energy decay of a variable coefficient wave equation with memory type acoustic boundary conditions abstract we study the energy decay for a variable coefficient wave equation with memory type acoustic boundary conditions boundary memory is described by an integral term applying the riemannian geometry method we obtain the uniform energy decay under some conditions on the memory function and the coefficient matrix

simultaneous exact approximate boundary controllability of thermo elastic plates with variable thermal coefficient and moment control abstract we study a controllability problem exact in the mechanical variables w w t and simultaneously approximate in the thermal variable of thermo elastic plates by means of boundary controls in the hinged dirichlet bc case when the thermal expansion term is variable in space

uniform stabilization of the damped cauchy ventcel problem with variable coefficients and dynamic boundary conditions in this paper the uniform stabilization of the cauchy ventcel problem with variable coefficients is considered and the uniform energy decay rate for the problem is established by riemannian geometry methods

the method of types information theory the method of types is one of the key technical tools in shannon theory and this tool is valuable also in other fields in this paper some key applications are presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method and a wide selection of further applications are surveyed these range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems while the method of types is suitable primarily for discrete memoryless models its extensions to certain models with memory are also discussed

higher order energy decay for damped wave equations with variable coefficients abstract under appropriate assumptions the higher order energy decay rates for the damped wave equations with variable coefficients c x u t t div a x u a x u t 0 in r n are established the results concern weighted in time and pointwise in time energy decay estimates we also obtain weighted l 2 estimates for spatial derivatives

stabilization of the wave equation with variable coefficients and a delay in dissipative boundary feedback we consider the stabilization of the wave equation with variable coefficients and a delay in the dissipative boundary feedback by virtue of the riemannian geometry methods the energy perturbed approach and the multiplier skills we establish the uniform stability of the energy of the closed loop system

stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks in this paper we consider in a bounded and smooth domain the wave equation with a delay term in the boundary condition we also consider the wave equation with a delayed velocity term and mixed dirichlet neumann boundary condition in both cases under suitable assumptions we prove exponential stability of the solution these results are obtained by introducing suitable energies and by using some observability inequalities if one of the above assumptions is not satisfied some instability results are also given by constructing some sequences of delays for which the energy of some solutions does not tend to zero

exact approximate boundary controllability of the thermoelastic plate with a curved middle surface abstract controllability properties of a thermoelastic plate with a curved middle surface are studied by the riemannian geometry approach and the multiplier technique we obtain simultaneously exact controllability of the displacement of the plate and approximate controllability of the temperature through three boundary controls under verifiable assumptions on the geometry of the middle surface

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

universal prediction this paper consists of an overview on universal prediction from an information theoretic perspective special attention is given to the notion of probability assignment under the self information loss function which is directly related to the theory of universal data compression both the probabilistic setting and the deterministic setting of the universal prediction problem are described with emphasis on the analogy and the differences between results in the two settings

exact boundary observability for a kind of second order quasilinear hyperbolic system abstract in this paper by means of a constructive method based on the existence and uniqueness of the semi global classical solution we establish the local exact boundary observability for a kind of second order quasilinear hyperbolic system in which the number of positive eigenvalues and the number of negative ones are not equal as an application we obtain the one sided local exact boundary observability and two sided local exact boundary observability with fewer observed values for first order quasilinear hyperbolic systems of diagonal form with boundary conditions in which the diagonal variables corresponding to the positive eigenvalues and those corresponding to the negative ones are decoupled

on the observability inequalities for exact controllability of wave equations with variable coefficients this paper deals with boundary exact controllability for the dynamics governed by the wave equation with nonconstant coefficients in the principal part subject to dirichlet or neumann boundary controls the observability inequalities are established by the riemannian geometry method under some geometric condition for the dirichlet problem and for the neumann problem respectively next a number of nontrivial examples are presented to verify the observability inequality in particular a counterexample is given without boundary exact controllability where the control is exerted on the whole boundary

global and exponential attractors for extensible thermoelastic plate with time varying delay abstract a class of nonlinear problems modeling thermoelastic extensible plates with rotational inertia and time dependent delay in the internal feedback are considered by virtue of galerkin method combined with the priori estimates we prove the existence and uniqueness of global solution the proof with or without rotational inertia does not depend on the parameters 1 and 2 of time dependent delay moreover the existence of compact global and exponential attractors is proved through a stabilizability estimate this estimate which is established under restrictions on 1 and 2 and independently of the rotational inertia parameter provides bounds on the attractors fractal dimension other property such as additional smoothness of global attractors with respect to parameter is also presented furthermore the existence of a generalized fractal exponential attractor is also derived finally we show that the family of global attractors is continuous with respect to the parameter in some sense

existence and decay of solutions for a viscoelastic wave equation with acoustic boundary conditions abstract in this paper we consider a multi dimensional damped semilinear viscoelastic wave equation with variable coefficient and acoustic boundary conditions first we prove a local existence theorem by using the faedo galerkin approximations combined with a contraction mapping theorem second we show that under suitable conditions on the initial data and the relaxation function the solution exists globally in time and we prove the uniform decay rate of the energy

the nonstochastic multiarmed bandit problem in the multiarmed bandit problem a gambler must decide which arm of k nonidentical slot machines to play in a sequence of trials so as to maximize his reward this classical problem has received much attention because of the simple model it provides of the trade off between exploration trying out each arm to find the best one and exploitation playing the arm believed to give the best payoff past solutions for the bandit problem have almost always relied on assumptions about the statistics of the slot machines in this work we make no statistical assumptions whatsoever about the nature of the process generating the payoffs of the slot machines we give a solution to the bandit problem in which an adversary rather than a well behaved stochastic process has complete control over the payoffs in a sequence of t plays we prove that the per round payoff of our algorithm approaches that of the best arm at the rate o t 1 2 we show by a matching lower bound that this is the best possible we also prove that our algorithm approaches the per round payoff of any set of strategies at a similar rate if the best strategy is chosen from a pool of n strategies then our algorithm approaches the per round payoff of the strategy at the rate o log n1 2 t 1 2 finally we apply our results to the problem of playing an unknown repeated matrix game we show that our algorithm approaches the minimax payoff of the unknown game at the rate o t 1 2

the capacity of the arbitrarily varying channel revisited positivity constraints a well known result of r ahlswede 1970 asserts that the deterministic code capacity of an arbitrarily varying channel avc under the average error probability criterion either equals its random code capacity or else is zero a necessary and sufficient condition is identified for deciding between these alternative namely the capacity is zero if and only if the avc is symmetrizable the capacity of the avc is determined with constraints on the transmitted codewords as well as on the channel state sequences and it is demonstrated that it may be positive but less than the corresponding random code capacity a special case of the results resolves a weakened version of a fundamental problem of coding theory

global smooth solutions for the quasilinear wave equation with boundary dissipation abstract we consider the existence of global solutions of the quasilinear wave equation with a boundary dissipation structure of an input output in high dimensions when initial data and boundary inputs are near a given equilibrium of the system our main tool is the geometrical analysis the main interest is to study the effect of the boundary dissipation structure on solutions of the quasilinear system we show that the existence of global solutions depends not only on this dissipation structure but also on a riemannian metric given by the coefficients and the equilibrium of the system some geometrical conditions on this riemannian metric are presented to guarantee the existence of global solutions in particular we prove that the norm of the state of the system decays exponentially if the input stops after a finite time which implies the exponential stabilization of the system by boundary feedback

communication over individual channels a communication problem in considered where no mathematical model is specified for the channel the achievable rates are determined as a function of the channel input and output sequences known a posteriori without assuming any a priori relation between them for discrete channels the empirical mutual information between the input and output sequences is shown to be achievable while for continuous channels the achievable rate is based on the empirical correlation between the sequences a rate adaptive scheme employing feedback which achieves these rates asymptotically with a guaranteed reliability without prior knowledge of the channel behavior is presented

inverse observability estimates for second order hyperbolic equations with variable coefficients abstract we consider a general second order hyperbolic equation defined on an open bounded domain r n with variable coefficients in both the elliptic principal part and in the first order terms as well at first no boundary conditions b c are imposed our main result theorem 3 5 is a reconstruction or inverse estimate for solutions w under checkable conditions on the coefficients of the principal part the h1 l2 energy at time t t or at time t 0 is dominated by the l2 norms of the boundary traces w a and wt modulo an interior lower order term once homogeneous b c are imposed our results yield under a uniqueness theorem needed to absorb the lower order term continuous observability estimates for both the dirichlet and neumann case with an explicit sharp observability time hence by duality exact controllability results moreover no artificial geometrical conditions are imposed on the controlled part of the boundary in the neumann case in contrast with existing literature the first step of our method employs a riemann geometry approach to reduce the original variable coefficient principal part problem in r n to a problem on an appropriate riemann manifold determined by the coefficients of the principal part where the principal part is the laplacian in our second step we employ explicit carleman estimates at the differential level to take care of the variable first order energy level terms in our third step we employ micro local analysis yielding a sharp trace estimate to remove artificial geometrical conditions on the controlled part of the boundary in the neumann case

stabilization of euler bernoulli plate equation with variable coefficients by nonlinear boundary feedback abstract the aim of this paper is to investigate the uniform stabilization of euler bernoulli plate equation with variable coefficients in the principle part subject to nonlinear boundary feedback laws the exponential or rational energy decay rate is obtained by the multiplier method and the riemannian geometry method

exact boundary observability for a kind of second order quasilinear hyperbolic systems and its applications abstract in this paper by means of a constructive method based on the existence and uniqueness of the semi global c 2 solution we establish the local exact boundary observability for a kind of second order quasilinear hyperbolic systems as an application we obtain the one sided local exact boundary observability for a kind of first order quasilinear hyperbolic systems of diagonal form with boundary conditions in which the diagonal variables corresponding to the positive eigenvalues and those corresponding to the negative eigenvalues are decoupled

average cost optimal stationary policies in infinite state markov decision processes with unbounded costs we deal with infinite state markov decision processes with unbounded costs three simple conditions based on the optimal discounted value function guarantee the existence of an expected average cost optimal stationary policy sufficient conditions are the existence of a distinguished state of smallest discounted value and a single stationary policy inducing an irreducible ergodic markov chain for which the average cost of a first passage from any state to the distinguished state is finite a result to verify this is also given two examples illustrate the ease of applying the criteria

optimal feedback production planning in a stochastic n machine flowshop we consider a production planning problem in an n machine flowshop subject to breakdown and repair of machines and to non negativity constraints on work in process the machine capacities and demand processes are assumed to be finite state markov chains the problem is to choose the rates of production on the n machines over time to minimize the expected discounted cost of production and inventory backlog over an infinite horizon it is formulated as a stochastic dynamic programming problem we show that the value function of the problem is locally lipschitz and is a solution to a dynamic programming equation together with a certain boundary condition we provide an interpretation of the boundary condition we also prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the value function finally we obtain a deterministic optimal control problem that is equivalent to the stochastic production planning problem under consideration

universal communication over arbitrarily varying channels consider the problem of universally communicating over an arbitrarily varying channel i e a channel comprised of an unknown arbitrary sequence of memoryless channels it is shown that there is a communication system using feedback and common randomness that asymptotically attains with high probability the capacity of the time averaged channel universally for every sequence of channels this attainable rate is optimal under certain conditions while no prior knowledge of the channel sequence is assumed the capacity of the time averaged channel meets or exceeds the traditional arbitrarily varying channel avc capacity for every memoryless avc defined over the same alphabets and therefore the system universally attains the random code avc capacity without knowledge of the avc parameters the presented system combines rateless coding with a universal prediction scheme for the input prior distribution from which the codebook is randomly drawn because at each point in time the future of the channel sequence is unknown to the communicators the adaptation of the input behavior by universally predicting the prior plays a major role in the result

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

uniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditions abstract a variable coefficient wave equation with nonlinear damped acoustic boundary conditions is considered the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients the uniform decay of the energy is achieved without any geometrical conditions on the shape of the dissipative portion of the boundary

rate of decay of solutions of the wave equation with arbitrary localized nonlinear damping abstract we study the rate of decay of solutions of the wave equation with localized nonlinear damping without any growth restriction and without any assumption on the dynamics providing regular initial data the asymptotic decay rates of the energy functional are obtained by solving nonlinear ode moreover we give explicit uniform decay rates of the energy more precisely we find that the energy decays uniformly at last as fast as 1 ln t 2 2 0 when the damping has a polynomial growth or sublinear and for an exponential damping at the origin the energy decays at last as fast as 1 ln ln t e 2 2 0

well posedness for a variable coefficient wave equation with nonlinear damped acoustic boundary conditions abstract we consider a variable coefficient wave equation with nonlinear damped acoustic boundary conditions well posedness in the hadamard sense for strong and weak solutions is proved by using the theory of nonlinear semigroups

sequential prediction of individual sequences under general loss functions we consider adaptive sequential prediction of arbitrary binary sequences when the performance is evaluated using a general loss function the goal is to predict on each individual sequence nearly as well as the best prediction strategy in a given comparison class of possibly adaptive prediction strategies called experts by using a general loss function we generalize previous work on universal prediction forecasting and data compression however here we restrict ourselves to the case when the comparison class is finite for a given sequence we define the regret as the total loss on the entire sequence suffered by the adaptive sequential predictor minus the total loss suffered by the predictor in the comparison class that performs best on that particular sequence we show that for a large class of loss functions the minimax regret is either spl theta log n or spl omega spl radic spl lscr log n depending on the loss function where n is the number of predictors in the comparison class and spl lscr is the length of the sequence to be predicted the former case was shown previously by vovk 1990 we give a simplified analysis with an explicit closed form for the constant in the minimax regret formula and give a probabilistic argument that shows this constant is the best possible some weak regularity conditions are imposed on the loss function in obtaining these results we also extend our analysis to the case of predicting arbitrary sequences that take real values in the interval 0 1

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

discounted stochastic fluid programs we consider optimal control problems for stochastic fluid models of the following type suppose z t is a continuous time markov chain with finite state space as long asz t z the dynamics of the system at timet are given by a functionb z u i whereu is a control we have to choose a cost rate functionc is given depending on the state and the action we want to control the system in such a way as to minimize the expected discounted cost over an infinite horizon we will call a problem of this type astochastic fluid program sfp they typically appear in production and telecommunication systems we formulate the optimization problem as a discrete time markov decision process and give conditions under which an optimal stationary policy exists furthermore we show how to solve sfps numerically using kushner s approximating markov chain approach last but not least we apply our results to a multiproduct manufacturing system without backlog

universal communication part ii channels with memory consider communication over a channel whose probabilistic model is completely unknown vector wise and is not assumed to be stationary communication over such channels is challenging because knowing the past does not indicate anything about the future the existence of reliable feedback and common randomness is assumed in a previous paper it was shown that the shannon capacity cannot be attained in general if the channel is not known an alternative notion of capacity was defined as the maximum rate of reliable communication by any block coding system used over consecutive blocks this rate was shown to be achievable for the modulo additive channel with an individual unknown noise sequence and not achievable for some channels with memory in this paper this capacity is shown to be achievable for general channel models possibly including memory as long as this memory fades with time in other words there exists a system with feedback and common randomness that without knowledge of the channel asymptotically performs as well as any block code which may be designed knowing the channel for channels in which memory does not fade with time a weaker type of capacity is shown to be achievable

uniform stabilization of the wave equation on compact manifolds and locally distributed damping a sharp result abstract let m g be an n dimensional n 2 compact riemannian manifold with or without boundary where g denotes a riemannian metric of class c this paper is concerned with the study of the wave equation on m g with locally distributed damping described by u t t g u a x g u t 0 on m 0 u 0 on m 0 where m represents the boundary of m and the last condition is dropped when m is boundaryless let 0 we prove that there exist an open subset v m and a smooth function f m r such that meas v meas m hess f g on v and inf x v f x 0 this function f is used in order to prove that if a x a 0 0 on an open subset m m that contains m v and if g is a monotonic increasing function such that k s g s k s for all s 1 then uniform and optimal decay rates of the energy hold therefore given an arbitrary 0 uniform and optimal decay rates of the energy hold if the damping is effective in a well chosen open subset with volume less than

average optimality in dynamic programming with general state space a markovian decision model with general state space compact action space and the average cost as criterion is considered the existence of an optimal policy is shown via an optimality inequality in terms of the minimal average cost g and a relative value function w the existence of some w is usually shown via relative compactness in a space of real valued functions on the state space here it shall be shown that one can instead do with pointwise relative compactness in the set of real numbers if one makes use of a generalized lower limit of functions an application to an inventory model is given

achieving the empirical capacity using feedback memoryless additive models we address the problem of universal communications over an unknown channel with an instantaneous noiseless feedback and show how rates corresponding to the empirical behavior of the channel can be attained although no rate can be guaranteed in advance first we consider a discrete modulo additive channel with alphabet x where the noise sequence zn is arbitrary and unknown and may causally depend on the transmitted and received sequences and on the encoder s message possibly in an adversarial fashion although the classical capacity of this channel is zero we show that rates approaching the empirical capacity log x h emp zn can be universally attained where h emp zn is the empirical entropy of zn for the more general setting where the channel can map its input to an output in an arbitrary unknown fashion subject only to causality we model the empirical channel actions as the modulo addition of a realized noise sequence and show that the same result applies if common randomness is available the results are proved constructively by providing a simple sequential transmission scheme approaching the empirical capacity

uniform exponential energy decay of wave equations in a bounded region with l2 0 l2 γ feedback control in the dirichlet boundary conditions etant donne un ouvert borne r n n 2 on considere l equation d onde w tt w dans o avec des conditions initiales w o x w o x l 2 w 1 o x w 1 x h 1 et des conditions aux limites non homogenes de type dirichlet w t u t sur o etant la frontiere de

energy decay for a nonlinear wave equation of variable coefficients with acoustic boundary conditions and a time varying delay in the boundary feedback abstract a variable coefficient wave equation with acoustic boundary conditions and a time varying delay in the boundary feedback is considered applying the riemannian geometry method we show that the decay rates of the nonlinear system with a time varying delay are described by solutions to a first order ode

a new global carleman estimate for cahn hilliard type equation and its applications abstract we establish a new carleman inequality for linear cahn hilliard type equation when the norms of right hand sides are in sobolev spaces of negative orders and apply it to obtain the unique continuation property ucp for cahn hilliard type equation with the coefficients of terms of lower order that are not regular and null controllability for semilinear cahn hilliard type equation whose semilinear term contains derivatives of first and second order of solutions

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

controllability for transmission wave plate equations on riemannian manifolds abstract in this paper we consider controllability for transmission system of coupling wave equations with euler bernoulli equations on riemannian manifolds we show that such a system is exactly controllable by boundary controls only along the exterior boundary which means there is no control on the interface of the transmission system our proofs rely on the hilbert uniqueness method hum and geometric multiplier method

the uniform distribution as a universal prior in this correspondence we discuss the properties of the uniform prior as a universal prior i e a prior that induces a mutual information that is simultaneously close to the capacity for all channels we determine bounds on the amount of the mutual information loss in using the uniform prior instead of the capacity achieving prior specifically for the class of binary input channels with any output alphabet we show that the z channel has the minimal mutual information with uniform prior out of all channels with a given capacity from this we conclude that the degradation of the mutual information with respect to the capacity is at most 0 011 bit and as was shown previously at most 6 a related result is that the capacity achieving prior for any channel is not far from uniform some of these results are extended to channels with nonbinary input

stabilization of the elastodynamic equations with a degenerate locally distributed dissipation we consider the dynamic elasticity equations with a locally distributed damping in a bounded domain the local dissipation of the form a x yt involves coefficients a that vanish on a negligible portion of the subset where the damping is effective using multiplier techniques interpolation inequalities and a judicious application of holder inequality we prove sharp energy decay estimates the results obtained generalize and improve on earlier works by nakao and the author in the framework of the ordinary wave equation

control and stabilization for the wave equation with variable coefficients in domains with moving boundary abstract the study of stabilization and control for pdes with variable coefficients involves higher level of complexity than the corresponding case of constant coefficients further compounding the complexity are the concern and effects of dynamic boundary motion the problem in its general form is extremely challenging to treat but under certain specific physical and geometric conditions such as the time likeness of the boundary and a limited speed of domain expansion energy decay estimates can be established and the exact controllability can also be obtained by control theoretic and riemannian geometric methods our approach here is based on the bochner technique of differential geometry in terms of riemannian metric and geometric multipliers by generalizing an energy identity method used earlier in bardos and chen 1981 concrete examples are also given to illustrate the geometric conditions and the theorems

asymptotic stability of the wave equation on compact manifolds and locally distributed damping a sharp result let m g be a n dimensional n geqq 2 compact riemannian manifold with boundary where g denotes a riemannian metric of class c this paper is concerned with the study of the wave equation on m g with locally distributed damping described by left begin array l u tt delta bf g u a x g u t 0 quad hbox on thinspace m times left 0 infty right u 0 hbox on partial m times left 0 infty right end array right where m represents the boundary of m and a x g ut is the damping term the main goal of the present manuscript is to generalize our previous result in cavalcanti et al trans ams 361 9 4561 4580 2009 treating the conjecture in a more general setting and extending the result for n dimensional compact riemannian manifolds m g with boundary in two ways i by reducing arbitrarily the region m ast subset m where the dissipative effect lies this gives us a totally sharp result with respect to the boundary measure and interior measure where the damping is effective ii by controlling the existence of subsets on the manifold that can be left without any dissipative mechanism namely a precise part of radially symmetric subsets an analogous result holds for compact riemannian manifolds without boundary

stabilization of transmission coupled wave and euler bernoulli equations on riemannian manifolds by nonlinear feedbacks abstract we consider the transmission system of coupling wave equations with euler bernoulli equations on riemannian manifolds by introducing nonlinear boundary feedback controls we establish the exponential and rational energy decay rate for the problem our proofs rely on the geometric multiplier method

convex stochastic fluid programs with average cost abstract we consider stochastic fluid programs under the average cost criterion these models have been introduced by the author in press math oper res and are of the following type suppose z t is a continuous time markov chain with finite state space as long as z t z the dynamics of the system at time t are given by a linear function b z a where a is a control we have to choose a convex cost rate function c is given depending on the state and the action we want to control the system in such a way as to minimize the expected average cost such models typically appear in production and telecommunication systems using a vanishing discount approach and a discretization technique we show that the relative value function satisfies a hjb equation and derive a verification theorem last but not least we apply our results to manufacturing systems and network problems

general decay of the solution for a viscoelastic wave equation with a time varying delay term in the internal feedback in this paper we consider a viscoelastic wave equation with a time varying delay term the coefficient of which is not necessarily positive by introducing suitable energy and lyapunov functionals under suitable assumptions we establish a general energy decay result from which the exponential and polynomial types of decay are only special cases