disorder induced transport i simple cubic lattice using a vax 11 780 a random walk motion is studied in a random field disordered system a non monotonic transport behaviour is observed as a function of local field intensity in contrast to the random walk motion in random percolating fractals the root mean square displacement here increases as a function of time faster than that of diffusion a crossover from diffusion to disorder induced transport is discussed and its spectral dimensionality is estimated

dwell time based observer design for unknown input switched linear systems without requiring strong detectability of subsystems this paper investigates the state observer design of a class of unknown input switched linear systems via mode dependent dwell time switchings the distinguishing feature of the proposed method is that strong detectability condition of subsystems of the switched systems is unnecessarily required first a time varying coordinate transformation is introduced to design a suitable reduced order observer for each subsystem then computable sufficient conditions on the synthesis of the observers are proposed in the framework of a mode dependent dwell time technique since the observer of an individual subsystem cannot be designed due to unavailability of strong detectability condition of the subsystem the state of the switched system is estimated under the condition of confining the dwell time by a pair of upper and lower bounds restricting the growth of the lyapunov function of the active subsystem and forcing energy of the overall switched system to decrease at switching instants finally an example is presented to demonstrate the effectiveness of the proposed method

to what class of fractals does the alexander orbach conjecture apply discussion de la decouverte numerique recente d alexander et orbach selon laquelle pour un agregat infini naissant en percolation le rapport d f d w dimension fractale de l agregat dimension fractale d une marche aleatoire dans l agregat est approximativement independant de d pour d 1

a characterization of compact perturbations of toeplitz operators let x be a bounded operator on the hardy space h 2 of the unit circle it has been a longstanding problem to determine whether the condition that t u xt u x is compact for every inner function u implies that x is a compact perturbation of a toeplitz operator we show that the answer is affirmative

independence properties in subalgebras of ultraproduct ii1 factors let mn be a sequence of finite factors with dim mn and denote by m mn their ultraproduct over a free ultrafilter we prove that if q m is either an ultraproduct q qn of subalgebras qn mn with qn mnqn mn n or the centralizer q b m of a separable amenable subalgebra b m then for any separable subspace x m q m there exists a diffuse abelian von neumann subalgebra in q which is free independent to x relative to q m some related independence properties for subalgebras in ultraproduct ii1 factors are also discussed

a double commutant relation in the calkin algebra on the bergman space abstract let t be the toeplitz algebra on the bergman space l a 2 b d v of the unit ball in c n we show that the image of t in the calkin algebra satisfies the double commutant relation t t this is a surprising result for it is the opposite of what happens in the hardy space case 16 17

holomorphic kernels and commuting operators necessary and sufficient conditions in terms of operator polynomials are obtained for an m tuple t tl t l of commuting bounded linear operators on a separable hilbert space x to extend to an m tuple s s1 sm of operators on some hilbert space x where each s is realized as a representation of the adjoint of a multiplication operator on the tensor product of a special type of functional hilbert spaces a1so necessary and sufficient conditions in terms of operator polynomials are obtained for t to have a commuting normal extension o introduction in this paper some results in 1 and 2 for a single bounded linear operator t on a separable hilbert space x are generalized to m commuting operators on x in 1 agler introduces a special class of functional hilbert spaces and describes conditions under which an operator t on x extends to m where m denotes the multiplication operator on x and m denotes the countable direct sum of m with itself special cases of spaces x of which the classical hardy space is the prototype are considered in 1 2 the relevant conditions for the kind of extension of t referred to above are expressed in terms of the positivity of certain operator polynomials involving t and t these conditions are closely related to the reproducing kernel associated with the space s in 2 necessary and sufficient conditions are also given for a contraction t to be subnormal these conditions are really the requirement that a certain sequence of polynomials in t and t be positive it is natural to seek generalizations of these results to m commuting operators t1 tm on x an appropriate model for this generalization is obtained by constructi ng a finite tensor product of spaces s and exploiting the well known fact that the reproducing kernel of such a tensor product is the product of the reproducing kernels of the illdividual spaces suitable modifications of the reproducing kernels which render them holomorphic on the unit polydisc can be used to describe analogous extension results for t t1 tm the question of t having a commuting normal extension n n1 nm turns out to have a direct link with the multi dimensional hausdorff moment problem from the theory of probability received by the editors march 21 1986 1980 mathematics subject classification primary 47a20 secondary 47b20 47b38

toeplitz projections and essential commutants abstract we construct a toeplitz projection for every regular a isometry t b h n on a complex hilbert space h and use it to determine the essential commutant of the set of all analytic toeplitz operators formed with respect to an essentially normal regular a isometry we show that the toeplitz projection annihilates the compact operators if and only if t possesses no joint eigenvalues as an application we deduce an essential version of the classical hartman wintner spectral inclusion theorem give a new proof of johnson and parrot s theorem on the essential commutant of abelian von neumann algebras for separable hilbert spaces and construct short exact sequences of toeplitz algebras

effective permeability of sandstone shale reservoirs by a random walk method a random walk algorithm for calculating the effective permeability of random mixtures of two finite permeability components e g sandstone and shale is introduced it is an extension of the ant in a labyrinth algorithm which only applies when one of the components has zero permeability numerical results obtained from the proposed random walk algorithm are shown to be in close agreement with those obtained from the conventional finite difference method on three dimensional cubic lattices in contrast it is shown that the hybrid random walk algorithms which have been used in the past to study the critical behaviour of two component random conductor mixtures are inadequate for the problem under consideration the proposed random walk algorithm provides a computationally efficient method for calculating the effective permeability and does not require the explicit solution of the fluid flow through the random mixture

resistance and related scaling properties of self avoiding random walks three scaling exponents for random and self avoiding chains are studied by direct renormalisation these describe the end to end resistance of a conducting chain the arc length of the shortest path traceable between the chain ends and the arc length of chain in no loop the scaling behaviours of these quantities are identical to first order in epsilon 4 d d is the space dimension for a long self avoiding chain the authors predict that each one one is proportional to the chain length

on the essential commutant of the toeplitz algebra on the bergman space let tt be the c c algebra generated by the toeplitz operators tf f l b dv tf f l b dv on the bergman space of the unit ball we show that the essential commutant of tt equals tg g vobdd k tg g vobdd k where vobddvobdd is the collection of bounded functions of vanishing oscillation on b and kk denotes the collection of compact operators on la2 b dv

boundedness and compactness of hankel operators on the sphere abstract we consider hankel operators on the hardy space of the unit sphere in c n we show that a large amount of information about the function f p f can be recovered from the hankel operator h f for example if h f is compact then the function f p f is necessarily in vmo

conductivity exponents from the analysis of series expansions for random resistor networks there has been considerable controversy in recent years over the value of the conductivity exponent t this exponent can be deduced from series expansions via the scaling relations t zeta d 2 nu where zeta is deduced from differences between the exponents of the resistive gamma r percolative gamma p and conductive gamma c susceptibility the author finds that allowance for non analytic confluent corrections to scaling and the use of recent pc estimates leads to estimates for gamma r gamma p and gamma c that are somewhat different to those of fisch and harris 1978 however the differences between these exponents do not change significantly moreover the change in accepted estimates of nu in the last five years cancels some of this remaining discrepancy and she concludes using the relation zeta gamma r gamma p that t 1 31 d 2 t 2 04 d 3 t 2 39 d 4 t 2 72 d 5 with an error of about or 0 10 in each case the d 2 estimate is in significantly better agreement with those of other methods than that of fisch and harris

stabilizability and insensitivity of switched linear systems this note identifies two types of stabilizability for switched systems the pointwise stabilizability and the consistent stabilizability necessary conditions and sufficient conditions for both types are presented for switched linear systems insensitivity issues are briefly addressed as well

the random normal superconductor mixture in one dimension two models for random two conductor mixtures by diffusion processes are considered in the one dimensional case it is shown that the two models are not in the same universality class this is seen to be an artefact of systems with pc 1 however a scaling theory proposed earlier is tested for this simple one dimensional case and confirmed

characterization and quantification of the cluster hopping mechanism responsible for transport in two component random networks a cluster hopping mechanism for transport in two component random networks below pc is proposed and shown to account for observed conductivity exponents key structures forming paths of least resistance are identified a novel computationally efficient method for determining exponents results

bmo in the bergman metric on bounded symmetric domains for bounded symmetric domains in cn a notion of bounded mean oscillation in terms of the bergman metric is introduced it is shown that for in l2 dv is in bmo if and only if the densely defined operator m p m p pm on l2 dv is bounded here m is multiplication by and p is the bergman projection with range the bergman subspace h2 dv la2 dv of holomorphic functions in l2 dv an analogous characterization of compactness for m p is provided by functions of vanishing mean oscillation at the boundary of

hopping conduction in insulator conductor superconductor mixtures the coherent medium approximation is applied to study the frequency dependent diffusion constant in two and three dimensional ant termite like mixtures where three types of jump rates normal metallic superconducting and insulating are distributed randomly the dc diffusion constant vanishes when p r pc where p and r are the probabilities that a given bond is metallic and superconducting respectively and z is the coordination number of the lattice pc rc identical to 2 z in the low frequency limit the real and imaginary parts of the ac diffusion constant go as a z d p r f omega and b z d p r g omega respectively a behaviour similar to the pure ant limit the behaviour of f omega and g omega is examined below at and above the percolation thresholds in both two and three dimensions the coefficients a and b of these leading terms diverge as r to rc superconducting region percolates indicating enhancement in the dielectric constant

improved overshoot estimation in pole placements and its application in observer based stabilization for switched systems in this note we first establish an improved and generalized overshoot estimation in pole placements then this estimation is applied to the observer based output feedback stabilization problem for switched linear systems with arbitrary switching frequency our results complement those results of cheng about the state feedback stabilization of switched linear systems

spectral mapping theorems for subnormal operators on etablit un calcul fonctionnel f f s pour des operateurs sous normaux s on etudie l espace associe a ce calcul on considere la caracterisation du spectre clos de f s en fonction de f

a stone weierstrass theorem for weak star approximation by rational functions abstract let k be a compact subset of the complex plane c and let be a finite positive borel measure on k define r to be the weak star closure in l of the algebra of rational functions with poles off k for f r we consider a f the weak star closure in l of the algebra generated by r and the complex conjugate f of f a problem which arises in connection with subnormal operators is to determine for which f r a f l we obtain a characterization of a f as precisely the functions in l which belong to r e for every restriction of to a level set e of f of positive measure this characterization gives a solution to the problem above

invariant subspaces for certain finite rank perturbations of diagonal operators abstract suppose that e k is an orthonormal basis for a separable infinite dimensional hilbert space h let d be a diagonal operator with respect to the orthonormal basis e k that is d k 1 k e k e k where k is a bounded sequence of complex numbers let t d u 1 v 1 u n v n improving a result of foias et al 2007 3 we show that if the vectors u 1 u n and v 1 v n satisfy an l 1 condition with respect to the orthonormal basis e k and if t is not a scalar multiple of the identity operator then t has a non trivial hyperinvariant subspace

schatten class membership of hankel operators on the unit sphere abstract let h 2 s be the hardy space on the unit sphere s in c n n 2 consider the hankel operator h f 1 p m f h 2 s where the symbol function f is allowed to be arbitrary in l 2 s d we show that for p 2 n h f is in the schatten class c p if and only if f p f belongs to the besov space b p to be more precise the if part of this statement is easy the main result of the paper is the only if part we also show that the membership h f c 2 n implies f p f 0 i e h f 0

function theory on cartan domains and the berezin toeplitz symbol calculus cn with dv z normalized lebesgue measure on 9 we let l l2 q dv be the usual space of lebesgue square integrable complex valued functions on 9 by h2 h2 q dv we denote the bergman subspace of l2 consisting of holomorphic functions the orthogonal projection operator from l2 onto h2 is denoted by p forf in l q the space of essentially bounded measurable functions on 9 we will consider the multiplication operator

parisi s mean field solution for spin glasses as an analytic continuation in the replica number parisi s replica symmetry breaking solution for spin glasses is extended to finite replica number n the free energy fp n obtained this way as well as its first two derivatives with respect to n are shown to join the corresponding values in the sherrington kirkpatrick sk solution at a characteristic value ns t where stability breaks down in the latter the continuation composed of the sk branch fsk n for n or ns t and the parisi branch fp n for 0 or n or ns t fulfils the requirements of convexity monotonicity and stability for all n

percolation cluster numbers it has recently been suggested that there may be an infinite number of independent exponents hidden in the tails of the probability distribution of average percolation cluster numbers a simple approximation of non gaussian effects was used to deduce this result and we show that this approximation is questionable extensive simulations of the cluster distribution have been made and an interesting dependence of the cumulants on concentration and range of summation has been observed

hypercyclic tuples of operators and somewhere dense orbits in this paper we prove that there are hypercyclic n 1 tuples of diagonal matrices on cn and that there are no hypercyclic n tuples of diagonalizable matrices on cn we use the last result to show that there are no hypercyclic subnormal tuples in infinite dimensions we then show that on real hilbert spaces there are tuples with somewhere dense orbits that are not dense but we also give sufficient conditions on a tuple to insure that a somewhere dense orbit on a real or complex space must be dense

diffusion in superconducting percolation networks number of sites visited two models of diffusion in superconducting percolation networks are studied on a one dimensional system the authors use chains of 5 105 sites and study the scaling properties of the mean squared displacement of termites which execute random walks on the network mean number of distinct sites visited and mean number of visits to the origin they find that although these quantities can be described by well defined scaling laws the values of the critical exponents appear to depend on the time interval in which the walks are studied they observe at least four different scaling regimes the implications of these results for higher dimensional systems are discussed

bergman commutators and norm ideals let p be the orthogonal projection from l2 b dv onto the bergman space la2 b dv of the unit ball in cn in this paper we characterize the membership of commutators of the form mf p in the norm ideal c where the symmetric gauge function is allowed to be arbitrary

exponential stabilization of discrete time switched linear systems this article studies the exponential stabilization problem for discrete time switched linear systems based on a control lyapunov function approach it is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control lyapunov function such a converse control lyapunov function theorem justifies many of the earlier synthesis methods that have adopted piecewise quadratic lyapunov functions for convenience or heuristic reasons in addition it is also proved that if a switched linear system is exponentially stabilizable then it must be stabilizable by a stationary suboptimal policy of a related switched linear quadratic regulator lqr problem motivated by some recent results of the switched lqr problem an efficient algorithm is proposed which is guaranteed to yield a control lyapunov function and a stabilizing policy whenever the system is exponentially stabilizable

some remarks on the critical behaviour of superconducting percolation networks recent relations that relate the exponent s of superconducting percolating networks to other percolation exponents are discussed the author analyses the available exact and numerical results for s to gain insight into the possible relation between s and the geometrical exponents of percolation and the structure of superconducting percolation networks the results are given geometrical interpretation the author also discusses the random walk statistics of the termite which executes a random walk on the superconducting percolation networks in particular the author proposes an expression for the mean number of distinct sites visited by the termite and interpret it in terms of the statistics of a random walk with a transition probability whose variance is infinite

coincidence of essential commutant and the double commutant relation in the calkin algebra let b be a von neumann algebra on a separable hilbert space h we show that if the dimension of b as a linear space is infinite then it has a proper c subalgebra a whose essential commutant in b h coincides with the essential commutant of b moreover if is the quotient map from b h to the calkin algebra b h k h then a b and a b

hochschild cohomology for von neumann algebras with cartan subalgebras the main result of this paper is that h n m m 0 n 1 for von neumann algebras m with cartan subalgebras and separable preduals

localization and the toeplitz algebra on the bergman space abstract let t f denote the toeplitz operator with symbol function f on the bergman space l a 2 b d v of the unit ball in c n it is a natural problem in the theory of toeplitz operators to determine the norm closure of the set t f f l b d v in b l a 2 b d v we show that the norm closure of t f f l b d v actually coincides with the toeplitz algebra t i e the c algebra generated by t f f l b d v a key ingredient in the proof is the class of weakly localized operators recently introduced by isralowitz mitkovski and wick our approach simultaneously gives us the somewhat surprising result that t also coincides with the c algebra generated by the class of weakly localized operators

on the essential commutant of analytic toeplitz operators associated with spherical isometries abstract let t b h n be an essentially normal spherical isometry with empty point spectrum on a separable complex hilbert space h and let a t b h be the unital dual operator algebra generated by t in this note we show that every operator s b h in the essential commutant of a t has the form s x k with a t toeplitz operator x and a compact operator k our proof actually covers a larger class of subnormal operator tuples called a isometries which includes for example the tuple t m z 1 m z n b h 2 n consisting of the multiplication operators with the coordinate functions on the hardy space h 2 associated with the normalized surface measure on the boundary d of a strictly pseudoconvex domain d c n as an application we determine the essential commutant of the set of all analytic toeplitz operators on h 2 and thus extend results proved by davidson 1977 6 for the unit disc and ding and sun 1997 11 for the unit ball

speculation on a scaling law for superconductor resistor mixture exponent s in a percolation system it is argued that looking for a relationship between the exponent s and the cluster exponents may be more promising than looking for one between the resistor insulator exponent t and the cluster exponents the author proposes s nu beta 2

on the relationship between the critical exponents of percolation conductivity and static exponents of percolation the author argues that the critical exponent t of random conductance networks near the percolation threshold is given by t d 1 nu for low dimensionalities and t 1 beta for high dimensionalities where nu is the correlation length exponent beta the backbone exponent and d is dimensionality the author argues that what separates the two regimes is a critical fractal dimensionality dl which equals 2 the author also argues that dl is also a critical fractal dimensionality for fractals such as lattice animals and diffusion limited aggregates the result for low dimensionalities has been also obtained by aharony and stauffer by a different argument

localization and berezin transform on the fock space abstract we introduce the notion of sufficiently localized operators on the fock space we show that if a is in the c algebra generated by the class of sufficiently localized operators then a is compact if and only if its berezin transform vanishes at infinity moreover we show that this class contains many familiar operators including all the toeplitz operators with bounded symbols

on operators commuting with toeplitz operators modulo the finite rank operators abstract let x be a bounded linear operator on the hardy space h2 of the unit disk we show that if x t xt is of finite rank for every inner function then x t f for some toeplitz operator t and some finite rank operator f on h2 this solves a variant of an open question where the compactness replaces the finite rank conditions

transport in one dimensional random resistor superconductor mixtures with random distribution of resistor strength the authors study the problem of transport in linear random resistor superconductor mixtures with a random distribution of resistor strength the superconductors with a concentration p are represented in the model as short circuits the resistor concentration is 1 p and their conductivity distribution is p sigma approximately sigma alpha alpha 0 the specific conductivity scales with the linear size l of the system as l alpha 1 alpha 1 p 1 1 alpha the mean square displacement x2 of a random walker in this system scales as x2 2 alpha 1 alpha 2 approximately 1 p 2 alpha 1 alpha t in the presence of a bias field they obtain x 1 1 alpha approximately 1 p 1 1 alpha t they present an exact enumeration method to study diffusion on those systems the numerical results confirm the above scaling relations

diffusion on percolation clusters at criticality the concept of fractal dimensionality is used to study the problem of diffusion on percolation clusters the authors find from monte carlo simulations that the fractal dimensionality of a random walk on a critical percolation cluster in three dimensional space is d 3 3 or 0 1 where the size of the cluster is restricted to be larger than the span of the walk and is d 3 9 or 0 1 for a walk on clusters not subject to this restriction for two dimensional space they find d approximately d approximately 2 7 or p0 1 the exponent d and d is related to the scaling of the average length r of n steps via rd varies as n the fracton dimensionality which is related to the density of states was found to be 1 26 or 0 1 these results are in good agreement with the predictions of alexander and orbach 1982

brief paper periodic stabilizability of switched linear control systems stabilizability via direct observer based state feedback control for discrete time switched linear control systems slcss is investigated in this paper for an slcs the control factors are not only the control input but also the switching signal and they need to be designed in order to stabilize the system as a result stabilization design for slcss is more complicated than that for non switched ones differently from the existing approaches a periodic switching signal and piecewise constant linear state feedback control are adopted to achieve periodic stabilizability for such systems it is highlighted that multiple feedback controllers need to be designed for one subsystem for discrete time slcss it is proved that reachability implies periodic stabilizability via state feedback a necessary and sufficient criterion for periodic stabilizability is also established two stabilization design algorithms are presented for real application moreover it is proved that reachability and observability imply periodic stabilizability via observer based feedback for discrete time slcss periodic detectability as the dual concept of periodic stabilizability is discussed and the stabilization design algorithms via observer based feedback are presented as well

termite and ant diffusions in the d dimensional lattice trapping model the coherent medium approximation of odagaki and lax 1981 is generalised to the trapping model the frequency dependent diffusion constant in the d dimensional hypercubic lattice is studied when the jump rate obeys a bimodal distribution the coherent medium approximation gives the correct static diffusion constant the imaginary part of the ac part of the diffusion constant vanishes linearly in frequency omega when d 2 as omega ln omega when d 2 and as omega d 2 when d 4 as omega 2 ln omega when d 4 and as omega d 2 when d 4 the termite limit is studied by taking the limit that one of the two jump rates probability p becomes infinite in the termite diffusion the static diffusion constant is critical at p 1 and the critical exponents are the same as those for the termite diffusion in the hopping model the ant or ant lion limit is defined by the limit of one jump rate being zero the imaginary and real parts of the ac diffusion constant vanish linearly and quadratically in frequency respectively the critical exponent of the leading real part of the diffusion constant is one less than the corresponding exponent for the ant diffusion in the hopping model below the percolation threshold while the leading imaginary part has the same critical exponent as those in the hopping model

first exit time of termites and random super normal conductor networks the resistance of a random super normal conductor network is calculated through the diffusion of a termite which performs a random walk on the normal bonds and has the same probability to exist from any point on a cluster of superconducting bonds the first time t that the termite exits at a distance r from the origin averaged over many configurations and runs is found to behave as t approximately r2k for r xi pc p s describes the divergence of the conductivity as p to pc p being the concentration of the superconductor scaling arguments are used to show that k 1 s 2 theta where 2 theta is the fractal dimension of random walks on single clusters at pc numerical simulations at two dimensions d 2 yields s 1 34 or 0 10 and k 1 34 or 0 03 in agreement with scaling the authors also show that the probability of return to the origin at time t behaves as t dk2 preliminary results at d 1 and other calculations methods are also discussed

on automorphisms of the toeplitz algebra in this paper we completely determine those c automorphisms of the full toeplitz algebra which have the form inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i compact operator where is a bi lipschitz homeomorphism of the unit circle

on the essential commutant of let t qc resp t be the c algebra generated by the toeplitz operators t qc resp t l on the hardy space h 2 of the unit circle a well known theorem of davidson asserts that t qc is the essential commutant of t we show that the essential commutant of t qc is strictly larger than t thus the image of t in the calkin algebra does not satisfy the double commutant relation we also give a criterion for membership in the essential commutant of t qc

the minimal normal extension problem for subnormal operators on etablit un calcul fonctionnel pour des operateurs sous normaux on montre que le probleme de theorie des operateurs est equivalent a un probleme de theorie des fonctions concernant la faible etoile densite d une certaine algebre de fonctions dans un certain espace l infini

diffusion on random systems above below and at their percolation threshold in two and three dimensions a detailed monte carlo study is presented for classical diffusion random walks on random l l triangular and l l l simple cubic lattices with l up to 4096 and 256 respectively the speed of a cyber 205 vector computer is found to be about one order of magnitude larger than that of a usual cdc cyber 76 computer to reach the asymptotic scaling regime walks with up to 10 million steps were simulated with about 10 jl steps in total for l 256 at the percolation threshold we review and extend the dynamical scaling description for the distance traveled as function of time the diffusivity above the threshold and the cluster radius below earlier discrepancies between scaling theory and computer experiment are shown to be due to insufficient monte carlo data the conductivity exponent is found to be 2 0 0 2 in three and 1 28 0 02 in two dimensions our data in three dimensions follow well the finite size scaling theory below the threshold the approach of the distance traveled to its asymptotic value is consistent with theoretical speculations and an exponent 2 5 independent of dimensionality the correction to scaling exponent at pc seems to be larger in two than in three dimensions

towards a functional calculus for subnormal tuples the minimal normal extension in this paper the study of a functional calculus for subnormal ntuples is initiated and the minimal normal extension problem for this functional calculus is explored this problem is shown to be equivalent to a mean approximation problem in several complex variables which is solved an analogous uniform approximation problem is also explored in addition these general results are applied together with the area and the the coarea formula from geometric measure theory to operators on bergman spaces and to the tensor product of two subnormal operators the minimal normal extension of the tensor product of the bergman shift with itself is completely determined an n tuple of commuting operators s s1 sn on a hilbert space z is subnormal if there is an n tuple n nl nn of commuting normal operators on a hilbert space z that contains z such that for 1 j n nj c and sj njlt for any commuting n tuple of operators s there is a notion of spectrum the taylor spectrum of s 30 also see 12 denoted by v s this spectrum is a nonempty compact subset of un in this general theory it is possible to define s for any function analytic in a neighborhood of v s this functional calculus generalizes the usual riesz functional calculus for a single operator when s is assumed to be a subnormal n tuple however a much richer functional calculus is possible in this case 0 s can be defined for functions 0 that are weak limits of analytic functions and 0 s becomes a subnormal operator the central question in this development is what are the properties of this operator 0 s and what are the relations between the operator and the function x more generally if s is an n tuple and xl xq are analytic functions defined in a neighborhood of the taylor spectrum of s then 0 s 0l s xq s is a commuting q tuple of operators if s is subnormal then 0 s can be defined for x 0l xq consisting of functions that are weak limits received by the editors january 31 1989 and in revised form july 6 1989 1980 mathematics subject classification 1985 revision primary 47b20 47a60 secondary 32a35 47b38 the results here were delivered in a talk at the american mathematical society summer institute in operator theory held at the university of new hampshire in july 1988 during the preparation of this paper partial support was furnished by national science foundation grant dms 87 00835 32 1991 american mathematical society 0002 9947 91 1 00 25 per page

technical communique observer driven switching stabilization of switched linear systems in this work we investigate the observer driven switching stabilization problem for a class of switched linear systems by incorporating the switched observer presented in sun wang xie and yu 2006 into the control loop we construct an observer driven path wise switching law for the switched linear system we prove that any stabilizable switched linear system is exponentially stable under the switching law and establish a weak version of the separation principle for switching and observer design

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

transport in a two component randomly composite material scaling theory and computer simulations of termite diffusion near the superconducting limit the question of transport in a random two component mixture is addressed to this end two models are precisely formulated that effectively extend to two component mixtures the de gennes ant model of one component systems we develop and test a scaling theory and we solve some of the problems associated with the limit where one of the components is superconducting our work provides the first practical realisation of the termite model of a random superconducting network which performs a normal walk in the normal regions of the material but performs a new and unique form of random walk in the superconducting regions we find that the divergence of the electrical conductivity at the percolation threshold can be described by this random walk and that the critical exponent s is given by s 1 3 f 0 1 in d 2 if we perturb away from the pure superconduct ing limit we find that the electrical properties can still be described by the random walk model with a crossover exponent i 0 4 d 2 moreover we find that the diffusion constant in this region is described by a scaling form so that data can be made to collapse upon a single curve whose form is governed by the exponents s and i

diffusion and fracton dimensionality on fractals and on percolation clusters the authors present simulations of diffusion on an exact fractal and on percolation clusters at criticality for two and three dimensions the results for the fractal support the rammal and toulouse proposition 1983 that ds n dn varies as b n s n the results for percolation are in excellent agreement with the alexander and orbach conjecture 1982 that the fracton dimensionality d 4 3

on schatten class perturbations of toeplitz operators let d denote the unit ball or the unit polydisc in cncn with n 2n 2 for 1 p 2n1 p 2n in the case of the ball and 1 p 1 p for the polydisc we show that a bounded operator s on the hardy space h2 d h2 d commutes with all analytic toeplitz operators modulo the schatten class spsp if and only if s x ks x k with an analytic toeplitz operator x and an operator k spk sp this partially answers a question of guo and wang 14 for 1 p 1 p and a strictly pseudoconvex or bounded symmetric and circled domain d cnd cn we show that a given operator s on h2 d h2 d is a schatten p class perturbation of a toeplitz operator if and only if t st s sp for every inner function on d

a local inequality for hankel operators on the sphere and its application abstract let h 2 s be the hardy space on the unit sphere s in c n we establish a local inequality for hankel operators h f 1 p m f h 2 s as an application of this local inequality we characterize the membership of h f in the lorentz like ideal c p 2 n p

the backbone and conductivity of random clusters the author studies the properties of the backbone of and conduction in random clusters which have homogeneous interior structure these include the largest percolation cluster at pc lattice animals and the witten sander ws aggregates for lattice animals the fractal dimension da of the backbone is estimated the for first time and is found to be about 1 14 at d 2 and about 1 39 at d 3 these values are much lower than the corresponding values for the animals themselves the fractal and spectral dimensions of the backbone of the ws aggregates are estimated to be about 1 25 and 1 06 at d 2 respectively a recent hypothesis which relates the fractal dimension of random walks on these clusters to those of the clusters and their backbones is also discussed it is shown that for the ws aggregates ds ds 2 on a bethe lattice i e at d infinity in contrast with ds 4 3 and ds 1 for percolation clusters and lattice animals the conductivity exponent ta of lattice animals is found to be ta d 2 approximately 0 73 and ta d 3 approximately 1 19 and ta d or 8 2 whereas for the ws aggregates the author finds tws d 2 approximately 0 67 and tws d 3 approximately 0 94 and tws d to infinity 1

derivations with values in ideals of semifinite von neumann algebras let m be a semifinite von neumann algebra with a faithful semifinite normal trace and let a be an arbitrary c subalgebra of m assume that e is a fully symmetric function space on 0 having fatou property and order continuous norm and e m is the corresponding symmetric operator space we prove that every derivation a e m e m m is inner strengthening earlier results by kaftal and weiss 28 in the case when m is a semifinite non finite factor we show that our assumptions on e 0 are sharp

the notion of a strange fractal phenomenon disorder induced walk it is argued that a random system coupled with a walk may cause an unusual phenomenon which shares some of the opposite properties of fractals