linearly implicit imex runge kutta methods for a class of degenerate convection diffusion problems multispecies kinematic flow models with strongly degenerate diffusive corrections give rise to systems of nonlinear convection diffusion equations of arbitrary size applications of these systems include models of polydisperse sedimentation and multiclass traffic flow implicit explicit imex runge kutta rk methods are suitable for the solution of these convection diffusion problems since the stability restrictions coming from the explicitly treated convective part are much less severe than those that would be deduced from an explicit treatment of the diffusive term these schemes usually combine an explicit rk scheme for the time integration of the convective part with a diagonally implicit one for the diffusive part in r burger p mulet and l m villada siam j sci comput 35 2013 pp b751 b777 a scheme of this type is proposed where the nonlinear and nonsmooth systems of algebraic equations arising in the implicit treatment of the degenerate diffusive part are solved by smoothing o

existence results for the flow of viscoelastic fluids with a differential constitutive law where 2 is the symmetric extra stress tensor the total stress is given by g pl i where p is the hydrodynamic pressure 4 is the rate of deformation tensor g u vu vu u being the velocity field a is the relaxation time a2 the retardation time 0 i a a1 and q is the fluid viscosity the symbol a d t denotes an objective frame indifferent derivative i 181 more precisely

cross validation for correlated data abstract k fold cross validation cv with squared error loss is widely used for evaluating predictive models especially when strong distributional assumptions cannot be taken however cv with sq

incompressible limit of the compressible nematic liquid crystal flow abstract this paper is concerned with the incompressible limit of the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions in r n n 2 3 the local and global existence of strong solutions for the incompressible system with small initial data is rigorously proved via the incompressible limit furthermore the convergence rates are obtained in some sense

a note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations abstract following the lead of carrillo arch ration mech anal 147 1999 269 361 recently several authors have used kru kov s device of doubling the variables to prove uniqueness results for entropy solutions of nonlinear degenerate parabolic equations in all these results the second order differential operator is not allowed to depend explicitly on the spatial variable which certainly restricts the range of applications of entropy solution theory the purpose of this paper is to extend a version of carrillo s uniqueness result to a class of degenerate parabolic equations with spatially dependent second order differential operator the class is large enough to encompass several interesting nonlinear partial differential equations coming from the theory of porous media flow and the phenomenological theory of sedimentation consolidation processes

local well posedness to the cauchy problem of the 2d compressible navier stokes smoluchowski equations with vacuum abstract this paper concerns the local strong solution to the compressible navier stokes smoluchowski equations with vacuum as far field density on the whole space r 2 without additional cho choe kim type compatibility conditions which provided the initial density and the initial particles density decay not too slow at infinity in particular we extend the results of ding et al 2016 13 and yang 2020 24 to the 2d case

adaptive multiresolution weno schemes for multi species kinematic flow models multi species kinematic flow models lead to strongly coupled nonlinear systems of first order spatially one dimensional conservation laws the number of unknowns the concentrations of the species may be arbitrarily high models of this class include a multi species generalization of the lighthill whitham richards traffic model and a model for the sedimentation of polydisperse suspensions their solutions typically involve kinematic shocks separating areas of constancy and should be approximated by high resolution schemes a fifth order weighted essentially non oscillatory weno scheme is combined with a multiresolution technique that adaptively generates a sparse point representation spr of the evolving numerical solution thus computational effort is concentrated on zones of strong variation near shocks numerical examples from the traffic and sedimentation models demonstrate the effectiveness of the resulting weno multiresolution weno mrs scheme

low mach number limit of the compressible navier stokes smoluchowski equations in multi dimensions this paper is concerned with the incompressible limit of the compressible navier stokes smoluchowski equations with periodic boundary conditions in multidimensions the authors establish the uniform stability of the local solution family which yields a lifespan of the navier stokes smoluchowski system then the local existence of strong solutions for the incompressible system with small initial data is rigorously proved via the incompressible limit furthermore the authors obtain the convergence rates in the case without external force this paper is concerned with the incompressible limit of the compressible navier stokes smoluchowski equations with periodic boundary conditions in multidimensions the authors establish the uniform stability of the local solution family which yields a lifespan of the navier stokes smoluchowski system then the local existence of strong solutions for the incompressible system with small initial data is rigorously proved via the incompressible limit furthermore the authors obtain the convergence rates in the case without external force

strongly degenerate parabolic hyperbolic systems modeling polydisperse sedimentation with compression we show how existing models for the sedimentation of monodisperse flocculated suspensions and of polydisperse suspensions of rigid spheres differing in size can be combined to yield a new theory of the sedimentation processes of polydisperse suspensions forming compressible sediments sedimentation with compression or sedimentation consolidation process for n solid particle species this theory reduces in one space dimension to an n times n coupled system of quasi linear degenerate convection diffusion equations analyses of the characteristic polynomials of the jacobian of the convective flux vector and of the diffusion matrix show that this system is of strongly degenerate parabolic hyperbolic type for arbitrary n and particle size distributions bounds for the eigenvalues of both matrices are derived the mathematical model for n 3 is illustrated by a numerical simulation obtained by the kurganov tadmor central difference scheme for convection diffusion problems the numerical scheme exploits

monotone difference approximations of bv solutions to degenerate convection diffusion equations we consider consistent conservative form monotone difference schemes for nonlinear convection diffusion equations in one space dimension since we allow the diffusion term to be strongly degenerate solutions can be discontinuous and in general are not uniquely determined by their data here we choose to work with weak solutions that belong to the bv in space and time class and in addition satisfy an entropy condition a recent result of wu and yin northeastern math j 5 1989 pp 395 422 states that these so called bv entropy weak solutions are unique the class of equations under consideration is very large and contains to mention only a few the heat equation the porous medium equation the two phase flow equation and hyperbolic conservation laws the difference schemes are shown to converge to the unique bv entropy weak solution of the problem in view of the classical theory for monotone difference approximations of conservation laws the main difficulty in obtaining a similar convergence theory in the present context is to show that the strongly degenerate discrete diffusion term is sufficiently smooth we provide the necessary regularity estimates by deriving and carefully analyzing a linear difference equation satisfied by the numerical flux of the difference schemes finally we make some concluding remarks about monotone difference schemes for multidimensional equations

local well posedness of the compressible navier stokes smoluchowski equations with vacuum abstract in this paper we prove the local well posedness of strong solutions to the compressible navier stokes smoluchowski equations with vacuum in a bounded domain r 3 without the standard compatibility conditions which improves the results obtained by huang et al discrete contin dyn syst ser s9 6 2016 1717 1752

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

a model of continuous sedimentation of flocculated suspensions in clarifier thickener units the chief purpose of this paper is to formulate and partly analyze a new mathematical model for continuous sedimentation consolidation processes of flocculated suspensions in clarifier thickener units this model appears in two variants for cylindrical and variable cross sectional area units respectively models 1 and 2 in both cases the governing equation is a scalar strongly degenerate parabolic equation in which both the convective and diffusion fluxes depend on parameters that are discontinuous functions of the depth variable the initial value problem for this equation is analyzed for model 1 we introduce a simple finite difference scheme and prove its convergence to a weak solution that satisfies an entropy condition a limited analysis of steady states as desired stationary modes of operation is performed numerical examples illustrate that the model realistically describes the dynamics of flocculated suspensions in clarifier thickeners

a cross validatory method for dependent data summary in this paper we extend the technique of cross validation to the case where observations form a general stationary sequence we call it h block cross validation because the idea is to reduce the training set by removing the h observations preceding and following the observation in the test set we propose taking h to be a fixed fraction of the sample size and we add a term to our h block cross validated estimate to compensate for the underuse of the sample the advantages of the proposed modification over the cross validation technique are demonstrated via simulation

central schemes and systems of conservation laws with discontinuous coefficients modeling gravity separation of polydisperse suspensions in this paper two existing one dimensional mathematical models one for continuous sedimentation of monodisperse suspensions and one for settling of polydisperse suspensions are combined into a model of continuous separation of polydisperse mixtures this model can be written as a first order system of conservation laws for the local concentrations of each particle species with a flux vector that depends discontinuously on the space variable this application motivates the extension of the kurganov tadmor central difference scheme to systems with discontinuous flux the new central schemes are based on discretizing an enlarged system in which the discontinuous coefficients are viewed as additional conservation laws these additional conservation laws can either be discretized and the evolution of the discontinuity parameters is calculated in each time step or solved exactly that is the discontinuity parameters are kept constant with respect to time numerical examples and an l1 error study show that the kurganov tadmor scheme with first order in time discretization produces spurious oscillations whereas its semi discrete version discretized by a second order runge kutta scheme produces good results the scheme with discontinuity parameters kept constant is slightly more accurate than when these are evolved numerical examples illustrate the application to separation of polydisperse suspensions

on the behaviour of marginal and conditional aic in linear mixed models in linear mixed models model selection frequently includes the selection of random effects two versions of the akaike information criterion aic have been used based either on the marginal or on the conditional distribution we show that the marginal aic is not an asymptotically unbiased estimator of the akaike information and favours smaller models without random effects for the conditional aic we show that ignoring estimation uncertainty in the random effects covariance matrix as is common practice induces a bias that can lead to the selection of any random effect not predicted to be exactly zero we derive an analytic representation of a corrected version of the conditional aic which avoids the high computational cost and imprecision of available numerical approximations an implementation in an r package r development core team 2010 is provided all theoretical results are illustrated in simulation studies and their impact in practice is investigated in an analysis of childhood malnutrition in zambia

maximum principle for optimal control of non well posed elliptic differential equations in this paper we shall study two optimal control problems p1 and p2 governed by some semilinear elliptic di erential equations which can admit more than one solution we shall call such systems non well posed systems we obtain the pontryagin maximum principle for problems p1 and p2 in the 6rst problem p1 the cost functional may be non smooth and the set of controls is convex while in the second problem p2 the cost functional is smooth and the set of controls is non convex in both problem p1 and problem p2 we consider some state constraint of integral type due to some practical interests many authors studied optimal control for elliptic di erential equations here we cite 1 10 12 15 however most of these works except for 7 10 13 deal with state equations which are governed by monotone operators and admit a unique solution corresponding to each control in such problems the pontryagin maximum principle was obtained by studying the variations of the state with respect to some perturbations of the control cf 1 2 12 15 in the present work the state equations are governed by non monotone operators and can admit more than one solution we cannot obtain the variations of the state with respect to the control with the same methods in 1 2 12 15 when the state equations admit more than one solution we even do not know how to make the sensitivity analysis of the state with respect to the control

hyperbolicity analysis of polydisperse sedimentation models via a secular equation for the flux jacobian polydisperse suspensions consist of small particles which are dispersed in a viscous fluid and which belong to a finite number n of species that differ in size or density spatially one dimensional kinematic models for the sedimentation of such mixtures are given by systems of n nonlinear first order conservation laws for the vector phi of the n local solids volume fractions of each species the problem of hyperbolicity of this system is considered here for the models due to masliyah lockett and bassoon batchelor and wen and hofler and schwarzer in each of these models the flux vector depends only on a small number m n of independent scalar functions of phi so its jacobian is a rank m perturbation of a diagonal matrix this allows us to identify its eigenvalues as the zeros of a particular rational function r lambda which in turn is related to the determinant of a certain m times m matrix the coefficients of r lambda follow from a representation formula due to anderson linear a

augmented lagrangian sqp methods for nonlinear optimalcontrol problems of tracking type an augmented lagrangian method with second order update is developed and its relationship to the sequential quadratic programming method is described the rate of convergence proof depends on a second order sufficient optimality condition which is shown to be satisfied for a class of nonlinear optimal control problems of tracking type numerical examples are included which demonstrate the globalizing effect of the augmented lagrangian method

monotone methods for semilinear elliptic equations in unbounded domains abstract monotone methods in conjuction with upper and lower solutions have proved to be extremely powerful tools in the study of nonlinear elliptic boundary value problems in bounded domains in this paper the theory is extended to unbounded not necessarily exterior domains and general linear boundary conditions

weakly dissipative solutions and weak strong uniqueness for the navier stokes smoluchowski system abstract this article deals with a fluid particle interaction model for the evolution of particles dispersed in a fluid the fluid flow is governed by the navier stokes equations for a compressible fluid while the evolution of the particle densities is given by the smoluchowski equation the coupling between the dispersed and dense phases is obtained through the drag forces that the fluid and the particles exert mutually the existence of weakly dissipative solutions is established under reasonable physical assumptions on the initial data the physical domain and the external potential furthermore a weak strong uniqueness result is established via the relative entropy method yielding that a weakly dissipative solution agrees with a classical solution with the same initial data when such a classical solution exists

relative entropy in multi phase models of 1d elastodynamics convergence of a non local to a local model abstract in this paper we study a local and a non local regularization of the system of nonlinear elastodynamics with a non convex energy we show that solutions of the non local model converge to those of the local model in a certain regime the arguments are based on the relative entropy framework and provide an example of how local and non local regularizations may compensate for non convexity of the energy and enable the use of the relative entropy stability theory even if the energy is not quasi or poly convex

nonhomogeneous dirichlet problems for degenerate parabolic hyperbolic equations the aim of the paper is to give a formulation for the initial boundary value problem of parabolic hyperbolic type in the case of nonhomogeneous boundary data a 0 here u u x t with x t q 0 t where is a bounded domain in n with smooth boundary and t 0 the function b is assumed to be nondecreasing allowing degeneration zones where b is constant is locally lipschitz continuous and g l 0 b after introducing the definition of an entropy solution to the above problem in the spirit of otto 14 we prove uniqueness of the solution in the proposed setting moreover we prove that the entropy solution previously defined can be obtained as the limit of solutions of regularized equations of nondegenerate parabolic type specifically the diffusion function b is approximated by functions b that are strictly increasing

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

a comparative study of ordinary cross validation v fold cross validation and the repeated learning testing methods summary concepts of v fold cross validation and repeated learning testing methods have been introduced here in many problems these methods are computationally much less expensive than ordinary cross validation and can be used in its place a comparative study of these three methods has been carried out in detail

global existence and large time behavior of classical solutions to the euler maxwell vlasov fokker planck system abstract we consider global classical solutions to the cauchy problem for an euler maxwell vlasov fokker planck system which is a fluid particle model describe the evolutions of disperse two phase flows in these two phase flows the compressible euler maxwell equations modeling a dense phase fluid and the vlasov fokker planck equation for the dispersed phase particles which is usually considered from the statistical view of point they are coupled through the friction force global existence of classical solutions to the cauchy problem in r 3 is established when initial data is a small perturbation of some given equilibrium the algebraic rate of convergence of solution toward the equilibrium state is also obtained under additional conditions on initial data the proof is based on the classical energy estimates and fourier multiplier technique which are considerably complicated and some new ideas and techniques are thus required

on strongly degenerate convection diffusion problems modeling sedimentation consolidation processes abstract we investigate initial boundary value problems for a quasilinear strongly degenerate convection diffusion equation with a discontinuous diffusion coefficient these problems come from the mathematical modeling of certain sedimentation consolidation processes the existence of entropy solutions belonging to bv is shown by the vanishing viscosity method the existence proof for one of the models includes a new regularity result for the integrated diffusion coefficient new uniqueness proofs for entropy solutions are also presented these proofs rely on a recent extension to second order equations of kru kov s method of doubling the variables the application to a sedimentation consolidation model is illustrated by two numerical examples

how biased is the apparent error rate of a prediction rule abstract a regression model is fitted to an observed set of data how accurate is the model for predicting future observations the apparent error rate tends to underestimate the true error rate because the data have been used twice both to fit the model and to check its accuracy we provide simple estimates for the downward bias of the apparent error rate the theory applies to general exponential family linear models and general measures of prediction error special attention is given to the case of logistic regression on binary data with error rates measured by the proportion of misclassified cases several connected ideas are compared mallows s cp cross validation generalized cross validation the bootstrap and akaike s information criterion

multilevel hierarchical modeling what it can and cannot do multilevel hierarchical modeling is a generalization of linear and generalized linear modeling in which regression coefficients are themselves given a model whose parameters are also estimated from data we illustrate the strengths and limitations of multilevel modeling through an example of the prediction of home radon levels in u s counties the multilevel model is highly effective for predictions at both levels of the model but could easily be misinterpreted for causal inference

an extension of pontryagin s principle for state constrained optimal control of semilinear elliptic equations and variational inequalities this paper deals with state constrained optimal control problems governed by semilinear elliptic equations or variational inequalities by using ekeland s principle a minimum principle of pontryagin s type under some stability conditions of the optimal cost with respect to the state constraints is derived

existence and stability for mathematical models of sedimentation consolidation processes in several space dimensions abstract in this paper we study several spatially multidimensional initial boundary value problems modelling sedimentation consolidation processes of a flocculated suspension this solid fluid mixture is considered as two superimposed continuous media differing in density and viscosity the phenomenological foundation and derivation of the mathematical model are based on the previous work by r burger et al 2000 z angew math mech 80 79 92 we study the full coupling of the conservation of mass equation and the conservation of linear momentum equation for different types of regularization we establish energy estimates the dissipative nature of the whole system assures the existence as well as the stability long time asymptotics of a solution of the system provided that the viscosities of the fluid are large enough moreover the energy estimates might serve as the foundation for the design of numerical algorithms to simulate the system

optimal control problems for semilinear non well posed parabolic differential equations this paper deals with necessary conditions for optimal control problem governed by some semilinear parabolic differential equation which may be non well posed state constrained problem is considered finally under some suitable assumptions we obtain the existence of optimal pairs

existence of solution for a micro macro model of polymeric fluid the fene model abstract we analyse a non linear micro macro model of polymeric fluids in the case of a shear flow more precisely we consider the fene dumbbell model which models polymers by nonlinear springs accounting for the finite extensibility of the polymer chain we prove the existence of a unique solution to the stochastic differential equation which rules the evolution of a representative polymer in the flow and next deduce a local in time existence and uniqueness result on the system coupling the stochastic differential equation and the momentum equation on the fluid

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

kernel regression estimation using repeated measurements data abstract the estimation of growth curves has been studied extensively in parametric situations here we consider the nonparametric estimation of an average growth curve suppose that there are observations from several experimental units each following the regression model y xi f xj e j 1 n where e1 e n are correlated zero mean errors and 0 x1 xn 1 are fixed constants we study some of the properties of a kernel estimator of f x asymptotic and finite sample results concerning the mean squared error of the estimator are obtained in particular the influence of correlation on the bandwidth minimizing mean squared error is discussed a data based method for selecting the bandwidth is illustrated in a data analysis most previous research on kernel regression estimators has involved uncorrelated errors we investigate how dependence of the errors changes the behavior of a kernel estimator our theorems concerning the asymptotic mean squared error show that the estimator cannot be consistent un

conditional akaike information for mixed effects models summary this paper focuses on the akaike information criterion aic for linear mixed effects models in the analysis of clustered data we make the distinction between questions regarding the population and questions regarding the particular clusters in the data we show that the aic in current use is not appropriate for the focus on clusters and we propose instead the conditional akaike information and its corresponding criterion the conditional aic caic the penalty term in caic is related to the effective degrees of freedom p for a linear mixed model proposed by hodges sargent 2001 p reflects an intermediate level of complexity between a fixed effects model with no cluster effect and a corresponding model with fixed cluster effects the caic is defined for both maximum likelihood and residual maximum likelihood estimation a pharmacokinetics data appli cation is used to illuminate the distinction between the two inference settings and to illustrate the use of the conditional aic in model selection

generalized least squares inference in panel and multilevel models with serial correlation and fixed effects in this paper i consider generalized least squares gls estimation in fixed effects panel and multilevel models with autocorrelation the presence of fixed effects complicates implementation of gls as estimating the fixed effects will typically render standard estimators of the covariance parameters necessary for obtaining feasible gls estimates inconsistent i focus on the case where the disturbances follow an ar p process and offer a simple to implement bias correction for the ar coefficients the usefulness of gls and the derived bias correction for the parameters of the autoregressive process is illustrated through a simulation study which uses data from the current population survey

a semi implicit monotone difference scheme for an initial boundary value problem of a strongly degenerate parabolic equation modeling sedimentation consolidation processes we prove the convergence of a semi implicit monotone finite difference scheme approximating an initial boundary value problem for a spatially one dimensional quasilinear strongly degenerate parabolic equation which is supplied with two different inhomogeneous flux type boundary conditions this problem arises in the modeling of the sedimentation consolidation process we formulate the definition of entropy solution of the model in the sense of kruzkov and prove convergence of the scheme to the unique bv entropy solution of the problem up to satisfaction of one of the boundary conditions

operator spltting methods for systems of convection diffusion equations nonlinear error mechanisms and correction strategies abstract many numerical methods for systems of convection diffusion equations are based on an operator splitting formulation where convective and diffusive forces are accounted for in separate substeps we describe the nonlinear mechanism of the splitting error in such numerical methods in the one dimensional case a mechanism that is intimately linked to the local linearizations introduced implicitly in the hyperbolic convection steps by the use of an entropy condition for convection dominated flows we demonstrate that operator splitting methods typically generate a numerical widening of viscous fronts unless the splitting step is of the same magnitude as the diffusion scale to compensate for the potentially damaging splitting error we propose a corrected operator splitting cos method for general systems of convection diffusion equations with the ability of correctly resolving the nonlinear balance between the convective and diffusive forces in particular cos produces viscous shocks with a correct structure also when the splitting step is large a front tracking method for systems of conservation laws which in turn relies heavily on a riemann solver constitutes an important part of our cos strategy the proposed cos method is successfully applied to a system modeling two phase multicomponent flow in porous media and a triangular system modeling three phase flow

counting degrees of freedom in hierarchical and other richly parameterised models summary drawing on linear model theory we rigorously extend the notion of degrees of freedom to richly parameterised models including linear hierarchical and random effect models some smoothers and spatial models and combinations of these the number of degrees of freedom is often much smaller than the number of parameters our notion of degrees of freedom is compatible with similar ideas long associated with smoothers but is applicable to new classes of models and can be interpreted using the projection theory of linear models we use an example to illustrate the two applications of setting prior distributions for variances and fixing model complexity by fixing degrees of freedom

kernel smoothing of data with correlated errors abstract kernel smoothing is a common method of estimating the mean function in the nonparametric regression model y f x e where f x is a smooth deterministic mean function and e is an error process with mean zero in this article the mean squared error of kernel estimators is computed for processes with correlated errors and the estimators are shown to be consistent when the sequence of error processes converges to a mixing sequence the standard techniques for bandwidth selection such as cross validation and generalized cross validation are shown to perform very badly when the errors are correlated standard selection techniques are shown to favor undersmoothing when the correlations are predominantly positive and oversmoothing when negative the selection criteria can however be adjusted to correct for the effect of correlation in simulations the standard selection criteria are shown to behave as predicted the corrected criteria are shown to be very effective when the correlation functi

a note on conditional aic for linear mixed effects models the conventional model selection criterion aic has been applied to choose candidate models in mixed effects models by the consideration of marginal likelihood vaida and blanchard 2005 demonstrated that such a marginal aic and its small sample correction are inappropriate when the research focus is on clusters correspondingly these authors suggested to use conditional aic the conditional aic is derived under the assumptions of the variance covariance matrix or scaled variance covariance matrix of random effects being known we develop a general conditional aic but without these strong assumptions this allows vaida and blanchard s conditional aic to be applied in a wide range simulation studies show that the proposed method is promising

necessary conditions for optimal control of distributed parameter systems the ekeland variational principle is used to prove a maximum principle for the optimal controls of a general semilinear evolutionary control system in a banach space with strictly convex dual the boundary constraint is of general type which includes the optimal periodic control problem as a special case

convergence of diffusive bgk approximations for nonlinear strongly parabolic systems we study a class of bgk approximations of parabolic systems in one space dimension we prove stability and existence of global solutions for this model moreover under certain conditions we prove a rigorous result of convergence toward the formal limit by using compensated compactness techniques

entropy solutions for nonlinear degenerate problems we consider a class of elliptic hyperbolic degenerate equations g u delta b u divg phi u f with dirichlet homogeneous boundary conditions and a class of elliptic parabolic hyperbolic degenerate equations g u t delta b u divg phi u f with homogeneous dirichlet conditions and initial conditions existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function satisfying rather general conditions comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for continuous

global well posedness for a smoluchowski equation coupled with navier stokes equations in 2d we prove global existence for a nonlinear smoluchowski equation a nonlinear fokker planck equation coupled with navier stokes equations in 2d the proof uses a deteriorating regularity estimate in the spirit of 5 see also 1

optimal control of problems governed by abstract elliptic variational inequalities with state constraints in this paper we investigate optimal control problems governed by elliptic variational inequalities with additional state constraints we present a relaxed formulation for the problem with penalization methods and approximation techniques we give qualification conditions to get first order optimality conditions

distributed control of systems governed by a general class of quasilinear elliptic equations abstract in this paper we are concerned with optimal control problems governed by a general class of quasilinear elliptic equations our aim is to prove existence of solution and derive optimality conditions in order to deal with this last question we begin investigating differentiability of state solution of equation with respect to the control second term of equation obtaining it only in certain cases a perturbation method is used to treat other cases as a consequence of the optimality system regularity of optimal control and state is establised

convergence of a finite volume scheme for nonlinear degenerate parabolic equations one approximates the entropy weak solution u of a nonlinear parabolic degenerate equation u t rm div mathbf q f u delta phi u 0 by a piecewise constant function u mathcal d using a discretization mathcal d in space and time and a finite volume scheme the convergence of u mathcal d to u is shown as the size of the space and time steps tend to zero in a first step estimates on u mathcal d are used to prove the convergence up to a subsequence of u mathcal d to a measure valued entropy solution called here an entropy process solution a result of uniqueness of the entropy process solution is proved yielding the strong convergence of u mathcal d to it u some on a model equation are shown

simulation of fluid and particles flows asymptotic preserving schemes for bubbling and flowing regimes in this work we propose asymptotic preserving numerical schemes for the bubbling and flowing regimes of particles immersed in a fluid treated by two phase flow models the description comprises compressible euler equations for the dense phase fluid and a kinetic fokker planck equation for the disperse phase particles coupled through friction terms we show numerical simulations in the relevant case of gravity in the one dimensional case demonstrating the overall behavior of the schemes

a new approach to optimal control of ill posed semilinear elliptic equations in the absence of convexity abstract an optimal control problem governed by a class of ill posed semilinear elliptic equations in the absence of convexity is studied in this paper firstly by using a variant of the penalization method the pontryagin s maximum principle for the initial problem is obtained secondly an existence result is also proved

local polynomial mixed effects models for longitudinal data we consider a nonparametric mixed effects model yi tij tij vi tij i tij j 1 2 ni i 1 2 n for longitudinal data we propose combining local polynomial kernel regression and linear mixed effects lme model techniques to estimate both fixedeffects population curve t and random effects curves vi t the resulting estimator called the local polynomial lme llme estimator takes the local correlation structure of the longitudinal data into account naturally we also propose new bandwidth selection strategies for estimating t and vi t simulation studies show that our estimator for t is superior to the existing estimators in the sense of mean squared errors the asymptotic bias variance mean squared errors and asymptotic normality are established for the llme estimators of t when ni is bounded and n tends to infinity our llme estimator converges in a standard nonparametric rate and the asymptotic bias and variance are essentially the same as those of the kernel generalized esti