problem of the dead zones but also cancel the restrictive assumption in the previous literature that the states are all available for measurement two simulation examples are provided to show the effectiveness of the proposed approach

robust adaptive neural network control for a class of uncertain mimo nonlinear systems with input nonlinearities in this paper robust adaptive neural network nn control is investigated for a general class of uncertain multiple input multiple output mimo nonlinear systems with unknown control coefficient matrices and input nonlinearities for nonsymmetric input nonlinearities of saturation and deadzone variable structure control vsc in combination with backstepping and lyapunov synthesis is proposed for adaptive nn control design with guaranteed stability in the proposed adaptive nn control the usual assumption on nonsingularity of nn approximation for unknown control coefficient matrices and boundary assumption between nn approximation error and control input have been eliminated command filters are presented to implement physical constraints on the virtual control laws then the tedious analytic computations of time derivatives of virtual control laws are canceled it is proved that the proposed robust backstepping control is able to guarantee semiglobal uniform ultimate boundedness of all signals in the closed loop system finally simulation results are presented to illustrate the effectiveness of the proposed adaptive nn control

the δn statistic for the β hermite ensemble abstract the fluctuation n of the n th unfolded eigenvalue was recently characterized for the classical gaussian ensembles of n n random matrices goe gue gse it is investigated here for the hermite ensemble as a function of the reciprocal of the temperature by monte carlo simulations the ensemble averaged fluctuation n 2 and the autocorrelation function vary logarithmically with n for any 0 1 n n the simple logarithmic behavior of the higher order moments of n reported in the literature for the goe 1 and the gue 2 holds for any 0 and is accounted for by gaussian distributions whose variances depend linearly on ln n

non polynomial spline approach to the solution of a system of third order boundary value problems we use a quartic spline equivalent nonpolynomial spline functions to develop a numerical method for computing approximations to the solution of a system of third order boundary value problems associated with obstacle unilateral and contact problems we show that the present method gives approximations which are better than those produced by other collocation finite difference and spline methods a numerical example is given to illustrate the applicability and efficiency of the new method

quadratic non polynomial spline approach to the solution of a system of second order boundary value problems a quadratic non polynomial spline functions based method is developed to find approximations solution to a system of second order boundary value problems associated with obstacle unilateral and contact problems the present approach has less computational cost and gives better approximations than those produced by other collocation finite difference and spline methods convergence analysis of the method is discussed a numerical example is given to illustrate practical usefulness of the new method

a combined backstepping and stochastic small gain approach to robust adaptive fuzzy output feedback control in this paper an adaptive fuzzy output feedback control approach is investigated for a class of stochastic nonlinear strict feedback systems without the requirement of states measurement the stochastic nonlinear system addressed in this paper is assumed to possess unstructured uncertainties unknown nonlinear functions and in the presence of unmodeled dynamics dynamics disturbances fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states by combining the backstepping design technique with the stochastic small gain approach a new adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that the closed loop system is input state practically stability isps in probability and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters simulation results are included to indicate that the proposed adaptive fuzzy control approach has a satisfactory control performance in addition the simulation comparisons with the previous methods show that the proposed adaptive fuzzy control approach has robustness to the dynamical uncertainties

wavelet analysis and scaling properties of time series we propose a wavelet based method for the characterization of the scaling behavior of nonstationary time series it makes use of the built in ability of the wavelets for capturing the trends in a data set in variable window sizes discrete wavelets from the daubechies family are used to illustrate the efficacy of this procedure after studying binomial multifractal time series with the present and earlier approaches of detrending for comparison we analyze the time series of averaged spin density in the 2d ising model at the critical temperature along with several experimental data sets possessing multifractal behavior

observer based adaptive neural network control for nonlinear stochastic systems with time delay this paper considers the problem of observer based adaptive neural network nn control for a class of single input single output strict feedback nonlinear stochastic systems with unknown time delays dynamic surface control is used to avoid the so called explosion of complexity in the backstepping design process radial basis function nns are directly utilized to approximate the unknown and desired control input signals instead of the unknown nonlinear functions the proposed adaptive nn output feedback controller can guarantee all the signals in the closed loop system to be mean square semi globally uniformly ultimately bounded simulation results are provided to demonstrate the effectiveness of the proposed methods

observer based fuzzy adaptive control for strict feedback nonlinear systems in this paper a new fuzzy adaptive control approach is developed for a class of siso strict feedback nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is introduced for state estimation as well as system identification under the framework of the backstepping design fuzzy adaptive output feedback control is constructed recursively it is proven that the proposed fuzzy adaptive control approach guarantees the semi global boundedness property for all the signals and the tracking error to a small neighborhood of the origin simulation studies are included to illustrate the effectiveness of the proposed approach

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

multifractal detrended cross correlation analysis of coding and non coding dna sequences through chaos game representation abstract we propose a new approach combining the chaos game representation and the two dimensional multifractal detrended cross correlation analysis methods to examine multifractal behavior in power law cross correlation between any pair of nucleotide sequences of unequal lengths in this work we analyzed the characteristic behavior of coding and non coding dna sequences of eight prokaryotes the results show the presence of strong multifractal nature between coding and non coding sequences of all data sets we found that this integrative approach helps us to consider complete dna sequences for characterization and further it may be useful for classification clustering identification of class affiliation of nucleotide sequences etc with high precision

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

a novel control design on discrete time takagi sugeno fuzzy systems with time varying delays this paper focuses on analyzing a new model transformation of discrete time takagi sugeno t s fuzzy systems with time varying delays and applying it to dynamic output feedback dof controller design a new comparison model is proposed by employing a new approximation for time varying delay state and then a delay partitioning method is used to analyze the scaled small gain of this comparison model a sufficient condition on discrete time t s fuzzy systems with time varying delays which guarantees the corresponding closed loop system to be asymptotically stable and has an induced l2 disturbance attenuation performance is derived by employing the scaled small gain theorem then the solvability condition for the induced l2 dof control is also established by which the dof controller can be solved as linear matrix inequality optimization problems finally examples are provided to illustrate the effectiveness of the proposed approaches

nonpolynomial spline approach to the solution of a system of second order boundary value problems we use a cubic spline equivalent nonpolynomial spline functions to develop a numerical method for computing approximations to the solution of a system of second order boundary value problems associated with obstacle unilateral and contact problems we show that the present method gives approximations which are better than those produced by other collocation finite difference and spline methods convergence analysis of the method is discussed a numerical example is given to illustrate practical usefulness of our method

observer based adaptive fuzzy tracking control of mimo stochastic nonlinear systems with unknown control directions and unknown dead zones in this paper an adaptive fuzzy backstepping output feedback tracking control approach is proposed for a class of multi input and multi output mimo stochastic nonlinear systems the mimo stochastic nonlinear systems under study are assumed to possess unstructured uncertainties unknown dead zones and unknown control directions by using a linear state transformation the unknown control coefficients and the unknown slopes characteristic of the dead zones are lumped together and the original system is transformed to a new system on which the control design becomes feasible fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states by introducing a special nussbaum gain function into the backstepping control design a stable adaptive fuzzy output feedback tracking control scheme is developed the main features of the proposed adaptive control approach are that it can guarantee the stability of the closed loop system and the tracking errors converge to a small neighborhood of zero moreover it can solve the problems of unknown control direction unknown dead zone and unmeasured states simultaneously two simulation examples are provided to show the effectiveness of the proposed approach

multiresolution analysis of fluctuations in non stationary time series through discrete wavelets abstract we illustrate the efficacy of a discrete wavelet based approach to characterize fluctuations in non stationary time series the present approach complements the multifractal detrended fluctuation analysis mf dfa method and is quite accurate for small size data sets as compared to polynomial fits in the mf dfa a single daubechies wavelet is used here for detrending purposes the natural built in variable window size in wavelet transforms makes this procedure well suited for non stationary data we illustrate the working of this method through the analysis of binomial multifractal model for this model our results compare well with those calculated analytically and obtained numerically through mf dfa to show the efficacy of this approach for finite data sets we also do the above comparison for gaussian white noise time series of different sizes in addition we analyze time series of three experimental data sets of tokamak plasma and also spin density fluctuations in 2d ising model

multifractal formalism for fractal signals the structure function approach versus the wavelet transform modulus maxima method several attempts have been made recently to generalize the multifractal formalism originally introduced for singular measures to fractal signals we report on a systematic comparison between the structure function approach pioneered by parisi and frisch in 2 proceedings of the international school on turbulence and predictability in geophysical fluid dynamics and climate dynamics edited by m ghil r benzi and g parisi north holland amsterdam 1985 p 84 to account for the multifractal nature of fully developed turbulent signals and an alternative method we have developed within the framework of the wavelet transform analysis we comment on the intrinsic limitations of the structure function approach this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases we demonstrate that our method based on the wavelet transform modulus maxima representation works in most situations and is likely to be the ground of a unified multifractal description of self affine distributions our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations

wavelet transform of multifractals we present the wavelet transform as a mathematical microscope which is well suited for studying the local scaling properties of fractal objects we apply this technique to probability measures on self similar cantor sets and to the golden mean trajectories on two tori at the onset of chaos

adaptive backstepping controller design for stochastic jump systems in this technical note we improve the results in a paper by shi et al in which problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps were considered however the system considered is switching stochastically between different subsystems the dynamics of the jump system can not stay on each sliding surface of subsystems forever therefore it is difficult to determine whether the closed loop system is stochastically stable in this technical note the backstepping techniques are adopted to overcome the problem in a paper by shi et al the resulting closed loop system is bounded in probability it has been shown that the adaptive control problem for the markovian jump systems is solvable if a set of coupled linear matrix inequalities lmis have solutions a numerical example is given to show the potential of the proposed techniques

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

a smooth approximation based on exponential spline solutions for nonlinear fourth order two point boundary value problems methods of order two four and six based on exponential spline functions consisting of a polynomial part of degree three and an exponential part is developed to find approximation of linear and nonlinear fourth order two point boundary value problems it is shown that the free parameter k of the exponential part can be used to raise the order of accuracy of the new scheme convergence analysis of these methods is shown along with numerical examples each for linear and nonlinear are included to illustrate the practical usefulness of our methods

solution of the system of fourth order boundary value problems using cubic spline a system of fourth order boundary value problems associated with obstacle unilateral and contact problems is solved using cubic spline since the solution of system of fourth order bvp with boundary conditions in terms of values of function and first derivatives is not found in the literature so in this paper the boundary conditions are considered in terms of values of function and not only in first derivatives but in terms of second derivatives as well three examples are considered for the numerical illustration of the method developed it has been observed that the method developed in this paper is better than the other collocation finite difference and spline methods

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

a class of methods based on non polynomial spline functions for the solution of a special fourth order boundary value problems with engineering applications we use a quintic non polynomial spline functions to develop a numerical method for computing approximations to the solution of a system of fourth order boundary value problems associated with plate deflection theory we show that the present family of methods gives better approximations and generalize all the existing finite difference and spline functions based methods up to order six convergence of the methods is shown through standard convergence analysis numerical exampls are given to illustrate the applicability and efficiency of the new method

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

comparison of multifractal and thermodynamical properties of fractal and natural spectra in this paper we explain the multifractal and thermodynamical properties of deterministic fractal spectra and compare the most relevant behaviors with those obtained for some natural spectra with multifractal properties in particular we compare the heat capacity c t derived from cantor set type spectra with the ones obtained from several atomic spectra we nd that although many of the properties of deterministic fractals previously reported are also reproduced in natural fractals oscillations of c t in log scale new features appear in the natural case the mean value of c t is not always related to the multifractal properties and the oscillations are present in cases for which they disappear in deterministic fractals c 2000 elsevier science b v all rights reserved

difference in nature of correlation between nasdaq and bse indices abstract we apply a recently developed wavelet based approach to characterize the correlation and scaling properties of non stationary financial time series this approach is local in nature and it makes use of wavelets from the daubechies family for detrending purpose the built in variable windows in wavelet transform makes this procedure well suited for the non stationary data we analyze daily price of nasdaq composite index for a period of 20 years and bse sensex index over a period of 15 years it is found that the long range correlation as well as fractal behavior for both the stock index values differ from each other significantly strong non statistical long range correlation is observed in bse index whose removal revealed a gaussian random noise character for the corresponding fluctuation the nasdaq index on the other hand showed a multifractal behavior with long range statistical correlation

spectral fluctuation characterization of random matrix ensembles through wavelets a recently developed wavelet based approach is employed to characterize the scaling behaviour of spectral fluctuations of random matrix ensembles as well as complex atomic systems our study clearly reveals anti persistent behaviour and supports the fourier power spectral analysis it also finds evidence for multi fractal nature in the atomic spectra the multi resolution and localization nature of the discrete wavelets ideally characterizes the fluctuations in these time series some of which are not stationary

robust adaptive control of a class of nonlinear systems with unknown dead zone this paper deals with the adaptive control of a class of continuous time nonlinear dynamic systems preceded by an unknown dead zone by using a new description of a dead zone and by exploring the properties of this dead zone model intuitively and mathematically a robust adaptive control scheme is developed without constructing the dead zone inverse the new control scheme ensures global stability of the adaptive system and achieves desired tracking precision simulations performed on a typical nonlinear system illustrate and clarify the validity of this approach

a numerical and asymptotic study of some third order ordinary differential equations relevant to draining and coating flows some draining or coating fluid flow problems in which surface tension forces are important can be described by third order ordinary differential equations accurate computations are provided here