energy decay for timoshenko systems of memory type abstract linear systems of timoshenko type equations for beams including a memory term are studied the exponential decay is proved for exponential kernels while polynomial kernels are shown to lead to a polynomial decay the optimality of the results is also investigated

logarithmic stabilization of the euler bernoulli transmission plate equation with locally distributed kelvin voigt damping abstract in this work we consider a transmission problem for a plate equation where one small part of the domain is made of a viscoelastic material with kelvin voigt constitutive relation we apply the general results due to burq s 10 in the study of asymptotic behavior of solutions and prove that the semigroup associated to the system is logarithmically stable the main ingredient of the proof is the carleman estimates the method consist to use carleman estimates to obtain information on the resolvent for high frequency

nonparametric estimation of a multivariate distribution in the presence of censoring summary this paper presents examples of situations in which one wishes to estimate a multivariate distribution from data that may be right censored a distinction is made between what we term homogeneous and heterogeneous censoring it is shown how a multivariate empirical survivor function must be constructed in order to be considered a nonparametric maximum likelihood estimate of the underlying survivor function a closed form solution similar to the product limit estimate of kaplan and meier is possible with homogeneous censoring but an iterative method such as the em algorithm is required with heterogeneous censoring an example is given in which an anomaly is produced if censored multivariate data are analyzed as a series of univariate variables this anomaly is shown to disappear if

energy decay estimates for the damped plate equation with a local degenerated dissipation we consider the euler bernoulli plate equation in a bounded open set of r2 with a degenerated local damping term this dissipation is effective in a subset of and the damping coefficient may vanish in some subset of dimension one of we show that the usual observability inequality for the undamped problem implies polynomial decay estimates for the damped problem our method can be applied for other pde s such as the wave equation or the schrodinger equation

rank tests for association with right censored data summary rank tests for association between a time variable and a continuous covariate and between two time variables are given in the presence of censoring in the first case these tests are related to the semiparametric tests of cox 1972 and prentice 1978 but differ in that the covariate is replaced by a score computed from its rank in the second case the test statistic is again a simple inner product which in the proportional hazards model reduces to the correlation between the two vectors of log rank scores the loss of efficiency arising from incorrect score functions is also explored when there is no censoring in this paper we consider a general model for association between pairs of observations in which either variable or both variables may be right censored the aim is to develop tests based on the generalized ranks of both variables which have maximal power at alternatives which are near to the null hypothesis of independence attention will be concentrated on two special cases of interest in survival analysis tests for association between a censored survival time and a possibly censored continuous covariate and tests for association between the times to different events beginning with cox 1972 the first situation has been studied extensively in a semiparametric set up in which information based on ranks is used for the time variable but exact values are used for the covariate procedures which use only the ranks of both variables have been developed by brown hollander korwar 1974 and more recently by o brien 1978 however neither of these procedures have been developed with a particular model in mind and one of the achievements of the present paper is to derive rank tests with good local power when a particular model such as the proportional hazards model holds in the case of a proportional hazards model with a continuous covariate the present development may be preferable to the semiparametric methods when the functional form of the relation ship between the hazard and the covariate is not known in advance or when errors or outliers may exist in the observed covariate values thus significance levels may be obtained which are not inflated by multiple regroupings or transformations of the covariate data although it would be expected that parametric model building with variables found to be associated with survival would often be carried out in further analyses

unique continuation for the linearized benjamin bona mahony equation with space dependent potential in this paper we analyze a unique continuation problem for the linearized benjamin bona mahony equation with space dependent potential in a bounded interval with dirichlet boundary conditions the underlying cauchy problem is a characteristic one we prove two unique continuation results by means of spectral analysis and the generalized eigenvector expansion of the solution instead of the usual holmgren type method or carleman type estimates it is found that the unique continuation property depends very strongly on the nature of the potential and in particular on its zero set and not only on its boundedness or integrability properties

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

goodness of fit tests for log linear models in sparse contingency tables abstract the asymptotic normality of the likelihood ratio goodness of fit statistic is demonstrated for testing the fit of log linear models with closed form maximum likelihood estimates in sparse contingency tables unlike the traditional chi squared theory the number of categories in the table increases as the sample size increases but not all of the expected frequencies are required to become large some results of a small monte carlo study are presented the traditional chi squared approximation is reasonably accurate for the pearson statistic for many sparse tables but cases are presented for which it fails the normal approximation can be much more accurate than the chi squared approximation for the likelihood ratio statistic but the bias of estimated moments is a potential problem for very sparse tables

exponential stability of nondissipative linear system in banach space and application to unbounded bilinear systems abstract we consider linear control systems of the form d z t d t a z t b z t where is a real parameter a is the infinitesimal generator of a linear c 0 semigroup of contractions s 0 t on a banach space x and the linear perturbation b is a relatively bounded operator with respect to a we provide necessary and sufficient conditions for exponential stability of the above system our stability results are then applied to establish uniform exponential stabilization of linear and bilinear systems with unbounded control operators applications to hyperbolic like equations are considered

a general decay result for a memory type timoshenko thermoelasticity system with second sound abstract in this paper we consider a system of timoshenko thermoelasticity with second sound in the presence of an infinite history term we prove under suitable conditions on the coefficients and the relaxation function a general decay result from which the exponential and polynomial decay estimates are only special cases we also establish a lack of exponential decay result and discuss the optimality for some situation

on timoshenko type systems with type iii thermoelasticity asymptotic behavior abstract in this study we consider a thermoelastic beam system where the oscillations are defined by the timoshenko model and heat conduction is given by the green and naghdi theories we provide an explicit characterization of the decay rate which can be exponential or polynomial depending on the relationship between the coefficients of the wave propagation speed

the damped string problem revisited abstract we revisit the damped string equation on a compact interval with a variety of boundary conditions and derive an infinite sequence of trace formulas associated with it employing methods familiar from supersymmetric quantum mechanics we also derive completeness and riesz basis results with parentheses for the associated root functions under less smoothness assumptions on the coefficients than usual using operator theoretic methods rather than detailed eigenvalue and root function asymptotics only

tests of independence for bivariate data with random censoring a contingency table approach procedures are proposed for testing the hypothesis of independence between two discrete or discretized random variables one or both of which may be randomly censored the censoring mechanisms can be either independent bivariate censoring or identical univariate censoring the proposed tests reduce to goodness of fit tests for log linear models applied to either complete or incomplete contingency tables three examples are analyzed for illustrative purposes

weighted l2 estimates for dissipative wave equations with variable coefficients abstract we establish weighted l 2 estimates for the wave equation with variable damping u t t u a u t 0 in r n where a x a 0 1 x with a 0 0 and 0 1 in particular we show that the energy of solutions decays at a polynomial rate t n 2 1 if a x a 0 x for large x we derive these results by strengthening significantly the multiplier method this approach can be adapted to other hyperbolic equations with damping

energy decay rate of wave equations with indefinite damping abstract we consider the one dimensional wave equation with an indefinite sign damping and a zero order potential term using a shooting method we establish the asymptotic expansion of eigenvalues and eigenvectors of the damped wave equation for a large class of coefficients in addition if the damping coefficient is more positive than negative we prove that the energy of system decays uniformly exponentially to zero this sharp result generalizes a previous work of freitas and zuazua 1996

existence and energy decay rates of solutions to the variable coefficient euler bernoulli plate with a delay in localized nonlinear internal feedback abstract this paper is concerned with the existence and energy decay estimates of solutions to the variable coefficient euler bernoulli plate with a delay in localized nonlinear internal feedback the existence of solutions to the nonlinear system is obtained by using galerkin method combined with some energy estimates furthermore applying riemannian geometry method we establish uniform decay rates of the plate equation with variable coefficients and a nonlinear delay term

boundary stabilization of a 1 d wave equation with in domain antidamping we consider the problem of boundary stabilization of a 1 d one dimensional wave equation with an internal spatially varying antidamping term this term puts all the eigenvalues of the open loop system in the right half of the complex plane we design a feedback law based on the backstepping method and prove exponential stability of the closed loop system with a desired decay rate for plants with constant parameters the control gains are found in closed form our design also produces a new lyapunov function for the classical wave equation with passive boundary damping

well posedness and stability of a hinged plate equation with a localized nonlinear structural damping abstract we consider an n dimensional plate equation in a bounded domain with a locally distributed nonlinear dissipation involving the laplacian the dissipation is effective in a neighborhood of a suitable portion of the boundary when the space dimension equals two the associated linear equation corresponds to the plate equation with a localized viscoelastic or structural damping first we prove existence uniqueness and smoothness results then using an appropriate perturbed energy coupled with multiplier technique we directly prove exponential and polynomial decay estimates for the underlying energy to the author s best knowledge the perturbed energy approach is new in the framework of stabilization of second order evolution equations with locally distributed damping

exponential stability of an abstract nondissipative linear system in this paper we consider an abstract linear system with perturbation of the form frac dy dt ay varepsilon by on a hilbert space cal h where a is skew adjoint b is bounded and varepsilon is a positive parameter motivated by a work of freitas and zuazua on the one dimensional wave equation with indefinite viscous damping p freitas and e zuazua j differential equations 132 1996 pp 338 352 we obtain a sufficient condition for exponential stability of the above system when b is not a dissipative operator we also obtain a hautus type criterion for exact controllability of system a g where g is a bounded linear operator from another hilbert space to cal h our result about the stability is then applied to establish the exponential stability of several elastic systems with indefinite viscous damping as well as the exponential stabilization of the elastic systems with noncolocated observation and control

mildly dissipative nonlinear timoshenko systems global existence and exponential stability we consider nonlinear systems of timoshenko type in a one dimensional bounded domain the system has a dissipative mechanism being present only in the equation for the rotation angle it is a damping effect through heat conduction the global existence of small smooth solutions as well as the exponential stability are investigated

a concordance test for independence in the presence of censoring an extension of the definition of kendall s coefficient of concordance is proposed for testing independence in bivariate censored survival times the test statistic counts the number of known concordances minus the number of known discordances the variance of the statistic is calculated for an random censorship model which however does not require independence of the components of the censoring distribution two examples are given

energy methods for quasilinear hyperbolic initial boundary value problems applications to elastodynamics the aim of this paper is to show how energy methods can be used to establish local in time existence of smooth solutions to certain initial boundary value problems for systems of quasilinear hyperbolic partial differential equations our particular objective is to treat the equations of nonlinear elastodynamics

a spillover phenomenon in the optimal location of actuators in this paper we are interested in finding the optimal location and shape of the actuators in a stabilization problem namely we consider the one dimensional wave equation damped by an internal feedback supported on a subdomain omega of given length the criterion we want to optimize represents the rate of decay of the total energy of the system it theoretically involves all the eigenmodes of the operator from an engineering point of view it seems more realistic to consider only a finite number of modes say the n first ones in that context we are able to prove existence and uniqueness of an optimal domain omega n it is the better possible location for the actuators we characterize this optimal domain and we point out the following strange phenomenon at least for small lengths the optimal domain omega n which is the better one for the n first modes is actually the worse one for the n 1th mode this looks like the well known spillover phenomenon in control theory at last we will give some possible extension and open problems in higher dimension

testing the assumption of independence of truncation time and failure time summary for data subject to random censorship it is well known that the assumption of independence between censoring time and failure time cannot be tested nonparametrically for data subject to random truncation however it is possible to test independence of truncation time and failure time a statistic generalizing kendall s tau is proposed for testing the independence assumption and asymptotic properties under the null hypothesis are derived a conditional permutation test is also derived for small data sets generalization to allow right censoring and an application to truncated linear regression are also briefly discussed

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

asymptotic stability for intermittently controlled second order evolution equations motivated by several works on ordinary differential equations we are interested in the asymptotic stability of intermittently controlled partial differential equations we give a condition of asymptotic stability for second order evolution equations uniformly damped by an on off feedback this result extends to the case of partial differential equations a previous result of r a smith concerning ordinary differential equations

time reversal focusing of the initial state for kirchhoff plate consider a kirchhoff plate partial t 2 u delta 2 u partial t 2 delta u 0 in omega times 0 t with boundary data u delta u 0 on partial omega times 0 t and unknown initial data u cdot 0 u 0 and partial t u cdot 0 u 1 in omega we study an inverse problem of determining u 0 u 1 from an interior observation u omega times 0 t here omega is a bounded domain omega a nonempty open subset of omega and t 0 a suitable time duration by means of an iterative time reversal technique we derive an asymptotic formula of reconstructing u 0 u 1 approximately with a logarithmical convergence rate for smooth initial data the convergence becomes uniform and exponential when omega omega t satisfies the geometric control condition introduced by bardos lebeau and rauch

on a mixed problem with a nonlinear acoustic boundary condition for a non locally reacting boundaries abstract we discuss global solvability to the mixed problem for a nonlinear wave equation in domains with non locally reacting boundaries and nonlinear acoustic boundary condition we prove the existence and uniqueness of solution additionally using the method of nakao we demonstrate the decay of the associated energy stability

on conditions for asymptotic stability of dissipative infinite dimensional systems with intermittent damping abstract we study the asymptotic stability of a dissipative evolution in a hilbert space subject to intermittent damping we observe that even if the intermittence satisfies a persistent excitation condition if the hilbert space is infinite dimensional then the system needs not being asymptotically stable not even in the weak sense exponential stability is recovered under a generalized observability inequality allowing for time domains that are not intervals weak asymptotic stability is obtained under a similarly generalized unique continuation principle finally strong asymptotic stability is proved for intermittences that do not necessarily satisfy some persistent excitation condition evaluating their total contribution to the decay of the trajectories of the damped system our results are discussed using the example of the wave equation schrodinger s equation and for strong stability also the special case of finite dimensional systems

nonparametric bivariate estimation with randomly censored data summary the estimation of a bivariate distribution function with randomly censored data is considered it is assumed that the censoring occurs independently of the lifetimes and that deaths and losses which occur simultaneously can be separated two estimators are developed a reduced sample estimator and a self consistent one it is shown that the latter estimator satisfies a nonparametric likelihood function and is unique up to the final uncensored values in any dimension it jumps at the points of double deaths in both dimensions some key word8 censored data kaplan meier estimator life table product limit estimator survival estimation

achieving arbitrarily large decay in the damped wave equation we exhibit a sequence of viscous dampings for the fixed string that yields arbitrarily fast attenuation of any and all initial disturbances the limit case produces extinction of all solutions in finite time

stability results for the wave equation with indefinite damping abstract the one dimensional wave equation with damping of indefinite sign in a bounded interval with dirichlet boundary conditions is considered it is proved that solutions decay uniformly exponentially to zero provided the damping potential is in thebv class has positive average is small enough and satisfies a finite number of further constraints guaranteeing that the derivative of the real part of the eigenvalues is negative when the damping vanishes this sharp result completes a previous one by the first author showing that an indefinite sign damping always produces unstable solutions if it is large enough and it answers by the afirmative to a conjecture concerning small damping terms the method of proof relies on the developments by s cox and the second author on the high frequency asymptotic expansion of the spectrum for damped wave equations and on the characterization of the decay rate in terms of the spectral abscissa

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

perturbing the critically damped wave equation we consider the wave equation with viscous damping the equation is said to be critically damped when the damping is that value for which the spectral abscissa of the associated wave operator is minimized within the class of constant dampings the critically damped wave operator possesses a nonsemisimple eigenvalue we present a detailed study of the splitting of this eigenvalue under bounded perturbations of the damping and subsequently show that the critical choice is a local minimizes of the spectral abscissa over lines in the class of all bounded dampings

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

multiple imputation of industry and occupation codes in census public use samples using bayesian logistic regression abstract we describe methods used to create a new census data base that can be used to study comparability of industry and occupation classification systems this project represents the most extensive application of multiple imputation to date and the modeling effort was considerable as well hundreds of logistic regressions were estimated one goal of this article is to summarize the strategies used in the project so that researchers can better understand how the new data bases were created another goal is to show how modifications of maximum likelihood methods were made for the modeling and imputation phases of the project to multiply impute 1980 census comparable codes for industries and occupations in two 1970 census public use samples logistic regression models were estimated with flattening constants for many of the regression models considered the data were too sparse to support conventional maximum likelihood analysis so some alternative had to be employed these methods solve existence and

general stability of a viscoelastic variable coefficients plate equation with time varying delay in localized nonlinear internal feedback abstract this paper is concerned with the decay properties of a memory type euler bernoulli plate equation with variable coefficients and time varying delay in localized nonlinear internal feedback by using piecewise multiplier method and riemannian geometric analysis we establish the explicit and general decay rates of system whose nonlinear internal feedbacks act on a suitable subregion

exponential stability of the plate equations with potential of second order and indefinite damping we study the exponential stability of the plate equations with potential of second order and indefinite sign damping term by means of a global carleman type estimate and the usual perturbation method we show that the energy of the system decays exponentially provided that the negative damping is sufficiently small both the energy decay rate and the upper bound estimate on the negative damping are given explicitly

stabilization of high eigenfrequencies of a beam equation with generalized viscous damping in this paper using the one dimensional vibrating beam equation with generalized viscous damping as a model of vibration of flexible robot arms it is shown that for such a system the high eigenmodes decay at a uniform rate the proof is obtained by perturbation theory of linear operators y h luo acta math sinica 32 1991 pp 556 563 and asymptotic estimates of eigenvectors based on an earlier work of g b birkhoff and m h stone feedback control for this class of system is investigated and a finite dimensional controller is presented for an exponentially stable closed loop system our method may be used to study nondissipative systems

stabilization of the wave equations with potential and indefinite damping by means of global carleman type estimate we study the stabilization problem of the wave equations with potential and indefinite damping the energy decay rate of the system is given explicitly also we obtain an upper bound estimate on the negative damping to guarantee the energy of the system decays exponentially

the rate at which energy decays in a viscously damped hinged euler bernoulli beam we study the best decay rate of the solutions of a damped euler bernoulli beam equation with a homogeneous dirichlet boundary conditions we show that the fastest decay rate is given by the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup if the damping coefficient is in l infty 0 1

exponential decay of energy of evolution equations with locally distributed damping consider an evolution equation with energy dissipation frac partial partial t y x t ay x t by x t on a bounded x domain omega where by signifies a dissipative perturbation to an otherwise energy conserving system this dissipation may be due to medium impurities viscous effects or artificially imposed dampers and stabilizers it is distributed over only part of the domain omega the question of when the dissipation is effective enough to cause uniform exponential decay of energy is examined because of the locally distributed nature of energy dissipation the problem lacks coercivity and is not directly solvable by energy identities thus to get conditions sufficient for uniform exponential decay a different approach needs to be taken provided here is a set of tight sufficient conditions in terms of the influence of the dissipative operatorbon the separated eigenmodes or clustered eigenmodes ofa the main theorems are general enough to treat the wave and bea

bresse system with indefinite damping abstract we consider the bresse system in a bounded domain 0 l r 1 the system has an indefinite damping mechanism i e with a damping function a a x possibly changing sign presented only in the equation for the rotation angle we shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case and provided a 1 l 0 l a x d x 0 and a a l 2 for small enough in the arguments we shall also give a new proof of exponential stability for the constant case a a

local existence of solution for the initial boundary value problem of fully nonlinear wave equation on considere l existence locale par rapport au temps des solutions pour le probleme aux valeurs limites et initiales d une equation d onde totalement non lineaire

timoshenko systems with indefinite damping abstract we consider the timoshenko system in a bounded domain 0 l r 1 the system has an indefinite damping mechanism i e with a damping function a a x possibly changing sign present only in the equation for the rotation angle we shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case and provided a 0 l a x d x 0 and a a l 2 for small enough the decay rate will be described explicitly in the arguments we shall also give a new proof of exponential stability for the constant case a a moreover we give a precise description of the decay rate and demonstrate that the system has the spectrum determined growth sdg property i e the type of the induced semigroup coincides with the spectral bound for its generator

global existence asymptotic behavior and uniform attractors for a non autonomous timoshenko system of thermoelasticity of type iii with a time varying delay abstract in this paper we first establish the global existence by using the variable norm technique of kato and semigroup method second under suitable assumptions on the data we obtain the asymptotic behavior of the solution last we prove the existence of a uniform attractor by using the method of uniform contractive functions

eigenvalue asymptotics inverse problems and a trace formula for the linear damped wave equation abstract we determine the general form of the asymptotics for dirichlet eigenvalues of the one dimensional linear damped wave operator as a consequence we obtain that given a spectrum corresponding to a constant damping term this determines the damping term in a unique fashion we also derive a trace formula for this problem

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

on the spectrum of euler bernoulli beam equation with kelvin voigt damping abstract the spectral property of an euler bernoulli beam equation with clamped boundary conditions and internal kelvin voigt damping is considered the essential spectrum of the system operator is rigorously identified to be an interval on the left real axis under some assumptions on the coefficients it is shown that the essential spectrum contains continuous spectrum only and the point spectrum consists of isolated eigenvalues of finite algebraic multiplicity the asymptotic behavior of eigenvalues is presented

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

exponential stability for wave equations with non dissipative damping abstract we consider the nonlinear wave equation u t t u x x a x u t 0 in a bounded interval 0 l r 1 the function a is allowed to change sign but has to satisfy a 1 l 0 l a x d x 0 for this non dissipative situation we prove the exponential stability of the corresponding linearized system for i possibly large a l with small a a l 2 and ii a class of pairs a l with possibly negative moment 0 l a x sin 2 x l d x estimates for the decay rate are also given in terms of a moreover we show the global existence of smooth small solutions to the corresponding nonlinear system if additionally the negative part of a is small enough

exponential stability of wave equations with potential and indefinite damping abstract first we consider the linear wave equation u t t u x x a x u t b x u 0 on a bounded interval 0 l r the damping function a is allowed to change its sign if a 1 l 0 l a x d x is positive and the spectrum of the operator x x b is negative exponential stability is proved for small a a l 2 explicit estimates of the decay rate are given in terms of a and the largest eigenvalue of x x b second we show the existence of a global small smooth solution of the corresponding nonlinear wave equation u t t u x x a x u t b x u 0 if additionally the negative part of a is small enough compared with

a stability result of a timoshenko system with a delay term in the internal feedback abstract in this paper we consider a timoshenko system with a delay term in the feedback and prove a stability result the beam is clamped at the endpoints and has in addition to an internal damping a feedback with a delay under an appropriate assumption on the weights of the two feedbacks we prove the well posedness of the system and establish an exponential decay result for the case of equal speed wave propagation

polynomial stability of the timoshenko system by one boundary damping abstract in this paper we study the indirect boundary stabilization of the timoshenko system with only one dissipation law this system which models the dynamics of a beam is a hyperbolic system with two wave speeds assuming that the wave speeds are equal we prove non uniform stability and an optimal polynomial energy decay rate is obtained otherwise if the ratio of the wave speeds is a rational number we show that the decay rate is of polynomial type

decay rate estimates for the quasi linear timoshenko system with nonlinear control and damping terms in this work we consider a class of quasi linear timoshenko systems with nonlinear control and damping terms we investigate the stabilization of weak solutions to the initial boundary value problem and obtain explicit decay rate estimation depending on control and damping terms

general energy decay in a timoshenko type system of thermoelasticity of type iii with a viscoelastic damping in this paper we consider a one dimensional linear thermoelastic system of timoshenko type where the heat conduction is given by green and naghdi theories we prove a general decay result from which the exponential and polynomial decays are only special cases

parameter estimation in spatially extended systems the karhunen loeve and galerkin multiple shooting approach parameter estimation for spatiotemporal dynamics for coupled map lattices and continuous time domain systems is shown using a combination of multiple shooting karhunen loeve decomposition and galerkin s projection methodologies the resulting advantages in estimating parameters have been studied and discussed for chaotic and turbulent dynamics using small amounts of data from subsystems availability of only scalar and noisy time series data effects of space time parameter variations and in the presence of multiple time scales

a note on stabilization of locally damped wave equations with time delay abstract in this paper we consider the wave equation with internal distributed time delay and local damping in a bounded and smooth domain r n when the local damping acts on a neighborhood of a suitable part of the boundary of we show that an exponential stability result holds if the coefficient of the delay term is sufficiently small

local controllability to stationary trajectories of a burgers equation with nonlocal viscosity abstract this article studies the local controllability to trajectories of a burgers equation with nonlocal viscosity by linearization we are led to an equation with a non local term whose controllability properties are analyzed by using fourier decomposition and biorthogonal techniques once the existence of controls is proved and the dependence of their norms with respect to the time is established for the linearized model a fixed point method allows us to deduce the result for the nonlinear initial problem

linear models random censoring and synthetic data summary estimators for the linear model in the presence of censoring are available a new extension of the least squares estimator to censored data is equivalent to applying the ordinary least squares estimator to synthetic times time constructed by magnifying the gaps between successive order statistics under suitable regularity conditions the synthetic data estimator is fisher consistent and asymptotically normal examples facilitate com parison of the synthetic data estimator with estimators proposed by buckley james 1979 and by koul susarla van ryzin 1981 the entire lifetime of a person a machine a plant or an animal is not always observable some lifetimes may be censored in that only a lower bound for the lifetime is recorded statisticians are often interested in modelling the distribution of the true lifetimes as a function of covariates when censoring is present a proportional hazards model is often used when there is no censoring linear models are often used for ad hoc modelling of dependent variables miller halpern 1982 survey the methods that have been proposed for the linear model in the presence of censoring this paper describes a closed form method which is consistent and asymptotically normal this method incorporates censor ing in a natural way section 2 formulates classical least squares estimation in a manner that generalizes to accommodate random right censoring section 3 gives some theoretical results for the simplest nontrivial linear model the two sample case section 4 contains examples and the final section discusses the role of this estimator the covariate vector of the ith person will be denoted by xi and usually includes one as the first component the true lifetime yi follows a linear model if its conditional distribution given xi is

the conditional distribution of goodness of fit statistics for discrete data abstract i consider the distribution of pearson s statistic and of the likelihood ratio goodness of fit statistic for discrete data in the important case where the data are extensive but sparse it is argued that the appropriate reference distribution is conditional on the sufficient statistic for the unknown regression parameters the first three conditional asymptotic cumulants are derived by edgeworth expansion and these are used for the computation of tail probabilities the principal advantage of the limit considered here as opposed to the more usual x 2 limit is that the cell counts need not be large

frictional versus viscoelastic damping in timoshenko systems with different speeds of wave propagation abstract we consider the decay rate of timoshenko type equations for beams with frictional damping and memory effect in an interval when the speeds of wave propagation are different we show that the solution energy of timoshenko systems decays at the rate t 1 under only basic conditions on the memory kernels without any decaying conditions the proof is based on some appropriate functionals and it improves the previously related results in the literature

on the stabilization of timoshenko systems with memory and different speeds of wave propagation in this work we consider a one dimensional timoshenko system with different speeds of wave propagation and with only one control given by a viscoelastic term on the angular rotation equation for a wide class of relaxation functions and for sufficiently regular initial data we establish a general decay result for the energy of solution unlike the past history and internal feedback cases the second energy is not necessarily decreasing to overcome this difficulty a precise estimate of the second energy in terms of the initial data and the relaxation function is proved

boundary control of an anti stable wave equation with anti damping on the uncontrolled boundary abstract much of the boundary control of wave equations in one dimension is based on a single principle passivity under the assumption that control is applied through neumann actuation on one boundary and the other boundary satisfies a homogeneous dirichlet boundary condition we have recently expanded the scope of tractable problems by allowing destabilizing anti stiffness a robin type condition on the uncontrolled boundary where the uncontrolled system has a finite number of positive real eigenvalues in this paper we go further and develop a methodology for the case where the uncontrolled boundary condition has anti damping which makes the real parts of all the eigenvalues of the uncontrolled system positive and arbitrarily high i e the system is anti stable exponentially stable in negative time using a conceptually novel integral transformation we obtain extremely simple explicit formulae for the gain functions for the case with only boundary sensing available at the same end with actuation we design backstepping observers which are dual to the backstepping controllers and have explicit output injection gains we then combine the control and observer designs into an output feedback compensator and prove the exponential stability of the closed loop system

nonparametric estimation of a bivariate survival function in the presence of censoring a new family of estimators of a bivariate survival function based on censored vectors is obtained from a decomposition of the bivariate survival function these estimators are uniformly consistent under bivariate censoring and are self consistent under univariate censoring

stabilization of the euler bernoulli plate with variable coefficients by nonlinear internal feedback we consider the energy decay for solutions of the euler bernoulli plate equation with variable coefficients where a nonlinear internal feedback acts in a suitable subregion of the domain the riemannian geometric method is used to deal with variable coefficient problems when the feedback region has a structure similar to that for the wave equation with constant coefficients we establish the stabilization of the system in the case of fixed boundary conditions several energy decay rates are established according to various growth restrictions on the nonlinear feedback near the origin and at infinity we further show that unlike for the case of constant coefficients choices of such feedback regions depend not only on the type of boundary conditions but also on the curvature of a riemannian metric based on the coefficients of the system

the damped wave equation with unbounded damping abstract we analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity we prove the generation of a contraction semigroup study the relation between the spectra of the semigroup generator and the associated quadratic operator function the convergence of non real eigenvalues in the asymptotic regime of diverging damping on a subdomain and we investigate the appearance of essential spectrum on the negative real axis we further show that the presence of the latter prevents exponential estimates for the semigroup and turns out to be a robust effect that cannot be easily canceled by adding a positive potential these analytic results are illustrated by examples

locally distributed control and damping for the conservative systems in this paper we note the equivalence between exact controllability and exponential stabilizability for an abstract conservative system with bounded control this enables us to establish a frequency domain characterization for the exact controllability uniform exponential decay property of second order elastic systems such as the wave equation and the petrovsky equation with locally distributed control damping a piecewise multiplier method for frequency domain is introduced for several classes of pdes on regions which are not necessarily smooth we obtain a sufficient condition for the subregion on which the application of control damping will yield the exact controllability uniform exponential decay property this result provides useful information for designing the location of controllers dampers for distributed systems with a law of conservation

asymptotic stability for bresse systems abstract in this paper consider a vibrating system of bresse type in a one dimensional bounded domain with a nonlinear damping acting in the equation of the shear angle displacement and nonlinear localized damping in other equations we show the asymptotic stability without imposing conditions about the equal speed wave propagation using a method developed by lasiecka and tataru 9

instability results for the damped wave equation in unbounded domains abstract we extend some previous results for the damped wave equation in bounded domains in r d to the unbounded case in particular we show that if the damping term is of the form a with bounded a taking on negative values on a set of positive measure then there will always exist unbounded solutions for sufficiently large positive in order to prove these results we generalize some existing results on the asymptotic behaviour of eigencurves of one parameter families of schrodinger operators to the unbounded case which we believe to be of interest in their own right

stability of a nonuniform rayleigh beam with indefinite damping abstract this is a continuation of our earlier work j m wang g q xu s p yung exponential stability for variable coefficients rayleigh beams under boundary feedback control a riesz basis approach systems control lett 51 1 2004 33 50 on the study of a nonhomogeneous rayleigh beam and this time the stabilization is achieved via an internal damping instead of the boundary feedbacks we continue to address a conjecture of guo basis property of a rayleigh beam with boundary stabilization j optim theory appl 112 3 2002 529 547 in this paper and demonstrate how the damping term can affect the decay rate asymptotically by a detailed spectral analysis we obtain a necessary condition for the stability and establish the riesz basis property as well as the spectrum determined growth condition for the system furthermore when the damping is indefinite we provide a condition on how negative the damping can be without destroying the exponential stability

interval estimation of slope with right censored data summary a new method for point and interval estimation of a slope that uses randomly right censored data is presented the new method is based on inverting a censored data version of a test for association a simulation study shows that the new method compares favourably with a method due to buckley james 1979 in this paper we consider nonparametric estimation of the slope parameter in a simple linear regression model when the data are randomly right censored the three main nonparametric methods for the estimation of slope in a linear regression model are due to miller 1976 buckley james 1979 and to koul susarla van ryzin 1981 a fourth method due to cox 1972 though used extensively in the regression analysis of right censored data is not directly comparable to the first three methods because it is based on a proportional hazards model miller halpern 1982 compare the four methods and come out generally in favour of the cox and buckley james methods finding that the other two methods have some methodological weaknesses miller halpern conclude that the choice between the cox and buckley james methods must be based on the appropriateness of the proportional hazards model or the linear model in this paper we propose a new method for point and interval estimation of the slope parameter in a simple linear regression model under suitable regularity conditions the

on the spectrum of evolution operators generated by hyperbolic systems abstract we prove that the asymptotic behavior of semigroups generated by mixed initial value problems for hyperbolic systems in one space variable is determined by the zeroes of the characteristic equation the proof is based on the following reduction principle we construct a reduced system which is much simpler than the given one such that the difference of the semigroups is a compact operator the construction of the reduced system is presented in the non autonomous case because it has implifications in the study of systems which are time periodic

optimal shape and position of the actuators for the stabilization of a string abstract the energy in a string subject to constant viscous damping k on a subset of length l 0 decays exponentially in time we consider the problem of optimizing the decay rate for the which are the unions of at most n intervals this rate is given by the spectral abscissa of the linear operator associated to the wave equation we are interested in small values of k therefore we consider the derivative of the spectral abscissa at k 0 we prove that except for the case l 1 2 when the number of intervals is not fixed a priori an optimal domain does not exist we study numerically the case of one or two intervals using a genetic algorithm these numerical results are not intuitive in particular the optimal position of one interval is never at the middle of the string