robust model based and model assisted predictors of the finite population total the prediction approach to finite population inference has received considerable attention in recent years under this approach the finite population is assumed to be a realization from a superpopulation described by a known probability model usually a linear model the prediction approach is often criticized for its lack of robustness against model misspecification in this article we revisit this important issue and introduce a new robust prediction approach in which the superpopulation model is chosen adaptively from the well known box cox class of probability distributions the richness of the box cox class ensures robustness in our model based prediction approach we explain how our robust model based predictor can be adjusted to handle zero observations for the study variable and to achieve the design unbiasedness and benchmarking properties we demonstrate the robustness of our proposed predictors using a monte carlo simulation study and a real life example

homogenization limits and wigner transforms we present a theory for carrying out homogenization limits for quadratic functions called energy densities of solutions of initial value problems ivps with anti self adjoint spatial pseudo differential operators pdos the approach is based on the introduction of phase space wigner matrix measures that are calculated by solving kinetic equations involving the spectral properties of the pdo the weak limits of the energy densities are then obtained by taking moments of the wigner measure the very general theory is illustrated by typical examples like semi classical limits of schrodinger equations with or without a periodic potential the homogenization limit of the acoustic equation in a periodic medium and the classical limit of the dirac equation 1997 john wiley sons inc

the l2 boundedness of pseudodifferential operators on donne une nouvelle demonstration du theoreme de calderon vaillancourt on obtient la l 2 continuite de a x d si le symbole a x satisfait a certaines conditions

multiphase semiclassical approximation of an electron in a one dimensional crystalline lattice i homogeneous problems we present a computational approach for the wkb approximation of the wave function of an electron moving in a periodic one dimensional crystal lattice we derive a nonstrictly hyperbolic system for the phase and the intensity where the flux functions originate from the bloch spectrum of the schrodinger operator relying on the framework of the multibranch entropy solutions introduced by brenier and corrias we compute efficiently multiphase solutions using well adapted and simple numerical schemes in this first part we present computational results for vanishing exterior potentials which demonstrate the effectiveness of the proposed method

local and global well posedness of the fractional order epdiff equation on r d abstract of concern is the study of fractional order sobolev type metrics on the group of h diffeomorphism of r d and on its sobolev completions d q r d it is shown that the h s sobolev metric induces a strong and smooth riemannian metric on the banach manifolds d s r d for s 1 d 2 as a consequence a global well posedness result of the corresponding geodesic equations both on the banach manifold d s r d and on the smooth regular frechet lie group of all h diffeomorphisms is obtained in addition a local existence result for the geodesic equation for metrics of order 1 2 s 1 d 2 is derived

on discrete time diagonal and d stability abstract this paper introduces four discrete time analogs of different types of matrix stability diagonal simultaneous vertex and d stability the last three being defined in terms of a certain associated polytope of matrices the diagonal stability of any vertex of this polytope is shown to imply its simultaneous stability and hence d stability of the vertices it is shown by a counterexample that d stability as in the continuous time case is not equivalent to diagonal stability several important classes for which this equivalence is true are identified it is shown that simultaneous stability of the vertices is equivalent to the simultaneous stability of the whole polytope and it is conjectured that this equivalence holds without the requirement of simultaneity some other conjectures relating the four types of stability are made and it is shown that in the 2 x 2 case all four are equivalent

wkb analysis for nonlinear schrodinger equations with potential we justify the wkb analysis for the semiclassical nonlinear schrodinger equation with a subquadratic potential this concerns subcritical critical and supercritical cases as far as the geometrical optics method is concerned in the supercritical case this extends a previous result by e grenier we also have to restrict to nonlinearities which are defocusing and cubic at the origin but besides subquadratic potentials we consider initial phases which may be unbounded for this we construct solutions for some compressible euler equations with unbounded source term and unbounded initial velocity

complex d convergence and diagonal convergence of matrices abstract in this paper types of convergence also referred to as schur stability for complex matrices are studied in particular it is proven that for complex matrices of order n 3 diagonal convergence d c convergence and boundary convergence are all equivalent an example of a 4 by 4 matrix that is d c convergent but not diagonally convergent is constructed

the estimation of the mean squared error of small area estimators abstract small area estimation has received considerable attention in recent years because of a growing demand for reliable small area statistics the direct survey estimators based only on the data from a given small area or small domain are likely to yield unacceptably large standard errors because of small sample size in the domain therefore alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the efficiency these estimators use models either implicitly or explicitly that connect the small areas through supplementary e g census and administrative data for example simple synthetic estimators are based on implicit modeling in this article three small area models of battese harter and fuller 1988 dempster rubin and tsutakawa 1981 and fay and herriot 1979 are investigated these models are all special cases of a general mixed linear model involving fixed and random effects and a small area mean can be expr

the cubic fourth order schrodinger equation fourth order schrodinger equations have been introduced by karpman and shagalov to take into account the role of small fourth order dispersion terms in the propagation of intense laser beams in a bulk medium with kerr nonlinearity in this paper we investigate the cubic defocusing fourth order schrodinger equation i tu 2u u 2u 0 in arbitrary space dimension rn for arbitrary initial data we prove that the equation is globally well posed when n 8 and ill posed when n 9 with the additional important information that scattering holds true when 5 n 8

spectrally stable matrices abstract given an n n complex matrix a define the matrix polytope determined by a as p a ad d diag d 1 d n 1 d i 1 i 1 n we investigate the class of matrices a such that every eigenvalue of every member of p a is contained in the convex hull of the eigenvalues of the extreme points of p a

geometric optics and instability for semi classical schrodinger equations we prove some instability phenomena for semi classical linear or nonlinear schrodinger equations for some perturbations of the data we show that for very small times we can neglect the laplacian and the mechanism is the same as for the corresponding ordinary differential equation our approach allows smaller perturbations of the data where the instability occurs for times such that the problem cannot be reduced to the study of an ordinary differential equation

loss of regularity for supercritical nonlinear schrodinger equations we consider the nonlinear schrodinger equation with defocusing smooth nonlinearity below the critical sobolev regularity it is known that the cauchy problem is ill posed we show that this is even worse namely that there is a loss of regularity in the spirit of the result due to g lebeau in the case of the wave equation as a consequence the cauchy problem for energy supercritical equations is not well posed in the sense of hadamard we reduce the problem to a supercritical wkb analysis for super cubic smooth nonlinearity this analysis is new and relies on the introduction of a modulated energy functional a la brenier

on fourier time splitting methods for nonlinear schrodinger equations in the semiclassical limit we prove an error estimate for a lie trotter splitting operator associated with the schrodinger poisson equation in the semiclassical regime when the wkb approximation is valid in finite time and so long as the solution to a compressible euler poisson equation is smooth the error between the numerical solution and the exact solution is controlled in sobolev spaces in a suitable phase amplitude representation as a corollary we infer the numerical convergence of the quadratic observables with a time step independent of the planck constant a similar result is established for the nonlinear schrodinger equation in the weakly nonlinear regime the function u e u e t x is complex valued and the space variable x belongs to r d the presence of the parameter e is motivated by the semiclassical limit e 0 physically e corresponds to a small ratio between microscopic and macroscopic quantities so the limit e 0 is expected to yield a relevant approximation see e g 18 and references therein the parameter 0 measures the strength of nonlinear interactions in the wkb regime which is recalled below the nonlinearity is negligible if 1 it has a leading order moderate influence if 1 weakly nonlinear regime and its influence is very strong in the regime e 0i f 0 the case 0 1 is not considered here but it should be considered as similar to the case 0 see 9 in this paper we consider mostly two families of nonlinearity nonlocal nonlinearity in the case 0 f k local or nonlocal nonlinearity in the case 1 the first case includes the schrodinger poisson system in space dimension d 3 f 1 r hence k x cd x d 2 the second case includes the cubic nonlinearity focusing or defocusing we will also discuss why the case of the cubic nonlinearity is not treated in the regime 0 see remark 6 3 our analysis is limited to bounded time intervals so the exponentials are controlled which is the reason why we do not keep track of such factors when they are eventually included in a uniform constant the reason why the analysis is bound to finite time intervals is in the case 0 that the solution of the euler poisson equation generically develops

sharp estimates for pseudo differential operators with symbols of limited smoothness and commutators we consider here pseudo differential operators whose symbol x is not infinitely smooth with respect to x decomposing such symbols into four sometimes five components and using tools of paradifferential calculus we derive sharp estimates on the action of such pseudo differential operators on sobolev spaces and give explicit expressions for their operator norm in terms of the symbol x we also study commutator estimates involving such operators and generalize or improve the so called kato ponce and calderon coifman meyer estimates in various ways

estimation of finite population domain means a model assisted empirical best prediction approach in this article we introduce a general methodology for producing a model assisted empirical best predictor ebp of a finite population domain mean using data from a complex survey our method improves on the commonly used design consistent survey estimator by using a suitable mixed model such a model combines information from related sources such as census and administrative data unlike a purely model based ebp the proposed model assisted ebp converges in probability to the customary design consistent estimator as the domain and sample sizes increase the convergence in probability is shown to hold with respect to the sampling design irrespective of the assumed mixed model a property commonly known as design consistency this property ensures robustness of the proposed predictor against possible model failures in addition the convergence in probability is shown to be valid with respect to the assumed mixed model model consistency a new mean squared prediction error mspe estimator is proposed

strichartz inequalities and the nonlinear schrodinger equation on compact manifolds kklwe prove strichartz estimates with fractional loss of derivatives for the schrodinger equation on any riemannian compact manifold as a consequence we infer low regularity local well posedness results in any dimension as well as global existence results for the cauchy problem of nonlinear schrodinger equations on surfaces in the case of defocusing polynomial nonlinearities and on three manifolds in the case of cubic defocusing nonlinearities we also discuss the optimality of these strichartz estimates on spheres

geometric optics and boundary layers for nonlinear schrodinger equations we justify supercritical geometric optics in small time for the defocusing semiclassical nonlinear schrodinger equation for a large class of non necessarily homogeneous nonlinearities the case of a half space with neumann boundary condition is also studied

supercritical geometric optics for nonlinear schrodinger equations we consider the small time semi classical limit for nonlinear schrodinger equations with defocusing smooth nonlinearity for a super cubic nonlinearity the limiting system is not directly hyperbolic due to the presence of vacuum to overcome this issue we introduce new unknown functions which are defined nonlinearly in terms of the wave function itself this approach provides a local version of the modulated energy functional introduced by y brenier the system we obtain is hyperbolic symmetric and the justification of wkb analysis follows

large time wkb approximation for multi dimensional semiclassical schrodinger poisson system abstract we consider the semiclassical schrodinger poisson system with a special initial data of wkb type such that the solution of the limiting hydrodynamical equation becomes time global in dimensions at least three we give an example of such initial data in the focusing case via the analysis of the compressible euler poisson equations this example is a large data with radial symmetry and is beyond the reach of the previous results because the phase part decays too slowly extending previous results in this direction we justify the wkb approximation of the solution with this data for an arbitrarily large interval of r

global well posedness and scattering for the energy critical nonlinear schrodinger equation in r 3 we obtain global well posedness scattering and global l 10 spacetime bounds for energy class solutions to the quintic defocusing schrodinger equa tion in r 1 3 which is energy critical in particular this establishes global existence of classical solutions our work extends the results of bourgain 4 and grillakis 20 which handled the radial case the method is similar in spirit to the induction on energy strategy of bourgain 4 but we perform the induction analysis in both frequency space and physical space simultaneously and replace the morawetz inequality by an interaction variant first used in 12 13 the principal advantage of the interaction morawetz estimate is that it is not localized to the spatial origin and so is better able to handle nonradial solutions in particular this interaction estimate together with an almost conservation argument controlling the movement of l 2 mass in fre quency space rules out the possibility of energy concentration

instabilities for supercritical schrodinger equations in analytic manifolds in this paper we consider supercritical nonlinear schrodinger equations in an analytic riemannian manifold md g where the metric g is analytic using an analytic wkb method we are able to construct an ansatz for the semiclassical equation for times independent of the small parameter these approximate solutions will help to show two different types of instabilities the first is in the energy space and the second is an immediate loss of regularity in higher sobolev norms

robust empirical bayes estimation of means from stratified samples abstract this article considers simultaneous estimation of means from several strata where each stratum contains a finite number of elements for example quite often estimates of annual incomes unemployment rates and so forth must be made simultaneously for many areas our results find application in small area estimation where very few samples are available from an individual area and an estimate of a certain area mean or simultaneous estimates of several area means can be improved by incorporating information from similar neighboring areas ghosh and meeden 1986 considered empirical bayes estimation of the finite population mean assuming a normal superpopulation model their estimators generalize automatically when one estimates a vector of stratum means this article relaxes the normality assumption and assumes instead that the posterior expectation of any stratum mean is a linear function of the sample observations this is the so called posterior linearity property as described in ericson 1

constrained bayes estimation with applications abstract bayesian techniques are widely used in these days for simultaneous estimation of several parameters in compound decision problems often however the main objective is to produce an ensemble of parameter estimates whose histogram is in some sense close to the histogram of population parameters this is for example the situation in subgroup analysis where the problem is not only to estimate the different components of a parameter vector but also to identify the parameters that are above and the others that are below a certain specified cutoff point we have proposed in this paper bayes estimates in a very general context that meet this need these estimates are obtained by matching the first two moments of the histogram of the estimates and the posterior expectations of the first two moments of the histogram of the parameters and minimizing subject to these conditions the posterior expectation of the euclidean distance between the estimates and the parameters several applications of the m

empirical bayes estimation of finite population means from complex surveys abstract estimation of finite population means is considered when samples are collected using a stratified sampling design finite populations for different strata are assumed to be realizations from different superpopulations the true means of the observations lie on a regression surface with random intercepts for different strata the true sampling variances are also different and random for different strata the strata are connected through two common prior distributions one for the intercepts and another for the sampling variances for all the strata the model is appropriate in two important survey situations first it can be applied to repeated surveys where the physical characteristics of the sampling units change slowly over time second the model is appropriate in small area estimation problems where a very few samples are available for any particular area empirical bayes estimators of the finite population means are shown to be asymptotically optimal in the sense of robbins the proposed emp

classes of schur d stable matrices abstract it is shown that vertex stability implies schur d stability for real 3 3 matrices also principally nilpotent n n complex matrices are shown to be perfectly schur d stable and additional characterizations of these matrices are given

universal dynamics for the defocusing logarithmic schrodinger equation we consider the nonlinear schrodinger equation with a logarithmic nonlinearity in a dispersive regime we show that the presence of the nonlinearity affects the large time behavior of the solution the dispersion is faster than usual by a logarithmic factor in time and the positive sobolev norms of the solution grow logarithmically in time moreover after rescaling in space by the dispersion rate the modulus of the solution converges to a universal gaussian profile these properties are suggested by explicit computations in the case of gaussian initial data and remain when an extra power like nonlinearity is present in the equation one of the key steps of the proof consists in using the madelung transform to reduce the equation to a variant of the isothermal compressible euler equation whose large time behavior turns out to be governed by a parabolic equation involving a fokker planck operator

semi classical limit of schrodinger poisson equations in space dimension n 3 abstract we prove the existence of solutions to the schrodinger poisson system on a time interval independent of the planck constant when the doping profile does not necessarily decrease at infinity in the presence of a subquadratic external potential the lack of integrability of the doping profile is resolved by working in zhidkov spaces in space dimension at least three we infer that the main quadratic quantities position density and modified momentum density converge strongly as the planck constant goes to zero when the doping profile is integrable we prove pointwise convergence

l infty l ill posedness for a class of equations arising in hydrodynamics we give a new approach to studying norm inflation in some critical spaces for a wide class of equations arising in hydrodynamics as an application we prove strong ill posedness of the n dimensional euler equations in the class c 1 cap l 2 omega and also in c k cap l 2 omega where omega can be the whole space a smooth bounded domain or the torus we also apply our method to the oldroyd b surface quasi geostrophic and boussinesq systems

nonlinear schrodinger equations and sharp interpolation estimates a sharp sufficient condition for global existence is obtained for the nonlinear schrodinger equation begin array 20 c nls 2i phi t delta phi left phi right 2 sigma phi 0 x in mathbb r n t in mathbb r end array in the case 2 n this condition is in terms of an exact stationary solution nonlinear ground state of nls it is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of nirenberg and gagliardo

low mach number limit of the full navier stokes equations the low mach number limit for classical solutions of the full navier stokes equations is here studied the combined effects of large temperature variations and thermal conduction are taken into account in particular we consider general initial data the equations lead to a singular problem depending on a small scaling parameter whose linearized system is not uniformly well posed yet it is proved that solutions exist and they are uniformly bounded for a time interval which is independent of the mach number ma 0 1 the reynolds number re 1 and the peclet number pe 1 based on uniform estimates in sobolev spaces and using a theorem of g metivier s schochet 30 we next prove that the penalized terms converge strongly to zero this allows us to rigorously justify at least in the whole space case the well known computations given in the introduction of p l lions book 26

semiclassical limit of the gross pitaevskii equation in an exterior domain in this paper we study the semiclassical limit of the gross pitaevskii equation a cubic nonlinear schrodinger equation with the neumann boundary condition in an exterior domain we prove that before the formation of singularities in the limit system the quantum density and the quantum momentum converge to the unique solution of the compressible euler equation with the slip boundary condition as the scaling parameter approaches 0

on scattering for the quintic defocusing nonlinear schrodinger equation on r t2 we consider the problem of large data scattering for the quintic nonlinear schrodinger equation on r t2 this equation is critical both at the level of energy and mass most notably we exhibit a new type of profile a large scale profile that controls the asymptotic behavior of the solutions 2014 wiley periodicals inc

multiplicative perturbations of stable and convergent operators abstract some familiar classes of stable hilbert space operators are studied to determine how they overlap and where the unitary similarity classes of their members lie analogous but less familiar classes of convergent operators are examined with the same aim the classes considered are often sets of products m a where m is a given set of diagonal or hermitian matrices and a is a single matrix the a s for which m a is a set of stable or convergent operators are sometimes characterized

wkb analysis of the schrodinger kdv system abstract we consider the behavior of solutions to the water wave interaction equations in the limit e 0 to justify the semiclassical approximation we reduce the water wave interaction equation into some hyperbolic dispersive system by using a modified madelung transform the reduced system causes loss of derivatives which prevents us to apply the classical energy method to prove the existence of solution to overcome this difficulty we introduce a modified energy method and construct the solution to the reduced system

robust schur stability of a polytope of polynomials the main objective of the authors is to provide a necessary and sufficient condition for a polytope of polynomials to have all its zeros inside the unit circle the criterion obtained serves as a discrete time counterpart for results in s bialas 1985 and f fu and b r barmish 1987 for the continuous case also the results are reduced to operations on n 1 n 1 matrices it is concluded that by the edge result of a c bartlett et al 1987 it suffices to check the exposed edges in order to determine whether a polytope of polynomials has all its zeros in a simply connected region d

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

existence and uniqueness of two dimensional euler poisson system and wkb approximation to the nonlinear schrodinger poisson system in this paper we study a dispersive euler poisson system in two dimensional euclidean space our aim is to show unique existence and the zero dispersion limit of the time local weak solution since one may not use dispersive structure in the zero dispersion limit when reducing the regularity lack of critical embedding h1 l becomes a bottleneck we hence employ an estimate on the best constant of the gagliardo nirenberg inequality by this argument a reasonable convergence rate for the zero dispersion limit is deduced with a slight loss we also consider the semiclassical limit problem of the schrodinger poisson system in two dimensions

empirical bayes estimation in finite population sampling abstract empirical bayes methods are becoming increasingly popular in statistics robbins 1955 introduced the method in the context of nonparametric estimation of a completely unspecified prior distribution subsequently the method has been explored very successfully in a series of articles by efron and morris 1973 1975 1977 in a parametric framework in the efron morris setup a family of parametric distributions is used as possible priors but only when one or more of the parameters of the family of prior distributions is estimated from the data morris 1983 listed a number of areas where empirical bayes methods are used one of the main features of empirical bayes analysis is to borrow strength from the ensemble that is use information from similar sources in constructing estimators and predictors in addition to the most directly available source of information there are some situations in finite population sampling where such methods might be suitable for instance in many repetitive surve

monotonicity properties of norms abstract we consider several properties that might be described as monotonicity or absoluteness that a norm may or may not have and give a complete set of implications among them we also consider some related hadamard product inequalities under various normalizations

on the design consistency property of hierarchical bayes estimators in finite population sampling we obtain a limit of a hierarchical bayes estimator of a finite population mean when the sample size is large the limit is in the sense of ordinary calculus where the sample observations are treated as fixed quantities our result suggests a simple way to correct the hierarchical bayes estimator to achieve design consistency a well known property in the traditional randomization approach to finite population sampling we also suggest three different measures of uncertainty of our proposed estimator

on schur d stable matrices abstract it is shown that vertex stability implies schur d stability for real 2 2 matrices and real n n tridiagonal matrices additional results describing the class of n n complex schur d stable matrices are given

pseudo differential energy estimates of singular perturbations in this paper we study singular limits of hyperbolic systems which exhibit large time oscillations and in particular pseudo differential energy estimates that enable us to obtain uniform existence time and a priori bounds on the solutions 1997 john wiley sons inc

global existence and scattering for rough solutions of a nonlinear schr odinger equation on r 3 we prove global existence and scattering for the defocusing cubic nonlinear schrodinger equation in h s r 3 for s 4 the main new estimate in the argument is a morawetz type inequality for the solution this estimate bounds k x t k l 4 r3 r whereas the well known morawetz type estimate of lin strauss controls r 1 0 r r3 x t 4 x dxdt

blowup of smooth solutions to the compressible navier stokes equation with compact density we present a sufficient condition on the blowup of smooth solutions to the compressible navier stokes equations in arbitrary space dimensions with initial density of compact support as an immediate application it is shown that any smooth solutions to the compressible navier stokes equations for polytropic fluids in the absence of heat conduction will blow up in finite time as long as the initial densities have compact support and an upper bound which depends only on the initial data on the blowup time follows from our elementary analysis immediately another implication is that there is no global small decay in time or even bounded in the case that all the viscosity coefficients are positive smooth solutions to the compressible navier stokes equations for polytropic fluids no matter how small the initial data are as long as the initial density is of compact support this is in contrast to the classical theory of global existence of small solutions to the same system with initial data being a small perturbation of a constant state that is not a vacuum the blowup of smooth solutions to the compressible euler system with initial density and velocity of compact support is a simple consequence of our argument 1998 john wiley sons inc

the limit from the schrodinger poisson to the vlasov poisson equations with general data in one dimension we deal with the classical limit of the schrodinger poisson system to the vlasov poisson equations as the planck constant e goes to zero this limit is also frequently called the semiclassical limit the coupled schrodinger poisson system for the wave functions j t x is transformed to the wigner poisson equations for a phase space function f t x for the case of the so called completely mixed state i e j 1 2 under additional assumptions on the potential this classical limit was solved in 1993 by p l lions and t paul in 23 and independently by p a markowich and n j mauser in 26 with strong assumptions on the initial data the so called pure state case where only one or a finite number of wave functions j t x are considered has been open up to now we prove here for general initial data the pure state as well as the mixed state case of the wave functions in one space dimension that the wigner measure f t x which is a weak limit of f t x as tends to 0 satisfies the classical one dimensional vlasov poisson equations as a by product we have improved the decay assumption on the initial data of one dimensional vlasov poisson equations in 38 for the existence of global weak solutions with measures as initial data the equations we regard are widely used in quantum classical transport and semiconductor theory as a nonlinear one particle mean field approximation of the linear n electron schrodinger hamilton equation

bohmian measures and their classical limit abstract we consider a class of phase space measures which naturally arise in the bohmian interpretation of quantum mechanics we study the classical limit of these so called bohmian measures in dependence on the scale of oscillations and concentrations of the sequence of wave functions under consideration the obtained results are consequently compared to those derived via semi classical wigner measures to this end we shall also give a connection to the theory of young measures and prove several new results on wigner measures themselves our analysis gives new insight on oscillation and concentration effects in the semi classical regime

propagation of oscillations in real vanishing viscosity limit in this paper we study viscous perturbations of quasilinear hyperbolic systems in several space dimensions the equations involve a singular parameter which goes to zero they arise in realistic models of compressible flow the large scale motions in the atmosphere 12 they come also from theoretical considerations in non linear geometric optics 4 5 we prove that solutions u exist on a domain of space time independent on open image in new window

global well posedness and scattering for the defocusing energy critical nonlinear schrodinger equation in r1 4 we obtain global well posedness scattering uniform regularity and global l6t x spacetime bounds for energy space solutions to the defocusing energy critical nonlinear schrodinger equation in a 4 our arguments closely follow those of colliander keel et al though our derivation of the frequency localized interaction morawetz estimate is somewhat simpler as a consequence our method yields a better bound on the l6t x norm

large time existence for 3d water waves and asymptotics we rigorously justify in 3d the main asymptotic models used in coastal oceanography including shallow water equations boussinesq systems kadomtsev petviashvili kp approximation green naghdi equations serre approximation and full dispersion model we first introduce a variable nondimensionalized version of the water waves equations which vary from shallow to deep water and which involves four dimensionless parameters using a nonlocal energy adapted to the equations we can prove a well posedness theorem uniformly with respect to all the parameters its validity ranges therefore from shallow to deep water from small to large surface and bottom variations and from fully to weakly transverse waves

empirical bayes estimation for the finite population mean on the current occasion abstract many finite populations which are sampled repeatedly change slowly over time then estimation of finite population characteristics for the current occasion l may be improved by the use of data from previous surveys in this article we investigate the use of empirical bayes procedures based on two superpopulation models each model has the same first stage the values of the population units on the ith occasion are a random sample from the normal distribution with mean i and variance 2 i at the second stage we assume that either a 1 l are a random sample from the normal distribution with mean and variance 2 or b given 2 i and i has the normal distribution with mean and variance 2 i independently for each i whereas the 2 i are a random sample from the inverse gamma distribution with parameters 2 and 2 in a the 2 i and 2 are assumed to be unknown whereas in b and are unknown we develop empirical bayes point estimators and confide

a stability criterion for two fluid interfaces and applications we derive a new stability criterion for two fluid interfaces that ensures the existence of stable local solutions that do not break down too fast due to kelvin helmholtz instabilities it can be seen both as a two fluid generalization of the rayleigh taylor criterion and as a nonlinear version of the kelvin stability condition we show that gravity can control the inertial effects of the shear up to frequencies that are high enough for the surface tension to play a relevant role this explains why surface tension is a necessary condition for well posedness while the low frequency main dynamics of interfacial waves are unaffected by it in order to derive a practical version of this criterion we work with a nondimensionalized version of the equations and allow for the possibility of various asymptotic regimes such as the shallow water limit this limit being singular we have to derive a new symbolic analysis of the dirichlet neumann operator that includes an infinitely smoothing tail accounting for the contribution of the bottom we then validate our criterion by comparison with experimental data in two important settings air water interfaces and internal waves the good agreement we observe allows us to discuss the scenario of wave breaking and the behavior of water brine interfaces and to propose a formula for the maximal amplitude of interfacial waves we also show how to rigorously justify two fluid asymptotic models used for applications and how to relate some of their properties to kelvin helmholtz instabilities

on the semiclassical limit of the general modified nls equation we study the semiclassical limit of the so called general modified nonlinear schrodinger equation for initial data with sobolev regularity before shocks appear in the limit system the strict hyperbolicity and genuine nonlinearity are proved for the dispersion limit of the cubic nonlinear case the limiting transition from the mnls equation to the nls equation is also discussed

some bayesian and non bayesian procedures for the analysis of comparative experiments and for small area estimation computational aspects frequentist properties and relationships abstract the estimation of a treatment contrast from experimental data and the estimation of a small area mean are special cases of the prediction of the realization of a linear combination of fixed and random effects in a possibly unbalanced two part mixed linear model in this article a bayesian approach to point and interval prediction is presented and its computational requirements are examined differences between the bayesian approach and the traditional classical approach are discussed in general terms and in addition in terms of two examples taken from the literature 1 the comparison of drug formulations in a bioavailability trial westlake and 2 the estimation of corn crop areas using satellite data battese harter and fuller some deficiencies in the classical approach are pointed out and the bayesian approach is considered from a frequentist perspective it is shown via a monte carlo study that for certain noninformative choices of the prior distribution the frequentist prop

counter examples to concentration cancellation we study the existence and the asymptotic behavior of large amplitude high frequency oscillating waves subjected to the two dimensional burger equation this program is achieved by developing tools related to supercritical wkb analysis by selecting solutions which are divergence free we show that incompressible or compressible two dimensional euler equations are not locally closed for the weak l2 topology

well posedness of the water waves equations 1 1 presentation of the problem the water waves problem for an ideal liquid consists of describing the motion of the free surface and the evolution of the velocity field of a layer of perfect incompressible irrotational fluid under the influence of gravity in this paper we restrict our attention to the case when the surface is a graph parameterized by a function x where t denotes the time variable and x xi xd rd the horizontal spatial variables the method developed here works equally well for any integer d 1 but the only physically relevant cases are of course d 1 and d 2 the layer of fluid is also delimited from below by a not necessarily flat bottom parameterized by a time independent function b x we denote by q t the fluid domain at time t the incompressibility of the fluids is expressed by 1 1 div v 0 in qu t 0

using empirical bayes methods in biopharmaceutical research a compound sampling model where a unit specific parameter is sampled from a prior distribution and then observed are generated by a sampling distribution depending on the parameter underlies a wide variety of biopharmaceutical data for example in a multi centre clinical trial the true treatment effect varies from centre to centre observed treatment effects deviate from these true effects through sampling variation knowledge of the prior distribution allows use of bayesian analysis to compute the posterior distribution of clinic specific treatment effects frequently summarized by the posterior mean and variance more commonly with the prior not completely specified observed data can be used to estimate the prior and use it to produce the posterior distribution an empirical bayes or variance component analysis in the empirical bayes model the estimated prior mean gives the typical treatment effect and the estimated prior standard deviation indicates the heterogeneity of treatment effects in both the bayes and empirical bayes approaches estimated clinic effects are shrunken towards a common value from estimates based on single clinics this shrinkage produces more efficient estimates in addition the compound model helps structure approaches to ranking and selection provides adjustments for multiplicity allows estimation of the histogram of clinic specific effects and structures incorporation of external information this paper outlines the empirical bayes approach coverage will include development and comparison of approaches based on parametric priors for example a gaussian prior with unknown mean and variance and non parametric priors discussion of the importance of accounting for uncertainty in the estimated prior comparison of the output and interpretation of fixed and random effects approaches to estimating population values estimating histograms and identification of key considerations in the use and interpretation of empirical bayes methods

quasi linear bayes estimation in stratified finite populations in this paper a bayesian least squares approximation is proposed for descriptive inference in a finite population when a categorical auxiliary variable is known a hierarchical model ii analysis of variance is assumed the solution consists of a projection on the vector of group totals and on the between and within sums of squares the approximation can be seen as a normal approximation of the joint distribution of the statistic and of the parameter of interest conditional on two discrete variables these denote attribution to one group and selection in the sample the main consequence of the conditioning is that conjectures about non normality can be taken into account the solution is compared with others that have been published

derivation of the zakharov equations this article continues the study initiated in 27 7 of the validity of the zakharov model which describes langmuir turbulence we give an existence theorem for a class of singular quasilinear equations this theorem is valid for prepared initial data we apply this result to the euler maxwell equations which describes laser plasma interactions to obtain in a high frequency limit an asymptotic estimate that describes solutions of the euler maxwell equations in terms of wkb approximate solutions the leading terms of which are solutions of the zakharov equations due to the transparency properties of the euler maxwell equations evidenced in 27 this study is carried out in a supercritical highly nonlinear regime in such a regime resonances between plasma waves electromagnetric waves and acoustic waves could create instabilities in small time the key of this work is the control of these resonances the proof involves the techniques of geometric optics of joly metivier and rauch 12 13 recent results by lannes on norms of pseudodifferential operators 14 and a semiclassical paradifferential calculus

on fourier time splitting methods for nonlinear schrodinger equations in the semi classical limit ii analytic regularity we consider the time discretization based on lie trotter splitting for the nonlinear schrodinger equation in the semi classical limit with initial data under the form of wkb states we show that both the exact and the numerical solutions keep a wkb structure on a time interval independent of the planck constant we prove error estimates which show that the quadratic observables can be computed with a time step independent of the planck constant the functional framework is based on time dependent analytic spaces in order to overcome a previously encountered loss of regularity phenomenon

generalized linear models for small area estimation abstract bayesian methods have been used quite extensively in recent years for solving small area estimation problems particularly effective in this regard has been the hierarchical or empirical bayes approach which is especially suitable for a systematic connection of local areas through models however the development to date has mainly concentrated on continuous valued variates often the survey data are discrete or categorical so that hierarchical or empirical bayes techniques designed for continuous variates are inappropriate this article considers hierarchical bayes generalized linear models for a unified analysis of both discrete and continuous data a general theorem is provided that ensures the propriety of posteriors under diffuse priors this result is then extended to the case of spatial generalized linear models the hierarchical bayes procedure is implemented via markov chain monte carlo integration techniques two examples one featuring spatial correlation structure are given to illu

schur type stability properties and complex diagonal scaling we introduce new classes of n by n matrices with complex entries which can be scaled by a diagonal matrix with complex entries to be normal or hermitian and study the schur type stability properties of these matrices

multiphase semiclassical approximation of an electron in a one dimensional crystalline lattice iii from ab initio models to wkb for schrodinger poisson this work is concerned with the semiclassical approximation of the schrodinger poisson equation modeling ballistic transport in a 1d periodic potential by means of wkb techniques it is derived by considering the mean field limit of a n body quantum problem then k multivalued solutions are adapted to the treatment of this weakly nonlinear system obtained after homogenization without taking into account for pauli s exclusion principle numerical experiments display the behaviour of self consistent wave packets and screening effects

a unified jackknife theory for empirical best prediction with m estimation the paper presents a unified jackknife theory for a fairly general class of mixed models which includes some of the widely used mixed linear models and generalized linear mixed models as special cases the paper develops jackknife theory for the important but so far neglected prediction problem for the general mixed model for estimation of fixed parameters a jackknife method is considered for a general class of m estimators which includes the maximum likelihood residual maximum likelihood and anova estimators for mixed linear models and the recently developed method of simulated moments estimators for generalized linear mixed models for both the prediction and estimation problems a jackknife method is used to obtain estimators of the mean squared errors mse asymptotic unbiasedness of the mse estimators is shown to hold essentially under certain moment conditions simulation studies undertaken support our theoretical results 1 introduction due to the advent of high speed computers and powerful software computer oriented statistical methods including various resampling methods have received considerable attention in recent years as statisticians are constantly facing complex problems the jackknife method is one such simple resampling method which is very popular among survey samplers primarily due