asymptotic behaviour of some bootstrap estimators the aim of this paper is to present a theoretical analysis of three bootstrap estimators commonly used in system identification the main results concern the local convergence and accuracy properties of the estimators both iterative and on line versions are examined

an inequality by which to adjust the lms algorithm step size this paper gives a method for differentiating between the transient and steady states in the lms algorithm using inequalities among a set of output errors based on these inequalities it also gives an algorithm for automatic step size adjustment to both improve the convergence rate and reduce steady state parameter estimation errors

insensitizing controls for the 1 d wave equation we study the insensitizing controllability property of the one dimensional wave equation observed in some open set in two cases when the control acts in an interior region and when it acts on the boundary in both cases when the control time is sufficiently large the e insensitizing controllability holds moreover for the boundary controlled equation the exact insensitizing controllability also holds

the steiglitz mcbride identification algorithm revisited convergence analysis and accuracy aspects the convergence and accuracy properties of the steiglitz and mcbride identification method are examined the analysis is valid for a sufficiently large number of data it is shown that the method can converge to the true parameter vector only when the additive output noise is white in that case the method is proved to be locally convergent to the true parameters the global convergence properties are also investigated it is pointed out that the method is not always globally convergent some sufficient conditions guaranteeing global convergence are given assuming convergence takes place the estimates are shown to be asymptotically gaussian distributed an explicit expression is given for their asymptotic covariance matrix

new adaptive iir filtering algorithms based on the steiglitz mcbride method this correspondence introduces a family of algorithms based on the steiglitz mcbride sm method for adaptive iir filtering the main feature of the proposed algorithms is to remove the parameter bias induced by colored measurement noise the conceptual similarities between the sm method and the equation error method are explored in order to analyze some properties of the new algorithms the main analysis results concern the consistency of the parameter estimates and local convergence a set of simulations in a system identification configuration is included in order to verify the improved performance of the new algorithms based on the sm method

ground state solutions for the electrostatic nonlinear klein gordon maxwell system abstract in this paper we study the nonlinear klein gordon equation coupled with the maxwell equation in the electrostatic case p u m 2 e 2 u f u in r 3 e e u 2 in r 3 where m e 0 benci and fortunato 2002 3 and d aprile and mugnai 2004 6 showed that for any u h 1 r 3 the second equation of problem p has a unique solution u d 1 2 r 3 the map u h 1 r 3 u d 1 2 r 3 is continuously differentiable and u e 0 furthermore we prove that max e u u u 0 where u u u 2 then we consider the ground state solution of problem p with f u u p 2 u 2 p 6

applications of a variable step size algorithm to qcee adaptive iir filters the quadratic constraint equation error qcee method was proposed by ho and chan see ibid vol 43 no 1 p 51 62 1995 to achieve bias removal for the equation error adaptive iir filters however this approach is limited to slow convergence in estimation when a small step size is used large step sizes lead to significant misadjustment this article presents a variable step size vss technique to greatly improve the qcee under its quadratic constraint to achieve both fast convergence and reduced misadjustment for adaptive iir filters

infinitely many solutions and least energy solutions for klein gordon maxwell systems with general superlinear nonlinearity abstract this paper is concerned with the following klein gordon maxwell system u v x u 2 u f x u x r 3 u 2 x r 3 where 0 is a constant v c r 3 r f c r 3 r r and f is superlinear at infinity using some weaker superlinear conditions instead of the common super cubic conditions on f we prove that the above system has 1 infinitely many solutions when v x is coercive and sign changing 2 a least energy solution when v x is positive periodic these results improve the related ones in the literature

stochastic mean square performance analysis of an adaptive hammerstein filter this paper presents an almost sure mean square performance analysis of an adaptive hammerstein filter for the case when the measurement noise in the desired response signal is a martingale difference sequence the system model consists of a series connection of a memoryless nonlinearity followed by a recursive linear filter a bound for the long term time average of the squared a posteriori estimation error of the adaptive filter is derived using a basic set of assumptions on the operating environment this bound consists of two terms one of which is proportional to a parameter that depends on the step size sequences of the algorithm and the other that is inversely proportional to the maximum value of the increment process associated with the coefficients of the underlying system one consequence of this result is that the long term time average of the squared a posteriori estimation error can be made arbitrarily close to its minimum possible value when the underlying system is time invariant

on a new adaptive lattice algorithm for recursive filters a new and simplified adaptive algorithm is presented for lattice structured recursive filters implementing the two multiplier form based on itakura and saito a comparison is also presented between the results obtained from this new algorithm and the algorithm introduced recently by parikh ahmed and stearns

very robust low complexity lattice filters in this paper a novel lattice filter structure is derived by combining the tapped numerator and injected numerator lattices y c lim on the synthesis of iir digital filters derived from single channel ar lattice network ieee trans acoust speech signal process vol assp 32 no 4 pp 741 749 august 1984 the injector coefficients are optimized for finite wordlength performance while the tapped coefficients synthesize the transfer function of the filters for an n th order digital filter the proposed tapped numerator and injected numerator hybrid lattice structure after optimization has only 2n 1 multipliers it is not only canonic in the number of multipliers but also possesses much improved finite wordlength properties such as very low parameter sensitivity and very uniform signal powers across signal nodes the excellent finite wordlength performance of the proposed structure is demonstrated with a design example and compared with those of traditional structures including several well known lattice structures

a new normalized relatively stable lattice structure this paper proposes a new lattice filter structure that has the following properties when the filter is linear time invariant lti it is equivalent to the celebrated gray markel lattice when the lattice parameters vary with time it sustains arbitrary rates of time variations without sacrificing a prescribed degree of stability provided that the lattice coefficients are magnitude bounded in a region where all lti lattices have the same degree of stability we also show that the resulting ltv lattice obeys an energy contraction condition this structure thus generalizes the normalized gray markel lattice which has similar properties but only with respect to stability as opposed to relative stability

positive ground state solutions for the critical klein gordon maxwell system with potentials abstract this paper deals with the klein gordon maxwell system when the nonlinearity exhibits critical growth we prove the existence of positive ground state solutions for this system when a periodic potential v is introduced the method combines the minimization of the corresponding euler lagrange functional on the nehari manifold with the brezis and nirenberg technique

fast rls type algorithm for unbiased equation error adaptive iir filtering based on approximate inverse power iteration in this paper a fast approximate inverse power aip iteration is applied to compute recursively the total least squares tls solution for unbiased equation error adaptive infinite impulse response iir filtering which is established by approximating the well known inverse power iteration with galerkin method the aip algorithm is based on an interesting modification of the inverse power iteration in which the first entry of the parameter vector is constrained to the negative one the distinctive feature of the proposed algorithm lies in its high computational efficiency which is characterized by efficient computation of the fast gain vector fgv adaptation of the interesting modification of the inverse power iteration and rank one update of the augmented correlation matrix the shift structure of the input data vector is exploited to develop a fast algorithm for computing the gain vector this fgv algorithm can be implemented at a numerical cost lower than the well known fast kalman algorithm since the first entry of the parameter vector has been fixed as the negative one and the weight vector is updated along the input data vector a very efficient aip algorithm is obtained by using the fgv algorithm the proposed aip algorithm is of computational complexity o l per iteration moreover with no need to use the well known matrix inversion lemma the aip algorithm has another attractive feature of numerical stability the proposed algorithm is shown to have global convergence simulation examples are included to demonstrate the effectiveness of the proposed aip algorithm

a new framework for convergence analysis and algorithm development of adaptive iir filters a parameterization of an adaptive infinite impulse response iir filter s poles is developed based on balanced realization theory from this we develop a local approximation of the actual adapted pole parameters in which convergence speed is related to a certain eigenvalue spread this in turn is shown to relate to the hankel singular values of the system to be identified as well as certain coefficient sensitivity functions of the adapted filter the local approximation is not restricted to stationary points at these points however it is equivalent to a hessian approximation with the benefit of decomposing the hessian matrix into terms related to the aforementioned singular values and sensitivity functions the description of the adaptation process by means of the developed approximation leads to a greater understanding of the effects on convergence speed of factors such as the hankel singular values of the system its order the distribution of its poles and the choice of adapted parameters in particular the use of direct form and lattice parameters are compared in detail based on these properties a new adaptive iir algorithm with faster convergence and relatively low computational complexity has recently been proposed which is briefly mentioned results also indicate a potential for variable gain algorithms

a local result on insensitizing controls for a semilinear heat equation with nonlinear boundary fourier conditions in this paper we present a local result on the existence of insensitizing controls for a semilinear heat equation when nonlinear boundary conditions of the form partial n y f y 0 are considered the problem leads to an analysis of a special type of nonlinear null controllability problem a sharp study of the linear case and a later application of an appropriate fixed point argument constitute the scheme of the proof of the main result the boundary conditions we are dealing with lead us to seek a fixed point and thus also control functions in certain holder spaces the main strategy in this paper is the construction of controls with holderian regularity starting from l2 controls in the linear case sufficient regularity in the data and appropriate assumptions on the right hand side term xi of the equation are required

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

simplified gradient calculation in adaptive iir lattice filters a simplified algorithm is presented for computing the gradient in adaptive iir infinite impulse response lattice filters for a filter with n zeros and n poles this algorithm requires only order n computations several computer simulations were performed to compare the performance of the proposed o n formulation and the conventional o n sup 2 formulation and no difference in their behavior was found in these simulations the full hessian and the diagonal hessian adaptive algorithms were used in a system identification configuration it is concluded that the proposed method allows the development of robust adaptive iir algorithms with a cost proportional to the filter order

an algorithm for efficient unbiased equation error infinite impulse response adaptive filtering an algorithm for efficiently adjusting the coefficients of equation error infinite impulse response iir adaptive filters is described unlike the recursive least squares rls algorithm the proposed algorithm yields unbiased filter coefficients simulations involving the identification of unknown pole zero systems demonstrate the algorithm s improved performance over the equation error rls algorithm

adaptive laguerre lattice filters adaptive laguerre based filters provide an attractive alternative to adaptive fir filters in the sense that they require fewer parameters to model a linear time invariant system with a long impulse response we present an adaptive laguerre lattice structure that combines the desirable features of the laguerre structure i e guaranteed stability unique global minimum and small number of parameters m for a prescribed level of modeling error with the numerical robustness and low computational complexity of adaptive fir lattice structures the proposed configuration is based on an extension to the iir case of the fir lattice filter it is a cascade of identical sections but with a single pole all pass filter replacing the delay element used in the conventional fir lattice filter we utilize this structure to obtain computationally efficient adaptive algorithms o m computations per time instant our adaptive laguerre lattice filter is an extension of the gradient adaptive lattice gal technique and it demonstrates the same desirable properties namely 1 excellent steady state behavior 2 relatively fast initial convergence comparable with that of an rls algorithm for laguerre structure and good numerical stability simulation results indicate that for systems with poles close to the unit circle where an adaptive fir model of very high order would be required to meet a prescribed modeling error an adaptive laguerre lattice model of relatively low order achieves the prescribed bound after just a few updates of the recursions in the adaptive algorithm

adaptive lattice iir filtering revisited convergence issues and new algorithms with improved stability properties several algorithms for adaptive iir filters parameterized in lattice form can be found in the literature the salient feature of these structures when compared with the direct form is that ensuring stability is extremely easy on the other hand while computing the gradient signals that drive the direct form update algorithms is straightforward it is not so for the lattice algorithms this has led to simplified lattice algorithms using gradient approximations although in general these simplified schemes present the same stationary points as the original algorithms whether this is also true for convergent points has remained an open problem this also applies to nongradient based lattice algorithms such as hyperstability based and the steiglitz mcbride algorithms here we answer this question in the negative by showing that for several adaptive lattice algorithms there exist settings in which the stationary point corresponding to identification of the unknown system is not convergent in addition new lattice algorithms with properties are derived they are based on the cascade lattice structure which allows the derivation of sufficient conditions for local stability

an asymptotically periodic and asymptotically linear schrodinger equation with indefinite linear part abstract we consider the semilinear schrodinger equation u v x u f x u x r n u h 1 r n where v x is asymptotically periodic and sign changing f x u is asymptotically periodic in x and asymptotically linear as u under some weak assumptions on v and f we prove that the above problem has a nontrivial solution

bias removal in equation error adaptive iir filters in the equation error formulation of adaptive iir filters the estimated parameters contain bias when there is noise in the desired response a method that can eliminate this bias is investigated the idea is to maintain a quadratic constraint on the feedback coefficients so that the noise contributes only a constant term to the mean square error this term does not affect minimization and thus the bias is eliminated a quadratically constrained stochastic gradient search method is applied for optimization and convergence behavior when the noise is white is analyzed adaptation of the feedback fir filter in second order cascade form useful for stability monitoring is also considered when the noise is nonwhite the technique requires an adaptive whitening filter simulation results are included to demonstrate the bias removal capability of the method corroborate the theoretical developments and compare with existing techniques

exact controllability for multidimensional semilinear hyperbolic equations in this paper we obtain a global exact controllability result for a class of multidimensional semilinear hyperbolic equations with a superlinear nonlinearity and variable coefficients for this purpose we establish an observability estimate for the linear hyperbolic equation with an unbounded potential in which the crucial observability constant is estimated explicitly by a function of the norm of the potential such an estimate is obtained by a combination of a pointwise estimate and a global carleman estimate for the hyperbolic differential operators and analysis on the regularity of the optimal solution to an auxiliary optimal control problem

brief paper some properties of the output error method the output error identification method is studied in various respects the stationary points of the associated loss function are investigated sufficient conditions for a unique local minimum are given the loss functions can be minimized using a quasilinearization algorithm such an algorithm will give good local convergence it is however shown that global convergence does not always occur the output error method is also compared with some other estimation methods from the accuracy point of view it is proved that a prediction error method will give better accuracy an instrumental variable technique may give better or worse accuracy depending on the actual noise correlation

ground state solutions for generalized quasilinear schrodinger equations with variable potentials and berestycki lions nonlinearities by introducing some new tricks we prove that the following generalized quasilinear schrodinger equation div g2 u u g u g u u 2 v x u f u x rn admits two classes of ground state solutions under the general berestycki lions assumptions on the nonlinearity f which are almost necessary conditions as well as some weak assumptions on the potential v moreover we also give a minimax characterization of the ground state energy our results improve and complement the previous ones in the literature by introducing some new tricks we prove that the following generalized quasilinear schrodinger equation div g2 u u g u g u u 2 v x u f u x rn admits two classes of ground state solutions under the general berestycki lions assumptions on the nonlinearity f which are almost necessary conditions as well as some weak assumptions on the potential v moreover we also give a minimax characterization of the ground state energy our results improve and complement the previous ones in the literature

tracking characteristics of the constrained iir adaptive notch filter the tracking behavior of a constrained iir notch filter the coefficients of which are estimated using a constant step size gauss newton algorithm is studied using weak convergence theory and the concept of prescaling it is shown that the mean behavior of the adaptive filter coefficients can be studied by using an ordinary differential equation ode approximate and simple closed form results are derived for the tracking behavior of a second order notch filter computer simulations are presented to substantiate the analysis

insensitizing controls for a class of quasilinear parabolic equations abstract this paper is addressed to showing the existence of insensitizing controls for a class of quasilinear parabolic equations with homogeneous dirichlet boundary conditions as usual this insensitizing problem is reduced to a nonstandard null controllability problem of some nonlinear cascade system governed by a quasilinear parabolic equation and a linear parabolic equation nevertheless in order to solve the later quasilinear controllability problem by the fixed point technique we need to establish the null controllability of the linearized cascade parabolic system in the framework of classical solutions the key point is to find the desired control function in a holder space for given data with certain regularities

solutions of superlinear elliptic equations and their morse indices we consider here solutions of semilinear second order elliptic equations with superlinear nonlinearities and we present some relationships between their morse indices and some qualitative properties in particular we show that for uo subcritical nonlinearities bounds on solutions are equivalent to bounds on their morse indices

application of benveniste s convergence results in the study of adaptive iir filtering algorithms it is shown that the weak convergence results of a benveniste et al ieee trans automat contr vol ac 25 p 1042 58 dec 1980 can be used to prove convergence of some adaptive infinite impulse response iir filtering algorithms the association of the algorithms with some ordinary differential equations for constant gains which parallels the theory of l ljung et al 1983 is suitable for constant gain adaptive filtering applications convergence proofs for a prefiltering algorithm for a simple constant gain version of the recursive maximum likelihood algorithm and for the well known simple hyperstable adaptive recursive filter sharf algorithm are given as examples

explicit observability estimate for the wave equation with potential and its application by means of the carleman type estimate we obtain an explicit observability estimate for the wave equation with a potential as its application we get the exact internal controllability of the semilinear wave equations in any space dimensions

insensitizing controls for the parabolic equations with dynamic boundary conditions abstract this paper concerns with the insensitizing controllability property of the semilinear parabolic equation with dynamic boundary conditions this problem can be reduced to a relaxed controllability problem for a coupled parabolic system with dynamic boundary conditions an observability estimate for the corresponding coupled system with this type of boundary conditions is established whose proof relies on a new global carleman estimate

sufficient stability bounds for slowly varying direct form recursive linear filters and their applications in adaptive iir filters this article derives a sufficient time varying bound on the maximum variation of the coefficients of an exponentially stable time varying direct form homogeneous linear recursive filter the stability bound is less conservative than all previously derived bounds for time varying iir systems the bound is then applied to control the step size of output error adaptive iir filters to achieve bounded input bounded output bibo stability of the adaptive filter experimental results that demonstrate the good stability characteristics of the resulting algorithms are included this article also contains comparisons with other competing output error adaptive iir filters the results indicate that the stabilized method possesses better convergence behavior than other competing techniques

bias remedy least mean square equation error algorithm for iir parameter recursive estimation in the area of infinite impulse response iir system identification and adaptive filtering the equation error algorithms used for recursive estimation of the plant parameters are well known for their good convergence properties however these algorithms give biased parameter estimates in the presence of measurement noise a new algorithm is proposed on the basis of the least mean square equation error lmsee algorithm which manages to remedy the bias while retaining the parameter stability the so called bias remedy least mean square equation error brle algorithm has a simple form the compatibility of the concept of bias remedy with the stability requirement for the convergence procedure is supported by a practically meaningful theorem the behavior of the brle has been examined extensively in a series of computer simulations

asymptotically linear schrodinger equation with potential vanishing at infinity we are concerned with the existence of bound states and ground states of the following nonlinear schrodinger equation

null controllability for forward and backward stochastic parabolic equations this paper is concerned with the null controllability for general forward and backward linear stochastic parabolic equations to develop the duality argument we establish observability estimates for linear backward and forward stochastic parabolic equations with general coefficients by means of a global carleman estimate our carleman inequality theorem 6 1 and observability estimate theorem 2 3 for backward stochastic parabolic equations are new in their forms by adding a control variable to act on the white noise we give a partial solution to the null controllability of forward stochastic heat equations which was regarded as a challenging topic see pages 99 and 108 110 in barbu rascanu and tessitore appl math optim 47 2003 pp 97 120

ground state sign changing solutions for kirchhoff type problems in bounded domains abstract in the present paper we consider the existence of ground state sign changing solutions for a class of kirchhoff type problems 0 1 a b u 2 d x u f u x u 0 x where r n is a bounded domain with a smooth boundary n 1 2 3 a 0 b 0 and f c r r under some weak assumptions on f with the aid of some new analytical skills and non nehari manifold method we prove that 0 1 possesses one ground state sign changing solution u b and its energy is strictly larger than twice that of the ground state solutions of nehari type furthermore we establish the convergence property of u b as the parameter b 0 our results improve and generalize some results obtained by w shuai 2015 34

cascade lattice iir adaptive filters the feedback lattice filter forms including the two multiplier form and the normalized form are examined with respect to their relationships to the feedback direct form filter specifically the transformation matrix between the lattice forms and the direct form is derived parameter and state relationships between the lattice forms and the direct form are therefore obtained an iir filter structure the cascade lattice iir structure is constructed based on this structure three iir adaptive filtering algorithms in the two multiplier form can then be developed following the gradient approach the steiglitz mcbride approach and the hyperstability approach convergence of these algorithms is theoretically analyzed using either the ode approach or the hyperstability theorem these algorithms are then simplified into forms computationally as efficient as their corresponding direct form algorithms relationships of the simplified algorithms to the direct form algorithms are also studied which disclose a consistency in algorithm structure regardless of the filter form three normalized lattice algorithms can also be derived from the two multiplier lattice algorithms experimental results show much improved performance of the normalized lattice algorithms over the two multiplier lattice algorithms and the direct form algorithms

a variable step vs adaptive filter algorithm in recent work a new version of an lms algorithm has been developed which implements a variable feedback constant for each weight of an adaptive transversal filter this technique has been called the vs variable step algorithm and is an extension of earlier ideas in stochastic approximation for varying the step size in the method of steepest descents the method may be implemented in hardware with only modest increases in complexity approx 15 percent over the lms widrow hoff algorithm it is shown that an upper bound for the convergence time is the classical mean square error time constant and examples are given to demonstrate that for broad signal classes both narrow band and broad band the convergence time is reduced by a factor of up to 50 in noise canceller applications for the proper selection of variable step parameters finally the vs algorithm is applied to an iir filter and simulations are presented for applications of the vs fir and iir adaptive filters

insensitizing controls for a forward stochastic heat equation abstract the existence of insensitizing controls for a forward stochastic heat equation is considered to develop the duality we obtain observability estimates for linear forward and backward coupled stochastic heat equations with general coefficients by means of some global carleman estimates furthermore the constant in the observability inequality is estimated by an explicit function of the norm of the involved coefficients in the equation as far as we know our paper is the first one to address the problem of insensitizing controls for stochastic partial differential equations

a structural view of asymptotic convergence speed of adaptive iir filtering algorithms i infinite precision implementation for pt i see ibid vol 41 no 4 p 1493 1517 1993 finite precision fp implementation is the ultimately inevitable reality of all adaptive filters including adaptive infinite impulse response iir filters this paper continues to examine the asymptotic convergence speed of adaptive iir filters of various structures and algorithms including the simple constant gain type and the newton type but under fp implementation a stochastic differential equation sde approach is used in the analysis such an approach not only greatly simplifies the fp analysis which is traditionally very involved algebraically but it also provides valuable information about the first order as well as the second order moments that the latter are not available using the ordinary differential equation ode approach the asymptotic convergence speed as well as the convergent values of the pertinent moments of fp errors are examined in terms of unknown system pole zero locations the adverse effects of lightly damped low frequency ldlf poles resulting from fast sampling on the local transient and convergent behavior of various structures and algorithms are analyzed and compared the new results agree with the existing ones when reduced to the finite impulse response fir case in particular the explosive behavior of pertinent error variances of newton type iir algorithms when the forgetting factor spl lambda 1 is also concluded computer simulation verifies the predicted theoretical results

a stable and efficient adaptive notch filter for direct frequency estimation we investigate the problem of direct frequency estimation a new adaptive algorithm is developed for constrained pole zero notch filters the basic characteristic of this algorithm is that the notch filter is cascaded and hence purely parametrized by the notching frequencies this makes the algorithm much simpler and hence more efficient and more robust such that the poles and zeros are automatically located on the respective constrained circle no matter if the algorithm is implemented with infinite or finite precision the algorithm is analyzed and compared with some existing algorithms several numerical examples are given as well as the corresponding simulations

a structural view of stability in adaptive iir filters this correspondence deals with the stability issue in adaptive iir filters from a structural view a new condition under which the bounded input bounded output bibo stability of the filters can be ensured is derived based on this result a normal state space realization for second order iir filters is proposed it is shown that the adaptive iir filter realized with such a structure is bibo stable no matter it is implemented with infinite or finite precision this property is very important for real time applications though both the proposed and the normalized lattice based structures are bibo stable the former is simpler and has minimal pole sensitivities two adaptive iir filter structures are developed based on a cascade form of second order filters the first structure is fit for the filters whose poles are all complex and the second one is for the constrained notch filters simulations are given to demonstrate the performance of the proposed structures

existence of multiple solutions of kirchhoff type equation with sign changing potential abstract in this paper we study the existence of infinitely many nontrivial solutions for a class of nonlinear schrodinger kirchhoff type equation a b r n u 2 dx u v x u f x u in r n u x 0 as x where constants a 0 b 0 and the potential v x is allowed to be sign changing under general superlinear assumption on nonlinearity f x u we establish the existence of infinitely many solutions via variational methods which unifies and improves the recent results of wu 2011 9

null controllability of a class of newtonian filtration equations abstract in this paper we study the null controllability of a class of newtonian filtration equations using the properties of finite extinction time and finite speed of propagation we construct a control function in feedback form such that system is exactly null controllable at any time t 0 if we put a nonnegative constraint on the control function this system is not exactly null controllable any more but approximately null controllable for a long time

the poles and zeros of a linear time varying system abstract for linear time varying discrete time and continuous time systems a notion of poles and zeros is developed in terms of factorizations of operator polynomials with time varying coefficients in the discrete time case it is shown that the poles can be computed by solving a nonlinear recursion with time varying coefficients in the continuous time case the poles can be calculated by solving a nonlinear differential equation with time varying coefficients the theory is applied to the study of the zero input response and asymptotic stability it is shown that if a time varying analogue of the vandermonde matrix is invertible the zero input response can be decomposed into a sum of modes associated with the poles stability is then studied in terms of the components of the modal decomposition

persistence of excitation conditions and the convergence of adaptive schemes in the study of the behavior of adaptive filtering algorithms persistence of excitation of the input process arises as a sufficient condition for convergence and perhaps more importantly for convergence rate of the parameter estimates in this paper the underlying nature of the persistence requirement is presented and discussed relating its normal specification in terms of moment conditions with covariance decays etc to sample path properties deterministic and stochastic persistence conditions and persistence measures are treated as well as persistence conditions for output error equation error and adaptive control schemes

some results on the controllability of coupled semilinear wave equations the desensitizing control case first we consider a semilinear hyperbolic equation with partially known initial data in a bounded domain for this system we construct a locally distributed control that desensitizes a certain norm of the state this result is new and the method for proving it combines a judicious application of the carleman estimate and a localization technique then we discuss possible extensions of our result finally we apply our method to the exact controllability of two hyperbolic equations one semilinear and the other one linear coupled in cascade through the boundary the control acting in one equation only

acoustic echo cancellation do iir models offer better modeling capabilities than their fir counterparts the adequateness of iir models for acoustic echo cancellation is a long standing question and the answers found in the literature are conflicting we use the results from rational hankel norm and least squares approximation and we recall a test that provides a priori performance levels for fir and iir models we apply this test to the measured acoustic impulse responses upon comparing the performance levels of fir and iir models with the same number of free parameters we do not observe any significant gain from the use of iir models we attribute this phenomenon to the shape of the energy spectra of the acoustic impulse responses so tested which possess many strong and sharp peaks faithful modeling of these peaks requires many parameters irrespective of the type of the model

berestycki lions conditions on ground state solutions for kirchhoff type problems with variable potentials based on the strategy introduced by chen and tang adv nonlinear anal 9 496 515 2020 and some new tricks we prove that the nonlinear problem of kirchhoff type a b r3 u 2dx u v x u f u x r3 in h1 r3 admits two classes of ground state solutions under the general berestycki lions assumptions on the nonlinearity f which are almost necessary conditions as well as some weak assumptions on the potential v moreover we also give a simple minimax characterization of the ground state energy our results improve and extend recent theorems in several directions

efficient lattice realizations of adaptive iir algorithms computationally efficient adaptive iir filter algorithms are presented based on lattice realizations allowing the adaptive filter stability to be easily monitored new simplified recursive in order equations relating the parameters of the direct form realization with the ones of two lattice realizations are presented these equations lead to a simplified technique to compute the regressor vector and to a general method to implement any adaptive iir algorithm using lattice realization results indicate that the proposed lattice based algorithms converge to a set of parameters that realize the same transfer function as the corresponding direct form algorithms

steep potential well may help kirchhoff type equations to generate multiple solutions abstract in this paper we consider a nonlinear kirchhoff type problem with steep potential well a r 3 u 2 d x b u v x u f x u p 2 u in r 3 u h 1 r 3 where a b 0 2 p 4 v c r 3 r and f l r 3 r such problem cannot be studied by applying variational methods in a standard way even by restricting its corresponding energy functional on the nehari manifold because palais smale sequences may not be bounded in this paper we introduce a novel constraint method to prove the existence of one and two positive solutions under the different assumptions on v respectively we conclude that steep potential well v may help kirchhoff type equations to generate multiple solutions which has never been involved before

on critical klein gordon maxwell systems with super linear nonlinearities abstract this paper is concerned with two classes of critical klein gordon maxwell systems as follows u v x u 2 u f u u 5 x r 3 u 2 x r 3 and e 2 u v x u 2 u g x u k x u 5 x r 3 u 2 x r 3 where 0 e 0 v k c r 3 r f c r r and g c r 3 r r are super linear at infinity instead of the expression sufficiently large in the existing works we give a certain range 0 under which the first system admits a ground state solution when v is positive and periodic under some mild conditions on v k and g we show that the second system has at least one nontrivial solution provided e 0 e 0 where the bound e 0 0 is expressed explicitly in terms of v k and g

an unbiased equation error identifier and reduced order approximations the equation error ee identification technique is modified to remove the parameter bias problem induced by uncorrelated measurement errors the modification replaces a monic constraint with a unit norm constraint the asymptotic solution replaces a normal equation with an eigenequation the resulting algorithm is simpler than previous schemes while at the same time preserving the desirable properties of the conventional ee method simplicity of an on line algorithm unimodality of the performance surface and consistent identification in the sufficient order case in the more realistic undermodeled case a robustness result shows that the mean optimal parameter values of both the monic and unit norm ee schemes correspond to a stable transfer function for all degrees of undermodeling and for all stationary output disturbances provided the input sequence satisfies an autoregressive constraint otherwise an unstable model may result model approximation properties for the undermodeled case are exposed in detail for the case of autoregressive inputs although both the monic and unit norm variants provide pade approximation properties the unit norm version is capable of autocorrelation matching properties as as well and yields the optimal solution to a first and second order interpolation problem finally the mismodeling error for the undermodeled case is shown to be a well behaved function of the hankel singular values of the unknown system this modification allows ee methods to be admitted to the class of unbiased identification and approximation techniques

a matrix factorization based structure for digital filters in this correspondence a novel digital filter structure is derived using matrix factorization this structure called the lcw structure is an improved version of the so called lgs structure proposed by li gevers and sun ldquoperformance analysis of a new structure for digital filter implementation rdquo ieee transactions on circuits and systems i vol 47 no 4 pp 474 482 april 2000 for a digital filter of order this new structure requires 4n 1 multiplications and 4n 1 additions for computing one filter output sample instead of 7n 3 and 6n 3 respectively which are needed for the lgs structure an expression of the roundoff noise gain is derived for the lcw structure design examples are presented to demonstrate the behavior of this structure and to compare with several well known digital filter structures in terms of minimizing roundoff noise and implementation efficiency

solutions in spectral gaps for a nonlinear equation of schrodinger type abstract in this paper we study the existence of a nontrivial h2 r n solution for an equation of the form u x p x u x f x u x u x x r n r where p l r n is a periodic function we assume that the operator p h2 r n l2 r n l2 r n is strongly indefinite and invertible and that x r r is odd and satisfies some superlinear but subcritical growth conditions we extend the class of nonlinearities which has been studied up to now in particular under standard technical restrictions the existence of a solution is derived when lim x f x s f s 0 exists for all s r if we assume that f x s f s for all s r and a e on r n

some results on connecting orbits for a class of hamiltonian systems abstract the existence of various kinds of connecting orbits is established for a certain hamiltonian system as well as its time dependent analogue for the autonomous case our main assumption is that v has a global maximum e g at x o and we find a various kinds of orbits terminating at o for the time dependent case v has a local but not global maximum at x o and we find a homoclinic orbit emanating from and terminating at o keywords periodic solution

infinitely many solutions for a nonlinear klein gordon maxwell system abstract in this paper a nonlinear klein gordon maxwell system with solitary wave solution is considered using critical point theory we establish sufficient conditions for the existence of infinitely many solitary wave solutions results obtained complement and improve the existing ones

carleman estimates for stratified media abstract we consider anisotropic elliptic and parabolic operators in a bounded stratified media in r n characterized by discontinuities of the coefficients in one direction the surfaces of discontinuities cross the boundary of the domain we prove carleman estimates for these operators with an arbitrary observation region

existence of multiple solutions for modified schrdingerkirchhoffpoisson type systems via perturbation method with sign changing potential in this paper we prove the existence of positive solutions and negative solutions for the following modified schrdingerkirchhoffpoisson type systems a br3u2 u v x u u12u u2 f x u inr3 u2 inr3 where a 0 b0 v and f are continuous functions and v x is allowed to be sign changing under some certain assumptions on v and f we prove the existence of nontrivial nonnegative solutions nontrivial nonpositive solutions and sequence of high energy solutions via the perturbation method

an algorithm for unit norm equation error system identification based on the method of multipliers it is known that the unit norm constraint for equation error based system identification is superior to the monic constraint since it produces consistent estimates for white measurement noise and also presents better approximation properties in reduced order cases here a new algorithm for unit norm equation error adaptive filtering is proposed this scheme is inspired by the constrained optimization technique known as the method of multipliers an analysis of stationary points and mean convergence properties is developed

bifurcation in lp rn for a semilinear elliptic equation keywords lsp p bifurcation constrained minimization sobolev spaces nonlinear eigenvalue problem semilinear spectrum linearisation variational structure reference ana article 1988 001doi 10 1112 plms s3 57 3 511 record created on 2008 12 10 modified on 2016 08 08

existence and non existence of solitary waves for the critical klein gordon equation coupled with maxwell s equations abstract in this paper we investigate existence and non existence of solutions for a nonlinear elliptic system arising from the coupling of the nonlinear klein gordon equation with the maxwell equations when the nonlinearity exhibits critical growth we prove a non existence result by a poho aev type argument and then adding a suitable perturbation we recover existence of at least a radially symmetric solution we overcome the lack of compactness relying on the brezis nirenberg method

nonstationary homoclinic orbits for an infinite dimensional hamiltonian system we study the following system of diffusion equations on r rn tu xu v x u g t x v tv xv v x v f t x u where z u v r rn r2 v c rn r g t x v f t x u are periodic in t x and superlinear at infinity by a variant linking theorem and concentration compactness arguments we establish the existence of nonstationary homoclinic type solutions of least energy for this systems

adaptive algorithms for joint time delay estimation and iir filtering a new class of gradient based algorithms for joint adaptive time delay estimation and iir filtering for the recursive identification of systems with long pure delays is introduced the algorithms update an adaptive delay estimate and the coefficients of an iir filter using familiar gradient descent methods in addition interpolation of the input sequence is used to obtain delays that are not constrained to integer numbers of samples three algorithms using a direct form filter parametrization and one using a normalized lattice filter are derived and computer simulations are used to demonstrate their convergence and tracking properties

infinitely many standing wave solutions for the nonlinear klein gordon maxwell system with sign changing potential in this paper we study the infinitely many solutions for the nonlinear klein gordon maxwell system email protected v x u email protected email protected fu f x u email protected r 3 email protected email protected u 2 email protected r 3 where w 0 is a constant u f r 3 r the potential v x is allowed to be sign changing and the primitive of the nonlinearity f is of super linear growth near infinity our super linear conditions are weaker than the usual super linear conditions

a homotopy approach to improving pem identification of armax models homotopy methods are applied to the non convex optimization problem that arises in prediction error estimation using armax model structures a concrete algorithm is proposed and its performance is studied by monte carlo simulation

lattice form adaptive infinite impulse response filtering algorithm for active noise control in some situations of active noise control infinite impulse response iir filters are more suitable than finite impulse response fir filters owing to the poles in the transfer function a number of algorithms have been derived for applying iir filters in active noise control however most of them use the direct form iir filter structure which faces the difficulties of checking stability and relatively slow convergence speed for noise composed of narrow band components with large power disparity to overcome these difficulties along with using the direct form iir filters a new adaptive algorithm is proposed in this paper which uses and updates the lattice form adaptive iir filter in an active noise control system full mathematical derivations of the proposed algorithm are presented and the comparison between the proposed algorithm and the commonly used filtered u lms and filtered v lms algorithms shows the superiority of the proposed algorithm

ground state solutions of schrodinger poisson systems with variable potential and convolution nonlinearity abstract in the present paper we consider the following nonlinear schrodinger poisson system with convolution nonlinearity u v x u u i f u f u x r 3 u 2 x r 3 where 0 3 i r 3 r is the riesz potential v c r 3 0 f c r r and f t 0 t f s d s satisfies lim t f t t with min 2 6 4 by using some new analytic techniques and new inequalities we prove the above system admits a ground state solution under mild assumptions on v and f in particular our results cover and improve the existing ones for the schrodinger poisson system which can be considered as the limited problem when 0

stable and efficient lattice algorithms for adaptive iir filtering previous attempts at applying lattice structures to adaptive infinite impulse response iir filtering have met with gradient computations of o n sup 2 complexity to overcome this computational burden two new lattice based algorithms are proposed for adaptive iir filtering and system identification with both algorithms of o n complexity the first algorithm is a reinterpretation of the steiglitz mcbride method 1965 while the second is a variation on the output error method state space models are employed to make the derivations transparent and the methods can be extended to other parameterizations if desired the set of possible stationary points of the algorithms is shown to be consistent with the convergent points obtained from the direct form versions of the steiglitz mcbride and output error methods whose properties are well studied the derived algorithms are as computationally efficient as existing direct form based algorithms while overcoming the stability problems associated with time varying direct form filters

rational subspace estimation using adaptive lossless filters rational models have been studied as a tractable attempt to account for frequency dependencies using a finite parameter description in this context the following problem is addressed given time domain measurements estimate rational orthonormal spanning vectors for the signal and noise subspaces it is shown that the problem can be rephrased as adapting a lossless transfer matrix so as to maximize the power split between two sets of output bins an efficient and numerically robust adaptive filtering algorithm is derived for lossless multivariable lattice filters and the system can be programmed in real time using cordic processors the adaptive filter equations are consistent with the proper subspace identification if the subspace filter satisfies a sufficient order condition in under modeled scenarios the stable stationary points are characterized by a minimized rayleigh quotient which leads to good subspace fits the proposed adaptive filter makes real time rational subspace estimation an accessible alternative to computationally expensive offline techniques

compactness results for schrodinger equations with asymptotically linear terms abstract we study the nonlinear problem u v x f x u x r n lim x u x 0 where the schrodinger operator v is semibounded and the nonlinearity f is linearly bounded we establish compactness of palais smale sequences and cerami sequences for the associated energy functional under general spectral theoretic assumptions applying these results we obtain existence of three nontrivial solutions if the energy functional has a mountain pass geometry

some results on the controllability of forward stochastic heat equations with control on the drift abstract in this paper we establish the null approximate controllability for forward stochastic heat equations with control on the drift the null controllability is obtained by a time iteration method and an observability estimate on partial sums of eigenfunctions for elliptic operators as a consequence of the null controllability we obtain the observability estimate for backward stochastic heat equations which leads to a unique continuation property for backward stochastic heat equations and hence the desired approximate controllability for forward stochastic heat equations it deserves to point out that one needs to introduce a little stronger assumption on the controller for the approximate controllability of forward stochastic heat equations than that for the null controllability this is a new phenomenon arising in the study of the controllability problem for stochastic heat equations

desensitizing controls for semilinear wave equations abstract the desensitizing control problems for semilinear wave equations are studied when the nonlinearity f satisfies lim s f s s ln 2 s lim s f s ln 2 s 0 we obtain the existence of a control which desensitizes the boundary observation the proof is based on the combination of fixed point arguments and explicit observability estimates for the linearized wave equation with a potential that depends on both x and t the work solves the problem proposed by tebou 2011 in the one dimensional setting for the interior observation we assume that the nonlinearity is globally lipschitz under which the existence of e desensitizing controls is proved our proof is based on the fixed point arguments and the unique continuation property