stability radii of positive linear difference equations under affine parameter perturbations in this paper we study stability radii of positive linear difference equations under arbitrary affine parameter perturbations it is shown that real and complex stability radii of positive equations coincide for block diagonal disturbances moreover for these stability radii estimates and computable formulae are derived which generalize to positive linear difference equations known results obtained earlier for positive linear discrete time systems of the form x k 1 ax k email protected n some illustrative examples are given

dynamics of piecewise linear maps and sets of nonnegative matrices abstract we consider maps f k v min a k av and g k v max a k av where k is a finite set of nonnegative matrices and by min and max we mean component wise minimum and maximum we transfer known results about properties of g k to f k in particular we show existence of nonnegative generalized eigenvectors of f k give necessary and sufficient conditions for existence of strictly positive eigenvector of f k study dynamics of f k on the positive cone we show the existence and construct matrices a and b possibly not in k such that f k n v a n v and g k n v b n v for any strictly positive vector v

extension of the perron frobenius theorem to homogeneous systems this paper deals with a particular class of positive systems the state components of a positive system are positive or zero for all positive times these systems are often encountered in applied areas such as chemical engineering or biology it is shown that for this particular class the first orthant contains an invariant ray in its interior an invariant ray generalizes the concept of an eigenvector of linear systems to nonlinear homogeneous systems then sufficient conditions for uniqueness of this ray are given the main result states that the vector field on an invariant ray determines the stability properties of the zero solution with respect to initial conditions in the first orthant the asymptotic behavior of the solutions is examined finally we compare our results to the perron frobenius theorem which gives a detailed picture of the dynamical behavior of positive linear systems

perron frobenius theory of seminorms a topological approach for nonnegative matrices a the well known perron frobenius theory studies the spectral radius a rump has offered a way to generalize the theory to arbitrary complex matrices he replaced the usual eigenvalue problem with the equation ax x and he replaced a by the signed spectral radius which is the maximum that admits a nontrivial solution to that equation we generalize this notion by replacing the linear transformation a by a map f c n r whose coordinates are seminorms and we use the same definition of rump for the signed spectral radius many of the features of the perron frobenius theory remain true in this setting at the center of our discussion there is an alternative theorem relating the inequalities f x x and f x x which follows from topological principals this enables us to free the theory from matrix theoretic considerations and discuss it in the generality of seminorms some consequences for p matrices and d stable matrices are discussed

stability analysis for continuous time positive systems with time varying delays this note addresses the stability problem of continuous time positive systems with time varying delays it is shown that such a system is asymptotically stable for any continuous and bounded delay if and only if the sum of all the system matrices is a hurwitz matrix the result is a time varying version of the widely known asymptotic stability criterion for constant delay positive systems a numerical example illustrates the correctness of our result

refined similarity hypothesis using three dimensional local averages the refined similarity hypotheses of kolmogorov regarded as an important ingredient of intermittent turbulence has been tested in the past using one dimensional data and plausible surrogates of energy dissipation we employ data from direct numerical simulations at the microscale reynolds number r 650 on a periodic box of 4096 3 grid points to test the hypotheses using three dimensional averages in particular we study the small scale properties of the stochastic variable v u r re r 1 3 where u r is the longitudinal velocity increment and e r is the dissipation rate averaged over a three dimensional volume of linear size r we show that v is universal in the inertial subrange in the dissipation range the statistics of v are shown to depend solely on a local reynolds number

log poisson cascade description of turbulent velocity gradient statistics the log poisson phenomenological description of the turbulent energy cascade is evoked to discuss high order statistics of velocity derivatives and the mapping between their probability distribution functions at different reynolds numbers the striking confirmation of theoretical predictions suggests that numerical solutions of the flow obtained at low moderate reynolds numbers can play an important quantitative role in the analysis of experimental high reynolds number phenomena where small scales fluctuations are in general inaccessible from direct numerical simulations

the short cut test abstract the short cut test detects existence and uniqueness of laplacians on finitely ramified graph directed fractals previous results by sabot nussbaum and the author are improved and extended it opens up the way for further studies because it combines well established spectral dynamical and analytic techniques its algorithmic and recursive structure is designed to provide computable and flexible criteria

normal and anomalous scaling of turbulence a non gaussian model of the probability density function pdf of ensuremath delta u r is proposed to study how the scaling exponents s p of the structure function ensuremath delta u r p of finite reynolds number turbulence depends upon the taylor microscale reynolds number r ensuremath lambda here ensuremath delta u r is the longitudinal velocity difference across a distance r and is the statistical average the model not only predicts anomalous scaling s p lp 3 for pg3 observed in experiments at a finite reynolds number but also predicts that s p approaches normal scaling p 3 while r ensuremath lambda is very high hence in contrast to the prevailing multiscaling models the non gaussian pdf model suggests a completely different picture of scaling of isotropic turbulence the anomalous scaling observed in experiments is a finite reynolds number effect and the normal scaling is valid in the real kolmogorov inertial range corresponding to an infinite reynolds number

on positivity and stability of linear volterra systems with delay an explicit criterion for positivity of the solution semigroup of linear volterra integro differential systems with infinitely many delays is given then exponential asymptotic stability is studied and it is shown that roughly speaking a linear volterra integro differential system with delay is exponentially asymptotically stable if its characteristic equation has no zeros in the closed right half complex plane and the kernel part of the system exponentially decays in particular some simple criteria for exponential asymptotic stability of positive systems are presented finally two sufficient conditions for exponential asymptotic stability of positive systems subjected to structured perturbations and affine perturbations are given a simple example is given to illustrate the obtained results

brief stabilization of positive systems with first integrals positive systems possessing first integrals are considered these systems frequently occur in applications this paper is devoted to two stabilization problems the first is concerned with the design of feedbacks to stabilize a given level set secondly it is shown that the same feedback allows to globally stabilize an equilibrium point if it is asymptotically stable with respect to initial conditions in its level set two examples are provided and the results are compared with those in the literature

theorems of perron frobenius type for matrices without sign restrictions abstract the paper attempts to solve a problem which was called a challenge for the future in linear algebra appl we define and investigate a new quantity for real matrices the sign real spectral radius and derive various characterizations bounds and properties of it in certain aspects our quantity shows similar behavior to the perron root of a nonnegative matrix it is shown that our quantity also has intimate connections to the componentwise distance to the nearest singular matrix relations to the perron root of the entrywise absolute value of the matrix and to the number are given as well

stability radii of positive linear functional differential equations under multi perturbations we study stability radii of linear retarded systems described by general linear functional differential equations a lower and an upper bound for the complex stability radius with respect to multi perturbations are given furthermore in some special cases concerning the structure matrices the complex stability radius can precisely be computed via the associated transfer function then the class of positive linear retarded systems is studied in detail it is shown that for this class complex real and positive stability radius under multi perturbations or multi affine perturbations coincide and can be computed by simple formulae expressed in terms of the system matrices

locality and stability of the cascades of two dimensional turbulence we investigate and clarify the notion of locality as it pertains to the cascades of two dimensional turbulence the mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions first introduced by l vov and procaccia as a point of departure we use a revised version of the system of hypotheses that was proposed by frisch for three dimensional turbulence we show that both the enstrophy cascade and the inverse energy cascade are local in the sense of non perturbative statistical locality we also investigate the stability conditions for both cascades we have shown that statistical stability with respect to forcing applies unconditionally for the inverse energy cascade for the enstrophy cascade statistical stability requires large scale dissipation and a vanishing downscale energy dissipation a careful discussion of the subtle notion of locality is given at the end of the paper

closure approach to high order structure functions of turbulence let t p be the structure function of order p of turbulence first t2 is determined then t3 is derived from t2 and finally t p p 3 are derived from t2 and t3 this closure scheme is realized by a non gaussian statistical model we use it to study the scaling law of t p and we find that the available data on scaling exponents favor kolmogorov s 1941 theory rather than his 1962 theory we also predict the high order universal constants of inertial range scaling

eigenvalue regions for positive systems positive systems are systems in which the state variables take only nonnegative values for all times in this paper we derive eigenvalue regions for discrete and continuous time positive linear systems by resorting to the immediately available information on the values of the main diagonal entries of the system matrix

concave perron frobenius theory and applications many important results of classical perron frobenius theory can be extended from linear selfmappings of the standard cone in finite dimensional real space to concave selfmappings of this cone this is in particular true for minima of linear mappings albeit the spectrum of these special concave mappings is more intricate than that for linear mappings as classical perron frobenius theory has numerous applications there are many new applications for its concave extension 1991 mathematical subject classification primary 39a11 15a48 secondary 47h07 47h12

robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay this paper establishes the existence and uniqueness theorem of neutral stochastic functional differential equations with infinite delay and examines the almost sure stability of this solution with general decay rate this result may be used to examine almost sure robust stability to illustrate our idea more carefully we carefully discuss a scalar stochastic integro differential equation with neutral type and its asymptotic stability including the exponential stability and the polynomial stability

generalized eigenvectors and sets of nonnegative matrices abstract we present extensions of the perron frobenius theory for square irreducible nonnegative matrices after discussing structural properties of reducible nonnegative matrices we extend the theory to sets of nonnegative matrices which play an important role in several dynamic programming recursions e g markov decision processes and in mathematical economics e g leontief substitution systems a set k of in general reducible matrices is considered which is generated by all possible interchanges of corresponding rows selected from a fixed finite set of square nonnegative matrices a simultaneous block triangular decomposition of the set of matrices k is presented and characterized in terms of the maximal spectral radius the maximal index and generalized eigenvectors as a by product of our analysis we obtain a generalization of howard s policy iteration method

local energy flux and the refined similarity hypothesis in this paper we demonstrate the locality of energy transport for incompressible euler equations both in space and in scale the key to the proof is the proper definition of a local subscale flux t r which is supposed to be a measure of energy transfer to length scales l at the space point r kraichnan suggested that for such a quantity the refined similarity hypothesis will hold which kolmogorov originally assumed to hold instead for volume averaged dissipation we derive a local energy balance relation for the large scale motions which yields a natural definition of such a subscale flux for this definition a precise form of the refined similarity hypothesis is rigorously proved as a big o bound the established estimate is t r o l3h 1 in terms of the local holder exponenth at the point r which is also the estimate assumed in the parisi frisch multifractal model our method not only establishes locality of energy transfer but it also clarifies the physical reason that convection effects which naively violate locality do not contribute to the subscale flux in fact we show that as a consequence of incompressibility such effects enter into the local energy balance only as the divergence of a spatial current therefore they describe motion of energy in space and cancel in the integration over volume we also discuss theorems of onsager eyink and constantinet al on energy conservation for euler dynamics particularly to explain their relation with the parisi frisch model the constantinet al proof may be interpreted as giving a bound on the total flux t d d r t r of the form t r o lz3h 1 wherez3 is the third order scaling exponent or besov index in agreement with the multifractal model finally we discuss how the local estimates are related to the results of caffarelli kohn nirenberg on partial regularity for solutions of navier stokes equations they provide some heuristic support to a scenario proposed recently by pumir and siggia for singularities in the solutions of navier stokes with small enough viscosity

on linear copositive lyapunov functions and the stability of switched positive linear systems we consider the problem of common linear copositive lyapunov function existence for positive switched linear systems in particular we present a necessary and sufficient condition for the existence of such a function for switched systems with two constituent linear time invariant systems several applications of this result are also given

a variant of the meir keeler type theorem in ordered banach spaces abstract this paper discusses a projective variant of the fixed point theorem for a class of mappings satisfying the meir keeler type contraction condition in ordered banach spaces through projective metric we also prove a result on the chainability of the thompson s metric using an elementary argument

joint parameter estimation and symbol detection for linear or nonlinear unknown channels we present an iterative method for joint channel parameter estimation and symbol selection via the baum welch algorithm or equivalently the expectation maximization em algorithm channel parameters including noise variance are estimated using a maximum likelihood criterion the markovian properties of the channel state sequence enable us to calculate the required likelihood using a forward backward algorithm the calculated likelihood functions can easily give optimum decisions on information symbols which minimize the symbol error probability the proposed receiver can be used for both linear and nonlinear channels it improves the system throughput by making saving in the transmission of known symbols usually employed for channel identification simulation results which show fast convergence are presented

a nonlinear extension of the birkhoff jentzsch theorem abstract the birkhoff jentzsch theorem for linear positive operators is extended to a certain class of nonlinear positive operators these so called p ascending operators include concave operators and suprema of such operators for the underlying positive cone to be complete for hilbert s metric a necessary and sufficient condition is given from which various criteria for completeness are derived the extension made yields in particular a concave version of jentzsch s theorem

on the elimination of the sweeping interactions from theories of hydrodynamic turbulence in this paper we revisit the claim that the eulerian and quasi lagrangian same time correlation tensors are equal this statement allows us to transform the results of an msr quasi lagrangian statistical theory of hydrodynamic turbulence back to the eulerian representation we define a hierarchy of homogeneity symmetries between incremental homogeneity and global homogeneity it is shown that both the elimination of the sweeping interactions and the derivation of the 4 5 law require a homogeneity assumption stronger than incremental homogeneity but weaker than global homogeneity the quasi lagrangian transformation on the other hand requires an even stronger homogeneity assumption which is many time rather than one time but still weaker than many time global homogeneity we argue that it is possible to relax this stronger assumption and still preserve the conclusions derived from theoretical work based on the quasi lagrangian transformation

on the scaling of three dimensional homogeneous and isotropic turbulence abstract in this paper we investigate the scaling properties of three dimensional isotropic and homogeneous turbulence we analyze a new form of scaling extended self similarity recently introduced in the literature we found that anomalous scaling of the velocity structure functions is clearly detectable even at a moderate and low reynolds number and it extends over a much wider range of scales with respect to the inertial range

velocity probability density functions of high reynolds number turbulence abstract this paper deals with the probability density function pdf of velocity differences between two points separated by distance r measurements of pdfs were made for r lying in the inertial range for two different flows in a jet with r 852 and in a wind tunnel with r 2720 these pdfs have a characteristic non gaussian shape with exponential tails following kolmogorov s general ideas of log normality a new model for the pdf is developed which contains two parameters determined by experiments this empirical model agrees with the experimental results that the tails of the pdf deviate from a truly exponential behaviour in particular for small r in addition the model leads to the general scaling law ln e 2 r r 0 differenr from kolmogorov s third hypothesis ln e 2 ln r r 0 restricted to the inertial range only x is x x we develop also a formalism based on an extremum principle which is consistent with both the log normality of e and the above mentioned power law in this formalism can be interpreted as the codimension of dissipative structures and asymptotically varies as 1 ln r

the omega limit sets of ray contractive operators abstract in this paper we study the omega limit sets of a ray contractive map t without the compactness assumption on the orbits if there exists a compact subset of k the interior of a closed convex cone k such that t and t k 0 k then we are able to prove that x either consists of a single point or forms a cycle 2 periodic orbit for any x k

inertial range and the finite reynolds number effect of turbulence the kolmogorov law which is the unique exact relationship of inertial range statistics is applied to investigate the finite reynolds number effect in particular to study how the width of the inertial range of finite reynolds number turbulence changes with the taylor microscale reynolds number mathrm r ensuremath lambda it is found that there is no inertial range when mathrm r ensuremath lambda ensuremath leqslant 2000 and within tolerance of 1 error mathrm r ensuremath lambda should be higher than 10 4 in order to have an inertial range wider than one decade the so called inertial range found in experiments and simulations is just a scaling range and is not the same as kolmogorov s inertial range the finite reynolds number effect cannot be neglected within such a scaling range and should be considered in comparing experiments or simulations with theories of the inertial range statistics

multilocality and fusion rules on the generalized structure functions in two dimensional and three dimensional navier stokes turbulence using the fusion rules hypothesis for three dimensional and two dimensional navier stokes turbulence we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences we call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator multilocality the resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry our main result is that the fusion rules hypothesis implies both locality and multilocality in both the ir and uv limits for the downscale energy cascade of three dimensional navier stokes turbulence and the downscale enstrophy cascade and inverse energy cascade of two dimensional navier stokes turbulence we stress that these claims relate to nonperturbative locality of generalized structure functions on all orders and not the term by term perturbative locality of diagrammatic theories or closure models that involve only two point correlation and response functions

the perron frobenius theorem for homogeneous monotone functions if a is a nonnegative matrix whose associated directed graph is strongly connected the perron frobenius theorem asserts that a has an eigenvector in the positive cone r n we associate a directed graph to any homogeneous monotone function f r n r n and show that if the graph is strongly connected then f has a nonlinear eigenvector in r n several results in the literature emerge as corollaries our methods show that the perron frobenius theorem is really about the boundedness of invariant subsets in the hilbert projective metric they lead to further existence results and open problems

turbulent cascade and intermittency growth most embodiments of kolmogorov s idea of turbulent cascade rest on heuristic modelling rather than mathematical treatment of the navier stokes equations however low order systematic approximation via renormalized perturbation theory also exists it supports the 5 3 inertial range spectrum law and yields quantitatively good predictions of both the kolmogorov constant and the dissipation spectrum pressure plays an essential role in the inertial range this is highlighted by the qualitatively different predictions of the same theory applied to burgers turbulence a recent non perturbative analytical approach via nonlinear mapping of gaussian fields may contribute to the resolution of questions of intermittency corrections to the inertial and dissipation ranges again comparison with burgers turbulence is illuminating whatever the tools it is crucial that a theory be able to describe what happens at finite reynolds numbers both to understand the limit of infinite reynolds number and to interpret correctly the data from existing experiments and simulations

stability theory for nonnegative and compartmental dynamical systems with time delay abstract nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations and involve the exchange of nonnegative quantities between subsystems or compartments these models are widespread in biological and physical sciences and play a key role in understanding these processes a key physical limitation of such systems is that transfers between compartments is not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments in this paper we present necessary and sufficient conditions for stability of nonnegative and compartmental dynamical systems with time delay specifically asymptotic stability conditions for linear and nonlinear nonnegative dynamical systems with time delay are established using linear lyapunov krasovskii functionals

the contraction mapping approach to the perron frobenius theory why hilbert s metric the perron frobenius theorem says that if a is a nonnegative square matrix some power of which is positive then there exists an x0 such that anx anx converges to xn for all x 0 there are many classical proofs of this theorem all depending on a connection between positively of a matrix and properties of its eigenvalues a more modern proof due to garrett birkhoff is based on the observation that every linear transformation with a positive matrix may be viewed as a contraction mapping on the nonnegative orthant this observation turns the perron frobenius theorem into a special ease of the banach contraction mapping theorem furthermore it applies equally to linear transformations which are positive in a much more general sense the metric which birkhoff used to show that positive linear transformations correspond to contraction mappings is known as hilbert s projective metric the definition of this metric is rather complicated it is therefore natural to try to define another less complicated m

kolmogorov s contributions to the physical and geometrical understanding of small scale turbulence and recent developments this paper reviews how kolmogorov postulated for the first time the existence of a steady statistical state for small scale turbulence and its defining parameters of dissipation rate and kinematic viscosity thence he made quantitative predictions of the statistics by extending previous methods of dimensional scaling to multiscale random processes we present theoretical arguments and experimental evidence to indicate when the small scale motions might tend to a universal form paradoxically not necessarily in uniform flows when the large scales are gaussian and isotropic and discuss the implications for the kinematics and dynamics of the fact that there must be singularities in the velocity field associated with the inertial range spectrum these may be particular forms of eddy or eigenstructure such as spiral vortices which may not be unique to turbulent flows also they tend to lead to the notable spiral contours of scalars in turbulence whose self similar structure enables the boxcounting technique to be used to measure the capacity dk of the contours themselves or of their intersections with lines dk although the capacity a term invented by kolmogorov and studied thoroughly by kolmogorov tikhomirov is like the exponent 2p of a spectrum in being a measure of the distribution of length scales d being related to 2p in the limit of very high reynolds numbers the capacity is also different in that experimentally it can be evaluated at local regions within a flow and at lower values of the reynolds number thus kolmogorov tikhomirov provide the basis for a more widely applicable measure of the self similar structure of turbulence finally we also review how kolmogorov s concept of the universal spatial structure of the small scales together with appropriate additional physical hypotheses enables other aspects of turbulence to be understood at these scales in particular the general forms of the temporal statistics such as the highfrequency inertial range spectra in eulerian and lagrangian frames of reference and the perturbations to the small scales caused by non isotropic non gaussian and inhomogeneous large scale motions 1 kolmogorov s papers review and comments a introduction in this review we join with the other contributors to this special publication in celebrating some of kolmogorov s great contributions to fluid mechanics and mathematics and showing in some small way how his genius has inspired further

growth optimality for branching markov decision chains this paper considers a multiplicative process called branching markov decision chains in which the output at the end of the nth period equals the product of n nonnegative matrices chosen at the beginning of periods 1 n respectively times a positive fixed terminal reward vector it is assumed that the above transition matrices are drawn out of a finite set of matrices given in product form i e the rows of the matrices can be selected independently out of finite sets of nonnegative row vectors for each coordinate s we define the geometric and algebraic growth rates respectively of the sth coordinate of the stream of output these growth rates are defined so that the magnitude of the corresponding sequence is of the order nnk where is the geometric growth rate and k is the algebraic growth rate the main result of this paper is the constructive establishment of the existence of a transition matrix whose repeated use will guarantee for each coordinate the achievement of the best geometri

a constructive approach to linear lyapunov functions for positive switched systems using collatz wielandt sets we establish the link between linear lyapunov functions for positive switched systems and corresponding collatz wielandt sets this leads to an algorithm to compute a linear lyapunov function whenever a lyapunov function exists

attractors for differential equations with unbounded delays we prove the existence of attractors for some types of dierential problems contain ing in nite delays applications and examples are provided to illustrate the theory which is valid for both cases with and without explicit dependence of time and with or without uniqueness of solutions as well

characterizations of linear volterra integral equations with nonnegative kernels abstract we first introduce the notion of positive linear volterra integral equations then we offer a criterion for positive equations in terms of the resolvent in particular equations with nonnegative kernels are positive next we obtain a variant of the paley wiener theorem for equations of this class and its extension to perturbed equations furthermore we get a perron frobenius type theorem for linear volterra integral equations with nonnegative kernels finally we give a criterion for positivity of the initial function semigroup of linear volterra integral equations and provide a necessary and sufficient condition for exponential stability of the semigroups

a blind decision feedback equalizer incorporating fixed lag smoothing a new type of blind decision feedback equalizer dfe incorporating fixed lag smoothing is developed in this paper the structure is motivated by the fact that if we make full use of the dependence of the observed data on a given transmitted symbol delayed decisions may produce better estimates of that symbol to this end we use a hidden markov model hmm suboptimal formulation that offers a good tradeoff between computational complexity and bit error rate ber performance the proposed equalizer also provides estimates of the channel coefficients and operates adaptively so that it can adapt to a fading channel for instance by means of an online version of the expectation maximization em algorithm the resulting equalizer structure takes the form of a linear feedback system including a quantizer and hence it is easily implemented in fact because of its feedback structure the proposed equalizer shows some similarities with the well known dfe a full theoretical analysis of the initial version of the algorithm is not available but a characterization of a simplified version is provided we demonstrate that compared to the zero forcing dfe zf dfe the algorithm yields many improvements a large range of simulations on finite impulse response fir channels and on typical fading gsm channel models illustrate the potential of the proposed equalizer

binary tree models of high reynolds number turbulence we consider hierarchical models for turbulence that are simple generalizations of the standard gledzer ohkitani yamada shell models e b gledzer dokl akad nauk sssr 209 5 1973 sov phys dokl 18 216 1973 m yamada and k ohkitani j phys soc jpn 56 4210 1987 the density of degrees of freedom is constant in wave number space looking only at this behavior and at the quadratic invariants in the inviscid unforced limit the models can be thought of as systems living naturally in one spatial dimension but being qualitatively similar to hydrodynamics in two 2d and three dimensions we investigated cascade phenomena and intermittency in the different cases we observed and studied a forward cascade of enstrophy in the 2d case

observations on the stability properties of cooperative systems we extend two fundamental properties of positive linear time invariant lti systems to homogeneous cooperative systems specifically we demonstrate that such systems are d stable meaning that global asymptotic stability is preserved under diagonal scaling we also show that a delayed homogeneous cooperative system is globally asymptotically stable gas for all non negative delays if and only if the system is gas for zero delay

stability radii of higher order positive difference systems in this paper we study stability radii of positive polynomial matrices under affine perturbations of the coefficient matrices it is shown that the real and complex stability radii coincide moreover explicit formulas are derived for these stability radii and illustrated by some examples

from global scaling a la kolmogorov to local multifractal scaling in fully developed turbulence in the first part of the paper a modern presentation of scaling ideas is made it includes a reformulation of kolmogorov s 1941 theory bypassing the universality problem pointed out by landau and a presentation of the multifractal theory with emphasis on scaling rather than on cascades in the second part various historical aspects are discussed the importance of kolmogorov s rigorous derivation of the 4 5 l law for the third order structure function in his last 1941 turbulence paper is stressed this paper also contains evidence that he was aware of universality not being essential to the 1941 theory an inequality is established relating the exponents 2 p of the structure functions of order 2 p and the maximum velocity excursion it follows that models such as the obukhov kolmogorov 1962 log normal model in which 2 p does not increase monotonically are inconsistent with the basic physics of incompressible flow this result is independent of novikov s 1971 inequality in particular the proof presented here does not rely on the questionable relation proposed by obukhov and kolmogorov between instantaneous velocity increments and local averages of the dissipation

on stability and robust stability of positive linear volterra equations we first introduce the notion of positive linear volterra integrodifferential equations then we give some characterizations of these positive equations an explicit criterion and a perron frobenius type theorem for positive linear volterra integrodifferential equations are given then we offer a new criterion for uniformly asymptotic stability of positive equations finally we study stability radii of positive linear volterra integrodifferential equations it is proved that complex real and positive stability radii of positive linear volterra equations under structured perturbations or affine perturbations coincide and can be computed by explicit formulae to the best of our knowledge most of the results of this paper are new

on a class of positive linear differential equations with infinite delay abstract we give an explicit criterion for positivity of the solution semigroup of linear differential equations with infinite delay and a perron frobenius type theorem for positive equations furthermore a novel criterion for the exponential asymptotic stability of positive equations is presented finally we provide a sufficient condition for the exponential asymptotic stability of positive equations subjected to structured perturbations a simple example is given to illustrate the obtained results

denjoy wolff theorems hilbert metric nonexpansive maps and reproduction decimation operators let k be a closed cone with nonempty interior in a banach space x suppose that f intk intk is order preserving and homogeneous of degree one let q k 0 be a continuous homogeneous of degree one map such that q x 0 for all x k 0 let t x f x q f x we give conditions on the cone k and the map f which imply that there is a convex subset of k which contains the omega limit set x t for every x intk we show that these conditions are satisfied by reproduction decimation operators we also prove that x t k for a class of operator valued means

probability density functions skewness and flatness in large reynolds number turbulence probability density functions pdf of longitudinal velocity increments are measured in an experiment using low temperature helium gas in which a large domain of microscale reynolds numbers mathit r ensuremath lambda from 150 to 5040 is explored the technique of measurement which is essentially hot wire anemometry but operating in nonstandard conditions is described in the inertial range of scales and for a given scale of separation the pdf are found to be independent of the reynolds number at large mathit r ensuremath lambda measurements of the skewness and the flatness of the velocity derivatives are performed in a range of mathit r ensuremath lambda lying between 150 and 3200 the surprising result that we find is that these quantities first increase with the reynolds number up to mathit r ensuremath lambda ensuremath approxeq 700 and then cease to increase further indicating a transitional behavior textcopyright 1996 the american physical society

nonlinear perron frobenius theory in finite dimensions abstract a nonlinear perron frobenius theory in finite dimensions is described which applies to positively homogeneous and increasing maps sufficient conditions for the existence and uniqueness of eigenvectors in the interior of a cone are developed even when eigenvectors at the boundary of the cone exist several ways to benefit from nonlinearities are pointed out in order to show that the classical linear theory truly deserves nonlinear generalization the main technical novelties are a link between collatz wielandt numbers and g teaux derivatives and the almost one dimensional dynamics of the nonlinear map

scaling exponents of the second order structure function of turbulence the kolmogorov equation which is an exact relationship between the second order structure function and the third order structure function is applied to study the relative scaling of against according to the extended self similarity ess method it is found that the relative ess scaling exponent is greater than the real or theoretical inertial range scaling exponent of in the case of normal scaling as well as anomalous scaling when and when therefore the experimental and numerical results favours the kolmogorov 2 3 law rather than anomalous scaling previously the results were interpreted as clear evidence of anomalous scaling based upon the assumption that

stability radius of linear parameter varying systems and applications abstract in this paper we present a unifying approach to the problems of computing of stability radii of positive linear systems first we study stability radii of linear time invariant parameter varying differential systems a formula for the complex stability radius under multi perturbations is given then under hypotheses of positivity of the system matrices we prove that the complex real and positive stability radii of the system under multi perturbations or affine perturbations coincide and they are computed via simple formulae as applications we consider problems of computing of strong stability radii of linear time invariant time delay differential systems and computing of stability radii of positive linear functional differential equations under multi perturbations and affine perturbations we show that for a class of positive linear time delay differential systems the stability radii of the system under multi perturbations or affine perturbations are equal to the strong stability radii next we prove that the stability radii of a positive linear functional differential equation under multi perturbations or affine perturbations are equal to those of the associated linear time invariant parameter varying differential system in particular we get back some explicit formulas for these stability radii which are given recently in p h a ngoc strong stability radii of positive linear time delay systems internat j robust nonlinear control 15 2005 459 472 p h a ngoc n k son stability radii of positive linear functional differential equations under multi perturbations siam j control optim 43 2005 2278 2295 finally we give two examples to illustrate the obtained results

convexity and log convexity for the spectral radius abstract the starting point of this paper is a theorem by j f c kingman which asserts that if the entries of a nonnegative matrix are log convex functions of a variable then so is the spectral radius of the matrix a related result of j cohen asserts that the spectral radius of a nonnegative matrix is a convex function of the diagonal elements the first section of this paper gives a new unified proof of these results and also analyzes exactly when one has strict convexity the second section gives some very simple proofs of results of friedland and karlin concerning min max characterizations of the spectral radius of nonnegative matrices these arguments also yield as will be shown in another paper min max characterizations of the principal eigenvalue of second order elliptic boundary value problems on bounded domains the third section considers the cone k of nonnegative vectors in r n and continuous maps f k k which are homogeneous of degree one and preserve the partial order induced by k the cone spectral radius of such maps is defined and a direct generalization of kingman s theorem to a subclass of such nonlinear maps is given the final section of this paper treats a problem that arises in population biology if k 0 denotes the interior of k and f is as above when can one say that f has a unique eigenvector to within normalization in k 0 a subtle point to be noted is that f may have other eigenvectors in the boundary of k if u k 0 is an eigenvector of f u 1 and g x f x f x when can one say that for any x k 0 g p x the p th iterate of g acting on x converges geometrically to u the fourth section provides answers to these questions that are adequate for many of the population biology problems

on line estimation of hidden markov model parameters based on the kullback leibler information measure sequential or online hidden markov model hmm signal processing schemes are derived and their performance is illustrated by simulation the online algorithms are sequential expectation maximization em schemes and are derived by using stochastic approximations to maximize the kullback leibler information measure the schemes can be implemented either as filters or fixed lag or sawtooth lag smoothers they yield estimates of the hmm parameters including transition probabilities markov state levels and noise variance in contrast to the offline em algorithm baum welch scheme which uses the fixed interval forward backward scheme the online schemes have significantly reduced memory requirements and improved convergence and they can estimate hmm parameters that vary slowly with time or undergo infrequent jump changes similar techniques are used to derive online schemes for extracting finite state markov chains imbedded in a mixture of white gaussian noise wgn and deterministic signals of known functional form with unknown parameters