long time behavior of a model of extensible beams with nonlinear boundary dissipations abstract this paper is concerned with the long time behavior of a model of extensible beams u t t u x x x x m 0 l u x 2 d x u x x h defined in a bounded interval 0 l where m is a continuous nonnegative function and h is a static load to this problem little is known with nonlinear boundary conditions one considers the case where a nonlinear forcing interacts with the shear force at the boundary then the existence of a global attractor is proved with a sole boundary damping

adaptive stabilization of a kirchhoff s non linear beam with output disturbances abstract this paper is concerned with adaptive stabilization of an undamped non linear beam with disturbed outputs by boundary feedback control the adaptive controller is constructed by the concept of high gain adaptive feedback and the estimation mechanism for the unknown parameters of the measurement noise the global existence and uniqueness of the solution of the closed loop system is justified the stability of the closed loop system is proved such that the convergence of the system state to zero and the convergence of the estimated parameter to the unknown parameter are guaranteed for the smooth and small initial data

abstract volterra integrodifferential equations with applications to parabolic models with memory in this paper we are concerned with local existence regularity and continuous dependence upon the initial data of epsilon regular mild solutions for the abstract integrodifferential equation 1 2 we also present a result on unique continuation and a blow up alternative for an epsilon regular mild solution of 1 2 finally we apply our results to three interesting models navier stokes equations with memory diffusion equations with memory and a strongly damped plate equation with memory

classical solutions of nonlinear beam equations existence and stabilization in this paper we consider the large amplitude planar motion of a cantilevered beam with a feedback force and or torque proportional and acting opposite to the velocity angular velocity respectively applied at the free end we derive nonlinear equations of motion for such a beam based upon certain natural geometric assumptions we then prove the existence of classical solutions for these equations and show that all classical solutions are uniformly exponentially stable

global attractors for the extensible thermoelastic beam system abstract this work is focused on the dissipative system t t u x x x x u x x x u l 2 0 1 2 x x u f t x x x x t u g describing the dynamics of an extensible thermoelastic beam where the dissipation is entirely contributed by the second equation ruling the evolution of under natural boundary conditions we prove the existence of bounded absorbing sets when the external sources f and g are time independent the related semigroup of solutions is shown to possess the global attractor of optimal regularity for all parameters r the same result holds true when the first equation is replaced by t t u x x t t u x x x x u x x x u l 2 0 1 2 x x u f with 0 in both cases the solutions on the attractor are strong solutions

binary modulated signal detection in a bistable receiver with stochastic resonance abstract the archetypal bistable system can act as a nonlinear receiver for detecting binary signals modulated by amplitude frequency or phase the introduction of noise enhances signal detection for a certain range of noise intensity which is ascribed to non conventional stochastic resonance sr phenomena such as residual aperiodic sr and short time sr for the first time we unify binary modulated signal detection from the point of view of an approximate probability density model we develop both theoretical and numerical analyses of the receiver performance for each type of modulated signal the optimization of receiver parameters and comparisons of the optimal bistable receiver versus the linear matched filter are also investigated an interesting result is that the probability density model enables us to explore the sr range of noise intensity and the optimally tuned bistable receiver theoretically which may play a prominent role for nonlinear systems performing in noisy conditions

noisy fitzhugh nagumo model from single elements to globally coupled networks we study the noisy fitzhugh nagumo model representative of the dynamics of excitable neural elements and derive a fokker planck equation for both a single element and for a network of globally coupled elements we introduce an efficient way to numerically solve this fokker planck equation especially for large noise levels we show that contrary to the single element the network can undergo a hopf bifurcation as the coupling strength is increased furthermore we show that an external sinusoidal driving force leads to a classical resonance when its frequency matches the underlying system frequency this resonance is also investigated analytically by exploiting the different time scales in the problem

adaptive stabilization for a kirchhoff type nonlinear beam under boundary output feedback control abstract in this paper the boundary stabilization for a kirchhoff type nonlinear beam with one end fixed and control at the other end is considered a gain adaptive controller is designed in terms of measured end velocity the existence and uniqueness of the classical solution of the closed loop system are justified the exponential stability of the system is obtained

global attractor for a nonlinear plate equation with supported boundary conditions abstract in this paper we consider a two dimensional nonlinear equation w t t d 2 w e w t n 1 t 2 w x 2 d x d y w x x n 2 t 2 w y 2 d x d y w y y 0 which arises from the model of the viscoelastic thin rectangular plate with four edges supported by virtue of galerkin method combined with the priori estimates we prove the existence and uniqueness of the global solution under initial boundary data for the above equation especially the existence of the bounded absorbing set in space e and the existence of the global attractor of system is also obtained

hadamard well posedness for a class of nonlinear shallow shell problems abstract this paper is concerned with the nonlinear shallow shell model introduced in 1966 by w t koiter in on the nonlinear theory of thin elastic shells iii nederl akad wetensch proc ser b 69 1966 33 54 section 11 and later studied in m bernadou j t oden an existence theorem for a class of nonlinear shallow shell problems j math pures appl 9 60 3 1981 285 308 we consider a version of this model which is based upon the intrinsic shell modeling techniques introduced by michel delfour and jean paul zolesio we show existence and uniqueness of both regular and weak solutions to the dynamical model and that the solutions are continuous with respect to the initial data while existence and uniqueness of regular solutions to nonlinear dynamic shell equations has been known full hadamard well posedness of weak solutions as shown in this paper is a new result which solves an old open problem in the field

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

remark on the decay for damped string and beam equations where a is an operator in a hilbert space h m is a real function our results improve those obtained by de brito in a recent paper l we briefly recall the notation and the assumptions in l referring to this paper for other information on physical meaning existence and regularity theory applications and bibliography let a be a self adjoint positive operator in a real hilbert space h with dense domain v we assume that 5 0 is the least eigenvalue of a so a u au u 3 51 1 for u e v let m e cl be a real nondecreasing function such that m s 2 p ks k z 0 p real we have with the notation

stochastic euler bernoulli beam driven by additive white noise global random attractors and global dynamics abstract this paper concerns with the long time dynamical behavior of a stochastic euler bernoulli beam driven by additive white noise by verifying the existence of absorbing set and obtaining the stabilization estimation of the dynamical system induced by the beam the existence of global random attractors that attracts all bounded sets in phase space is proved furthermore the finite hausdorff dimension for the global random attractors is attained in light of the relationship between global random attractor and random invariant probability measure the global dynamics of the beam are analyzed according to numerical simulation on global random basic attractors and global random point attractors

parameter induced aperiodic stochastic resonance in the presence of multiplicative noise and additive noise abstract parameter induced aperiodic stochastic resonance sr in the presence of multiplicative and additive noise is investigated in detail using theoretical and numerical analysis we evaluate the dynamical probability density by which the bit error rate is defined as a quantity to optimize in the aperiodic sr problem via tuning the system parameters tuning the system parameters includes two cases one is parameter optimized and the other is parameter induced sr to distinguish them we use the conventional method in which sr is realized by varying the noise intensity essentially parameter induced sr is based on the cooperative effect between the stochastic subjected dynamical system and the input signal by changing the intrinsic characteristic of the nonlinear system via tuning the system parameters rather than by adding noise the theory is tested against numerical simulations

dynamics of a class of odes more general than almost periodic abstract a temporally global solution if it exists of a nonautonomous ordinary differential equation need not be periodic almost periodic or almost automorphic when the forcing term is periodic almost periodic or almost automorphic respectively an alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here specifically the class of functions consists of uniformly continuous functions defined on the real line and taking values in a banach space which have pre compact ranges besides periodic and almost periodic functions this class also includes many nonrecurrent functions assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts the existence of a special bounded entire solution as well the existence of stable and unstable manifolds of this solution are established moreover it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation in the stable case it is shown that this special solution is the pullback attractor of the system a class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a c 0 semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations

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

local and global well posedness of semilinear reissner mindlin timoshenko plate equations abstract this is a study of local and global well posedness of nonlinearly perturbed reissner mindlin timoshenko plate equations this pde system represents an extension of the timoshenko beam model to plates and accounts for shear deformations the primary feature of the considered model is the interplay between nonlinear viscous interior damping and nonlinear source terms the main results verify local and global existence of solutions as well as their continuous dependence on the initial data in the appropriate function spaces moreover a blow up result is proved for solutions with negative initial energy

boundary feedback stabilization of the undamped timoshenko beam with both ends free in this paper we study a boundary feedback system of a class of nonuniform undamped timoshenko beam with both ends free we give some sufficient conditions and some necessary conditions for the system to have exponential stability our method is based on the operator semigroup technique the multiplier technique and the contradiction argument of the frequency domain method

global solution and regularizing properties on a class of nonlinear evolution equation abstract in this paper we will consider the equation formula where formula the initial value problem is proved to be locally well posed for initial data taken ind a2 d a3 2 and globally well posed for small data in this case we also show the exponential decay of the solution as time goes to infinity the main result of this paper is to prove that the solution has the smooting effect property on the initial data this means that if the initial data belongs tod a2 d a3 2 then the solutionubelongs toc 0 d ak k n providedm n andrarec function

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

bayesian estimation of change points using the general linear model bayesian analysis is applied to the general linear model to develop a framework for studying different types of change in the mean value of time series and linear regressions the output of the bayesian analysis is the posterior distribution of change point location and amplitude this information provides a rational and relatively objective basis for making decisions as to where to locate a change point several examples of hydrological applications are presented to demonstrate the utility of the methodology

uniform stabilization of the dynamic elastica by boundary feedback it is proved that the dynamic elastica which is a nonlinear model describing the large deflecting motion of an inextensible beam can be uniformly exponentially stabilized by boundary velocity feedback

a framework of change point detection for multivariate hydrological series under changing environments not only univariate but also multivariate hydrological series might become nonstationary nonstationarity in forms of change point or trend has been widely studied for univariate hydrological series while it attracts attention only recently for multivariate hydrological series for multivariate series two types of change point need to be distinguished i e change point in marginal distributions and change point in the dependence structure among individual variables in this paper a three step framework is proposed to separately detect two types of change point in multivariate hydrological series i e change point detection for individual univariate series estimation of marginal distributions and change point detection for dependence structure the last step is implemented using both the cramer von mises statistic cvm method and the copula based likelihood ratio test clr method for clr three kinds of copula model symmetric asymmetric and pair copula are employed to construct the dependence structure of multivariate series monte carlo experiments indicate that clr is far more powerful than cvm in detecting the change point of dependence structure this framework is applied to the trivariate flood series composed of annual maxima daily discharge amdd annual maxima 3 day flood volume and annual maxima 15 day flood volume of the upper hanjiang river china it is found that each individual univariate flood series has a significant change point and the trivariate series presents a significant change point in dependence structure due to the abrupt change in the dependence structure between amdd and annual maxima 3 day flood volume all these changes are caused by the construction of the ankang reservoir this article is protected by copyright all rights reserved

on the kirchhoff plates equations with thermal effects and memory boundary conditions in this paper we study the existence of weak and strong global solutions and uniform decay of the energy to the kirchhoff plates equations with thermal effect and memory conditions working at the boundary we show that the dissipation produced by the memory effect not depend on the present values of temperature gradient that is we show that the dissipation produced by memory effect is strong enough to produce exponential decay of the solution provided the relaxation functions also decays exponentially when the relaxation functions decays polynomially we show that the solution decays polynomially with the same rate

on a structural acoustic model with interface a reissner mindlin plate or a timoshenko beam abstract this paper is concerned with a model which describes the interaction of sound and elastic waves in a structural acoustic chamber in which one wall is flexible and flat the model is new in the sense that the composite dynamics of the three dimensional structure is described by the linearized equations for a gas defined on the interior of the chamber and the reissner mindlin plate equations on the two dimensional flat wall of the chamber while if a two dimensional acoustic chamber is considered the timoshenko beam equations describe the deflections of the one dimensional wall with a view to achieving uniform stabilization of the structure linear feedback boundary damping is incorporated in the model viz in the wave equation for the gas and in the system of equations for the vibrations of the elastic medium we present the uniform stability result for the case of a two dimensional chamber and outline the method for the three dimensional model which shows strong resemblance with the system of dynamic plane elasticity

uniform stabilization of a nonlinear beam by nonlinear boundary feedback we consider the planar motion of a uniform prismatic beam of length l we want to derive a model that reflects the effect of stretching on bending which necessarily leads to nonlinear partial differential equations for the motion of the beam we will however assume that the constitutive equations for bending are linear this is in agreement with existing engineering literature see for example s and the bibliography therein it should be remarked that the effect of stretching on bending becomes significant if in particular a rigid rotation is superimposed on the motion we do not consider such a rotation here even though it could be handled within the present framework we assume that the beam in its reference state occupies the region described in rectangular coordinates by

long time dynamics of von karman semi flows with non linear boundary interior damping abstract we study von karman evolution equations with non linear dissipation and with partially clamped and partially free boundary conditions two distinctive mechanisms of dissipation are considered i internal dissipation generated by non linear operator and ii boundary dissipation generated by shear forces friction acting on a free part of the boundary the main emphasis is given to the effects of boundary dissipation under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension we also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which in turn depends on the behaviour at the origin of the functions describing the dissipation

comparison of aperiodic stochastic resonance in a bistable system realized by adding noise and by tuning system parameters two methods of realizing aperiodic stochastic resonance asr by adding noise and tuning system parameters in a bistable system after a scale transformation can be compared in a real parameter space in this space the resonance point of asr via adding noise denotes the extremum of a line segment whereas the method of tuning system parameters presents the extrema of a parameter plane we demonstrate that in terms of the system performance the method of tuning system parameters takes the precedence of the approach of adding noise for an adjustable bistable system besides adding noise can be viewed as a specific case of tuning system parameters further research shows that the optimal system found by tuning system parameters may be subthreshold or suprathreshold and the conventional asr effects might not occur in some suprathreshold optimal systems

global attractors for von karman evolutions with a nonlinear boundary dissipation abstract dynamic von karman equations with a nonlinear boundary dissipation are considered questions related to long time behaviour existence and structure of global attractors are studied it is shown that a nonlinear boundary dissipation with a large damping parameter leads to an existence of global compact attractor for all weak finite energy solutions this result has been known in the case of full interior dissipation but it is new in the case when the boundary damping is the main dissipative mechanism in the system in addition we prove that fractal dimension of the attractor is finite the proofs depend critically on the infinite speed of propagation associated with the von karman model considered

evaluation of stochastic resonance based detectors of weak harmonic signals in additive white gaussian noise a thorough evaluation of stochastic resonance in the framework of statistical detection theory is presented both as a nonlinear signal preprocessor and as a detector the pertinent receiver operating characteristics are compared with those of the known statistically optimum detector using extensive monte carlo simulations parameter optimization and computational budget aspects are discussed

uniform stabilizability of a full von karman system with nonlinear boundary feedback full von karman system accounting for in plane accelerations and describing the transient deformations of a thin elastic plate subject to edge loading is considered the energy dissipation is introduced via the nonlinear velocity feedback acting on a part of the edge of the plate it is known j puel and m tucsnak siam j control optim 33 1995 pp 255 273 that in the case of linear dissipation and star shaped domains boundary velocity feedback with the tangential derivatives of horizontal displacements leads to the exponential decay rates for the energy of the resulting closed loop system the main goal of the paper is to derive the uniform energy decay rates valid for the model without the above mentioned restrictions in particular it is shown that simple monotone nonlinear feedback without the tangential derivatives of the horizontal displacements provides the uniform decay rates for the energy in the absence of geometric hypotheses imposed on the controlled part of the boundary this is accomplished by establishing among other things sharp regularity results valid for the boundary traces of solutions corresponding to this nonlinear model and by employing a holmgren type uniqueness result proved recently in v isakov j differential equations 97 1997 pp 134 147 for the dynamical systems of elasticity which are overdetermined on the boundary

global attractors for von karman equations with nonlinear interior dissipation abstract in this paper we study the asymptotic behavior of weak solutions for von karman equations with nonlinear interior dissipation we prove the existence of a global attractor in the space w 2 2 l 2

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

stochastic nonlinear beam equations an extensible beam equation with a stochastic force of a white noise type is studied lyapunov functions techniques being used to prove existence of global mild solutions and asymptotic stability of the zero solution

limit behavior of the solution to nonlinear viscoelastic marguerre von karman shallow shell system abstract this paper is concerned with the nonlinear full marguerre von karman shallow shell system with a dissipative mechanism of memory type the model depends on one small parameter the main purpose of this paper is to show that as the parameter approaches zero the limiting system is the well known full von karman model with memory for thin plates

long time dynamics of an extensible plate equation with thermal memory abstract this work is concerned with long time dynamics of solutions of extensible plate equations with thermal memory the problem corresponds to a model of thermoelasticity based on a theory of non fourier heat flux by considering the case where rotational inertia is present we show that the thermal dissipation is sufficient to stabilize the system and guarantees the existence of a finite dimensional global attractor in addition the existence of exponential attractors is also considered

noise enhanced performance for an optimal bayesian estimator a novel instance of a stochastic resonance effect under the form of a noise improved performance is shown to be possible for an optimal bayesian estimator estimation of the frequency of a periodic signal corrupted by a phase noise is considered the optimal bayesian estimator achieving the minimum of the mean square estimation error is explicitly derived conditions are exhibited where this minimal error is reduced when the noise level is raised over some ranges where this occurs essentially with non gaussian noise in the tested configurations these results contribute a new step in the exploration of stochastic resonance and its potentialities for signal processing

stochastic resonance in discrete time nonlinear ar 1 models this paper deals with stochastic resonance this nonlinear physical phenomenon generally occurs in bistable systems excited by random input noise plus a sinusoid through its internal dynamics such a system forces cooperation between the input noise and the input sine provided the existence of fine tuning between the power noise and the dynamics the system reacts periodically at the frequency of the sine of particular interest is the fact that the local output signal to noise ratio presents a maximum when plotted against the input noise power the system resounds stochastically continuous time systems have already been studied we study the ability of intrinsically discrete time systems general nonlinear ar 1 models to produce stochastic resonance it is then suggested that such discrete systems can be used in signal processing

global attractor for a model of extensible beam with nonlinear damping and source terms abstract this paper is concerned with the existence of a global attractor for the nonlinear beam equation with nonlinear damping and source terms u t t 2 u m u 2 d x u f u g u t h in r where is a bounded domain of r n m is a nonnegative real function and h l 2 the nonlinearities f u and g u t are essentially u u u u and u t r u t respectively with r 0 and this kind of problem models vibrations of extensible beams and plates

trivariate statistical analysis of extreme rainfall events via the plackett family of copulas 1 recent hydrologic studies on multivariate stochastic analysis have indicated that copulas perform well for bivariate problems in particular the frank family of archimedean copulas has been a popular choice for a dependence model however there are limitations to extending such archimedean copulas to trivariate and higher dimensions with very specific restrictions on the kinds of dependencies that can be modeled in this study we examine a non archimedean copula from the plackett family that is founded on the theory of constant cross product ratio it is shown that the plackett family not only performs well at the bivariate level but also allows a trivariate stochastic analysis where the lower level dependencies between variables can be fully preserved while allowing for specificity at the trivariate level as well the feasible range of plackett parameters that would result in valid 3 copulas is determined numerically the trivariate plackett family of copulas is then applied to the study of temporal distribution of extreme rainfall events for several stations in indiana where the estimated parameters lie in the feasible region on the basis of a given rainfall depth and duration conditional expectations of rainfall features such as expected peak intensity time to peak and percentage cumulative rainfall at 10 cumulative time increments are evaluated the results of this study suggest that while the constant cross product ratio theory was conventionally applied to discrete type random variables it is also applicable to continuous random variables and that it provides further flexibility for multivariate stochastic analyses of rainfall

noise enhanced capacity via stochastic resonance in an asymmetric binary channel a nonlinear system is considered where an aperiodic binary input signal is added to an arbitrarily distributed noise and compared to a fixed threshold to determine the binary output signal noise enhancement of the transmission of the aperiodic signal via stochastic resonance is demonstrated and studied in this nonlinear information channel the characterization developed goes up to the calculation of the information capacity of the channel defined as the maximal achievable input output transinformation occurring when the statistics of the input signal is matched to the noise it is then demonstrated that a regime exists where the information capacity of the channel can be increased by means of an increase of the noise up to an optimal noise level where the capacity resonates at a maximum value the influence on this resonance of the noise distribution is also studied

multivariate hydrological frequency analysis using copulas 1 this article presents the modeling of multivariate extreme values using copulas our approach allows us to model the dependence structure independently of the marginal distributions which is not possible with standard classical methods the methodology has been applied on two different problems in hydrology the first application is concerned with the combined risk in the framework of frequency analysis four copulas have been tested on peak flows from the watershed of peribonka in quebec canada the second application relates to the joint modeling of peak flows and volumes three copulas have been applied to the watershed of the rimouski river in quebec canada this approach using copulas is promising since it allows us to take into account a wide range of correlation which can happen in hydrology

renyi entropy measure of noise aided information transmission in a binary channel this paper analyzes a binary channel by means of information measures based on the renyi entropy the analysis extends and contains as a special case the classic reference model of binary information transmission based on the shannon entropy measure the extended model is used to investigate further possibilities and properties of stochastic resonance or noise aided information transmission the results demonstrate that stochastic resonance occurs in the information channel and is registered by the renyi entropy measures at any finite order including the shannon order furthermore in definite conditions when seeking the renyi information measures that best exploit stochastic resonance then nontrivial orders differing from the shannon case usually emerge in this way through binary information transmission stochastic resonance identifies optimal renyi measures of information differing from the classic shannon measure a confrontation of the quantitative information measures with visual perception is also proposed in an experiment of noise aided binary image transmission

the existence of smooth solutions for a nonlinear beam with boundary input and output in this article a dynamical system modeling the bending vibrations of a quasilinear beam is considered where the nonlinearity comes from hooke s law we are concerned with the existence of local smooth solutions to this quasi linear beam with boundary input and output applying the evolution system theory we first show that a related linear system admits a unique smooth solution then some energy estimates for the linear system are established finally the existence of local smooth solutions to the quasi linear system is shown through fixed point arguments

uniform decay rates for nonlinear viscoelastic marguerre von karman equations abstract in this paper we consider a model of nonlinear viscoelastic shallow shell that is referred to as the full marguerre von karman under the presence of long time memory we show that the energy functional associated with the system decays exponentially to zero as time goes to infinity

statistical analysis of stochastic resonance in a simple setting a subthreshold signal may be detected if noise is added to the data we study a simple model consisting of a constant signal to which at uniformly spaced times independent and identically distributed noise variables with known distribution are added a detector records the times at which the noisy signal exceeds a threshold there is an optimal noise level called stochastic resonance we explore the detectability of the signal in a system with one or more detectors with different thresholds we use a statistical detectability measure the asymptotic variance of the best estimator of the signal from the thresholded data or equivalently the fisher information in the data in particular we determine optimal configurations of detectors varying the distances between the thresholds and the signal as well as the noise level the approach generalizes to nonconstant signals

on a global solution and asymptotic behaviour for the generalized damped extensible beam equation abstract we prove the existence and uniqueness of global solutions for the cauchy problem concerning the evolution equation u a 2 u m a 1 2 u 2 h au g u 0 suggested by the study of plates and beams where a is a linear operator in a hilbert space h and m and g are real functions we also study the asymptotic behaviour of the solutions under suitable growth assumptions on the nonlinear term g