existence for coupled pseudomonotone strongly monotone systems and application to a cahn hilliard model with elasticity abstract a system of two operator equations is considered one of pseudomonotone type and the other of strongly monotone type both being strongly coupled conditions are given that allow to reduce the solvability of this system to a single operator equation of a pseudomonotone mapping this result is applied to a coupled system consisting of a parabolic equation of fourth order in space of cahn hilliard type and a nonlinear elliptic equation of second order modeling a quasi steady mechanical equilibrium using an appropriate notion of weak solutions and a framework for evolution equations developed by groger 2001 the system is reduced to a single parabolic operator equation and the existence of solutions is shown under restrictions on the strength of the coupling

maximal parabolic regularity for divergence operators including mixed boundary conditions abstract we show that elliptic second order operators a of divergence type fulfill maximal parabolic regularity on distribution spaces even if the underlying domain is highly non smooth the coefficients of a are discontinuous and a is complemented with mixed boundary conditions applications to quasilinear parabolic equations with non smooth data are presented

an h s p text curl varomega estimate for the maxwell system we derive an h 0 s p text curl varomega estimate for the solutions of the maxwell type equations modeled with anisotropic and w s infty varomega regular coefficients here we obtain the regularity of the solutions for the integrability and smoothness indices p s in a plane domain characterized by the apriori lower upper bounds of a and the apriori upper bound of its holder semi norm of order s the proof relies on a perturbation argument generalizing groger s l p type estimate known for the elliptic problems to the maxwell system

a bayesian bootstrap for censored data a bayesian bootstrap for a censored data model is introduced its small sample distributional properties are discussed and found to be similar to efron s bootstrap for censored data in the absence of censoring the bayesian bootstrap for censored data reduces to rubin s bayesian bootstrap for complete data a first order large sample theory is developed this theory shows that both censored data bootstraps are consistent bootstraps for approximating the sampling distribution of the kaplan meier estimator it also shows that both bootstraps are consistent bootstraps for approximating a posterior distribution of the survival function with respect to each member of the class of conjugate beta neutral process priors

numerical identification of a robin coefficient in parabolic problems this paper studies a regularization approach for an inverse problem of estimating a spatially and temporally dependent robin coefficient arising in the analysis of convective heat transfer the parameter to state map is analyzed especially a differentiability result is established a regularization approach is proposed and the properties e g existence and optimality system of the functional are investigated a finite element method is adopted for discretizing the continuous optimization problem and the convergence of the finite element approximations as the mesh size and temporal step size tend to zero is established numerical results by the conjugate gradient method for oneand two dimensional problems are presented

a rank statistics approach to the consistency of a general bootstrap a general notion of a bootstrapped mean constructed by exchangeably weighting sample points is introduced consistency of this generalized bootstrapped mean which includes proposals of efron and rubin among others is proved by classical linear rank statistics theory the consistency of generalized bootstrapped empirical and quantile processes is also established

on maximal parabolic regularity for non autonomous parabolic operators abstract we consider linear inhomogeneous non autonomous parabolic problems associated to sesquilinear forms with discontinuous dependence of time we show that for these problems the property of maximal parabolic regularity can be extrapolated to time integrability exponents r 2 this allows us to prove maximal parabolic l r regularity for discontinuous non autonomous second order divergence form operators in very general geometric settings and to prove existence results for related quasilinear equations

bayesian bootstrap for proportional hazards models we propose two bayesian bootstrap extensions the binomial and poisson forms for proportional hazards models the binomial form bayesian bootstrap is the limit of the posterior distribution with a beta process prior as the amount of the prior information vanishes and thus can be considered as a default nonparametric bayesian analysis it is also the same as lo s bayesian bootstrap for censored data when covariates are absent the poisson form bayesian bootstrap is equivalent to the bayesian analysis with cox s profile likelihood when the baseline distribution is discrete thus when the data set has many ties simulation study suggests that the binomial form bayesian bootstrap performs better than standard frequentist procedures in the frequentist sense an advantage of the proposed bayesian bootstrap procedures over the standard bayesian analysis is conceptual and computational simplicity finally it is shown that both bayesian bootstrap posteriors are asymptotically equivalent to the sampling distribution of the maximum likelihood estimator

gradient based estimation of manning s friction coefficient from noisy data we study the numerical recovery of manning s roughness coefficient for the diffusive wave approximation of the shallow water equation we describe a conjugate gradient method for the numerical inversion numerical results for one dimensional models are presented to illustrate the feasibility of the approach also we provide a proof of the differentiability of the weak form with respect to the coefficient as well as the continuity and boundedness of the linearized operator under reasonable assumptions using the maximal parabolic regularity theory

on the structure of the fiber cone of ideals with analytic spread one for a given a local ring a m we study the fiber cone of ideals in a with analytic spread one in this case the fiber cone has a structure as a module over its noether normalization which is a polynomial ring in one variable over the residue field one may then apply the structure theorem for modules over a principal domain to get a complete description of the fiber cone as a module we analyze this structure in order to study and characterize in terms of the ideal itself the arithmetical properties and other numerical invariants of the fiber cone as multiplicity reduction number or castelnuovo mumford regularity

on the associated graded rings of parameter ideals in buchsbaum rings is an invariant 1 a of a not depending on the particular choice of a parameter ideal q of a where i a q and e a denote the length of the amodule a q and the multiplicity of a relative to q respectively this is equivalent to saying that every system a a ad of parameters for a is a weak a sequence i e the equality a ai a i a ai m holds for all 0 i d 1 21 thus every cohen macaulay local ring a is clearly buchsbaum with i a 0 and vice versa in this sense the notion of buchsbaum rings is an extension of that of cohen macaulay rings and is originated in an answer of vogel 29 to a problem of buchsbaum 11 notice that the concept of buchsbaum rings may be canonically generalized to that of buchsbaum modules cf e g 11 221 now let us fix a parameter ideal q of a and let g denote the associated graded ring g a ona q qn of q recall that the ring g is cohenmacaulay if a is so actually g is a polynomial ring over a q in this case then what happens when a is buchsbaum this is a motive problem in the present research and our conclusion is briefly stated

buchsbaumness in rees modules associated to ideals of minimal multiplicity in the equi i invariant case abstract the present article gives certain conditions for rees modules to obtain buchsbaumness suppose a given m primary ideal is of minimal multiplicity in the equi i invariant case then it is shown that the positively graded submodule of the rees module must be buchsbaum and moreover that the rees module itself is also buchsbaum if the dimension of a given module is greater than one

buchsbaumness of certain generalization of the associated graded modules in the equi i invariant case the present article introduces a generalization of the associated graded modules writing g a e suppose that the equi i invariant case occurs then it is shown that our graded module g a e is buchsbaum over r a for any 0 if the given a module e is so over a moreover it is also shown that e is buchsbaum over a iff g m e is so over r m for all 0 where m is the maximal ideal of a

the bayesian bootstrap the bayesian bootstrap is the bayesian analogue of the bootstrap instead of simulating the sampling distribution of a statistic estimating a parameter the bayesian bootstrap simulates the posterior distribution of the parameter operationally and inferentially the methods are quite similar because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions neither method should be applied without some consideration of the reasonableness of these model assumptions in this sense neither method is a true bootstrap procedure yielding inferences unaided by external assumptions

approximate bayesian inference with the weighted likelihood bootstrap we introduce the weighted likelihood bootstrap wlb as a way to simulate approximately from a posterior distribution this method is often easy to implement requiring only an algorithm for calculating the maximum likelihood estimator such as iteratively reweighted least squares in the generic weighting scheme the wlb is first order correct under quite general conditions inaccuracies can be removed by using the wlb as a source of samples in the sampling importance resampling sir algorithm which also allows incorporation of particular prior information the sir adjusted wlb can be a competitive alternative to other integration methods in certain models asymptotic expansions elucidate the second order properties of the wlb which is a generalization of rubin s bayesian bootstrap the calculation of approximate bayes factors for model comparison is also considered we note that given a sample simulated from the posterior distribution the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values a modification of this estimator that avoids instability is also noted these methods provide simple ways of calculating approximate bayes factors and posterior model probabilities for a very wide class of models

a large sample study of the bayesian bootstrap on donne une justification asymptotique du bootstrap bayesien on obtient des resultats lies a l article de rubin 1981 dans le meme sens que bickel et freedman 1981 et singh 1981 se rapportant a l article d efron 1979

the problem of regions in the problem of regions we wish to know which one of a discrete set of possibilities applies to a continuous parameter vector this problem arises in the following way we compute a descriptive statistic from a set of data notice an interesting feature and wish to assign a confidence level to that feature for example we compute a density estimate and notice that the estimate is bimodal what confidence can we assign to bimodality a natural way to measure confidence is via the bootstrap we compute our descriptive statistic on a large number of bootstrap data sets and record the proportion of times that the feature appears this seems like a plausible measure of confidence for the feature the paper studies the construction of such confidence values and examines to what extent they approximate frequentist p values and bayesian a posteriori probabilities we derive more accurate confidence levels using both frequentist and objective bayesian approaches the methods are illustrated with a number of examples including polynomial model selection and estimating the number of modes of a density

aw1 p estimate for solutions to mixed boundary value problems for second order elliptic differential equations on demontre que sous des hypotheses plutot faibles une solution d un probleme aux valeurs limites mixte pour une equation elliptique d ordre 2 est dans l espace de sobolev w 1 p pour p 2

optimal control for the thermistor problem this paper is concerned with the state constrained optimal control of the two dimensional thermistor problem a quasi linear coupled system of a parabolic and elliptic pde with mixed boundary conditions this system models the heating of a conducting material by means of direct current existence uniqueness and continuity for the state system are derived by employing maximal elliptic and parabolic regularity by similar arguments the linearized state system is discussed while the adjoint system involving measures is investigated using a duality argument these results allow us to derive first order necessary conditions for the optimal control problem

noetherian local rings with buchsbaum associated graded rings is an invariant of a not depending on the choice of a parameter ideal q of a where f a q and e q denote respectively the length of the a module a q and the multiplicity of a relative to q see section 2 for detail here recall that if a is buchsbaum the local ring a is cohen macaulay and dim a d dim a p for any prime ideal p p m of a moreover the local cohomology modules a i d of a are vector spaces that is m h a 0 and one has the equality

on rings with linear resolutions let r denote a positively graded noetherian ring over a field k r eori with r k and m the irrelevant maximal ideal generated by forms of degree 1 or let r be the m adic completion of such a ring if we consider x as a homomorphic image of a polynomial ring resp of a power series ring over k with a homogeneous defining ideal one may ask whether r has a minimal linear resolution as an s module cohen macaulay rings r of maximal embedding dimension e g have a linear resolution as sally showed in 9 she also proved formulas for the hilbert series hr and the poincari series pi pz schenzel lo later characterized cm rings r with a linear resolution and called these rings extremal he also gave formulas for hr and pi s goto see 3 1 below proved besides other facts the linearity of the resolution for buchsbaum rings of maximal embedding dimension i e edim r dim r e r i r 1 i r denotes the invariant of the buchsbaum ring r and a formula for hh in section 1 we generalize these results and characterize rings with a linear resolution which have a parameter system that forms a d sequence in the buchsbaum case we then show that the h pi and pf of such rings are determined by the embedding dimension the krull dimension the dimensions of the local cohomology modules as k vector spaces and what we call the type of r in section 2 we determine all buchsbaum rings r k r of maximal embedding dimension and multiplicity 2 sally proved in 8 that for a local cm ring r m of maximal embedding dimension the associated graded ring is also cm of maximal embedding dimension goto showed a similar result for buchsbaum rings of

integrability of displacement and stresses in linear and nonlinear elasticity with mixed boundary conditions abstract equations of linear and nonlinear infinitesimal elasticity with mixed boundary conditions are considered the bounded domain is assumed to have a lipschitz boundary and to satisfy additional regularity assumptions w 1 p regularity for the displacements and l p regularity for the stresses are proved for some p 2

classical solutions of drift diffusion equations for semiconductor devices the two dimensional case abstract we regard drift diffusion equations for semiconductor devices in lebesgue spaces to that end we reformulate the generalized van roosbroeck system as an evolution equation for the potentials to the driving forces of the currents of electrons and holes this evolution equation falls into a class of quasi linear parabolic systems which allow unique local in time solution in certain lebesgue spaces in particular it turns out that the divergence of the electron and hole currents is an integrable function hence gauss theorem applies and gives the foundation for space discretization of the equations by means of finite volume schemes moreover the strong differentiability of the electron and hole density in time is constitutive for the implicit time discretization scheme finite volume discretization of space and implicit time discretization are accepted custom in engineering and scientific computing this investigation puts special emphasis on non smooth spatial domains mixed boundary conditions and heterogeneous material compositions as required in electronic device simulation