stabilization of linear systems with distributed infinite input delays a low gain approach this paper investigates the stabilization problem of linear systems with distributed infinite input delays by introducing a stability result on systems with infinite delays it is shown that a stabilizable linear system with distributed infinite input delays can be globally asymptotically stabilized with low gain controllers as long as the open loop system is not exponentially unstable our result includes constant delay and bounded distributed delay as its special cases it should be noted that the stabilization problem of systems with distributed infinite input delays to our best knowledge has not been considered in existing literatures simulation examples are provided to illustrate the effectiveness of our theoretical results

twenty five years of multifractals in fully developed turbulence a tribute to giovanni paladin the paper on the multifractal nature of fully developed turbulence and chaotic systems by benzi et al 1984 j phys a math gen 17 3521 has been a starting point of many investigations on the different faces of self similarity and intermittency in turbulent phenomena since then the multifractal model has become a useful tool for the study of small scale turbulence in particular for detailed predictions of different eulerian and lagrangian statistical properties on the occasion of the 50th birthday of our unforgettable friend and colleague giovanni paladin 1958 1996 we review here the basic concepts and some applications of the multifractal model for turbulence

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

cascade structures and scaling exponents in a dynamical model of turbulence measurements and comparison a detailed examination of the cascade statistics and scaling exponents is carried out for a dynamical system model of fully developed turbulence called the goy shell model the convergence in time of the probability density functions and moments of the velocity fluctuations and their scaling exponents is studied with particular care with a large sample size 5 ifmmode times else texttimes fi 10 9 we demonstrate that there exists a finite cutoff for the velocity fluctuations at each inertial range wave number shell and the properties of the cutoff determine the scaling exponents of all moments this cutoff represents the most intermittent structures in the cascade dynamics and exhibits a power law dependence on wave number the accurately determined scaling exponents permit a detailed comparison with various phenomenological models describing the statistics of the energy cascade the consideration of the first and second derivatives of the scaling exponents with respect to the order of the moments p provides the evidence that the hierarchical structure model she and leveque phys rev lett 72 336 1994 predicts the best functional dependence on p of the scaling exponents in the goy shell model

dissipativity analysis for singular systems with time varying delays this paper is concerned with the dissipativity analysis problem for singular systems with time varying delays a delay dependent criterion is established to guarantee the dissipativity of the underlying systems using the delay partitioning technique all the results given in this paper are not only dependent upon the time delay but also dependent upon the number of delay partitions the effectiveness and the reduced conservatism of the derived results are demonstrated by two illustrative examples

alternating pushdown and stack automata the classes of languages accepted by alternating pushdown automata alternating stack automata and alternating nonerasing stack automata both with and without an auxiliary space bounded worktape are characterized in terms of complexity classes defined by time bounded deterministic turing machines it is also shown that alternating 2 way finite state machines accept only regular languages

alternation bounded auxiliary pushdown automata languages accepted by alternating auxiliary pushdown automata using simultaneously a n alternations and s n space are shown to be members of the class of languages accepted by nondeterministic turing machines using a n 2es n space for some c 0 this result is used to show that the hierarchy of classes of languages accepted by pushdown automata based on the number of alternations collapses at the second level of the hierarchy the power of alternation bounded pushdown automata without auxiliary storage is also investigated

bounded query classes polynomial time machines having restricted access to an np oracle are investigated restricted access means that the number of queries to the oracle is restricted or the way in which the queries are made is restricted e g queries made during truth table reductions very different kinds of such restrictions result in the same or comparable complexity classes in particular the class p text np o log n can be characterized in very different ways furthermore the boolean hierarchy is generalized in such a way that it is possible to characterize p text np and p text np o log n in terms of the generalization

model approximation for discrete time state delay systems in the t s fuzzy framework this paper is concerned with the problem of h model approximation for discrete time takagi sugeno t s fuzzy time delay systems for a given stable t s fuzzy system our attention is focused on the construction of a reduced order model which not only approximates the original system well in an h performance but is also translated into a linear lower dimensional system by applying the delay partitioning approach a delay dependent sufficient condition is proposed for the asymptotic stability with an h error performance for the error system then the h model approximation problem is solved by using the projection approach which casts the model approximation into a sequential minimization problem subject to linear matrix inequality lmi constraints by employing the cone complementary linearization algorithm moreover by further extending the results h model approximation with special structures is obtained i e delay free model and zero order model finally two numerical examples are provided to illustrate the effectiveness of the proposed methods

nondeterministic space is closed under complementation in this paper we show that nondeterministic space s n is closed under complementation for s n greater than or equal to log n it immediately follows that the context sensitive languages are closed under complementation thus settling a question raised by kuroda inform and control 7 1964 pp 207 233

internal positivity preserved model reduction this article studies model reduction of continuous time stable positive linear systems under the hankel norm h norm and h 2 norm performance the reduced order systems preserve the stability as well as the positivity of the original systems this is achieved by developing new necessary and sufficient conditions of the model reduction performances in which the lyapunov matrices are decoupled with the system matrices in this way the positivity constraints in the reduced order model can be imposed in a natural way as the model reduction performances are expressed in linear matrix inequalities with equality constraints the desired reduced order positive models can be obtained by using the cone complementarity linearisation iterative algorithm a numerical example is presented to illustrate the effectiveness of the given methods

hankel norm approximation of linear systems with time varying delay continuous and discrete cases this paper investigates the problem of hankel norm model reduction for linear systems with time varying delay in the state for a given stable system our attention is focused on the construction of reduced order model which guarantees the corresponding error system to be asymptotically stable and has a specified hankel norm error performance two different approaches are proposed to solve this problem one casts the model reduction into a convex optimization problem by using a linearization procedure and the other is based on the cone complementarity linearization idea which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints both continuous and discrete time cases are considered a numerical example is provided to show the effectiveness of the proposed theory

alternating and empty alternating auxiliary stack automata we consider variants of alternating auxiliary stack automata and characterize their computational power when the number of alternations is bounded by a constant or unlimited in this way we get new characterizations of np the polynomial hierarchy pspace and bounded query classes like co dp nl np 1 and 2p pnp o logn in a uniform framework

model reduction of discrete time interval type 2 t s fuzzy systems this paper addresses the model reduction problem of discrete time interval type 2 it2 takagi sugeno t s fuzzy systems which represent the discrete time nonlinear systems subject to uncertainty with the use of it2 fuzzy sets the uncertainty of the discrete time nonlinear system can be captured by the lower and upper membership functions for a given high order discrete time it2 t s fuzzy system the purpose is to find a lower dimensional system to approximate the original system to achieve the approximation performance an mathcal h infty norm is used to suppress the error between the original system and its simplified system by introducing a membership functions dependent technique and applying a convex linearization method a membership functions dependent condition which takes the information of membership functions into account is obtained to reduce the dimensions of system matrices and the number of fuzzy rules of the system all the obtained theorems are represented as in the form of linear matrix inequalities finally simulation results are demonstrated to show the effectiveness of the derived results

improved results on h model reduction for markovian jump systems with partly known transition probabilities abstract this paper is concerned with the model reduction problem for markovian jump systems with partly known transition probabilities by making use of an existing result on the convex properties of the transition probabilities an improved condition is first derived for the h performance analysis of the error system two different approaches one in terms of linear matrix inequalities lmis and another in the form of an iterative algorithm subject to lmi constraints are then proposed to find a reduced order model such that the h performance of the error system is bounded by a specified level the first approach is obtained using finsler s lemma and involves fewer decision variables than the existing method it is shown that the proposed methods cover some existing results as special cases finally the advantages of our results are clearly illustrated by a numerical example

harmonious representation of pdfs reflecting large deviations abstract the framework of multifractal analysis mfa is distilled to the most sophisticated one within this transparent framework it is shown that the harmonious representation of mfa utilizing two distinct tsallis distribution functions one for the tail part of probability density function pdf and the other for its center part explains the recently observed pdfs of turbulence in the highest accuracy superior to the analyses based on other models such as the log normal model and the p model

optimal time weighted h 2 model reduction for markovian jump systems this article addresses the optimal time weighted h 2 model reduction problem for markovian jump linear systems that is for a given mean square stable markovian jump system our aim is to find a mean square stable jump system of lower order such that the time weighted h 2 norm of the corresponding error system is minimised the time weighted h 2 norm of the system is first defined and then a computational method is constructed the computation requires the solution of two sets of recursive lyapunov type linear matrix equations associated with the markovian jump system to solve the optimal time weighted h 2 model reduction problem we propose a gradient flow method for its solution a necessary condition for minimality is derived and a computational procedure is provided to obtain the minimising reduced order model the necessary condition generalises the standard result for systems when markov jumps and the time weighting term do not appear finally two numerical examples are given to demonstrate the

a new probabilistic description for intermittent turbulence internal time abstract a new fractal model for intermittent turbulence is constructed on the basis of a hierarchical velocity correlation function which represents a self similar structure of turbulence the hierarchy is assumed to be obtained by a class of transformations such as the baker transformation the hierarchical function allows describing stochastically the nonlinear dissipative dynamics of intermittent turbulence the probabilistic description is done with time scales which have such a concept of age that the stronger the fluctuation is the younger it is in age the velocity correlation function which is observed in turbulent flow is expressed as having statistical weights proportional to the time scales we propose that the time scale called internal time exists in the nonlinear dissipative dynamics of turbulence a degree of intermittency is governed by the internal time the numerical results of the one dimensional energy spectrum function agree well over equilibrium range with experimental results mandelbrot s fractal dimension takes values ranging from 2 3 to 2 7 for the experimental results

intermittency as multifractality in history space temporal intermittency in a chaotic dynamical system can be regarded as a manifestation of the multifractal properties of the set of histories the renyi entropies kq which generalize the kolmogorov entropy k1 play a role analogous to the exponents tau q characterising the scaling properties of the moments of the mass distribution the authors introduce the topological entropy h lambda of the subset of histories with the same local expansion parameter they show that kq and h lambda are related to each other by means of a legendre transformation

an approximate approach to h sup 2 optimal model reduction deals with the problem of computing an h sub 2 optimal reduced order model for a given stable multivariable linear system by way of orthogonal projection the problem is formulated as that of minimizing the h sub 2 model reduction cost over the stiefel manifold so that the stability constraint on reduced order models is automatically satisfied and thus totally avoided in the new problem formulation the closed form expression for the gradient of the cost over the manifold is derived from which a gradient flow results as an ordinary differential equation ode a number of nice properties about such a flow are established furthermore two explicit iterative convergent algorithms are developed from the flow one has a constant step size and the other has a varying step size and is much more efficient both of them inherit the properties that the iterates remain on the manifold starting from any orthogonal initial point and that the model reduction cost is decreasing to minima along the iterates a procedure for closing the gap between the original and modified problem is proposed in the symmetric case the two problems are shown to be equivalent numerical examples are presented to illustrate the effectiveness of the proposed algorithms as well as convergence

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

two remarks on the power of counting the relationship between the polynomial hierarchy and valiant s class p is at present unknown we show that some low portions of the polynomial hierarchy namely deterministic polynomial algorithms using an np oracle at most a logarithmic number of times can be simulated by one p computation we also show that the class of problems solvable by polynomial time nondeterministic turing machines which accept whenever there is an odd number of accepting computations is idempotent that is closed under usage of oracles from the same class

internal time irreversibility and intermittency in the quasi self similarity of turbulence abstract we have presented the description of a dynamical regime inherent in a hierarchical velocity correlation function defined for the time series of turbulent velocities the regime is described with an average time scale termed the internal time which measures the rates of local energy transfers flowing through the hierarchy and of dissipation accompanying the energy flow viscosity of the fluid elongates the internal time in very small length scales in the neighborhood of the smallest scale enhancing its own effect on nonlinear action the elongation yields a time arrow resulting from the irreversibility of the dissipative nature we put a new interpretation on intermittency i e multifractal and also give an explanation that the multifractal structure of turbulence makes our hierarchical description possible our model demonstrates the experimental results of batchelor and townsend for the decay of turbulent flows

multiscaling and multifractality abstract a general scaling argument is presented which predicts for the two points correlation function for growth phenomena and critical phenomena a scaling form multiscaling of the type g r r r d d r r a r r where r is the distance from the origin r a characteristic length and a x is an amplitude a connection between multifractality and multiscaling is shown the numerical data of plischke and racz on diffusion limited aggregation and a soluble model for spinodal decomposition are found in agreement with such multiscaling form

aquifer operator scaling and the effect on solute mixing and dispersion 1 since aquifer parameters may have statistical dependence structures that are present across a huge range of scales the concepts of fractional brownian motion fbm have been used in both analytic and numerical stochastic settings most previous models have used isotropic scaling characterized by a single scalar hurst coefficient any real world anisotropy has been handled by an elliptical stretching random k field we define a d dimensional extension of fbm in which the fractional order integration may take on different orders in the d primary possibly nonorthogonal scaling directions and the degree of connectivity and long range dependence is freely assigned via a probability measure on the unit sphere this approach accounts for the different scaling found in the vertical versus horizontal directions in sedimentary aquifers and allows very general degrees of continuity of k in certain directions it also allows for the representation of fracture networks in a continuum setting the eigenvectors of the scaling matrix describe the primary fracture scaling directions and discrete weights of fractional integration represent fracture continuity that may be limited to a small number of directions in a numerical experiment the motion of solutes through 2 d operator fractional gaussian fields depends very much on transverse hurst coefficients transverse scaling in the range of fractional gaussian noise engenders greater plume mixing and a transition to a fickian regime higher orders of integration in the range of fractional brownian motion are associated with thicker layering of aquifer sediments and more preferential unmixed transport therefore direct representation of the unique directional scaling properties of an aquifer is important for realistic simulation of transport

generalized kolmogorov entropy in the dynamics of multifractal generation abstract we point out that applying a maximization principle on a tsallis like generalized form of the kolmogorov entropy for iterated function systems naturally provides a canonical statistical frame for the description of the multifractal measures generated by such dynamical processes multifractal spectra can then be characterized by usual statistical parameters in particular the temperature we show that in the limit of zero temperature the multifractal measure collapses to a homogeneous distribution over a fractal support for finite temperatures multifractal spectra are studied numerically in an illustrative example

gabor transform and intermittency in turbulence intermittency effects basically limited to the viscous subrange contaminate the gabor filtering analysis in the inertial subrange the contamination decreases with an increase in the quality factor of the filter and the gabor transform coefficients of turbulent velocity have scaling properties approaching the kolmogorov scaling in the limit of an infinitely long inertial range there is no anomalous scaling i e no non gaussianity the wavelet transform coefficients of turbulent velocity and its structure functions follow probability rules depending on the scales extracted by analyzing wavelet functions this anomalous scaling property is produced by the intermittency effects inherent in the viscous subrange the structure functions cannot extract properties in a pure inertial subrange

a parameterised model order reduction method for parametric systems based on laguerre polynomials abstractthis paper presents a laguerre polynomials based parametrised model order reduction method for the parametric system in time domain the method allows that the parametric dependence in system matrices is nonaffine the method is presented via reducing an approximate polynomial parametric system based on taylor expansion and laguerre polynomials resulting in a parametric reduced system that can accurately approximate the time response of the original parametric system over a wide range of parameter the reduced parametric system obtained by proposed method can be implemented by two algorithms algorithm 1 is a direct way that is suitable for single input multi output parametric systems algorithm 2 is presented based on a connection to the krylov subspace which is efficient and suitable for multi input multi output parametric systems the effectiveness of the proposed method is illustrated with two benchmarks in practical applications

novel dynamical scaling in kinetic growth phenomena abstract a novel dynamical scaling characterized by infinitely many growth exponents is presented this new behavior is manifested in the time dependent pair correlation function and therefore is amenable to direct experimental observation an exact analytical solution on the time dependent ginzburg landau model is obtained in the large n limit for a quench at zero temperature which exhibits such multiscaling behavior this new form of behavior reflects a morphological pattern in the growing domains and is expected in other growth phenomena as indicated by preliminary analysis on dla clusters a connection between multiscaling and multifractality is discussed

h model reduction of markovian jump linear systems abstract in this paper the h model reduction problem for linear systems that possess randomly jumping parameters is studied the development includes both the continuous and discrete cases it is shown that the reduced order models exist if a set of matrix inequalities is feasible an effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the model reduction solutions using the numerical solutions of the matrix inequalities the reduced order models can be obtained an example is given to illustrate the proposed model reduction method

h model reduction for discrete time delay systems delay independent and dependent approaches this paper investigates the problem of h model reduction for linear discrete time state delay systems for a given stable system our attention is focused on the construction of reduced order models which guarantee the corresponding error system to be asymptotically stable and have a prescribed h error performance both delay independent and dependent approaches are developed with sufficient conditions obtained for the existence of admissible reduced order solutions since these obtained conditions are not expressed as strict linear matrix inequalities lmis the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to lmi constraints which can be readily solved in standard numerical software in addition the development of reduced order models with special structures such as delay free models and zeroth order models is also addressed the approximation methods presented in this paper can be further extended to cope with systems with unc

some results on the behavior and estimation of the fractal dimensions of distributions on attractors the strong interest in recent years in analyzing chaotic dynamical systems according to their asymptotic behavior has led to various definitions of fractal dimension and corresponding methods of statistical estimation in this paper we first provide a rigorous mathematical framework for the study of dimension focusing on pointwise dimension x and the generalized renyi dimensionsd q and give a rigorous proof of inequalities first derived by grassberger and procaccia and hentschel and procaccia we then specialize to the problem of statistical estimation of the correlation dimension and information dimension it has been recognized for some time that the error estimates accompanying the usual procedures which generally involve least squares methods and nearest neighbor calculations grossly underestimate the true statistical error involved in least squares analyses of and we identify sources of error not previously discussed in the literature and address the problem of obtaining accurate error estimates we then develop an estimation procedure for which corrects for an important bias term the local measure density and provides confidence intervals for the general applicability of this method is illustrated with various numerical examples

ℋ model reduction for linear parameter varying systems with distributed delay this paper is concerned with the model reduction for linear parameter varying lpv systems with both discrete and distributed delays for a given stable system our attention is focused on the construction of reduced order models which approximate the original system well in an norm sense first a sufficient condition is proposed for the asymptotic stability with an performance of the error system by using the parameter dependent lyapunov functional method then the decoupling technique is applied such that there does not exist any product term between the lyapunov matrices and the system matrices in the parametrised linear matrix inequality plmi constraints thus a new sufficient condition is obtained based on the new condition two different approaches are developed to solve the model reduction problem one is the convex linearisation approach and the other is the projection approach finally a numerical example is provided to demonstrate the effectiveness of the proposed design method

reduced order model approximation of fuzzy switched systems with pre specified performance the reduced order model approximation problem for discrete time hybrid switched nonlinear systems is addressed via takagi sugeno t s fuzzy modelling in this paper for a high dimension hybrid switched nonlinear system our aim is on how to construct a reduced dimension hybrid switched model approximating its original high order model well with a pre specified system performance level firstly the mean square exponential stability analysis is provided in which it guarantees the given weighted h system performance level for the augmented error dynamic system by the average dwell time analysis approach and the hybrid switched lyapunov stability theory the solution of corresponding model reduction problem with pre specified performance is given by using the projection lemma the algorithm of the reduced order hybrid switched model parameters is designed by the cone complementary linearization technique finally the advantage and effectiveness of the proposed reduced order model approximation approach are shown by the simulation result

universal power law tails for singularity dominated strong fluctuations integrals of the type i t identical to integral integral dxdy delta t h x y are considered where h is a function from an ensemble labelled by parameters i can represent circulation times of fluid particles in the plane orbital periods or semiclassical densities of states for one dimensional hamiltonian systems spectral densities for two dimensional crystals or the strength of a wave pulse produced by propagation of a deformed step discontinuity as h varies over the ensemble i develops strong fluctuations associated with legendre singularities for unrestricted functions h the probability distribution p i describing the fluctuations of i decays according to a universal i 9 law obtained by a scaling argument involving arnold s classification of catastrophes if h is only quadratic in y p varies as i 10 if the integral defining i is one dimensional p varies as i 3 if it is three dimensional i decays no faster than i 48 the probability distribution of i identical to mod delta i delta t mod decays as i 2

brief lpv systems with parameter varying time delays analysis and control in this paper we address the analysis and state feedback synthesis problems for linear parameter varying lpv systems with parameter varying time delays it is assumed that the state space data and the time delays are dependent on parameters that are measurable in real time and vary in a compact set with bounded variation rates we explore the stability and the induced l 2 norm performance of these systems using parameter dependent lyapunov functionals in addition the design of parameter dependent state feedback controllers that guarantee desired l 2 gain performance is examined both analysis and synthesis conditions are formulated in terms of linear matrix inequalities lmis that can be solved via efficient interior point algorithms

pre specified performance based model reduction for time varying delay systems in fuzzy framework this paper attempts to provide a new solution to the model approximation problem for dynamic systems with time varying delays under the fuzzy framework for a given high order system our focus is on the construction of a reduced order model which approximates the original one in a prescribed error performance level and guarantees the asymptotic stability of the corresponding error system based on the reciprocally convex technique a less conservative stability condition is established for the dynamic error system with a given error performance index furthermore the reduced order model is eventually obtained by applying the projection approach which converts the model approximation into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm finally two numerical examples are provided to illustrate the effectiveness of the proposed method

small scale turbulence in the plankton low order deterministic chaos or high order stochasticity abstract almost all regions of the oceans are heavily influenced by the effects of physical processes such as turbulence which in turn influence the distribution and ecology of organisms that occupy these regions there is a real need for additional focus placed on the precise knowledge of both physical and biological processes which is often difficult using basic time series analysis in that way we applied nonlinear analysis techniques to high frequency time series of temperature salinity and phytoplankton concentrations recorded in different hydrodynamical regimes related to tidal forcing in a tidally mixed coastal ecosystem techniques devoted to the identification of low order deterministic chaos cannot find evidence of chaos while a lower dimensionality was identified in low hydrodynamic conditions the results rather suggest stochastic time series with many degrees of freedom no obvious attractor in phase space trajectory lle indistinguishable from zero absence of convergence of the correlation integral we then applied to these data specific multifractal analysis techniques and showed that these time series clearly exhibit high order stochasticity in addition the stochastic structure of purely passive scalars i e temperature and salinity remained invariant while the one of phytoplankton biomass must be regarded as highly structured in time by both hydrodynamic and advective processes

on h2 model reduction of bilinear systems the h 2 model reduction problem for continuous time bilinear systems is studied in this paper by defining the h 2 norm of bilinear systems in terms of the state space matrices the h 2 model reduction error is computed via the reachability or observability gramian necessary conditions for the reduced order bilinear models to be h 2 optimal are given the gradient flow approach is used to obtain the solution of the h 2 model reduction problem the formulation allows certain properties of the original models to be preserved in the reduced order models the model reduction procedure developed can also be applied to finite dimensional linear time invariant systems a numerical example is employed to illustrate the effectiveness of the proposed method

reliable h_ infty control for discrete time fuzzy systems with infinite distributed delay in this paper the problem of reliable h control is investigated for discrete time takagi sugeno t s fuzzy systems with infinite distributed delay and actuator faults a discrete time homogeneous markov chain is used to represent the stochastic behavior of actuator faults in terms of a stochastic fuzzy lyapunov functional a sufficient condition is proposed to ensure that the resultant closed loop system is exponentially stable in the mean square sense with an h performance index based on the derived condition the reliable h control problem is solved and an explicit expression of the desired controller is also given the case of no failure in the actuator is also considered a numerical example is given to demonstrate that our results are effective and less conservative

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

multiscaling transformation in dynamical systems and turbulence abstract multiscaling is a scaling law where the exponent is slowing varying with the length scale pseudo algebraic law we discuss its origin as a consequences of multifractility and the existence of a lower cutoff in the calculation of correlation functions in different contexts we derive some exact results in the case of two scale cantor sets which can be extended to other fractal structures such as strange attractors of chaotic systems in fully developed turbulence the cutoff is naturally introduced by the viscosity and our approach leads to the prediction of an intermediate dissipation range which can be tested experimentally