a new a posteriori error estimate for the morley element in this paper we present a posteriori error analysis for the nonconforming morley element of the fourth order elliptic equation we propose a new residual based a posteriori error estimator and prove its reliability and efficiency these results refine those of beirao da veiga et al numer math 106 165 179 2007 by dropping two edge jump terms in both the energy norm of the error and the estimator and those of wang and zhang local a priori and a posteriori error estimates of finite elements for biharmonic equation research report 13 2006 by showing the efficiency in the sense of verfurth a review of a posteriori error estimation and adaptive mesh refinement techniques wiley teubner new york 1996 moreover the normal component in the estimators of beirao da veiga et al numer math 106 165 179 2007 and wang and zhang local a priori and a posteriori error estimates of finite elements for biharmonic equation research report 13 2006 is dropped and therefore only the tangential component of the stress on each edge comes into the estimator in addition we generalize these results to three dimensional case

ℋ 2 filtering of discrete time markov jump linear systems through linear matrix inequalities this paper addresses the 2 filtering design problem of discrete time markov jump linear systems first under the assumption that the markov parameter is measured the main contribution is on the lmi characterisation of all filters such that the estimation error remains bounded by a given 2 norm level yielding the complete solution of the mode dependent filtering design problem based on this result a robust filter design to deal with convex bounded parameter uncertainty is considered second from the same lmi characterisation a design procedure for mode independent filtering design is proposed some examples are solved for illustration and comparison

robust linear filtering for discrete time hybrid markov linear systems in this paper we consider the robust linear filtering of hybrid discrete time markovian jump linear systems we assume that only an output of the system is available and therefore the values of the jump parameter are not known it is desired to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the square error we consider uncertainties on the parameters of the possible modes of operation of the system a linear matrix inequalities lmi formulation is proposed to solve the problem for the case in which there are no uncertainties on the modes of operation of the system we show that the lmi formulation provides a filter with the same stationary mean square error as the one obtained from the riccati equation approach

a convex programming approach to h2 control of discrete time markovian jump linear systems in this paper we consider the h control problem for the class of discrete time 2 linear systems with parameters subject to markovian jumps using a convex programming approach we generalize the definition of the h norm from the deter2 ministic case to the markovian jump case and set a link between this norm and the observability and controllability gramians conditions for existence and derivation of a mean square stabilizing controller for a markovian jump linear system using convex analysis are established the main contribution of the paper is to provide a convex programming formulation to the h control problem so that several 2 important cases to our knowledge not analysed in previous work can be addressed regarding the transition matrix p for the markov chain two ij situations are considered the case in which it is exactly known and the case in which it is not exactly known but belongs to an appropriated convex set regarding the state variable and the jump variable the cases in which t

a two grid discretization scheme of non conforming finite elements for transmission eigenvalues abstract in this paper for the helmholtz transmission eigenvalue problem we propose a two grid discretization scheme of non conforming finite elements with this scheme the solution of the transmission eigenvalue problem on a fine grid h is reduced to the solution of the primal and dual eigenvalue problem on a much coarser grid h and the solutions of two linear algebraic systems with the same positive definite hermitian and block diagonal coefficient matrix on the fine grid h we prove the resulting solution still maintains an asymptotically optimal accuracy and we report some numerical examples in two dimension and three dimension on the modified zienkiewicz element to validate the efficiency of our approach for solving transmission eigenvalues

stationary filter for linear minimum mean square error estimator of discrete time markovian jump systems we derive in this paper a stationary filter for the linear minimum mean square error estimator lmmse of discrete time markovian jump linear systems mjlss we obtain the convergence of the error covariance matrix of the lmmse to a stationary value under the assumption of mean square stability of the mjls and ergodicity of the associated markov chain it is shown that there exists a unique solution for the stationary riccati filter equation and moreover this solution is the limit of the error covariance matrix of the lmmse the advantage of this scheme is that it is very easy to implement and all calculations can be performed off line leading to a linear time invariant filter

nonexistence of holomorphic submersions between complex unit balls equivariant with respect to a lattice and their generalizations in this article we prove first of all the nonexistence of holomorphic submersions other than covering maps between compact quotients of complex unit balls with a proof that works equally well in a more general equivariant setting for a non equidimensional surjective holomorphic map between compact ball quotients our method applies to show that the set of critical values must be nonempty and of codimension 1 in the equivariant setting the line of arguments extend to holomorphic mappings of maximal rank into the complex projective space or the complex euclidean space yielding in the latter case a lower estimate on the dimension of the singular locus of certain holomorphic maps defined by integrating holomorphic 1 forms in another direction we extend the nonexistence statement on holomorphic submersions to the case of ball quotients of finite volume provided that the target complex unit ball is of dimension m 2 giving in particular a new proof that a local biholomorphism between noncompact m ball quotients of finite volume must be a covering map whenever m 2 finally combining our results with hermitian metric rigidity we show that any holomorphic submersion from a bounded symmetric domain into a complex unit ball equivariant with respect to a lattice must factor through a canonical projection to yield an automorphism of the complex unit ball provided that either the lattice is cocompact or the ball is of dimension at least 2

a type of adaptive c0 non conforming finite element method for the helmholtz transmission eigenvalue problem abstract the transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering in this paper for the helmholtz transmission eigenvalue problem in r d d 2 3 we discuss the a posteriori error estimates and adaptive algorithm of a type of c 0 non conforming finite elements including the morley zienkiewicz element and the modified zienkiewicz element we give the a posteriori error estimators for approximate eigenpair and prove their reliability and efficiency for eigenfunctions we also analyze their reliability for eigenvalues numerical results not only in r 2 but also in r 3 indicate that the a posteriori error estimators are sharp and the adaptive algorithm is efficient for computing real and complex transmission eigenvalues as expected

the adaptive ciarlet raviart mixed method for biharmonic problems with simply supported boundary condition abstract in this paper we study the adaptive fashion of the ciarlet raviart mixed method for biharmonic equation eigenvalue problem with simply supported boundary condition in r d we propose an a posteriori error indicator of the ciarlet raviart approximate solution for the biharmonic equation and an a posteriori error indicator of the ciarlet raviart approximate eigenfuction and prove the reliability and efficiency of the indicators we also give an a posteriori error indicator for the approximate eigenvalue and prove its reliability we design an adaptive ciarlet raviart mixed method with piecewise polynomials of degree less than or equal to m and numerical experiments show that numerical eigenvalues obtained by the method can achieve the optimal convergence order o d o f 2 m d d 2 m 2 3 d 3 m 3

linear minimum mean square filter for discrete time linear systems with markov jumps and multiplicative noises in this paper we obtain the linear minimum mean square estimator lmmse for discrete time linear systems subject to state and measurement multiplicative noises and markov jumps on the parameters it is assumed that the markov chain is not available by using geometric arguments we obtain a kalman type filter conveniently implementable in a recurrence form the stationary case is also studied and a proof for the convergence of the error covariance matrix of the lmmse to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated markov chain is obtained it is shown that there exists a unique positive semi definite solution for the stationary riccati like filter equation and moreover this solution is the limit of the error covariance matrix of the lmmse the advantage of this scheme is that it is very easy to implement and all calculations can be performed offline

mixed methods for the helmholtz transmission eigenvalues the ciarlet raviart mixed finite element method is popular for the biharmonic equations in this paper we apply this method to the helmholtz transmission eigenvalue problem which is quadratic and

a c0ipg method and its error estimates for the helmholtz transmission eigenvalue problem abstract the interior penalty methods using c 0 lagrange elements c 0 ipg developed in the last decade for the fourth order problems are an interesting topic in academia at present in this paper we apply the methods to the helmholtz transmission eigenvalue problem which is quadratic and non self adjoint and has important applications in the inverse scattering theory we propose a discrete scheme present a complete error analysis and first prove the c 0 ipg method can capture smooth eigenpairs efficiently using the argument in this paper we can prove that the c 0 ipg methods for the fourth order eigenvalue problems in the existing literature can also capture smooth eigenpairs efficiently numerical examples confirm our theoretical analysis

controllability observability and discrete time markovian jump linear quadratic control this paper is concerned with the controllability and observability of discrete time linear systems that possess randomly jumping parameters described by finite stale markov processes and the relationship between these properties and the solution of the infinite time jump linear quadratic jlq optimal control problem the solution of the markovian jlq problem with finite or infinite time horizons is known necessary and sufficient conditions for the existence of optimal constant control laws that lead to finite optimal expected costs as the time horizon becomes infinite are also known sufficient conditions for these steady state control laws to stabilize the controlled system are also available chizeck et al 1986 these conditions are not easy to test however various definitions of controllability and observability for stochastic systems exist in the literature these definitions are unfortunately not related to the steady state jlq control problem in a manner that is analogous to the role of deter

h and h 2 filtering for linear systems with uncertain markov transitions this paper is concerned with h and h 2 filtering for markovian jump linear systems with uncertain transition probabilities motivated by the fact that the existing results either impose severe restrictions on some key matrices or introduce some unnecessary matrix variables this paper is focused on developing a new approach to systematically relax these restrictions for filter design by applying a novel technique to eliminate the product terms between the lyapunov matrices and the filter parameters an improved condition is first obtained for analyzing the h performance of the filtering error system then sufficient conditions in terms of linear matrix inequalities are presented for designing filters with a guaranteed h filtering performance level the proposed method is further extended to h 2 filtering theoretical analyses followed by a few numerical examples show that the proposed filter design method outperforms some existing results with respect to reduction of conservatism or variables needed for computation the filter design problems for both continuous time and discrete time markovian jump linear systems are addressed in a unified framework

mixed methods for the elastic transmission eigenvalue problem abstract the elastic transmission eigenvalue problem is quadratic in the eigenvalue parameter nonselfadjoint and of fourth order in this paper we apply the ciarlet raviart mixed method to this problem give a mixed variational form and establish two mixed methods using the classical lagrange finite element and the spectral element respectively we deduce the error estimates of the discrete eigenpairs theoretical analysis and numerical experiments show that these two methods are simple and easy to implement and can efficiently compute real and complex elastic transmission eigenvalues

a properly embedded holomorphic disc in the ball with finite area and dense boundary in this paper we construct a properly embedded holomorphic disc in the unit ball mathbb b 2 of mathbb c 2 having a surprising combination of properties on the one hand it has finite area and hence is the zero set of a bounded holomorphic function on mathbb b 2 on the other hand its boundary curve is everywhere dense in the sphere b mathbb b 2 a similar result is proved in higher dimensions our construction is based on an approximation result in contact geometry also proved in the paper

mixed h sub 2 h sub spl infin control of discrete time markovian jump linear systems in this paper we consider the mixed h sub 2 h sub spl infin control problem for the class of discrete time linear systems with parameters subject to markovian jump linear systems it is assumed that both the state variable and the jump variable are available to the controller the transition probability matrix may not be exactly known but belongs to an appropriate convex set for this controlled discrete time markovian jump linear system the problem of interest can be stated in the following way find a robust with respect to the uncertainty on the transition markov probability matrix mean square stabilizing state and jump feedback controller that minimizes an upper bound for the h sub spl infin norm under the restriction that the h sub spl infin norm is less than a prespecified value spl delta the problem of the determination of the smallest h sub spl infin norm is also addressed we present an approximate version of these problems via linear matrix inequality optimization

linear minimum mean square filters for markov jump linear systems this paper studies optimal mean square error estimation for discrete time linear systems with observed markov jump parameters new linear estimators are introduced by considering a cluster information structure in the filter design the set of filters constructed in this way can be ordered in a lattice according to the refines of clusters of the markov chain including the linear markovian estimator at one end with only one cluster and the kalman filter at the other end with as many clusters as markov states the higher is the number of clusters the heavier are precomputations and smaller is the estimation error for embedded sequences of partitions so that the cardinality and choice of the clusters allows for a tradeoff between performance and computational requirements in this paper we propose the estimator give the formulas for precomputation of gains present some properties and give an illustrative numerical example

an lmi approach for h2 and h reduced order filtering of uncertain discrete time markov and bernoulli jump linear systems abstract this paper proposes a new approach based on parameter dependent linear matrix inequality lmi conditions associated with a scalar parameter that are sufficient to provide robust h 2 and h reduced order mode dependent partially mode dependent or mode independent filters for discrete time markov jump linear systems mjls with time invariant uncertain transition probabilities time invariant uncertainties in the state space matrices of the modes can be handled as well as main difference with respect to the existing approaches in the literature the filter matrices are obtained directly from the slack variables introduced in the conditions moreover the proposed conditions become also necessary for a particular choice of the scalar parameter when mode dependent full order filters are designed for systems without uncertainties additionally for precisely known generalized bernoulli jump systems i e the case where all the rows of the transition probability matrix are equal optimal solutions are obtained for both mode dependent and mode independent full order filters examples including one motivated by a practical application are presented to illustrate the proposed approach

new methods for mode independent robust control of markov jump linear systems abstract this paper treats the h 2 and h controls of linear systems with markov jump disturbances via new design methods based on linear matrix inequalities lmis the proposed techniques are especially tailored to the scenario where the jump process cannot be measured and apply to homogeneous markov chains of any structure in the scenario of polytopic uncertainty affecting the system matrices new uncertainty dependent methods are introduced for the design of robust controllers several numerical examples illustrate situations where the proposed techniques are less conservative than the ones found in the literature

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

recursive integral method for transmission eigenvalues the transmission eigenvalue problem arose in the inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse problems for target identification and nondestructive testing the problem is numerically challenging because of the nonself adjointness and complicated spectrum in this talk we introduce a novel recursive contour integral method using the spectrum projection the method can compute both real and complex eigenvalues and does not require any a priori information numerical examples show that the method is effective and robust

robust mode independent filtering for discrete time markov jump linear systems with multiplicative noises this paper deals with the robust mode independent linear filtering problem for discrete time markov jump linear systems with multiplicative noises it is assumed that the values of the markov chain are not available and that the parameters of the systems are subject to convex polytopic uncertainties the goal is to design a mode independent that is one that doesn t depend on the markov jump parameter dynamic linear filter such that the closed loop system is mean square stable and minimises an upper bound for the stationary expected value of the square error a linear matrix inequalities lmi formulation based on a parameter dependent lyapunov procedure is proposed to solve the problem the paper concludes with an illustrative example

a c0ip method of transmission eigenvalues for elastic waves abstract this paper develops a discontinuous galerkin method to compute a few smallest elasticity transmission eigenvalues which are of practical importance in inverse elastic scattering theory for high order problems comparing with classical conforming finite element methods discontinuous galerkin methods use simpler basis functions which make the numerical implementation much easier in this paper we propose an interior penalty discontinuous galerkin method using c 0 lagrange elements c 0 ip for the elastic transmission eigenvalue problem and prove the optimal convergence numerical examples are presented to validate its effectiveness both real and complex eigenvalues can be obtained

an efficient spectral galerkin approximation based on dimension reduction scheme for transmission eigenvalues in polar geometries abstract in this paper we put forward an efficient spectral galerkin approximation in view of dimension reduction scheme for transmission eigenvalue problem in polar geometries firstly we turn the original problem into an equivalent fourth order nonlinear eigenvalue problem then the fourth order nonlinear eigenvalue problem is transformed into a coupled fourth order linear eigenvalue system by introducing an auxiliary poisson equation secondly based on polar coordinate transformation we further reduce the coupled fourth order linear eigenvalue system to a series of equivalent one dimensional eigenvalue systems thirdly we derive the essential polar condition and introduce the appropriate weighted sobolev space according to the polar condition and establish the weak form and the corresponding discrete form in addition by utilizing spectral theory of compact operators we prove the error estimates of approximation eigenvalues and eigenvectors for each one dimensional eigenvalue system finally we provide ample numerical experiments and the numerical results show the effectiveness of the algorithm and the correctness of the theoretical results

h2 filtering for discrete time hidden markov jump systems abstractin this paper we consider the h2 filtering problem for a discrete time markov jump linear systemin which the markov parameter is not available in the spirit of active fault tolerant control systems it is supposed that there is a discrete time hidden markov model k k in which the observable part k represents the information coming from a detector and available to the filter while the hidden part k of the process represents the dynamics of the real system several models found in the literature are encompassed by this framework like the complete observation case the clustering information case the mode independent case and markov models in fault tolerant control we start by analysing an auxiliary filtering problem in which it is assumed that both k k are available to the filter so that necessary and sufficient conditions in terms of lmi linear matrix inequalities for the existence of the optimal filter can be obtained in the sequel we consider the realistic case

output feedback control of markov jump linear systems in continuous time this paper addresses the dynamic output feedback control problem of continuous time markovian jump linear systems the fundamental point in the analysis is an lmi characterization comprising all dynamical compensators that stabilize the closed loop system in the mean square sense the h sub 2 and h sub spl infin norm control problems are studied and the h sub 2 and h sub spl infin filtering problems are solved as a by product