on the multifractal nature of fully developed turbulence and chaotic systems it is generally argued that the energy dissipation of three dimensional turbulent flow is concentrated on a set with non integer hausdorff dimension recently in order to explain experimental data it has been proposed that this set does not possess a global dilatation invariance it can be considered to be a multifractal set the authors review the concept of multifractal sets in both turbulent flows and dynamical systems using a generalisation of the beta model

numerical methods for the estimation of multifractal singularity spectra on sampled data physical variables in scale invariant systems often show chaotic turbulent like behavior commonly associated to the existence of an underlying fractal or multifractal structure however the assessment of multifractality over experimental discretized data requires of appropriate methods and to establish criteria to measure the confidence degree on the estimates in this paper we have evaluated the quality of different techniques used for multifractal analysis we have tested four different techniques the moment m method the wavelet transform modulus maxima wtmm method the gradient modulus wavelet projection gmwp method and the gradient histogram gh method which are used to estimate the singularity spectra of multifractal signals the test consists in analyzing synthetic multifractal 1d signals with given multifractal spectrum we have compared the results studying the sensibility of each method to the length of the series size of the ensemble and type of spectrum our results show that gmwp method is the one attaining the best performance providing reliable estimates which can be improved when the statistics is increased all the other methods are affected by problems such as the linearization of the right tail of the spectrum and some of them are very demanding in data

left symmetric algebras from linear functions abstract in this paper some left symmetric algebras are constructed from linear functions they include a kind of simple left symmetric algebras and some examples appearing in mathematical physics their complete classification is also given which shows that they can be regarded as generalization of certain two dimensional left symmetric algebras

on fermionic novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus they are a class of left symmetric algebras with commutative right multiplication operators which can be viewed as bosonic fermionic novikov algebras are a class of left symmetric algebras with anti commutative right multiplication operators they correspond to a certain hamiltonian superoperator in a supervariable in this paper we commence a study on fermionic novikov algebras from the algebraic point of view we will show that any fermionic novikov algebra in dimension 3 must be bosonic moreover we give the classification of real fermionic novikov algebras on four dimensional nilpotent lie algebras and some examples in higher dimensions as a corollary we obtain kinds of four dimensional real fermionic novikov algebras which are not bosonic all of these examples will serve as a guide for further development including the application in physics

infinitely divisible distributions in turbulence the imbedding of the scale similarity of random fields into the theory of infinitely divisible probability distributions is considered the general probability distribution for the breakdown coefficients of turbulent energy dissipation is obtained along with corresponding similarity exponents related issues of self similarity and asymptotic behavior of statistical characteristics are also considered

left symmetric algebra structures on the w algebra w 2 2 we study the compatible left symmetric algebra structures on the w algebra w 2 2 with some natural grading conditions the results of earlier work on left symmetric algebra structures on the virasoro algebra play an essential role in determining these compatible structures as a corollary any such left symmetric algebra contains an infinite dimensional trivial subalgebra that is also a submodule of the regular module

the realization of non transitive novikov algebras novikov algebras were introduced in connection with hydrodynamic type poisson brackets and hamiltonian operators in the formal variational calculus we have given a kind of realization of transitive novikov algebras through the novikov algebras given by s gelfand and their compatible infinitesimal deformations in bai and meng 2001 j phys a math gen 34 3363 72 as a further and continuous study we extend this realization theory to the non transitive novikov algebras in the paper in two and three dimensions we find that all non transitive novikov algebras also can be realized as the novikov algebras given by s gelfand and their compatible infinitesimal deformations moreover they have simpler formulae

self similarity properties of natural images resemble those of turbulent flows we show that the statistics of an edge type variable in natural images exhibits self similarity properties which resemble those of local energy dissipation in turbulent flows our results show that selfsimilarity and extended self similarity hold remarkably for the statistics of the local edge variance and that the very same models can be used to predict all of the associated exponents these results suggest using natural images as a laboratory for testing more elaborate scaling models of interest for the statistical description of turbulent flows the properties we have exhibited are relevant for the modeling of the early visual system they should be included in models designed for the prediction of receptive fields s0031 9007 97 05190 9

dynamical pulse width modulation control of nonlinear systems abstract the design of dynamical stabilizing pulse width modulated controllers is addressed in full generality for the class of analytical nonlinear single input single output systems expressible in fliess local generalized observability canonical form

design of p i controllers for dc to dc power supplies via extended linearization in this article the method of extended linearization is used for designing stabilizing non linear proportional integral p i controllers which regulate to a constant value either the average output voltage or the average input current of pwm controlled dc to dc power converters such as the boost the buck boost and the cuk converters the design is carried out on the basis of the ziegler nichols p i controller design method applied to a family of linearized transfer function models of converters parametrized by constant operating equilibrium points of the average pwm controlled circuit

a unified algebraic approach to the classical yang baxter equation in this paper the different operator forms of the classical yang baxter equation are given in the tensor expression through a unified algebraic method it is closely related to left symmetric algebras which play an important role in many fields in mathematics and mathematical physics by studying the relations between left symmetric algebras and the classical yang baxter equation we can construct left symmetric algebras from certain classical r matrices and conversely there is a natural classical r matrix constructed from a left symmetric algebra which corresponds to a parakahler structure in geometry moreover the former in a special case gives an algebraic interpretation of the left symmetry as a lie bracket left twisted by a classical r matrix

abelian hessian algebra and commutative frobenius algebra in this paper we study the structure of an abelian hessian algebra first we show that it can be decomposed into unital abelian hessian algebras and a complete abelian hessian algebra abbreviated by caha then we show that a unital one is in fact a hyperbolic extension of a caha next we investigate the structure of caha by studying double filtration obtained canonically from lower and upper annihilator series this double filtration together with j invariant of ternary cubic form give a complete classification of caha up to dimension 6

a stochastic model of human gait dynamics abstract we present a stochastic model of gait rhythm dynamics based on transitions between different neural centers that reproduces distinctive statistical properties of normal human walking by tuning one model parameter the transition hopping range the model can describe alterations in gait dynamics from childhood to adulthood including a decrease in the correlation and volatility exponents with maturation the model also generates time series with multifractal spectra whose broadness depends only on this parameter moreover we find that the volatility exponent increases monotonically as a function of the width of the multifractal spectrum suggesting the possibility of a change in multifractality with maturation

non abelian phase spaces for a vector space v its phase space t v is the vector space v v together with the canonical symplectic form on it since the vector space is the same as an abelian lie algebra the natural question is given a lie algebra g does there exist a phase space t g in general the answer is negative below for a large class of lie algebras g the phase space t g is constructed three examples are treated in detail g gl v g d rn the lie algebra of vector fields on rn and current algebras

measuring daily value at risk of ssec index a new approach based on multifractal analysis and extreme value theory abstract recent studies in the econophysics literature reveal that price variability has fractal and multifractal characteristics not only in developed financial markets but also in emerging markets taking high frequency intraday quotes of the shanghai stock exchange component ssec index as example this paper proposes a new method to measure daily value at risk var by combining the newly introduced multifractal volatility mfv model and the extreme value theory evt method two var backtesting techniques are then employed to compare the performance of the model with that of a group of linear and nonlinear generalized autoregressive conditional heteroskedasticity garch models the empirical results show the multifractal nature of price volatility in chinese stock market var measures based on the multifractal volatility model and evt method outperform many garch type models at high risk levels

exact linearization in switched mode dc to dc power converters three popular dc to dc switched mode power converters buck boost and buck boost are shown to be in the same orbit of structural equivalence as a second order controllable circuit in brunovsky canonical form the equivalence is achievable under non linear feedback and explicit local difleomorphic state coordinate transformations the implications of local exact linearizability of this class of systems in the design of variable structure feedback control laws or pulse width modulation strategies is thoroughly discussed

the generating index of an n lie algebra we introduce a notion of generating index of an n lie algebra the classification of the complex n lie algebras with the generating index n is given we also introduce a notion of an eigenvalue number of an n lie algebra which is used to interpret the complex n lie algebras with the generating index n 1 in particular we give some classification results of the complex 3 lie algebras with the generating index 4 moreover we show that the generating index of a metric 3 lie algebra which is neither simple nor nilpotent is greater than 4 this work provides a new structural tool to study n lie algebras

a multifractal wavelet model with application to network traffic we develop a new multiscale modeling framework for characterizing positive valued data with long range dependent correlations 1 f noise using the haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results the model provides a rapid o n cascade algorithm for synthesizing n point data sets we study both the second order and multifractal properties of the model the latter after a tutorial overview of multifractal analysis we derive a scheme for matching the model to real data observations and to demonstrate its effectiveness apply the model to network traffic synthesis the flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics variance time plots and moment scaling and queuing behavior although for illustrative purposes we focus on applications in network traffic modeling the multifractal wavelet model could be useful in a number of other areas involving positive data including image processing finance and geophysics

microcanonical multifractal formalism a geometrical approach to multifractal systems part i singularity analysis multifractal formalism in the microcanonical framework has proved to be a valuable approach to understand and analyze complex signals typically associated with natural phenomena in scale invariant systems in this paper we discuss the multifractal microcanonical formalism in a comprehensive unified way including new theoretical proofs and validation tests on real signals so completing some known gaps in the foundations of this theory we also review the latest advances and describe the present perspectives in this field some technical details on the implementation of involved algorithms and relevant open issues are also discussed

application of the microcanonical multifractal formalism to monofractal systems the design of appropriate multifractal analysis algorithms able to correctly characterize the scaling properties of multifractal systems from experimental discretized data is a major challenge in the study of such scale invariant systems in the recent years a growing interest for the application of the microcanonical formalism has taken place as it allows a precise localization of the fractal components as well as a statistical characterization of the system in this paper we deal with the specific problems arising when systems that are strictly monofractal are analyzed using some standard microcanonical multifractal methods we discuss the adaptations of these methods needed to give an appropriate treatment of monofractal systems

feedback control of nonlinear systems by extended linearization for single input multiple output nonlinear systems we consider a design method based on the family of linearizations of the system parameterized by constant operating points nonlinear state feedback control laws and observer state feedback control laws are designed such that the eigenvalues of the family of linearized closed loop systems are placed at specified values that are locally invariant with respect to the closed loop operating point the method is illustrated by application to the problem of automatically balancing an inverted pendulum

commutative post lie algebra structures on lie algebras abstract we show that any cpa structure commutative post lie algebra structure on a perfect lie algebra is trivial furthermore we give a general decomposition of inner cpa structures and classify all cpa structures on complete lie algebras as a special case we obtain the cpa structures of parabolic subalgebras of semisimple lie algebras

the multifractal structure of contrast changes in natural images from sharp edges to textures we present a formalism that leads naturally to a hierarchical description of the different contrast structures in images providing precise definitions of sharp edges and other texture components within this formalism we achieve a decomposition of pixels of the image in sets the fractal components of the image such that each set contains only points characterized by a fixed strength of the singularity of the contrast gradient in its neighborhood a crucial role in this description of images is played by the behavior of contrast differences under changes in scale contrary to naive scaling ideas where the image is thought to have uniform transformation properties field 1987 each of these fractal components has its own transformation law and scaling exponents a conjecture on their biological relevance is also given

pseudo riemannian novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus pseudo riemannian novikov algebras denote novikov algebras with nondegenerate invariant symmetric bilinear forms in this paper we find that there is a remarkable geometry on pseudo riemannian novikov algebras and give a special class of pseudo riemannian novikov algebras

edges transitions and criticality in this article various notions of edges encountered in digital image processing are reviewed in terms of compact representation or completion we show that critical exponents defined in statistical physics lead to a much more coherent definition of edges consistent across the scales in acquisitions of natural phenomena such as high resolution natural images or turbulent acquisitions edges belong to the multiscale hierarchy of an underlying dynamics they are understood from a statistical perspective well adapted to fit the case of natural images numerical computation methods for the evaluation of critical exponents in the non ergodic case are recalled which apply for the vast majority of natural images we study the framework of reconstructible systems in a microcanonical formulation show how it redefines edge completion and how it can be used to evaluate and assess quantitatively the adequation of edges as candidates for compact representations we study with particular attention the case of turbulent data in which edges in the classical sense are particularly challenged tests are conducted and evaluated on a standard database for natural images we test the newly introduced compact representation as an ideal candidate for evaluating turbulent cascading properties of complex images and we show better reconstruction performance than the classical tested methods highlightsclassical edge detection algorithms are reviewed in terms of completion a new edge detection scheme based on multiscale hierarchical classification assessing the consistency of edges across scales evaluating edge performance through the framework of reconstructible systems comparing the performance with classical edge operators

multifractal structure of chaotically advected chemical fields the structure of the concentration field of a decaying substance produced by chemical sources and advected by a smooth incompressible two dimensional flow is investigated we focus our attention on the nonuniformities of the h older exponent of the resulting filamental chemical field they appear most evidently in the case of open flows where irregularities of the field exhibit strong spatial intermittency as they are restricted to a fractal manifold nonuniformities of the h older exponent of the chemical field in closed flows appears as a consequence of the nonuniform stretching of the fluid elements we study how this affects the scaling exponents of the structure functions displaying anomalous scaling and relate the scaling exponents to the distribution of local lyapunov exponents of the advection dynamics theoretical predictions are compared with numerical experiments

from rota baxter algebras to pre lie algebras rota baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics rota baxter algebras provide a construction of pre lie algebras from associative algebras in this paper we give all rota baxter operators of weight 1 on complex associative algebras in dimension 3 and their corresponding pre lie algebras

reconstructing images from their most singular fractal manifold real world images are complex objects difficult to describe but at the same time possessing a high degree of redundancy a previous on the statistical properties of natural images reveals that natural images can be viewed through different partitions which are essentially fractal in nature one particular fractal component related to the most singular sharpest transitions in the image seems to be highly informative about the whole scene we show how to decompose the image into their fractal components we see that the most singular component is related to but not coincident with the edges of the objects present in the scenes we propose a new simple method to reconstruct the image with information contained in that most informative component we see that the quality of the reconstruction is strongly dependent on the capability to extract the relevant edges in the determination of the most singular set we discuss the results from the perspective of coding proposing this method as a starting point for future developments

holder exponent spectra for human gait abstract the stride interval time series in normal human gait is not strictly constant but fluctuates from step to step in a complex manner more precisely it has been shown that the control process for human gait is a fractal random phenomenon that is one with a long term memory herein we study the holder exponent spectra for the slow normal and fast gaits of 10 young healthy men in both free and metronomically triggered conditions and establish that the stride interval time series is more complex than a monofractal phenomenon a slightly multifractal and non stationary time series under the three different gait conditions emerges

left symmetric algebras for mathfrak gl n we study the classification problem for left symmetric algebras with commutation lie algebra gr n in characteristic 0 the problem is equivalent to the classification of etale affine representations of g n algebraic invariant theory is used to characterize those modules for the algebraic group sl n which belong to affine etale representations of gr n from the classification of these modules we obtain the solution of the classification problem for gl n as another application of our approach we exhibit left symmetric algebra structures on certain reductive lie algebras with a one dimensional center and a non simple semisimple ideal

empirical evidences of a common multifractal signature in economic biological and physical systems abstract recent developments in microcanonical multifractal formalism have lead to a sensible improvement in the numerical techniques for the determination of the multifractal characteristics of real signals with the aid of these techniques we have found empirical evidence of a common multifractal signature in six very different systems ranging from stock market time series to sea surface temperature records these systems are not only found to be multifractal but their singularity spectra are coincident we propose an explanation of this striking coincidence in terms of a cascade process and analyze its consequences

polynomial alternatives for the group of affine motions it is known that every polycyclic by finite group even if it admits no affine structure allows a polynomial structure of bounded degree a major obstacle to a further development of the theory of these polynomial structures is that the group of the polynomial diffeomorphisms of mathbb r n in contrast to the group of affine motions is no longer a finite dimensional lie group in this paper we construct a family of finite dimensional lie groups even linear algebraic groups of polynomial diffeomorphisms which we call weighted groups of polynomial diffeomorphisms it turns out that every polycyclic by finite group admits a polynomial structure via these weighted groups in the nilpotent and other case s we can sharpen by specifying a nice set of weights the existence results obtained in earlier work we introduce unipotent polynomial structures of nilpotent groups and show how the existence of such polynomial structures is closely related to the existence of simply transitive actions of the corresponding mal cev completion this and other properties provide a strong analogy with the situation of affine structures and simply transitive affine actions considered e g in the work of fried goldman and hirsch

on the realization of transitive novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in the formal variational calculus it is well known that the radical of a finite dimensional novikov algebra is transitive in this paper we prove that a kind realization of novikov algebras given by s gel fand is transitive and we give a deformation theory of novikov algebras in two and three dimensions we find that all transitive novikov algebras can be realized as the novikov algebras given by s gel fand and their compatible infinitesimal deformations

three dimensional wavelet based multifractal method the need for revisiting the multifractal description of turbulence dissipation data we generalize the wavelet transform modulus maxima wtmm method to multifractal analysis of 3d random fields this method is calibrated on synthetic 3d monofractal fractional brownian fields and on 3d multifractal singular cascade measures as well as their random function counterpart obtained by fractional integration then we apply the 3d wtmm method to the dissipation field issued from 3d isotropic turbulence simulations we comment on the need to revisit previous box counting analyses which have failed to estimate correctly the corresponding multifractal spectra because of their intrinsic inability to master nonconservative singular cascade measures

multifractal geometry in stock market time series it has been recently noticed that time series of returns in stock markets are of multifractal multiscaling character in that context multifractality has been always evidenced by its statistical signature i e the scaling exponents associated to a related variable however a direct geometrical framework much more revealing about the underlying dynamics is possible in this paper we present the techniques allowing the multifractal decomposition we will show that there exists a particular fractal component the most singular manifold msm which contains the relevant information about the dynamics of the series it is possible to reconstruct the series at a given precision from the msm we analyze the dynamics of the msm which shows revealing features about the evolution of this type of series