multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

unified hybridization of discontinuous galerkin mixed and continuous galerkin methods for second order elliptic problems we introduce a unifying framework for hybridization of finite element methods for second order elliptic problems the methods fitting in the framework are a general class of mixed dual finite element methods including hybridized mixed continuous galerkin nonconforming and a new wide class of hybridizable discontinuous galerkin methods the distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements since the associated matrix is sparse symmetric and positive definite these methods can be efficiently implemented moreover the framework allows in a single implementation the use of different methods in different elements or subdomains of the computational domain which are then automatically coupled finally the framework brings about a new point of view thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom

numerical index of absolute sums of banach spaces abstract we study the numerical index of absolute sums of banach spaces giving general conditions which imply that the numerical index of the sum is less or equal than the infimum of the numerical indices of the summands and we provide some examples where the equality holds covering the already known case of c 0 l 1 and l sums and giving as a new result the case of e sums where e has the rnp and n e 1 in particular for finite dimensional e with n e 1 we also show that the numerical index of a banach space z which contains a dense union of increasing one complemented subspaces is greater or equal than the limit superior of the numerical indices of those subspaces using these results we give a detailed short proof of the already known fact that for a fixed p the numerical indices of all infinite dimensional l p spaces coincide

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

estimating parameters of a nonlinear dynamical system a method based on a modified newton raphson scheme is presented to estimate parameters of a nonlinear dynamical system from the time series data of the variables the method removes some of the problems associated with the standard synchronization based methods an important achievement of this method is that it is possible to determine the exact form of dynamical equations for systems with quadratic nonlinearity

the fourier version of the variational theory of complex rays for medium frequency acoustics the variational theory of complex rays vtcr is a wave based computational approach dedicated to the resolution of medium frequency problems it uses a variational formulation of the problem which enables one to use any type of shape function within the substructures provided that it satisfies the governing equation thus the solution can be approximated using plane waves which is very interesting in the medium frequency vibration domain and also leads to a strong convergence of the method in the previous works this was shown in the case of acoustic problems in which the amplitudes of the plane waves were calculated as wavebands in this paper we propose a new approximation of these amplitudes based on fourier series we show that this approach increases the robustness of the method makes it more efficient numerically and extends its applicability to somewhat higher frequencies

corner treatments for high order local absorbing boundary conditions in high frequency acoustic scattering this paper deals with the design and validation of accurate local absorbing boundary conditions set on convex polygonal computational domains for the finite element solution of high frequency acoustic scattering problems while high order absorbing boundary conditions habcs are accurate for smooth fictitious boundaries the precision of the solution drops in the presence of corners if no specific treatment is applied we present and analyze two strategies to preserve the accuracy of pade type habcs at corners first by using compatibility relations derived for right angle corners and second by regularizing the boundary at the corner we show that the former strategy is well adapted to right corners and efficient for nearly right corners while the later is better for very obtuse corners numerical results are proposed to analyze and compare the approaches for two and three dimensional problems

green function discretization for numerical solution of the helmholtz equation abstract a discretization method based on free space green function interpolation with a minimuml2norm property has been developed for numerical solution of the helmholtz equation it has been shown to produce accurate solutions with less than three points per wave which implies a manyfold improvement in solution efficiency over previous methods the accuracy of the method does not break down formally until the grid resolution approaches two points per wave

optimized schwarz methods without overlap for the helmholtz equation the classical schwarz method is a domain decomposition method to solve elliptic partial differential equations in parallel convergence is achieved through overlap of the subdomains we study in this paper a variant of the schwarz method which converges without overlap for the helmholtz equation we show that the key ingredients for such an algorithm are the transmission conditions we derive optimal transmission conditions which lead to convergence of the algorithm in a finite number of steps these conditions are however nonlocal in nature and we introduce local approximations which we optimize for performance of the schwarz method this leads to an algorithm in the class of optimized schwarz methods we present an asymptotic analysis of the optimized schwarz method for two types of transmission conditions robin conditions and transmission conditions with second order tangential derivatives numerical results illustrate the effectiveness of the optimized schwarz method on a model problem and on a problem from industry

adaptive approximation method for joint parameter estimation and identical synchronization of chaotic systems we introduce a numerical approximation method for estimating an unknown parameter of a primary chaotic system which is partially observed through a scalar time series specifically we show that the recursive minimization of a suitably designed cost function that involves the dynamic state of a fully observed secondary system and the observed time series can lead to the identical synchronization of the two systems and the accurate estimation of the unknown parameter the salient feature of the proposed technique is that the only external input to the secondary system is the unknown parameter which needs to be adjusted we present numerical examples for the lorenz system which show how our algorithm can be considerably faster than some previously proposed methods

estimation of parameters in nonlinear systems using balanced synchronization using synchronization between observations and a model with undetermined parameters is a natural way to complete the specification of the model the quality of the synchronization a cost function to be minimized typically is evaluated by a least squares difference between the data time series and the model time series if the coupling between the data and the model is too strong this cost function is small for any data and any model and the variation of the cost function with respect to the parameters of interest is too small to permit selection of an optimal value of the parameters we introduce two methods for balancing the competing desires of a small cost function for the quality of the synchronization and the numerical ability to determine parameters accurately one method of balanced synchronization adds to the synchronization cost function a requirement that the conditional lyapunov exponent of the model system conditioned on being driven by the data remain negative but small in magnitude the other method allows the coupling between the data and the model to vary in time according to the error in synchronization this method succeeds because the data and the model exhibit generalized synchronization in the region where the parameters of the model are well determined examples are explored which have deterministic chaos with and without noise in the data signal

dispersive and dissipative behaviour of high order discontinuous galerkin finite element methods the dispersive and dissipative properties of hp version discontinuous galerkin finite element approximation are studied in three different limits for the small wave number limit hk 0 we show the discontinuous galerkin gives a higher order of accuracy than the standard galerkin procedure thereby confirming the conjectures of hu and atkins j comput phys 182 2 2002 516 if the mesh is fixed and the order p is increased it is shown that the dissipation and dispersion errors decay at a super exponential rate when the order p is much larger than hk finally if the order is chosen so that 2p 1 hk for some fixed constant 1 then it is shown that an exponential rate of decay is obtained

on the polynomial numerical index of the real spaces c0 l1 and l abstract we give a lower bound for the polynomial numerical index of order k for real lush spaces we use this bound to compute the polynomial numerical index of order 2 of the real spaces c 0 l 1 and l finally we present an example of a real banach space x whose polynomial numerical indices are positive while the ones of its bidual are zero

discontinuous galerkin methods for the helmholtz equation with large wave number this paper develops and analyzes some interior penalty discontinuous galerkin ipdg methods using piecewise linear polynomials for the helmholtz equation with the first order absorbing boundary condition in two and three dimensions it is proved that the proposed discontinuous galerkin methods are stable hence well posed without any mesh constraint for each fixed wave number k optimal order with respect to h error estimate in the broken h 1 norm and suboptimal order estimate in the l 2 norm are derived without any mesh constraint the latter estimate improves to optimal order when the mesh size h is restricted to the preasymptotic regime i e k 2 h gtrsim 1 numerical experiments are also presented to gauge the theoretical result and to numerically examine the pollution effect with respect to k in the error bounds the novelties of the proposed ipdg methods include the following first the methods penalize not only the jumps of the function values across the element edges but also the jumps of the normal and tangential derivatives second the penalty parameters are taken as complex numbers of positive imaginary parts so essentially and practically no constraint is imposed on the penalty parameters since the helmholtz problem is a non hermitian and indefinite linear problem as expected the crucial and the most difficult part of the whole analysis is to establish the stability estimates i e a priori estimates for the numerical solutions to this end the cruxes of our analysis are to establish and to make use of a local version of the rellich identity for the laplacian and to mimic the stability analysis for the pde solutions given in p cummings analysis of finite element based numerical methods for acoustic waves elastic waves and fluid solid interactions in the frequency domain ph d thesis the university of tennessee knoxville tn 2001 p cummings and x feng math models methods appl sci 16 2006 pp 139 160 u hetmaniuk commun math sci 5 2007 pp 665 678

efficiency of higher order finite elements for the analysis of seismic wave propagation the analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process to perform accurate numerical investigations by the finite differences or finite element method one must consider a specific problem known as the numerical dispersion of waves numerical dispersion may increase the numerical error during the propagation process as the wave velocity phase and group depends on the features of the numerical model in this paper the numerical modelling of wave propagation by the finite element method is thus analyzed and dis cussed for linear constitutive laws numerical dispersion is analyzed herein through 1d computations investigating the accuracy of higher order 15 node finite elements towards numerical dispersion concerning the numerical analy sis of wave attenuation a rheological interpretation of the classical rayleigh assumption has for instance been previously proposed in this journal

strong peak points and strongly norm attaining points with applications to denseness and polynomial numerical indices abstract using the variational method it is shown that the set of all strong peak functions in a closed algebra a of c b k is dense if and only if the set of all strong peak points is a norming subset of a as a corollary we can induce the denseness of strong peak functions on other certain spaces in case that a set of uniformly strongly exposed points of a banach space x is a norming subset of p x n then the set of all strongly norm attaining elements in p x n is dense in particular the set of all points at which the norm of p x n is frechet differentiable is a dense g subset in the last part using reisner s graph theoretic approach we construct some strongly norm attaining polynomials on a cl space with an absolute norm then we show that for a finite dimensional complex banach space x with an absolute norm its polynomial numerical indices are one if and only if x is isometric to l n moreover we give a characterization of the set of all complex extreme points of the unit ball of a cl space with an absolute norm

parameter estimation through ignorance dynamical modeling lies at the heart of our understanding of physical systems its role in science is deeper than mere operational forecasting in that it allows us to evaluate the adequacy of the mathematical structure of our models despite the importance of model parameters there is no general method of parameter estimation outside linear systems a relatively simple method of parameter estimation for nonlinear systems is introduced based on variations in the accuracy of probability forecasts it is illustrated on the logistic map the henon map and the 12 dimensional lorenz96 flow and its ability to outperform linear least squares in these systems is explored at various noise levels and sampling rates as expected it is more effective when the forecast error distributions are non gaussian the method selects parameter values by minimizing a proper local skill score for continuous probability forecasts as a function of the parameter values this approach is easier to implement in practice than alternative nonlinear methods based on the geometry of attractors or the ability of the model to shadow the observations direct measures of inadequacy in the model the implied ignorance and the information deficit are introduced

parameter estimation of dynamical systems via a chaotic ant swarm through the construction of suitable objective function the parameter estimation of the dynamical system could be converted to the problem of parameter optimization based on the chaotic ant swarm optimization approach we investigate the problem of parameter optimization for the dynamical systems in the presence of noise we systematically analyze the basic relationships among the complexity of objective function the length of time series and the performance of the searching algorithm furthermore we consider the effect of measurable additive noise on the objective function numerical simulations are also provided to show the effectiveness and feasibility of the proposed methods

discontinuous galerkin methods with plane waves for time harmonic problems a general framework for discontinuous galerkin methods in the frequency domain with numerical flux is presented the main feature of the method is the use of plane waves instead of polynomials to approximate the solution in each element the method is formulated for a general system of linear hyperbolic equations and is applied to problems of aeroacoustic propagation by solving the two dimensional linearized euler equations it is found that the method requires only a small number of elements per wavelength to obtain accurate solutions and that it is more efficient than high order drp schemes in addition the conditioning of the method is found to be high but not critical in practice it is shown that the ultra weak variational formulation is in fact a subset of the present discontinuous galerkin method a special extension of the method is devised in order to deal with singular solutions generated by point sources like monopoles or dipoles aeroacoustic problems with non uniform flows are also considered and results are presented for the sound radiated from a two dimensional jet

a symmetric trefftz dg formulation based on a local boundary element method for the solution of the helmholtz equation a general symmetric trefftz discontinuous galerkin method is built for solving the helmholtz equation with piecewise constant coefficients the construction of the corresponding local solutions to the helmholtz equation is based on a boundary element method a series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters and more importantly its outstanding ability to reduce the instabilities known as the pollution effect in the literature on numerical simulations of long range wave propagation

failure of parameter identification based on adaptive synchronization techniques in this paper several examples as well as their numerical simulations are provided to show some possible failures of parameter identification based on the so called adaptive synchronization techniques these failures might arise not only when the synchronized orbit produced by the driving system is designed to be either some kind of equilibrium or to be some kind of periodic orbit but also when this orbit is deliberately designed to be chaotic the reason for emergence of these failures is theoretically analyzed in the paper and the boundedness of all trajectories generated by the coupled systems is rigorously proved moreover synchronization techniques are proposed to realize complete synchronization and unknown parameter identification in a class of systems where nonlinear terms are not globally lipschitz in addition unknown parameter identification is studied in coupled systems with time delays

recovering unknown model parameters contained in a class of time variant chaotic dynamical systems abstract this work deals mainly with the problem of recovering all unknown parameters for a class of time variant chaotic dynamical systems from given time sequence based on synchronization between a chaotic sender system and an additional receiver system a procedure which combines a linear feedback technique with updated feedback gain and an adapted control strategy associated with the law of estimated parameters is developed to dynamically determine the values of unknown parameters contained in the sender system to promote widespread applications the structure of the receiver system can be independent of that of the sender system the effectiveness of this procedure is guaranteed by the periodic version of the classical lasalle invariance principle of differential equations illustrations are presented for a harmonically excited duffing oscillator and a four dimensional chaotic oscillator the numerical results reveal the present procedure not only can precisely recover unknown model parameters but also can rapidly response to sudden changes in unknown parameters in addition it has great robustness against the disturbance of noise

a nearly optimal galerkin projected residual finite element method for helmholtz problem a finite element formulation for scalar and linear second order boundary value problems is introduced the new method relies on a variational formulation obtained following the usual path of appending to the galerkin variational formulation a balanced residual form of the governing partial differential equation computed within each element the novelty consists of projecting the residual in a subspace defined for each element which gives rise to the name of the method galerkin projected residual gpr this subspace is built by systematically exploring some a priori criteria either based on the physics or on the underlying mathematics the method can be used to stabilize a variety of problems here it is applied to helmholtz equation where standard galerkin formulations are known to present poor approximations for high wave numbers the method is formally introduced along with some numerical examples that are used to assess the improvements achieved

single shooting homotopy method for parameter identification in dynamical systems an algorithm for identifying parameters in dynamical systems is developed in this work using homotopy transformations and the single shooting method the equations governing the dynamics of the mathematical model are augmented with observer like homotopy terms that smooth the objective function as a result premature convergence to a local minimum is avoided and the obtained parameter estimates are globally optimal numerical examples are presented to demonstrate the application of the proposed approach to chaotic systems

use of synchronization and adaptive control in parameter estimation from a time series a technique is introduced for estimating unknown parameters when a time series of only one variable from a multivariate nonlinear dynamical system is given the technique employs a combination of two different control methods linear feedback for synchronizing system variables and adaptive control and is based on dynamic minimization of synchronization error the technique is shown to work even when the unknown parameters appear in the evolution equations of the variables other than the one for which the time series is given the technique not only establishes that explicit detailed information about all system variables and parameters is contained in a scalar time series but also gives a way to extract it out under suitable conditions illustrations are presented for lorenz and rossler systems and a nonlinear dynamical system in plasma physics also it is found that the technique is reasonably stable against noise in the given time series and the estimated value of a parameter fluctuates around the correct value with the error of estimation growing linearly with the noise strength for small noise

numerical peak holomorphic functions on banach spaces abstract we introduce the notion of numerical strong peak function and investigate the denseness of the norm and numerical peak functions on complex banach spaces let a b b x x be the banach space of all bounded continuous functions f on the unit ball b x of a banach space x and their restrictions f b x to the open unit ball are holomorphic in finite dimensional spaces we show that the intersection of the set of all norm peak functions and the set of all numerical peak functions is a dense g subset of a b b x x we also prove that if x is a smooth banach space with the radon nikod m property then the set of all numerical strong peak functions is dense in a b b x x in particular when x l p 1 p or x l 1 it is shown that the intersection of the set of all norm strong peak functions and the set of all numerical strong peak functions is a dense g subset of a b b x x as an application the existence and properties of numerical boundary of a b b x x are studied finally the numerical peak function in a b b x x is characterized when x c k and some negative results on the denseness of numerical strong peak holomorphic functions are given

limit theorems for the numerical index abstract we improve on a limit theorem see martin et al 2011 13 th 5 1 for numerical index n for large classes of banach spaces including vector valued l p spaces and l p sums of banach spaces where 1 p we introduce two conditions on a banach space x a local characterization condition lcc and a global characterization condition gcc we prove that if a norm on x satisfies the lcc then n x lim m n x m an analogous result in which n will be replaced by a directed infinite set s will be proved for x satisfying the gcc we also present examples of banach spaces satisfying the above mentioned conditions

a phase based hybridizable discontinuous galerkin method for the numerical solution of the helmholtz equation we introduce a new hybridizable discontinuous galerkin hdg method for the numerical solution of the helmholtz equation over a wide range of wave frequencies our approach combines the hdg methodology with geometrical optics in a fashion that allows us to take advantage of the strengths of these two methodologies the phase based hdg method is devised as follows first we enrich the local approximation spaces with precomputed phases which are solutions of the eikonal equation in geometrical optics second we propose a novel scheme that combines the hdg method with ray tracing to compute multivalued solution of the eikonal equation third we utilize the proper orthogonal decomposition to remove redundant modes and obtain locally orthogonal basis functions which are then used to construct the global approximation spaces of the phase based hdg method and fourth we propose an appropriate choice of the stabilization parameter to guarantee stability and accuracy for the proposed method numerical experiments presented show that optimal orders of convergence are achieved that the number of degrees of freedom to achieve a given accuracy is independent of the wave number and that the number of unknowns required to achieve a given accuracy with the proposed method is orders of magnitude smaller than that with the standard finite element method

on a recursive method for the estimation of unknown parameters of partially observed chaotic systems we investigate a recently proposed method for on line parameter estimation and synchronization in chaotic systems this novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series it works by periodically updating the parameter of interest in a secondary system with the same functional form as the primary one but no explicit coupling between their dynamic variables in order to minimize a suitably defined cost function in this paper we review the basics of the method and investigate its robustness and new extensions in particular we study the performance of the novel technique in the presence of noise either observational i e an additive contamination of the observed time series or dynamical i e a random perturbation of the system dynamics and when there is a mismatch between the primary and secondary systems numerical results including comparisons with other techniques are presented finally we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations

synchronization based estimation of all parameters of chaotic systems from time series by a simple combination of adaptive scheme and linear feedback with the updated feedback strength for a large class of chaotic systems it is proved rigorously by using the invariance principle of differential equations that all unknown model parameters can be estimated dynamically this approach supplies a systematic and analytical procedure for estimating parameters from time series and it is simple to implement in practice in addition this method is quite robust against the effect of noise and able to respond rapidly to changes in operating parameters of the experimental system lorenz and r ossler hyperchaos systems are used to illustrate the validity of this technique

lushness numerical index one and duality we construct an example of a banach space which is not lush but whose dual space is lush this example shows that lushness is not equivalent to numerical index one a characterization of lushness for some quotient spaces of l1 spaces and new results on c rich subspaces of scalar or vector valued c k spaces are also presented

application of an ultra weak variational formulation of elliptic pdes to the two dimensional helmholtz problem a new technique to solve elliptic linear pdes called ultra weak variational formulation uwvf in this paper is introduced in b despres c r acad sci paris 318 1994 pp 939 944 this paper is devoted to an evaluation of the potentialities of this technique it is applied to a model wave problem the two dimensional helmholtz problem the new method is presented in three parts following the same style of presentation as the classical one of the finite elements method even though they are definitely conceptually different methods the first part is committed to the variational formulation and to the continuous problem the second part defines the discretization process using a galerkin procedure the third part actually studies the efficiency of the technique from the order of convergence point of view this is achieved using theoretical proofs and a series of numerical experiments in particular it is proven and shown the order of convergence is lower bounded by a linear function of the number of degrees of freedom an application to scattering problems is presented in a fourth part

evaluation of dynamical models dissipative synchronization and other techniques some recent developments for the validation of nonlinear models built from data are reviewed besides giving an overall view of the field a procedure is proposed and investigated based on the concept of dissipative synchronization between the data and the model which is very useful in validating models that should reproduce dominant dynamical features like bifurcations of the original system in order to assess the discriminating power of the procedure four well known benchmarks have been used namely duffing ueda duffingholmes and van der pol oscillators plus the henon map the procedure developed for discrete time systems is focused on the dynamical properties of the model rather than on statistical issues for all the systems investigated it is shown that the discriminating power of the procedure is similar to that of bifurcation diagrams which in turn is much greater than say that of correlation dimension but at a much lower computational cost

a comparison of two trefftz type methods the ultraweak variational formulation and the least squares method for solving shortwave 2 d helmholtz problems trefftz methods for the numerical solution of partial differential equations pdes on a given domain involve trial functions which are defined in subdomains are generally discontinuous and are solutions of the governing pde or its adjoint within each subdomain the boundary conditions and matching conditions between subdomains must be enforced separately an interesting novel result presented in this paper is that the least squares method lsm and the ultraweak variational formulation two methods already established for solving the helmholtz equation can be derived in the framework of the trefftz type methods in the first case the boundary conditions and interelement continuity are enforced by means of a least squares procedure in the second a galerkin type weighted residual method is used another goal of the work is to assess the relative efficiency of each method for solving shortwave problems in acoustics and to study the stability of each method the numerical performance of each scheme is assessed with reference to two 2 d test problems acoustic propagation in an uniform soft walled duct and propagation in an l shaped domain the latter involving singular behaviour at a sharp corner

the unit ball of the complex mathcal p 3h let h be a two dimensional complex hilbert space and mathcal p 3h the space of 3 homogeneous polynomials on h we give a characterization of the extreme points of its unit ball mathsf b mathcal p 3h from which we deduce that the unit sphere of mathcal p 3h is the disjoint union of the sets of its extreme and smooth points we also show that an extreme point of mathsf b mathcal p 3h remains extreme as considered as an element of mathsf b mathcal l 3h finally we make a few remarks about the geometry of the unit ball of the predual of mathcal p 3h and give a characterization of its smooth points

polynomial numerical indices of banach spaces with 1 unconditional bases abstract the only infinite dimensional complex space with 1 unconditional basis which has polynomial numerical index of order 2 equal to 1 is c0 in the real case there is no space of this type we also show that in the complex case if x is an infinite dimensional banach sequence space with absolute norm whose kothe dual is norming and has polynomial numerical index of order 2 equal to 1 then c 0 x l in the real case again there is no space of this type

parameter and state estimation of experimental chaotic systems using synchronization we examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems we focus on important aspects of this problem that have received little attention previously and we explore them using experiments and simulations with the chaotic colpitts oscillator as an example system we explore the impact of model imperfection on the ability to extract valid information from an experimental system we compare two optimization methods an initial value method and a constrained method each of these involves coupling the model equations to the experimental data in order to regularize the chaotic motions on the synchronization manifold we explore both time dependent and time independent coupling and discuss the use of periodic impulse coupling we also examine both optimized and fixed or manually adjusted coupling for the case of an optimized time dependent coupling function u t we find a robust structure which includes sharp peaks and intervals where it is zero this structure shows a strong correlation with the location in phase space and appears to depend on noise imperfections of the model and the lyapunov direction vectors for time independent coupling we find the counterintuitive result that often the optimal rms error in fitting the model to the data initially increases with coupling strength comparison of this result with that obtained using simulated data may provide one measure of model imperfection the constrained method with time dependent coupling appears to have benefits in synchronizing long data sets with minimal impact while the initial value method with time independent coupling tends to be substantially faster more flexible and easier to use we also describe a method of coupling which is useful for sparse experimental data sets our use of the colpitts oscillator allows us to explore in detail the case of a system with one positive lyapunov exponent the methods we explored are easily extended to driven systems such as neurons with time dependent injected current they are expected to be of value in nonchaotic systems as well software is available on request

realization of parameters identification in only locally lipschitzian dynamical systems with multiple types of time delays most of the existing results for identifying parameters in dynamical systems through adaptive coupling techniques always require a uniform lipschitz condition on system vector fields however it is not this requirement but the only locally lipschitz condition that is more suitable for many nonlinear systems in real applications also time delays sometimes are essential for modeling real systems so that in addition to the discrete form time delays in the distributed form could be considered this paper thus considers the problem of parameters identification in only locally lipschitzian dynamical systems with multiple types of time delays through adaptive coupling techniques in particular the paper proposes some linear independence conditions for realization of parameters identification in both nonautonomous and autonomous systems and draws a comparison between these conditions and the persistent of excitation condition which is used frequently in the literature moreover the paper proposes an index t

optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems based on the lyapunov stability and adaptive synchronization theory optimization design of adaptive controllers and parameter observers with controllable gain coefficient are investigated in detail the linear errors of corresponding variables and parameters are used to construct different appropriate positive lyapunov functions v and the parameter observers and adaptive controllers are approached analytically by simplifying the differential inequality dv dt 0 particularly an optional gain coefficient is selected in the parameter observers and positive lyapunov function which decides the transient period to identify the unknown parameters and reach synchronization the scheme is used to study the synchronization of two non identical hyperchaotic rossler systems the theoretical and numerical results confirm that the four unknown parameters in the drive system are estimated exactly and the two hyperchaotic systems reach complete synchronization when the controllers and parameter observers work on the driven system to confirm the model independence of this scheme an alternative hyperchaotic system is investigated whereby the results confirm that the five unknown parameters are identified rapidly and exactly and that the two hyperchaotic systems reach complete synchronization as well

on the numerical radius of operators in lebesgue spaces we show that the absolute numerical index of the space lp is p 1pq 1q where 1p 1q 1 in other words we prove that sup x p 1 tx d x lp x p 1 p 1pq 1q t for every t l lp and that this inequality is the best possible when the dimension of lp is greater than one we also give lower bounds for the best constant of equivalence between the numerical radius and the operator norm in lp for atomless when restricting to rank one operators or narrow operators

overview of the discontinuous enrichment method the ultra weak variational formulation and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons

some geometric properties of disk algebras abstract in this paper we study some geometrical properties of certain classes of uniform algebras in particular the ball algebra a u b x of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex banach space x we prove that a u b x has k numerical index 1 for every k the lushness and also the ahsp moreover the disk algebra a d and more in general any uniform algebra whose choquet boundary has no isolated points is proved to have the polynomial daugavet property most of those properties are extended to the vector valued version a x of a uniform algebra a

the perfectly matched layer for the ultra weak variational formulation of the 3d helmholtz equation we investigate the feasibility of using the perfectly matched layer pml as an absorbing boundary condition for the ultra weak variational formulation uwvf of the 3d helmholtz equation the pml is derived using complex stretching of the spatial variables this leads to a modified helmholtz equation for which the uwvf can be derived in the standard discrete uwvf the approximating subspace is constructed from local solutions of the helmholtz equation in previous studies plane wave basis functions have been advocated because they simplify the building of the uwvf matrices for the pml domain we propose a special set of plane wave basis functions which allow fast computations and efficiently reduce spurious numerical reflections the method is validated by numerical experiments in comparison to a low order absorbing boundary condition the pml shows superior performance copyright 2004 john wiley sons ltd

on a second numerical index for banach spaces we introduce a second numerical index for real banach spaces with non trivial lie algebra as the best constant of equivalence between the numerical radius and the quotient of the operator norm modulo the lie algebra we present a number of examples and results concerning absolute sums duality vector valued function spaces which show that in many cases the behaviour of this second numerical index differs from the one of the classical numerical index as main results we prove that hilbert spaces have second numerical index one and that they are the only spaces with this property among the class of banach spaces with one unconditional basis and non trivial lie algebra besides an application to the bishop phelps bollobas property for the numerical radius is given

a discontinuous finite element method at element level for helmholtz equation abstract a discontinuous finite element formulation is presented for helmholtz equation continuity is relaxed locally in the interior of the element instead of across the element edges the interior shape functions can be viewed as discontinuous bubbles and the corresponding degrees of freedom can be eliminated at element level by static condensation yielding a global matrix topologically equivalent to those of classical c0 finite element approximations the discontinuous bubbles are introduced to consistently add stability to the formulation preserving the optimal rates of convergence and improving accuracy a crucial point of the discontinuous formulation relies on the choice of the stabilization parameters related to the weak enforcement of continuity inside each element explicit values of these stabilization parameters minimizing the pollution effect are presented for uniform meshes the accuracy and stability of the proposed formulation for bilinear shape functions are demonstrated in several numerical examples

polynomial numerical indices of banach spaces with absolute norm abstract we study when a banach space with absolute norm may have polynomial numerical indices equal to one in the real case we show that a banach space x with absolute norm which has the radon nikod m property or is asplund satisfies n 2 x 1 unless it is one dimensional in the complex case we show that the only banach spaces x with absolute norm and the radon nikod m property which satisfy n 2 x 1 are the spaces l m also the only asplund complex space x with absolute norm which satisfies n 2 x 1 is c 0

on the numerical index of banach spaces we give a partial answer to the problem of computing the numerical index of lp space 1 p also we give an estimate of the numerical index of the two dimensional real space lp2 1 p for the lp space we show that its numerical index is greater than the lp space one

a high order absorbing boundary condition for 2d time harmonic elastodynamic scattering problems abstract in this paper we are concerned with the construction of a new high order absorbing boundary condition abc for 2d elastic scattering problems it is defined by an approximate local dirichlet to neumann dtn map first we explain the derivation of this approximation next a detailed analytical study in terms of hankel functions in the circular case is addressed the new abc is compared with the standard low order lysmer kuhlemeyer abc finally its accuracy and efficiency are investigated for various numerical examples particularly at high frequencies

dispersion analysis of plane wave discontinuous galerkin methods summary the plane wave dg pwdg method for the helmholtz equation was introduced and analyzed in gittelson c hiptmair r and perugia i plane wave discontinuous galerkin methods analysis of the h version math model numer anal 43 2009 297 331 as a generalization of the so called ultra weak variational formulation see o cessenat and b despres application of an ultra weak variational formulation of elliptic pdes to the two dimensional helmholtz equation siam j numer anal 35 1998 pp 255 299 the method relies on trefftz type local trial spaces spanned by plane waves of different directions and links cells of the mesh through numerical fluxes in the spirit of dg methods we conduct a partly empirical dispersion analysis of the method in a discrete translation invariant setting by studying the mismatch of wave numbers of discrete and continuous plane waves traveling in the same direction we find agreement of the wave numbers for directions represented in the local trial spaces for other directions the pwdg methods turn out to incur both phase and amplitude errors this manifests itself as a pollution effect haunting the h version of the method our dispersion analysis allows a quantitative prediction of the strength of this effect and its dependence on the wave number and number of plane waves copyright 2014 john wiley sons ltd