an invariant observer for a chemostat model in this paper we tackle the problem of designing an invariant observer for a chemostat model with adjustable and robust convergence the main idea of the paper is to build a new class of observers for chemostat model using hidden symmetries the effectiveness of the proposed observer is shown through simulations

quadratic weighted median filters for edge enhancement of noisy images quadratic volterra filters are effective in image sharpening applications the linear combination of polynomial terms however yields poor performance in noisy environments weighted median wm filters in contrast are well known for their outlier suppression and detail preservation properties the wm sample selection methodology is naturally extended to the quadratic sample case yielding a filter structure referred to as quadratic weighted median qwm that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers arising in the higher order statistics of environment noise through statistical analysis of higher order samples it is shown that although the parent gaussian distribution is light tailed the higher order terms exhibit heavy tailed distributions the optimal combination of terms contributing to a quadratic system i e cross and square is approached from a maximum likelihood perspective which yields the wm processing of these terms the proposed qwm filter structure is analyzed through determination of the output variance and breakdown probability the studies show that the qwm exhibits lower variance and breakdown probability indicating the robustness of the proposed structure the performance of the qwm filter is tested on constant regions edges and real images and compared to its weighted sum dual the quadratic volterra filter the simulation results show that the proposed method simultaneously suppresses the noise and enhances image details compared with the quadratic volterra sharpener the qwm filter exhibits superior qualitative and quantitative performance in noisy image sharpening

alpha trimmed means and their relationship to median filters suppose that x is a finite set of n numbers the trimmed mean of x is obtained by sorting x into ascending order removing trimming a fixed fraction alpha 0 leq alpha leq 0 5 from the high and low ends of the sorted set and computing the average of the remaining values when applied to a sliding window of length lw the trimming process is called trim filtering for 0 5 the trimmed mean of a set is the median of the set and the filtering operation is called median filtering repeated application of a median filter to the output of a previous median filter of the same length lw eventually produces a signal which is invariant to median filtering this final signal is called the root signal this paper explains the relationship between trimmed means and median filters derives a simple straightforward and fast algorithm for applying a median filter and provides a new explanation of the convergence of repeated median filtering to the root signal the latter result incorporates an approach which permits generalization of the associated concepts to a larger class of index map filters

removal of high density salt and pepper noise in images with an iterative adaptive fuzzy filter using alpha trimmed mean suppression of impulse noise in images is an important problem in image processing in this paper we propose a novel adaptive iterative fuzzy filter for denoising images corrupted by impulse noise it operates in two stages detection of noisy pixels with an adaptive fuzzy detector followed by denoising using a weighted mean filter on the good pixels in the filter window experimental results demonstrate the algorithm to be superior to state of the art filters the filter is also shown to be robust to very high levels of noise retrieving meaningful detail at noise levels as high as 97

global existence and uniform decay for wave equation with dissipative term and boundary damping in this paper we prove the existence uniqueness and uniform stability of strong and weak solutions of the nonlinear wave equation u t email protected b x u t f u 0 in bounded domains with nonlinear damped boundary conditions given by email protected email protected g u t 0 with restrictions on function f u g u t and b x we prove the existence by means of the glerkin method and obtain the asymptotic behavior by using of the multiplier technique from the idea of kmornik and zuazua see 7

generalized mean median filtering for robust frequency selective applications huber proposed the pepsi family of epsi contaminated normal distributions to model environments characterized by heavy tailed distributions based on this two component mixture distribution mean median mem filters were proposed the mem filter output is a combination of the sample mean and the sample median where observation samples are weighted uniformly this property of mem filters constrains them to the class of smoothers lacking frequency selective filtering capabilities this paper extends mem filtering to the weighted sum median wsm filtering structure admitting real valued weights thereby enabling more general filtering characteristics i e bandpass and high pass filtering the proposed filter structure is also well motivated from a presented maximum likelihood ml estimate analysis under epsi contaminated statistics the ml analysis demonstrates the need for a combination of weighted sum ws and weighted median wm type filters for processing of signals corrupted by epsi contaminated noise the wsm filter is statistically analyzed through the determination of filter output variance and breakdown probability the combination parameter alpha is optimized to minimize the filter output variance which is a measure of noise attenuation capability moreover filter design procedures that yield a desired spectral response are detailed finally the proposed wsm filter structure is tested utilizing signal processing applications including low pass bandpass and high pass filtering and image processing applications including image sharpening and denoising evaluating and comparing the wsm filter performance to that of the ws wm and mem filters

adaptive alpha trimmed mean filters under deviations from assumed noise model alpha trimmed mean filters are widely used for the restoration of signals and images corrupted by additive non gaussian noise they are especially preferred if the underlying noise deviates from gaussian with the impulsive noise components the key design issue of these filters is to select its only parameter spl alpha optimally for a given noise type in image restoration adaptive filters utilize the flexibility of selecting spl alpha according to some local noise statistics in the present paper we first review the existing adaptive alpha trimmed mean filter schemes we then analyze the performance of these filters when the underlying noise distribution deviates from the gaussian and does not satisfy the assumptions such as symmetry specifically the clipping effect and the mixed noise cases are analyzed we also present a new adaptive alpha trimmed filter implementation that detects the nonsymmetry points locally and applies alpha trimmed mean filter that trims out the outlier pixels such as edges or impulsive noise according to this local decision comparisons of the speed and filtering performances under deviations from symmetry and gaussian assumptions show that the proposed filter is a very good alternative to the existing schemes

adaptive trimmed mean filters for image restoration an adaptive smoothing filter is proposed for reducing noise in digital signals of any dimensionality the adaptive procedure is based on the selection of an appropriate inner or outer trimmed mean filter according to local measurements of the tail behavior impulsivity of the noise process the set of trimmed means used provides robustness against a wide range of noise possibilities ranging from very shallow tailed to very heavy tailed a monte carlo analysis using a family of generalized exponential distributions supports the choice of the trimmed mean selected for measured values of an impulsivity statistic the assumption underlying the definition of the filter is that the signal to be filtered is locally smoothly varying and that the noise process is uncorrelated and derives from an unknown unimodal symmetric distribution for image processing applications a second statistic is used to mark the location of abrupt intensity changes or edges in the vicinity of an edge the trend preserving median filter is used since the impulsivity and edge statistics used in defining the adaptive filter are both functions of order statistics the extra computation required for their calculation is minimal examples are provided of the filter as applied to images corrupted by a variety of noises

global existence and uniform stabilization of a generalized dissipative klein gordon equation type with boundary damping in this paper we prove the existence uniqueness and uniform stability of strong and weak solutions of the nonlinear generalized klein gordon equation 1 1 1 see sec i in bounded domains with nonlinear damped boundary conditions given by 1 1 3 see sec i with some restrictions on function f u h u g ut and b x we prove the existence and uniqueness by means of nonlinear semigroup method and obtain the uniform stabilization by using the multiplier technique

boundary stabilization of nonlinear vibrations of a flexible structure in a bounded domain in rn abstract we study a problem of boundary stabilization of the vibrations of elastic structure governed by the nonlinear integro differential equation u a 2 b u 2 d x u f in a bounded domain in r n with a smooth boundary under mixed boundary conditions to stabilize this system we apply a velocity feedback control only on a part of the boundary we prove that the solution of such system is stable subject to some restriction on the uncertain disturbing force f we also estimate the total energy of the system over any time interval 0 t with a tolerance level of the disturbances finally we establish the uniform decay of solution by a direct method with an explicit form of exponential energy decay estimate when this disturbing force f is insignificant

some statistical properties of alpha trimmed mean and standard type m filters the statistical properties of two classes of filters generalizing the median filter are considered the two classes are the alpha trimmed mean alpha tm filter and the standard type m stm filter both of which are special cases of the l filter results are developed to quantify the white noise suppression and edge preservation characteristics of the filters by considering their output sequence error statistics it is shown that the alpha tm and stm filters perform better than the running mean and median filters in white noise suppression while they can be designed to be comparable to the median filter in edge preservation in the presence of noise

weighted iterative truncated mean filter the iterative truncated arithmetic mean itm filter was proposed recently it offers a way to estimate the sample median by simple arithmetic computing instead of the time consuming data sorting in this paper a rich class of filters named weighted itm witm filters are proposed by iteratively truncating the extreme samples the output of the witm filter converges to the weighted median proper stopping criterion makes the witm filters own merits of both the weighted mean and median filters and hence outperforms the both in some applications three structures are designed to enable the witm filters being low band and high pass filters properties of these filters are presented and analyzed experimental evaluations are carried out on both synthesis and real data to verify some properties of the witm filters

on existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions abstract we study the global existence of solutions of the nonlinear degenerate wave equation 0 x y y 0 in 0 y 0 on 1 0 y y f y g y 0 on 0 0 y x 0 y 0 y x 0 y 1 x in where y denotes the derivative of y with respect to parameter t f s c0 s s and g is a nondecreasing c1 function such that k1 s 2 g s s k2 s 2 for some k1 k2 0 with 0 0 if n 1 2 the existence of solutions is proved by means of the faedo galerkin method furthermore when 0 the uniform decay is obtained by making use of the perturbed energy method

iterative truncated arithmetic mean filter and its properties the arithmetic mean and the order statistical median are two fundamental operations in signal and image processing they have their own merits and limitations in noise attenuation and image structure preservation this paper proposes an iterative algorithm that truncates the extreme values of samples in the filter window to a dynamic threshold the resulting nonlinear filter shows some merits of both the fundamental operations some dynamic truncation thresholds are proposed that guarantee the filter output starting from the mean to approach the median of the input samples as a by product this paper unveils some statistics of a finite data set as the upper bounds of the deviation of the median from the mean some stopping criteria are suggested to facilitate edge preservation and noise attenuation for both the long and short tailed distributions although the proposed iterative truncated mean itm algorithm is not aimed at the median it offers a way to estimate the median by simple arithmetic computing some properties of the itm filters are analyzed and experimentally verified on synthetic data and real images

existence and exponential decay for a kirchhoff carrier model with viscosity abstract in this work we study the existence of global solutions and exponential decay for the following nonlinear problem formula where m is a c 1 function m 0 0 0

on exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback abstract the uniform stabilization of an originally regarded nondissipative system described by a semilinear wave equation with variable coefficients under the nonlinear boundary feedback is considered the existence of both weak and strong solutions to the system is proven by the galerkin method the exponential stability of the system is obtained by introducing an equivalent energy function and using the energy multiplier method on the riemannian manifold this equivalent energy function shows particularly that the system is essentially a dissipative system this result not only generalizes the result from constant coefficients to variable coefficients for these kinds of semilinear wave equations but also simplifies significantly the proof for constant coefficients case considered in a guesmia a new approach of stabilization of nondissipative distributed systems siam j control optim 42 2003 24 52 where the system is claimed to be nondissipative

global existence for the wave equation with nonlinear boundary damping and source terms abstract the paper deals with local and global existence for the solutions of the wave equation in bounded domains with nonlinear boundary damping and source terms the typical problem studied is u tt u 0 in 0 u 0 on 0 0 u u t m 2 u t u p 2 u on 0 1 u 0 x u 0 x u t 0 x u 1 x on where r n n 1 is a regular and bounded domain 0 1 m 1 2 p r where r 2 n 1 n 2 when n 3 r when n 1 2 and the initial data are in the energy space we prove local existence of the solutions in the energy space when m r r 1 p or n 1 2 and global existence when p m or the initial data are inside the potential well associated to the stationary problem

note on boundary stabilization of wave equations an energy decay rate is obtained for solutions of wave type equations in a bounded region in mathbb r n whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface unlike most previous results on this subject the results presented here are potentially valid for regions having connected boundaries

uniform decay of the solution to a wave equation with memory conditions on the boundary abstract a wave equation with variable coefficients in principal part and memory conditions on the boundary is considered the riemannian geometry method is applied to prove the exponential decay of the energy provided the relaxation function also decays exponentially

a new approach of stabilization of nondissipative distributed systems in this paper we propose a new approach to prove the nonlinear internal or boundary stabilization of certain nondissipative distributed systems the usual energy is not decreasing this approach leads to decay estimates known in the dissipative case when the integral inequalities method due to komornik exact controllability and stabilization the multiplier method masson paris john wiley chichester uk 1994 cannot be applied due to the lack of dissipativity first we study the stability of a semilinear wave equation with a nonlinear damping based on the equation u delta u h nabla u f u g u 0 we consider the general case with a function h satisfying a smallness condition and we obtain uniform decay of strong and weak solutions under weak growth assumptions on the feedback function and without any control of the sign of the derivative of the energy related with the above equation in the second part we consider the case h nabla u nabla phi cdot nabla u with phi in w 1 infty omega we prove some precise decay estimates exponential or polynomial of equivalent energy without any restriction on phi the same results will be proved in the case of boundary feedback finally we comment on some applications of our approach to certain nondissipative distributed systems some results of this paper were announced without proof in a guesmia c r acad sci paris ser i math 332 2001 pp 633 636