initial boundary value problem for the system of compressible adiabatic flow through porous media abstract we study the initial value problem for the system of compressible adiabatic flow through porous media in the one space dimension with fixed boundary condition under the restriction on the oscillations in the initial data we establish the global existence and large time behavior for the classical solutions via the combination of characteristic analysis and energy estimate methods the time asymptotic states for the solution are found and the exponential convergence to the asymptotic states is proved it is also shown that this problem can be approximated very well time asymptotically by an initial boundary problem for the related diffusion equations obtained from the original hyperbolic system by darcy s law provided that the initial total mass is the same the difference between these two solutions tends to zero exponentially fast as time goes to infinity in the sense of h 1 the diffusive phenomena caused by damping mechanism with boundary effects are thus observed

stabilization for wave equation of variable coefficients with balakrishnan taylor damping and source term abstract in this paper we consider the wave equation of variable coefficients with balakrishnan taylor damping time varying delay and source term by establishing some lyapunov functionals which are equivalent to the energy of the system and using the potential well method to deal with the source term we prove a general stability result

global smooth solutions and exponential stability for a nonlinear beam in this paper we consider a dynamical system with boundary input and output describing the bending vibrations of a quasi linear beam where the nonlinearity comes from hooke s law first we derive an existence result for short time solutions of the system of equations then we show that the structure of the boundary input and output forces the system to admit global solutions at least when the initial data and the boundary input are small in a certain sense in particular we prove that the norm of the state of the system decays exponentially if the input becomes zero after a finite time the input being zero can be understood as a boundary feedback

on a system of klein gordon type equations with acoustic boundary conditions we prove the existence uniqueness and uniform stabilization of global solutions for a generalized system of klein gordon type equations with acoustic boundary conditions on a portion of the boundary and the dirichlet boundary condition on the rest

moment methods for decision analysis decision models involving continuous probability distributions almost always require some form of approximation the usual approach to evaluating these kinds of models is to construct a discrete approximation for each continuous distribution and compute value lotteries and certain equivalents using these discrete approximations although decision analysts are quite comfortable with this approach there has been relatively little consideration of how these discrete approximations affect the results of the analysis in the first part of this paper we review three common methods of constructing discrete approximations and compare their performance in a simple example the results of the example suggest a different approach that offers potential improvements in accuracy and efficiency over the usual approach the basic idea is that given discrete approximations that accurately represent the moments of assessed input distributions we may easily and accurately compute the moments of the output distribution or value lotteries these moments then summarize what we know about the value lottery and certain equivalent and provide the basis for computing approximate value lotteries and certain equivalents in this paper we discuss the methods supporting this moment approach and evaluate their performance in the context of the example

global smooth solutions and stabilization of nonlinear elastodynamic systems with locally distributed dissipation we consider the existence of global solutions of the nonlinear elastodynamic system with a locally distributed damping in a bounded domain we assume that the energy function satisfies the strong ellipticity condition at the zero equilibrium the local dissipation is in the form a x u where the nonnegative function a x is only positive on a small portion of the domain we show the existence of global smooth solutions when initial data are small in particular we obtain the exponential decay of the energy which implies the exponential stabilization of the system by internal feedback

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

on anova expansions and strategies for choosing the anchor point the classic lebesgue anova expansion offers an elegant way to represent functions that depend on a high dimensional set of parameters and it often enables a substantial reduction in the evaluation cost of such functions once the anova representation is constructed unfortunately the construction of the expansion itself is expensive due to the need to evaluate high dimensional integrals a way around this is to consider an alternative formulation known as the anchored anova expansion this formulation requires no integrals but has an accuracy that depends sensitively on the choice of a special parameter known as the anchor point we present a comparative study of several strategies for the choice of this anchor point and argue that the optimal choice of this anchor point is the center point of a sparse grid quadrature this choice induces no additional cost and as we shall show results in a natural truncation of the anova expansion the efficiency and accuracy is illustrated through several standard benchmarks and this choice is shown to outperform the alternatives over a range of applications c 2010 elsevier inc all rights reserved

three point approximations for continuous random variables this paper compares a number of approximations used to estimate means and variances of continuous random variables and or to serve as substitutes for the probability distributions of such variables with particular emphasis on three point approximations numerical results from estimating means and variances of a set of beta distributions indicate surprisingly large differences in accuracy among approximations in current use with some of the most popular ones such as the pert and triangular density function approximations faring poorly a simple new three point approximation which is a straightforward extension of earlier work by pearson and tukey outperforms the others significantly in these tests and also performs well in related multivariate tests involving the dirichlet family of distributions it offers an attractive alternative to currently used approximations in a variety of applications

global solutions and blow up solutions for a nonlinear string with boundary input and output abstract in this paper we investigate the global solutions and blow up solutions for a nonlinear string with boundary input and output and prove that under some conditions the system has global solutions and blow up solutions respectively

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

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

an energy preserving nonlinear system modeling a string with input and output on the boundary abstract we study an energy conserving distributed parameter system described by a nonlinear string equation with the input and output at the boundary we prove the existence of global smooth solutions to this quasilinear hyperbolic system if the initial data and the boundary input are small if moreover the input function becomes zero after some finite time then the state trajectories decay exponentially

h stability for linear dynamic equations on time scales we study the h stability for linear dynamic equations on time scales and their perturbations by using the bihari type inequality on time scales and the unified time scale quadratic lyapunov functions

better estimation of pert activity time parameters this paper builds upon earlier work from the decision risk analysis area in presenting simple easy to use approximations for the mean and variance of pert activity times these approximations offer significant advantages over the pert formulas currently being taught and used as well as over recently proposed modifications for instance they are several orders of magnitude more accurate than their pert counterparts in estimating means and variances of beta distributions if the data required for all methods are obtained accurately moreover they utilize probability data that can be assessed more reliably than those required by the pert formulas while still requiring just three points from each activity time probability distribution using the proposed approximations can significantly improve the accuracy of probability statements about project completion time and their use complements ongoing efforts to improve pert analyses of networks involving multiple critical paths

a probabilistic interpretation of the final rankings in ahp abstract the analytic hierarchy process ahp has become a popular and practical tool for dealing with complex decision problems it provides a ranking for the decision alternatives this article recommends treating the pairwise comparison input data as random variables this will allow the determination of whether the differences between alternatives are statistically significant

modeling uncertainty in multi criteria decision analysis abstract his paper provides a review of multiple criteria decision analysis mcda for cases where attribute evaluations are uncertain the main aim is to identify different tools which can be used to represent uncertain evaluations and to broadly survey the available decision models that can be used to support uncertain decision making the review includes models using probabilities or probability like quantities explicit risk measures such as quantiles and variances fuzzy numbers and scenarios the practical assessment of uncertain outcomes and preferences associated with these outcomes is also discussed

stabilization of the variable coefficient structural acoustic model with curved middle surface and delay effects in the structural component abstract this paper is concerned with the uniform energy decay rates of a structural acoustic model which describes the interactions between the acoustic medium and the elastic structural in an acoustic chamber where one wall is flexible and curved the coupled system considered consists of a variable coefficient wave equation and a variable coefficient plate equation defined on the riemannian manifold with the coupling on the interface between the acoustic medium and the flexible wall both the components of the dynamics are subject to nonlinear boundary damping furthermore a nonlinear delay term acting in the boundary feedbacks of the structure component is considered the riemannian geometry method is applied to derive the energy estimates of the nonlinear coupled system with variable coefficients the uniform energy decay rates of the nonlinear variable coefficient structural acoustic system with delay effects on the riemannian manifold are quantified by a solution to a constructed nonlinear ode

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

energy decay and periodic solution for the wave equation in an exterior domain with half linear and nonlinear boundary dissipations abstract we first consider the wave equation in an exterior domain in r n with two separated boundary parts 0 1 on 0 the dirichlet condition u 0 0 is imposed while on 1 neumann type nonlinear boundary dissipation u g u t is assumed further a half linear localized dissipation is attached on for such a situation we derive a precise rate of decay of the energy e t for solutions of the initial boundary value problem we impose no geometrical condition on the shape of the boundary 0 1 secondly when a t periodic forcing term works we prove the existence of a t periodic solution on r under an additional growth assumption on x v and g v

correlations and copulas for decision and risk analysis the construction of a probabilistic model is a key step in most decision and risk analyses typically this is done by defining a joint distribution in terms of marginal and conditional distributions for the model s random variables we describe an alternative approach that uses a copula to construct joint distributions and pairwise correlations to incorporate dependence among the variables the approach is designed specifically to permit the use of an expert s subjective judgments of marginal distributions and correlations the copula that underlies the multivariate normal distribution provides the basis for modeling dependence but arbitrary marginals are allowed we discuss how correlations can be assessed using techniques that are familiar to decision analysts and we report the results of an empirical study of the accuracy of the assessment methods the approach is demonstrated in the context of a simple example including a study of the sensitivity of the results to the assessed correlations

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

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

operationalizing approximate multiattribute utility functions for use in practice abstract decision analysis provides defensible methods for rank ordering alternatives based on the calculation of expected utility this technique can be quite time consuming and conceptually difficult for the decision maker as many input parameters are needed to be assessed the recognition of such difficulties prompted researchers to call for simplifying approximations which retain the integrity of the original problem but relieve the assessment burden on the decision maker winkler 1982 this call has been answered with the recent development by kirkwood of taylor series approximations to expected utility which have never been applied in practice this paper further addresses the need to simplify decision analysis through the development of a simulation based technique which allows the kirkwood approximations to be used in practice the technique generates confidence intervals for the true but unknown certain equivalents which are used to rank order alternatives

controllability of the linear one dimensional wave equation with inner moving forces we address the null inner controllability of the one dimensional wave equation with supports of the controls that may vary with respect to the time variable we consider theoretical and numerical aspects assuming a geometric optic condition on the support of the controls we first prove a generalized observability inequality for the homogeneous wave equation implying the controllability we then introduce and prove the well posedness of a mixed formulation that characterizes the controls of minimal square integrable norm a numerical approximation of this formulation based on a conformal space time finite element method is then presented several numerical experiments are finally reported

stability and asymptotic behavior of perturbed difference systems the asymptotic behavior of the solutions of a class of functional difference equations is studied the results obtained which are applied to delay difference equations and summary difference equations give good estimates and explicit radius of attraction

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

using bayesian networks for bankruptcy prediction some methodological issues abstract this study provides operational guidance for building naive bayes bayesian network bn models for bankruptcy prediction first we suggest a heuristic method that guides the selection of bankruptcy predictors based on the correlations and partial correlations among variables the method aims at eliminating redundant and less relevant variables a naive bayes model is developed using the proposed heuristic method and is found to perform well based on a 10 fold validation analysis the developed naive bayes model consists of eight first order variables six of which are continuous we also provide guidance on building a cascaded model by selecting second order variables to compensate for missing values of first order variables second we analyze whether the number of states into which the six continuous variables are discretized has an impact on the model s performance our results show that the model s performance is the best when the number of states for discretization is either two or three starting from four states the performance starts to deteriorate probably due to over fitting finally we experiment whether modeling continuous variables with continuous distributions instead of discretizing them can improve the model s performance our finding suggests that this is not true one possible reason is that continuous distributions tested by the study do not represent well the underlying distributions of empirical data finally the results of this study could also be applicable to business decision making contexts other than bankruptcy prediction

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

a copulas based approach to modeling dependence in decision trees this paper presents a general framework based on copulas for modeling dependent multivariate uncertainties through the use of a decision tree the proposed dependent decision tree model allows multiple dependent uncertainties with arbitrary marginal distributions to be represented in a decision tree with a sequence of conditional probability distributions this general framework could be naturally applied in decision analysis and real options valuations as well as in more general applications of dependent probability trees while this approach to modeling dependencies can be based on several popular copula families as we illustrate we focus on the use of the normal copula and present an efficient computational method for multivariate decision and risk analysis that can be standardized for convenient application

the most critical path in a pert network a heuristic approach abstract the classical pert approach uses a deterministic critical path to estimate the probability of completing a project by a given deadline in general such a path is not the most critical path and does not provide the lowest probability of completion time this paper studies the most critical path problem and formulates it as an optimal path problem through a deterministic network with a two attribute fractional objective function a heuristic approach is developed for the optimal path problem which gives a solution to the most critical path problem the illustrative examples and computational results demonstrate that the proposed procedure provides critical activities and estimates for the probabilities of completion time that are more accurate than those resulting from the classical pert approach further our computational experiments show that the proposed heuristic performs well in identifying the most critical paths

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

estimating the impact of uncertainty on a deterministic multiattribute evaluation a method is presented to estimate the impact of uncertainty on the results of a multiattribute evaluation prior to conducting a complete probabilistic multiattribute utility analysis the method assumes that a deterministic analysis has been completed using a weighted additive multiattribute value evaluation function and that either an additive or multiplicative utility function is appropriate for the multiattribute utility analysis an approximation procedure is developed to estimate whether uncertainty about attribute levels could change the deterministic evaluation results an illustrative application investigates the accuracy of the procedure and its use to simplify analysis of the effects of uncertainty

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

variationally stable difference systems we characterize the h stability in variation for nonlinear difference systems via n similarity and lyapunov functions furthermore using lyapunov s method and comparison principle we obtain some results related to stability for the perturbations of nonlinear difference systems

quasilinear hyperbolic 2 2 systems with a free damping boundary condition we consider a quasilinear system of equations for two functions u x t v x t and a boundary function s t

observability inequalities for the transmission of shallow shells in this paper we establish some observability inequalities from both boundary and distributed controls for the transmission of shallow shell with a middle surface of any shape in particular if only the boundary controls are allowed we obtain the condition for the observability inequality on young s modulus and poisson s coefficient of the material which is similar as those in the case of wave and plate equations

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

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

a linear bayesian stochastic approximation to update project duration estimates by relaxing the unrealistic assumption of probabilistic independence on activity durations in a project this paper develops a hierarchical linear bayesian estimation model statistical dependence is established between activity duration and the amount of resource as well as between the amount of resource and the risk factor upon observation or assessment of the amount of resource required for an activity in near completion the posterior expectation and variance of the risk factor can be directly obtained in the bayesian scheme then the expected amount of resources required for and the expected duration of upcoming activities can be predicted we simulate an application project in which the proposed model tracks the varying critical path activities on a real time basis and updates the expected project duration throughout the entire project in the analysis the proposed model improves the prediction accuracy by 38 36 compared to the basic pert approach

uniform stabilization of a shallow shell model with nonlinear boundary feedbacks abstract we consider a dynamic linear shallow shell model subject to nonlinear dissipation active on a portion of its boundary in physical boundary conditions our main result is a uniform stabilization theorem which states a uniform decay rate of the resulting solutions mathematically the motion of a shell is described by a system of two coupled partial differential equations both of hyperbolic type i an elastic wave in the 2 d in plane displacement and ii a kirchhoff plate in the scalar normal displacement these pdes are defined on a 2 d riemann manifold solution of the uniform stabilization problem for the shell model combines a riemann geometric approach with microlocal analysis techniques the former provides an intrinsic coordinate free model as well as a preliminary observability type inequality the latter yield sharp trace estimates for the elastic wave critical for the very solution of the stabilization problem as well as sharp trace estimates for the kirchhoff plate which permit the elimination of geometrical conditions on the controlled portion of the boundary

risk taking in stochastic pert networks abstract this paper studies a pert problem which incorporates project managers risk taking behavior in stochastic environments in this stochastic pert network which we refer to as riskpert activity durations are nonnegative random variables and a project manager uses a disutility function to evaluate each path and chooses that path which maximizes his expected disutility as an optimal or critical path this path as opposed to the classical critical path is used as a basis to analyze the pert network and to estimate the probability of completion time the general riskpert is difficult to solve however special cases when activity durations are statistically independent and disutility functions are linear exponential quadratic or linear exponential are solvable exactly the illustrative examples demonstrate that riskpert captures managers risk taking behavior and provides results that are more realistic than those of the classical pert models furthermore this paper extends some of the riskpert models to include multi dimensional pert networks

decay of solutions of wave equations in a bounded region with boundary dissipation abstract an energy decay rate is obtained for solutions of wave type equations in a bounded region in rn whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface

polynomial decay of a variable coefficient wave equation with an acoustic undamped boundary condition abstract we consider a variable coefficient wave equation with an acoustic undamped condition this is a coupled system of second and first order in time partial differential equations with an acoustic boundary condition on the interface the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients we obtain the polynomial energy decay

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

observability inequalities for shallow shells we consider some observability inequalities from boundary for a general shallow shell with a middle surface of any shape at first an estimate is established by the geometric multiplier method in the case that no boundary conditions are imposed under some checkable geometric conditions then our results yield continuous observability estimates for two kinds of boundary conditions which have a physical meaning with an explicit observability time and hence by duality exact controllability results

an inverse problem for the schrodinger equation with variable coefficients and lower order terms abstract we study the uniqueness and stability for an inverse problem of schrodinger equation with variable coefficients and lower order terms we obtain a carleman estimate by which we recover the potential from partial boundary term

strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions we consider a wave equation with semilinear porous acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with possibly semilinear boundary conditions on the interface the results obtained are i strong stability for the linear model ii exponential decay rates for the energy of the linear model and iii local exponential decay rates for the energy of the semilinear model this work builds on a previous result showing generation of a well posed dynamical system the main tools used in the proofs are i the stability theorem of arendt batty ii energy methods used in the study of a wave equation with boundary damping and iii an abstract result of i lasiecka applicable to hyperbolic like systems with nonlinearly perturbed boundary conditions

discretizing distributions with exact moments error estimate and convergence analysis the maximum entropy principle is a powerful tool for solving underdetermined inverse problems this paper considers the problem of discretizing a continuous distribution which arises in various applied fields we obtain the approximating distribution by minimizing the kullback leibler information relative entropy of the unknown discrete distribution relative to an initial discretization based on a quadrature formula subject to some moment constraints we study the theoretical error bound and the convergence of this approximation method as the number of discrete points increases we prove that i the theoretical error bound of the approximate expectation of any bounded continuous function has at most the same order as the quadrature formula we start with and ii the approximate discrete distribution weakly converges to the given continuous distribution moreover we present some numerical examples that show the advantage of the method and apply to numerically solving an optimal portfolio problem

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

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

stability for semilinear hyperbolic coupled system with frictional and viscoelastic localized damping abstract in this paper we prove stability results for a semilinear hyperbolic coupled system subject to a viscoelastic localized damping acting in the first equation and a frictional localized one acting in the second equation of the system we divide the proof into two parts in the first part the equations are posed in a homogeneous medium with the damping acting in a boundary neighbourhood in the second part the equations posed in an inhomogeneous medium with the damping acting in a collar of the boundary and in an appropriate mesh in the interior due to the assumptions on the nonlinear function involving the frictional damping general decay rates are obtained to prove the results we used the tools of the microlocal analysis theory

perturbations of nonlinear systems of difference equations in this paper we study a general variational stability introduced mainly for non autonomous difference systems under summability conditions these systems remain stable for general perturbations

generating scenario trees for multistage decision problems in models of decision making under uncertainty we often are faced with the problem of representing the uncertainties in a form suitable for quantitative models if the uncertainties are expressed in terms of multivariate continuous distributions or a discrete distribution with far too many outcomes we normally face two possibilities either creating a decision model with internal sampling or trying to find a simple discrete approximation of the given distribution that serves as input to the model this paper presents a method based on nonlinear programming that can be used to generate a limited number of discrete outcomes that satisfy specified statistical properties users are free to specify any statistical properties they find relevant and the method can handle inconsistencies in the specifications the basic idea is to minimize some measure of distance between the statistical properties of the generated outcomes and the specified properties we illustrate the method by single and multiple period problems the results are encouraging in that a limited number of generated outcomes indeed have statistical properties that are close to or equal to the specifications we discuss how to verify that the relevant statistical properties are captured in these specifications and argue that what are the relevant properties will be problem dependent

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

certainty equivalents for three point discrete distribution approximations three point discrete distribution approximations are often used in decision and risk analyses to represent probability distributions for continuous random variables e g as probability nodes in decision or probability trees performance evaluations of such approximations have generally been based on their accuracies in estimating moments for the underlying distributions however moment based comparisons for recently proposed approximations have been limited moreover very little research has addressed the accuracies of any such approximations in representing expected utilities or certainty equivalents of the underlying distributions this is of potential concern since recent research shows three point discrete distribution approximations exist that match the first several moments of an underlying distribution exactly while counterintuitively approximating its certainty equivalents poorly this paper compares the best two approximations for estimating means and variances identified in an earlier study with promising approximations proposed more recently specifically it examines how accurately six simple general purpose three point approximations represent certainty equivalents for continuous random variables as the level of risk aversion is varied as well as how accurately they estimate means and variances the results show that several of these are quite accurate over a variety of test distributions when the level of risk aversion and the characteristics of the distributions are within reasonable bounds their robust performance is significant for decision analysis practice

using experts noisy quantile judgments to quantify risks theory and application to agribusiness motivated by a unique agribusiness setting this paper develops an optimization based approach to estimate the mean and standard deviation of probability distributions from noisy quantile judgments provided by experts the approach estimates the mean and standard deviations as weighted linear combinations of quantile judgments where the weights are explicit functions of the expert s judgmental errors the approach is analytically tractable and provides flexibility to elicit any set of quantiles from an expert the approach also establishes that using an expert s quantile judgments to deduce the distribution parameters is equivalent to collecting data with a specific sample size and enables combining the expert s judgments with those of other experts it also shows analytically that the weights for the mean add up to one and the weights for the standard deviation add up to zero these properties have been observed numerically in the literature in the last 30 years but without a systematic explanation th

explicit observability inequalities for the wave equation with lower order terms by means of carleman inequalities in this paper by means of carleman estimates and the usual energy estimate we obtain directly two observability inequalities for the linear wave equation with time variant nonsmooth lower order terms we do not need any unique continuation property of the linear equation a priori since this is actually one of the by products of our analysis furthermore the constant in the observability inequality is estimated by an explicit function of the norm of the involved coefficients in the equation also we apply our observability estimates to exact controllability for wave equations