hopf algebras having a dense big cell we discuss some axioms that ensure that a hopf algebra has its simple comodules classified using an analogue of the borel weil construction more precisely we show that a hopf algebra having a dense big cell satisfies the above requirement this method has its roots in the work of parshall and wang in the case of q deformed quantum groups gl and sl here we examine the example of universal cosovereign hopf algebras for which the weight group is the free group on two generators

higher order nonlinear degenerate parabolic equations this paper is concerned with nonlinear degenerate parabolic equations of the form ut 1 m 1 d f u d2m 1u 0 with f u u n n 1 near u 0 and d x under appropriate boundary conditions it is shown that there exists a weak solution u some of the main results of the paper are that u 0 if u0 0 and that the support of u t when u0 0 increases with t for the last property we require that n 2 and m 1

free probability for pairs of faces i we consider a notion of bi freeness for systems of non commutative random variables with two faces one of left variables and another of right variables this includes bi free convolution operations bi free cumulants the bi free central limit and bi freeness with amalgamation over an algebra b

free products of compact quantum groups we construct and study compact quantum groups from free products ofc algebras in this connection we discover two mysterious classes of natural compact quantum groups a u m anda o m thea u m s respectivelya o m s are non isomorphic to each other for differentm s and are not obtainable by the ordinary quantization method we also clarify some basic concepts in the theory of compact quantum groups

a noncommutative de finetti theorem for boolean independence abstract we introduce a family of quantum semigroups and its natural coactions on noncommutative polynomials we define three invariance conditions for the joint distribution of sequences of selfadjoint noncommutative random variables associated with these coactions for one of the invariance conditions we show that the joint distribution of an infinite sequence of noncommutative random variables satisfy it is equivalent to the fact that the sequence of the random variables is identically distributed and boolean independent with respect to the conditional expectation onto its tail algebra this is a boolean analogue of de finetti theorem on exchangeable sequences in the end of the paper we also discuss the other two invariance conditions which lead to some trivial results

quantum isometry groups examples and computations in this follow up of 4 where the quantum isometry group of a noncommutative manifold has been defined we explicitly compute such quantum groups for a number of classical as well as noncommutative manifolds including the spheres and the tori it is also proved that the quantum isometry group of an isospectral deformation of a classical or noncommutative manifold is a suitable deformation of the quantum isometry group of the original undeformed manifold

analysis of a thin film approximation for two fluid taylor couette flows abstract in this work we study the evolution of the interface between two different fluids in two concentric cylinders when the velocity is given by the navier stokes equation and one of the fluids is thin we present a formal asymptotic derivation of the evolution equation for the interface under different scaling assumptions for the surface tension we then study the different types of the stationary solutions and travelling waves for the resulting equation in particular we state a global well posedness result and using center manifold theory we obtain detailed information about the long time asymptotics of the solutions of the problem

the lubrication approximation for thin viscous films regularity and long time behavior of weak solutions we consider the fourth order degenerate diffusion equation in one space dimension this equation derived from a lubrication approximation models the surface tension dominated motion of thin viscous films and spreading droplets 15 the equation with f h h also models a thin neck of fluid in the hele shaw cell 10 11 23 in such problems h x t is the local thickness of the the film or neck this paper considers the properties of weak solutions that are more relevant to the droplet problem than to hele shaw for simplicity we consider periodic boundary conditions with the interpretation of modeling a periodic array of droplets we consider two problems the first has initial data h0 0 and f h h n 0 n 3 we show that there exists a weak nonnegative solution for all time also we show that this solution becomes a strong positive solution after some finite time t and asymptotically approaches its means as t the weak solution is in the classical sense of distributions for 3 8 n 3 and in a weaker sense introduced in 1 for the remaining 0 n 3 8 furthermore the solutions have high enough regularity to just include the unique source type solutions 2 with zero slope at the edge of the support they do not include any of the less regular solutions with positive slope at the edge of the support second we consider strictly positive initial data h0 m 0 and f h h n 0 n for this problem we show that even if a finite time singularity of the form h 0 does occur there exists a weak nonnegative solution for all time t this weak solution becomes strong and positive again after some critical time t as in the first problem we show that the solution approaches its mean as t the main technical idea is to introduce new classes of dissipative entropies to prove existence and higher regularity we show that these entropies are related to norms of the difference between the solution and its mean to prove the relaxation result 1996 john wiley sons inc

on regional nonlinear h filtering the structure of the nonlinear h filter in the neighborhood of the estimated trajectory is investigated and a bound on the size of the neighborhood that allows this structure is determined both for finite and infinite horizons riccati inequalities that depend on the estimated trajectory are derived for finding the filter gain matrix and an algorithm for calculating the bound on the size of the above neighborhood is presented explicit formulas are obtained in the infinite horizon case for the minimum achievable disturbance attenuation level the size of the neighborhood and the corresponding filter gain

validation of state space models from a single realization of non gaussian measurements a methodology is presented for testing whether a dynamic model in linear state space form accurately describes the system under consideration unlike existing procedures it is not necessary to assume that all of the random terms in the model are normally distributed the methodology is based on a single realization of observations and is relatively easy to implement since it relies on a normalized kalman filter state estimate the testing procedure rests on an asymptotic distribution theory for the filter estimate

quantum isometries and noncommutative spheres we introduce and study two new examples of noncommutative spheres the half liberated sphere and the free sphere together with the usual sphere these two spheres have the property that the corresponding quantum isometry group is easy in the representation theory sense we present as well some general comments on the axiomatization problem and on the untwisted and non easy case

filtering for a class of nonlinear discrete time stochastic systems with state delays in this paper the filtering problem is investigated for a class of nonlinear discrete time stochastic systems with state delays we aim at designing a full order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in the mean square for all admissible nonlinearities and time delays first an algebraic matrix inequality approach is developed to deal with the filter analysis problem and sufficient conditions are derived for the existence of the desired filters then based on the generalized inverse theory the filter design problem is tackled and a set of the desired filters is explicitly characterized a simulation example is provided to demonstrate the usefulness of the proposed design method

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

the full classification of orthogonal easy quantum groups we study easy quantum groups a combinatorial class of orthogonal quantum groups introduced by banica speicher in 2009 we show that there is a countable descending chain of easy quantum groups interpolating between bichon s free wreath product with the permutation group s n and a semi direct product of a permutation action of s n on a free product this reveals a series of new commutation relations interpolating between a free product construction and the tensor product furthermore we prove a dichotomy result saying that every hyperoctahedral easy quantum group is either part of our new interpolating series of quantum groups or belongs to a class of semi direct product quantum groups recently studied by the authors this completes the classification of easy quantum groups we also study combinatorial and operator algebraic aspects of the new interpolating series

the kantorovich inequality for error analysis of the kalman filter with unknown noise distributions the state space model with random noises is widely used to model dynamic systems in many practical problems the noise terms will have unknown probability distributions which is contrary to the usual assumption of gaussian noises made in state vector estimation this assumption is usually made for reasons of mathematical tractability a problem arises however in that inference based on the incorrect gaussian assumption can lead to misleading or erroneous conclusions this note shows how the kantorovich inequality from probability theory has potential for characterizing the estimation error of a kalman filter in such a non gaussian distribution free setting

optimal lower bounds on asymptotic support propagation rates for the thin film equation abstract we derive lower bounds on asymptotic support propagation rates for strong solutions of the cauchy problem for the thin film equation the bounds coincide up to a constant factor with the previously known upper bounds and thus are sharp our results hold in case of at most three spatial dimensions and n 1 2 92 the result is established using weighted backward entropy inequalities with singular weight functions to yield a differential inequality combined with some entropy production estimates the optimal rate of propagation is obtained to the best of our knowledge these are the first lower bounds on asymptotic support propagation rates for higher order nonnegativity preserving parabolic equations

well posedness for the navier slip thin film equation in the case of complete wetting we are interested in the thin film equation with zero contact angle and quadratic mobility modeling the spreading of a thin liquid film driven by capillarity and limited by viscosity in conjunction with a navier slip condition at the substrate this degenerate fourth order parabolic equation has the contact line as a free boundary from the analysis of the self similar source type solution one expects that the solution is smooth only as a function of two variables x x where x denotes the distance from the contact line with 13 14 0 6514 irrational therefore the well posedness theory is more subtle than in case of linear mobility coming from darcy dynamics or in case of the second order counterpart the porous medium equation here we prove global existence and uniqueness for one dimensional initial data that are close to traveling waves the main ingredients are maximal regularity estimates in weighted l2 spaces for the linearized evolution after suitable subtraction of a t b t x terms

quantum symmetry groups of finite spaces we determine the quantum automorphism groups of finite spaces these are compact matrix quantum groups in the sense of woronowicz

unbounded elements affiliated with c algebras and non compact quantum groups the affiliation relation that allows to include unbounded elements operators into thec algebra framework is introduced investigated and applied to the quantum group theory the quantum deformation of the two fold covering of the group of motions of euclidean plane is constructed a remarkable radius quantization is discovered it is also shown that the quantumsu 1 1 group does not exist on thec algebra level for real value of the deformation parameter

a noncommutative de finetti theorem invariance under quantum permutations is equivalent to freeness with amalgamation we show that the classical de finetti theorem has a canonical noncommutative counterpart if we strengthen exchangeability i e invariance of the joint distribution of the random variables under the action of the permutation group to invariance under the action of the quantum permutation group more precisely for an infinite sequence of noncommutative random variables x i i in mathbb n we prove that invariance of the joint distribution of the xi s under quantum permutations is equivalent to the fact that the xi s are identically distributed and free with respect to the conditional expectation onto the tail algebra of the xi s

quantum invariant families of matrices in free probability we consider self adjoint families of infinite matrices of noncommutative random variables such that the joint distribution of their entries is invariant under conjugation by a free quantum group for the free orthogonal and hyperoctahedral groups we obtain complete characterizations of the invariant families in terms of an operator valued r cyclicity condition this is a surprising contrast with the aldous hoover characterization of jointly exchangeable arrays

robust energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

robust kalman filtering for uncertain discrete time systems this paper is concerned with the problem of a kalman filter design for uncertain discrete time systems the system under consideration is subjected to time varying norm bounded parameter uncertainty in both the state and output matrices the problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties furthermore the guaranteed cost can be optimized by appropriately searching a scaling design parameter

nonnegative solutions of a fourth order nonlinear degenerate parabolic equation elena beretta michiel bertsch roberta dal passo communicated by m guatin o introduction in this paper we study nonnegative solutions of the fourth order equation 0 1 ut u uxxx x o where n is a real positive constant equation 0 1 is a nonlinear parabolic partial differential equation which is degenerate at points at which u vanishes it arises in several applications see the references in 2 4 5 6 in which u x t stands for a nonnegative quantity for example in the study of the dynamics of thin liquid films u denotes the thickness of the film or another relevant nonnegative quantity the case n 1 models the flow in a hele shaw cell while n 3 corresponds to viscous flow on a solid surface without slip driven by surface tension see also 6 7 8 for a related equation it is well known that fourth order equations do not satisfy a maximum principle in particular classical solutions of the linear equation ut u 0 may become negative in finite time bernis 8 friedman 2 have observed that if n is positive equation 0 1 has generalized solutions which remain nonnegative for all times in addition they show that the qualitative positivity of these solutions strongly depends on the value of n in more recent papers by kadanoff et al a combination of numerical calculations and matched asymptotics 4 and the analysis of travelling wave solutions 5 leads to results which suggest a very rich structure of the solutions of 0 1 it is the purpose of the present paper to clarify several aspects of the nonlinear equation 0 1 and its dependence on the parameter n our results lead to several conjectures and open problems as was pointed out in 4 for sufficiently small values of n solutions of 0 1 which are initially strictly positive may vanish at some point x 0 after a finite time to but to the best of our knowledge there is no rigorous proof of this phenomenon in the literature on the other hand it is of particular interest for applications for example if u denotes the thickness of a liquid film it implies that at time to the film breaks at xo

a characterization of freeness by invariance under quantum spreading we construct spaces of quantum increasing sequences which give quantum families of maps in the sense of so ltan we then introduce a notion of quantum spreadability for a sequence of noncommutative random variables by requiring their joint distribution to be invariant under taking quantum subsequences our main result is a free analogue of a theorem of ryll nardzewski for an infinite sequence of noncommutative random variables quantum spreadability is equivalent to free independence and identical distribution with respect to a conditional expectation introduction the study of random objects with distributional symmetries is an important subject in modern probability consider a sequence 1 2 of random variables such a sequence is called exchangeable if its distribution is invariant under finite permutations and spreadable if it is invariant under taking subsequences i e if 1 k d l1 lk for all k n and l1 lk in the 1930 s de finetti gave his famous characterization of infinite exchangeable sequences of random variables taking values in 0 1 as conditionally i i d this was extended to variables taking values in a compact hausdorff space by hewitt and savage 6 it was later discovered by ryll nardzewski that de finetti s theorem in fact holds under the apparently weaker condition of spreadability 12 for a comprehensive treatment of distributional symmetries in classical probability the reader is referred to the recent text of kallenberg 8 free probability developed by voiculescu in the 1980 s is based on the notion of free independence for random variables with the highest degree of noncommutativity remarkably there is a deep parallel between the theories of classical and free probability however it is only quite recently that this parallel has been extended to the study of distributional symmetries the breakthrough came with the work of kostler and speicher 10 who discovered that roughly speaking in free probability one should consider quantum distributional symmetries more specifically they defined the notion of quantum exchangeability for a sequence x1 x2 of noncommutative random variables by requiring that for each n n the joint distribution of x1 xn is invariant under the natural action of the quantum permutation group as n of wang 17 they then gave a free analogue of de finetti s theorem for an infinite sequence of noncommutative random variables quantum exchangeability is equivalent to free independence and identical distribution with respect to a conditional expectation 2010 mathematics subject classification 46l54 46l65 60g09

robust filtering for discrete time systems with bounded noise and parametric uncertainty this note presents a new approach to finite horizon guaranteed state prediction for discrete time systems affected by bounded noise and unknown but bounded parameter uncertainty our framework handles possibly nonlinear dependence of the state space matrices on the uncertain parameters the main result is that a minimal confidence ellipsoid for the state consistent with the measured output and the uncertainty description may be recursively computed in polynomial time using interior point methods for convex optimization with n states l uncertain parameters appearing linearly in the state space matrices with rank one matrix coefficients the worst case complexity grows as o l n l sup 3 5 with unstructured uncertainty in all system matrices the worst case complexity reduces to o n sup 3 5

nonlinear filtering methods for harmonic retrieval and model order selection in gaussian and non gaussian noise this paper addresses the problem of high resolution parameter estimation harmonic retrieval and model order selection for superimposed sinusoids the harmonic retrieval problem is analyzed using a nonlinear parameter estimation approach estimation is performed using several nonlinear estimators with signals embedded in white and colored gaussian noise simulation results demonstrate that the nonlinear filters perform close to the cramer rao bound model order selection is performed in gaussian and non gaussian noise the problem is formulated using a multiple hypothesis testing approach with assumed known a priori probabilities for each hypothesis parameter estimation is performed using the extended kalman filter when the noise is gaussian the extended high order filter ehof is implemented in non gaussian noise simulation results demonstrate excellent performance in selecting the correct model order and estimating the signal parameters

recursive consistent estimation with bounded noise estimation problems with bounded uniformly distributed noise arise naturally in reconstruction problems from over complete linear expansions with subtractive dithered quantization we present a simple recursive algorithm for such bounded noise estimation problems the mean square error mse of the algorithm is almost o 1 n sup 2 where n is the number of samples this rate is faster than the o 1 n mse obtained by standard recursive least squares estimation and is optimal to within a constant factor

robust estimation and filtering in the presence of bounded noise optimal algorithms for robust estimation and filtering are constructed the noise is considered a deterministic variable belonging to a set described by a norm previous results obtained for complete one to one and approximate information by m milanese and r tempo ibid vol 30 p 730 8 1985 are extended to partial and approximate information this information is considered useful in dealing with dynamic systems not completely identifiable and or with two different sources of noise such as process and measurement noise for different norms characterizing the noise optimal algorithms in a min max sense are shown in particular for hilbert norms a linear optimal algorithm is the well known minimum variance estimator for l sub infinity norm an optimal algorithm computable by linear programming is presented state estimation is formalized in the context of the general theory for stable systems an approximate state estimation is obtained by neglecting higher order powers an upper bound determining the approximation introduced is derived a numerical example illustrates the application of the theory

delay dependent robust h sub spl infin and l sub 2 l sub spl infin filtering for a class of uncertain nonlinear time delay systems this note presents delay dependent robust h sub spl infin and l sub 2 l sub spl infin filter designs for a class of nonlinear systems with multiple time varying delays in the state and parameter uncertainties residing in a polytope the nonlinearities are assumed to satisfy global lipschitz conditions attention is focused on the design of robust full order and reduced order filters guaranteeing a prescribed noise attenuation level in an h sub spl infin or l sub 2 l sub spl infin sense the admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms

quantum bernstein s theorem and the hyperoctahedral quantum group we study an extension of bernstein theorem to the setting of quantum groups for a d tuple of free identically distributed random variables we consider a problem of preservation of freeness under the transformations from the free orthogonal quantum group for a subset not contained in the hyperoctahedral quantum group we prove that preservation of freeness characterizes wigner s semicircle law we show that freeness is always preserved if the quantum subset is contained in the hyperoctahedral quantum group we provide examples of quantum subsets which show that our result is an extension of results known in the literature we study an extension of bernstein theorem to the setting of quantum groups for a d tuple of free identically distributed random variables we consider a problem of preservation of freeness under the transformations from the free orthogonal quantum group for a subset not contained in the hyperoctahedral quantum group we prove that preservation of freeness characterizes wigner s semicircle law we show that freeness is always preserved if the quantum subset is contained in the hyperoctahedral quantum group we provide examples of quantum subsets which show that our result is an extension of results known in the literature

a delay dependent approach to h filtering for stochastic delayed jumping systems with sensor non linearities in this paper a delay dependent approach is developed to deal with the stochastic h filtering problem for a class of ito type stochastic time delay jumping systems subject to both the sensor non linearities and the exogenous non linear disturbances the time delays enter into the system states the sensor non linearities and the external non linear disturbances the purpose of the addressed filtering problem is to seek an h filter such that in the simultaneous presence of non linear disturbances sensor non linearity as well as markovian jumping parameters the filtering error dynamics for the stochastic time delay system is stochastically stable with a guaranteed disturbance rejection attenuation level by using ito s differential formula and the lyapunov stability theory we develop a linear matrix inequality approach to derive sufficient conditions under which the desired filters exist these conditions are dependent on the length of the time delay we then characterize the expression of the fi

de finetti theorems for braided parafermions the classical de finetti theorem in probability theory relates symmetry under the permutation group with the independence of random variables this result has application in quantum information here we study states that are invariant with respect to a natural action of the braid group and we emphasize the pictorial formulation and interpretation of our results we prove a new type of de finetti theorem for the four string double braid group acting on the parafermion algebra to braid qudits a natural symmetry in the quon language for quantum information we prove that a braid invariant state is extremal if and only if it is a product state furthermore we provide an explicit characterization of braid invariant states on the parafermion algebra including finding a distinction that depends on whether the order of the parafermion algebra is square free we characterize the extremal nature of product states an inverse de finetti theorem

stochastic aspects of easy quantum groups we consider several orthogonal quantum groups satisfying the easiness assumption axiomatized in our previous paper for each of them we discuss the computation of the asymptotic law of tr uk with respect to the haar measure u being the fundamental representation for the classical groups on sn we recover in this way some well known results of diaconis and shahshahani

error constrained filtering for a class of nonlinear time varying delay systems with non gaussian noises in this technical note the quadratic error constrained filtering problem is formulated and investigated for discrete time varying nonlinear systems with state delays and non gaussian noises both the lipschitz like and ellipsoid bounded nonlinearities are considered the non gaussian noises are assumed to be unknown bounded and confined to specified ellipsoidal sets the aim of the addressed filtering problem is to develop a recursive algorithm based on the semi definite programme method such that for the admissible time delays nonlinear parameters and external bounded noise disturbances the quadratic estimation error is not more than a certain optimized upper bound at every time step the filter parameters are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi definite programme method a simulation example is exploited to illustrate the effectiveness of the proposed design procedures

min max kalman filtering abstract the problem of h optimal state estimation of linear continuous time systems that are measured with an additive white noise is addressed the relevant cost function is the expected value of the standard h performance index with respect to the measurement noise statistics the solution is obtained by applying the matrix version of the maximum principle to the solution of the min max problem in which the estimator tries to minimize the mean square estimation error and the exogenous disturbance tries to maximize it while being penalized for its energy the solution is given in terms of two coupled riccati difference equations from which the filter gains are derived in the case where an infinite penalty is imposed on the energy of the exogenous disturbance the celebrated kalman filter is recovered in the stationary case where all the signals are stationary an upper bound on the solutions of the coupled riccati equations is obtained via a solution of coupled linear matrix inequalities the resulting filter then guarantees a bound on the estimation error covariance matrix an illustrative example is given where the velocity of a maneuvering target has to be estimated utilizing noisy measurements of the position

minimum entropy filtering for multivariate stochastic systems with non gaussian noises in this note a minimum entropy filtering algorithm is presented for a class of multivariate dynamic stochastic systems which are represented by a set of time varying difference equations and are subjected to the multivariate non gaussian stochastic inputs several new concepts including the hybrid random vector hybrid probability and hybrid entropy are firstly established to describe the probabilistic property of the estimation errors new relationships are provided between the probability density functions pdfs of the multivariate stochastic input and output for different mapping cases recursive algorithms are then proposed to design the real time sub optimal filter so that the hybrid entropy of the estimation error can be minimized finally an improved algorithm is provided through the on line tuning of the weighting matrices so as to guarantee the local stability of the error system

thin film approximations of the two phase stokes problem abstract passing to the limit of small layer thickness in the two phase stokes problem we obtain when including only gravity resp surface tension effects a strongly coupled parabolic system of second resp fourth order in the non degenerate case we prove that the corresponding evolution problems are locally well posed for the gravity driven flow though we have to assume that the less dense fluid lies on top of the less dense layer moreover we show that the solutions converge exponentially fast towards a flat steady state which is uniquely determined by the volume of the two fluids provided they are initially close to this rest state

smooth zero contact angle solutions to a thin film equation around the steady state in the simplest case of a linearly degenerate mobility we view the thin film equation as a classical free boundary problem our focus is on the regularity of solutions and of their free boundary in the complete wetting regime which prescribes zero slope at the free boundary in order to rule out of the analysis possible changes in the topology of the positivity set we zoom into the free boundary by looking at perturbations of the stationary solution our strategy is based on a priori energy type estimates which provide minimal conditions on the initial datum under which a unique global solution exists in fact this solution turns out to be smooth for positive times and to converge to the stationary solution for large times as a consequence we obtain smoothness and large time behavior of the free boundary

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

on the structure of quantum automorphism groups we compute the k theory of quantum automorphism groups of finite dimensional c algebras in the sense of wang the results show in particular that the c algebras of functions on the quantum permutation groups s n are pairwise non isomorphic for different values of n along the way we discuss some general facts regarding torsion in discrete quantum groups in fact the duals of quantum automorphism groups are the most basic examples of discrete quantum groups exhibiting genuine quantum torsion phenomena

on the classification of easy quantum groups abstract in 2009 banica and speicher began to study the compact quantum groups g with s n g o n whose intertwiner spaces are induced by some partitions these so called easy quantum groups have a deep connection to combinatorics we continue their work on classifying these objects by introducing some new examples of easy quantum groups in particular we show that the six easy groups o n s n h n b n s n and b n split into seven cases o n s n h n b n s n b n and b n on the side of free easy quantum groups also we give a complete classification in the half liberated and in the nonhyperoctahedral case

de finetti theorem on the car algebra the symmetric states on a quasi local c algebra on the infinite set of indices j are those invariant under the action of the group of the permutations moving only a finite but arbitrary number of elements of j the celebrated de finetti theorem describes the structure of the symmetric states i e exchangeable probability measures in classical probability in the present paper we extend the de finetti theorem to the case of the car algebra that is for physical systems describing fermions namely after showing that a symmetric state is automatically even under the natural action of the parity automorphism we prove that the compact convex set of such states is a choquet simplex whose extremal i e ergodic w r t the action of the group of permutations previously described are precisely the product states in the sense of araki moriya in order to do that we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self containing interest

faithfulness of free product states abstract it is proved that the free product state in the reduced free product of c algebras is faithful if the initial states are faithful

asymptotic infinitesimal freeness with amalgamation for haar quantum unitary random matrices we consider the limiting distribution of u na nu n and bn and more general expressions where an and bn are n n matrices with entries in a unital c algebra mathcal b which have limiting mathcal b valued distributions as n and un is a n n haar distributed quantum unitary random matrix with entries independent from mathcal b under a boundedness assumption we show that u na nu n and bn are asymptotically free with amalgamation over mathcal b moreover this also holds in the stronger infinitesimal sense of belinschi shlyakhtenko

brief robust h filtering with error variance constraints for discrete time varying systems with uncertainty the robust h filtering problem with error variance constraints is considered for discrete time varying systems subject to norm bounded parameter uncertainties in both the state and the output matrices of the state space model sufficient conditions for a finite horizon filter to satisfy state estimation error variance constraints as well as prescribed h performance for all admissible perturbations are given in terms of two discrete riccati difference equations which are of a form suitable for recursive computation the results are extended to cover the case of stationary filtering over an infinite horizon for uncertain time invariant systems

non crossing cumulants of type b we establish connections between the lattices of non crossing partitions of type b introduced by v reiner and the framework of the free probability theory of d voiculescu lattices of non crossing partitions of type a up to now have played an important role in the combinatorics of free probability primarily via the non crossing cumulants of r speicher here we introduce the concept of non crossing cumulant of type b the inspiration for its definition is found by looking at an operation of restricted convolution of multiplicative functions studied in parallel for functions on symmetric groups in type a and on hyperoctahedral groups in type b the non crossing cumulants of type b live in an appropriate framework of non commutative probability space of type b and are closely related to a type b analogue for the r transform of voiculescu which is the free probabilistic counterpart of the fourier transform by starting from a condition of vanishing of mixed cumulants of type b we obtain an analogue of type b for the concept of free independence for random variables in a non commutative probability space

variance constrained filtering for uncertain stochastic systems with missing measurements in this note we consider a new filtering problem for linear uncertain discrete time stochastic systems with missing measurements the parameter uncertainties are allowed to be norm bounded and enter into the state matrix the system measurements may be unavailable i e missing data at any sample time and the probability of the occurrence of missing data is assumed to be known the purpose of this problem is to design a linear filter such that for all admissible parameter uncertainties and all possible incomplete observations the error state of the filtering process is mean square bounded and the steady state variance of the estimation error of each state is not more than the individual prescribed upper bound it is shown that the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like inequalities or linear matrix inequalities the explicit expression of the desired robust filters is parameterized and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

the extended kalman filter as an exponential observer for nonlinear systems we analyze the behavior of the extended kalman filter as a state estimator for nonlinear deterministic systems using the direct method of lyapunov we prove that under certain conditions the extended kalman filter is an exponential observer i e the dynamics of the estimation error is exponentially stable furthermore we discuss a generalization of the kalman filter with exponential data weighting to nonlinear systems

a noncommutative extended de finetti theorem abstract the extended de finetti theorem characterizes exchangeable infinite sequences of random variables as conditionally i i d and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability our main result is a noncommutative version of this theorem in contrast to the classical result of ryll nardzewski exchangeability turns out to be stronger than spreadability for infinite sequences of noncommutative random variables out of our investigations emerges noncommutative conditional independence in terms of a von neumann algebraic structure closely related to popa s notion of commuting squares and kummerer s generalized bernoulli shifts our main result is applicable to classical probability quantum probability in particular free probability braid group representations and jones subfactors

de finetti theorems for easy quantum groups we study sequences of noncommutative random variables which are invariant under quantum transformations coming from an orthogonal quantum group satisfying the easiness condition axiomatized in our previous paper for 10 easy quantum groups we obtain de finetti type theorems characterizing the joint distribution of any infinite quantum invariant sequence in particular we give a new and unified proof of the classical results of de finetti and freedman for the easy groups sn on which is based on the combinatorial theory of cumulants we also recover the free de finetti theorem of kostler and speicher and the characterization of operator valued free semicircular families due to curran we consider also finite sequences and prove an approximation result in the spirit of diaconis and freedman

delay dependent stabilization of stochastic interval delay systems with nonlinear disturbances in this paper a delay dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time delay interval systems with nonlinear disturbances the system matrices are assumed to be uncertain within given intervals the time delays appear in both the system states and the nonlinear disturbances and the stochastic perturbation is in the form of a brownian motion the purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that for all admissible interval uncertainties and nonlinear disturbances the closed loop system is asymptotically stable in the mean square where the stability criteria are dependent on the length of the time delay and therefore less conservative by using ito s differential formula and the lyapunov stability theory sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems then the controller gain is characterized in terms of the solution to a delay dependent linear matrix inequality lmi which can be easily solved by using available software packages a numerical example is exploited to demonstrate the effectiveness of the proposed design procedure

a justification for the thin film approximation of stokes flow with surface tension in the free boundary problem of stokes flow driven by surface tension we pass to the limit of small layer thickness it is rigorously shown that in this limit the evolution is given by the well known thin film equation the main techniques are appropriate scaling and uniform energy estimates in sobolev spaces of sufficiently high order based on parabolicity

general de finetti type theorems in noncommutative probability we prove general de finetti type theorems for classical and free independence the de finetti type theorems work for all non easy quantum groups which generalize a recent work of banica curran and speicher we determine maximal distributional symmetries which means the corresponding de finetti type theorem fails if a sequence of random variables satisfy more symmetry relations other than the maximal one in addition we define boolean quantum semigroups in analogous to the easy quantum groups by universal conditions on matrix coordinate generators and an orthogonal projection then we show a general de finetti type theorem for boolean independence