on prediction properties of kriging uniform error bounds and robustness kriging based on gaussian random fields is widely used in reconstructing unknown functions the kriging method has pointwise predictive distributions which are computationally simple however in m

boundary effect on asymptotic behaviour of solutions to the p system with linear damping we consider the asymptotic behaviour of solutions to the p system with linear damping on the half line r 0 vt ux 0 ut p v x u with the dirichlet boundary condition u x 0 0 or the neumann boundary condition ux x 0 0 the initial date v0 u0 x has the constant state v u at x l hsiao and t p liu commun math phys 143 1992 599 605 have shown that the solution to the corresponding cauchy problem behaves like diffusion wave and k nishihara j differential equations131 1996 171 188 137 1997 384 395 has proved its optimal convergence rate our main concern in this paper is the boundary effect in the case of null dirichlet boundary condition on u the solution v u is proved to tend to v 0 as t tends to infinity its optimal convergence rate is also obtained by using the green function of the diffusion equation with constant coefficients in the case of null neumann boundary condition on u v 0 t is conservative and v 0 t v0 0 by virtue of the first equation so that v x t is expected to tend to the diffusion wave v x t connecting v0 0 and v in fact the solution v u x t is proved to tend to v x t 0 in the special case v0 0 v the optimal convergence rate is also obtained however this is not known in the case v0 0 v

scaling variables and asymptotic expansions in damped wave equations abstract we study the long time behavior of small solutions to the nonlinear damped wave equationeu u a u n u u u r 0 whereeis a positive not necessarily small parameter we assume that the diffusion coefficienta converges to positive limitsa as and that the nonlinearity n u u u vanishes sufficiently fast asu 0 introducing scaling variables and using various energy estimates we compute an asymptotic expansion of the solutionu in powers of 1 2as and we show that this expansion is entirely determined up to the second order by a linear parabolic equation which depends only on the limiting valuesa in particular this implies that the small solutions of the damped wave equation behave for large like those of the parabolic equation obtained by settinge 0

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

existence and asymptotic behavior of global smooth solution for p system with damping and boundary effect abstract in this paper we study the existence and asymptotic behavior of global smooth solution for p system with damping on the strip 0 1 0 v t u x 0 u t p v x u with the null dirichlet boundary condition u 0 t u 1 t 0 first we prove the existence of the global smooth solution under the assumption that only the c 0 norm of the first derivatives of the initial data is sufficiently small while the c 0 norm of the initial data is not necessarily small second when the initial data is in c 2 and the c 0 norm of the first derivatives of the initial data is large enough then the first derivatives of the corresponding c 2 smooth solution must blow up in finite time finally we consider the asymptotic behavior of the global smooth solution precisely we show that the solution of this problem tends to the corresponding nonlinear diffusive wave governed by the classical darcy s law exponentially fast as time goes to infinity in the sense of h 1 norm provided the initial total mass is the same and thus justifies the validity of darcy s law in large time

robust estimation of mean squared error of small area estimators abstract a well known model due to fay and herriot for estimating small area domain means i is considered given i s it is assumed that the survey estimators y i are independent with means i and known variances di i 1 t further the i s are assumed to be independent with means x i and unknown variance a where x i is a vector of benchmark variables related to i and is a vector of regression parameters an empirical best linear unbiased prediction eblup estimator or an empirical linear bayes estimator t i y of i is obtained it is shown that an estimator of mean squared error mse of t t y derived by prasad and rao under normality of i and y i given i is robust with respect to nonnormality of the i s specifically it is shown that the prasad rao estimator of mse is correct to terms of order o t 1 for large t assuming only certain moment conditions on the i s and normally distributed survey errors results of a simulation study on the accur

existence and non existence of global solutions of the cauchy problem for higher order semilinear pseudo hyperbolic equations abstract we consider the cauchy problem for a higher order pseudo hyperbolic equation using the l p l q type estimation for the corresponding linear problem the existence and non existence criteria of global solutions are found the existence and uniqueness of smooth global solutions are also investigated we also establish the behavior of solutions and their derivatives as t

best asymptotic profile for linear damped p system with boundary effect abstract this paper is devoted to the study of the 2 2 linear damped p system with boundary effect by a heuristic analysis we realize that the best asymptotic profile for the original solution is the parabolic solution of the ibvp for the corresponding porous media equation with a specified initial data in particular we further show the convergence rates of the original solution to its best asymptotic profile which are much better than the existing rates obtained in the previous works the approach adopted in the paper is the elementary weighted energy method with green function method together

on parametric bootstrap methods for small area prediction summary the particularly wide range of applications of small area prediction e g in policy making decisions has meant that this topic has received substantial attention in recent years the problems of estimating mean squared predictive error of correcting that estimator for bias and of constructing prediction intervals have been addressed by various workers although existing methodology is still restricted to a narrow range of models to overcome this difficulty we develop new bootstrap based methods which are applicable in very general settings for constructing bias corrected estimators of mean squared error and for computing prediction regions unlike existing techniques which are based largely on taylor expansions our bias corrected mean squared error estimators do not require analytical calculation they also have the property that they are non negative our prediction intervals have a high degree of coverage accuracy o n 3 where n is the number of areas if double bootstrap methods are employed the techniques do not depend on the form of the small area estimator and are applicable to general two level small area models where the variables at either level can be discrete or continuous and in particular can be non normal most importantly the new methods are simple and easy to apply

on measuring the variability of small area estimators under a basic area level model summary in this paper based on a basic area level model we obtain second order accurate approxi mations to the mean squared error of model based small area estimators using the fay herriot 1979 iterative method of estimating the model variance based on weighted residual sum of squares we also obtain mean squared error estimators unbiased to second order based on simulations we compare the finite sample performance of our mean squared error estimators with those based on method of moments maximum likelihood and residual maximum likelihood estimators of the model variance our results suggest that the fay herriot method performs better in terms of relative bias of mean squared error estimators than the other methods across different combinations of number of areas pattern of sampling variances and distribution of small area effects we also derive a noninformative prior on the model parameters for which the posterior variance of a small area mean is second order unbiased for the mean squared error the posterior variance based on such a prior possesses both bayesian and frequentist interpretations

critical exponent for nonlinear wave equations with frictional and viscoelastic damping terms abstract in this paper we study the cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms our aim is to obtain the threshold to classify the global existence of solutions for small initial data or the finite time blow up of solutions under the growth condition of the nonlinearity

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

critical exponents for semilinear dissipative wave equations in rn abstract we shall present new critical exponents 1 2m n with m 1 2 to the cauchy problem utt u ut u p 1u with the initial data u 0 u 1 h 1 r n l m r n l 2 r n l m r n that is the small data global existence property can be derived to the cauchy problem above with power 1 2m n

convergence to strong nonlinear diffusion waves for solutions to p system with damping in this paper we consider the so called p system with linear damping and we will prove an optimal decay estimates without any smallness conditions on the initial error more precisely if we restrict the initial data v0 u0 in the space h3 r l1 r h2 r l1 r then we can derive faster decay estimates than those given in p marcati m mei b rubino optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping j math fluid mech 7 2 2005 224 240 h zhao convergence to strong nonlinear diffusion waves for solutions of p system with damping j differential equations 174 1 2001 200 236 and m jian c zhu convergence to strong nonlinear diffusion waves for solutions to p system with damping on quadrant j differential equations 246 1 2009 50 77

nonparametric estimation of mean squared prediction error in nested error regression models nested error regression models are widely used for analyzing clustered data for example they are often applied to two stage sample surveys and in biology and econometrics prediction is usually the main goal of such analyses and mean squared prediction error is the main way in which prediction performance is measured in this paper we suggest a new approach to estimating mean squared prediction error we introduce a matched moment double bootstrap algorithm enabling the notorious underestimation of the naive mean squared error estimator to be substantially reduced our approach does not require specific assumptions about the distributions of errors additionally it is simple and easy to apply this is achieved through using monte carlo simulation to implicitly develop formulae which in a more conventional approach would be derived laboriously by mathematical arguments

critical exponent for semilinear damped wave equations in the n dimensional half space abstract we generalize a previous result of ikehata math methods appl sci in press which studies the critical exponent problem of a semilinear damped wave equation in the one dimensional half space to the general n dimensional half space case that is to say one can show the small data global existence of solutions of a mixed problem for the equation utt u ut u p with the power p satisfying p n 1 2 n 1 if we deal with the problem in the n dimensional half space

wave equations with time dependent dissipation ii effective dissipation abstract this article is intended to present a construction of structural representations of solutions to the cauchy problem for wave equations with time dependent dissipation above scaling these representations are used to give estimates of the solution and its derivatives based on l q r n q 2 the article represents the second part within a series in jens wirth wave equations with time dependent dissipation i non effective dissipation j differential equations 222 2 2006 487 514 weak dissipations below scaling were discussed

semiparametric inference in generalized mixed effects models summary the paper presents a study of the generalized partially linear model including random effects in its linear part we propose an estimator that combines likelihood approaches for mixed effects models with kernel methods following the methodology of hardie and co workers we introduce a test for the hypothesis of a parametric mixed effects model against the alternative of a semiparametric mixed effects model the critical values are estimated by using a bootstrap procedure the asymptotic theory for the methods is provided as are the results of a simulation study these verify the feasibility and the excellent behaviour of the methods for samples of even moderate size the usefulness of the methodology is illustrated with an application in which the objective is to estimate forest coverage in galicia spain

convergence to nonlinear diffusion waves for solutions of p system with time dependent damping abstract in this paper we study the cauchy problem for the hyperbolic p system with time gradually degenerate damping term 1 1 t u for 0 1 and show that the damped p system has a couple of global solutions uniquely and such solutions tend time asymptotically to the shifted nonlinear diffusion waves which are the solutions of the corresponding nonlinear parabolic equation governed by the darcy s law we further derive the convergence rates when the initial perturbations are in l 2 the approach adopted is the technical time weighted energy method

decidability and complexity of simultaneous rigid e unification with one variable and related results we show that simultaneous rigid e unification or sreu for short is decidable and in fact exptime complete in the case of one variable this result implies that the for all there exists for all f

logic with equality partisan corroboration and shifted pairing herbrand s theorem plays a fundamental role in automated theorem proving methods based on tableaux the crucial step in procedures based on such methods can be described as the corroboration problem or the herbrand skeleton problem where given a positive integer m called multiplicity and a quantifier free formula one seeks a valid disjunction of m instantiations of that formula in the presence of equality which is the case in this paper this problem was recently shown to be undecidable the main contributions of this paper are two theorems the first the partisan corroboration theorem relates corroboration problems with different multiplicities the second the shifted pairing theorem is a finite tree automata formalization of a technique for proving undecidability results through direct encodings of valid turing machine computations these theorems are used in the paper to explain and sharpen several recent undecidability results related to the corroboration problem the simultaneous rigid e unification problem and the prenex fragment of intuitionistic logic with equality

generalization of likelihood ratio tests under nonstandard conditions in this paper we analyze the statistic which is the difference in the values of an estimating function evaluated at its local maxima on two different subsets of the parameter space assuming that the true parameter is in each subset but possibly on the boundary our results extend known methods by covering a large class of estimation problems which allow sampling from nonidentically distributed random variables specifically the existence and consistency of the local maximum estimators and asymptotic properties of useful hypothesis tests are obtained under certain law of large number and central limit type assumptions other models covered include those with general log likelihoods and or covariates as an example the large sample theory of two way nested random variance components models with covariates is derived from our main results

weighted l2 estimates for dissipative wave equations with variable coefficients abstract we establish weighted l 2 estimates for the wave equation with variable damping u t t u a u t 0 in r n where a x a 0 1 x with a 0 0 and 0 1 in particular we show that the energy of solutions decays at a polynomial rate t n 2 1 if a x a 0 x for large x we derive these results by strengthening significantly the multiplier method this approach can be adapted to other hyperbolic equations with damping

convergence to strong nonlinear diffusion waves for solutions to p system with damping on quadrant in this paper we consider the so called p system with linear damping on quadrant we show that for a certain class of given large initial data v0 x u0 x the corresponding initial boundary value problem admits a unique global smooth solution v x t u x t and such a solution tends time asymptotically at the lp 2 p optimal decay rates to the corresponding nonlinear diffusion wave v x t u x t which satisfies 1 9 provided the corresponding prescribed initial error function v0 x u0 x lies in h3 r l1 r h2 r l1 r

penalized balanced sampling summary linear mixed models are flexible and extensible models that c over a wide range of statistical methods they have found many uses in estimation for complex surveys particularly in small area estimation and in extensions of generalized regression estimation they have also been used as a means of relaxing constraints in calibration estimatio n the purpose of this work is to consider methods by which linear mixed models may be used at the design stage of a survey this paper reviews the ideas of balanced sampling and the cube algorithm and proposes an implementation of the cube algorithm by which penalized balanced samples can be selected such samples have the property that horvitz thompson estimators from penalized balanced samples behave like linear mixed model assisted survey regression estimators from unbalanced samples the methodology is evaluated by using nonparametric and temporal linear mixed models in simulation experiments and by using a spatial linear mixed model in an artificial but realistic sampling application motivated by a 1991 1996 environmental protection agency survey of lakes in the northeastern states of the united states

empirical bayes estimates of age standardized relative risks for use in disease mapping there have been many attempts in recent years to map incidence and mortality from diseases such as cancer such maps usually display either relative rates in each district as measured by a standardized mortality ratio smr or some similar index or the statistical significance level for a test of the difference between the rates in that district and elsewhere neither of these approaches is fully satisfactory and we propose a new approach using empirical bayes estimation the resulting estimators represent a weighted compromise between the smr the overall mean relative rate and a local mean of the relative rate in nearby areas the compromise solution depends on the reliability of each individual smr and on estimates of the overall amount of dispersion of relative rates over different districts

the e ms algorithm model selection with incomplete data we propose a procedure associated with the idea of the e m algorithm for model selection in the presence of missing data the idea extends the concept of parameters to include both the model and the parameters under the model and thus allows the model to be part of the e m iterations we develop the procedure known as the e ms algorithm under the assumption that the class of candidate models is finite some special cases of the procedure are considered including e ms with the generalized information criteria gic and e ms with the adaptive fence af jiang et al we prove numerical convergence of the e ms algorithm as well as consistency in model selection of the limiting model of the e ms convergence for e ms with gic and e ms with af we study the impact on model selection of different missing data mechanisms furthermore we carry out extensive simulation studies on the finite sample performance of the e ms with comparisons to other procedures the methodology is also illustrated on a real dat

asymptotic behaviors of solutions of quasilinear hyperbolic equations with linear damping ii this paper as a follow up to the recent work of k nishihara 1997 j differential equations133 384 395 is concerned with the asymptotic behaviors of the solution of quasilinear hyperbolic equation with linear damping vtt a vx x vt 0 a v 0forallv r which satisfies the following prescribed initial condition v t x vt t x t 0 v0 x v1 x x r compared with the results obtained by k nishihara the main novelties of our present paper lie in the following first we recover all the results obtained by k nishihara under some other smallness assumptions on the initial data v0 x v1 x which are much weaker than those needed in k nishihara s arguments second under some additional assumptions on the nonlinear function a v and on the initial data v0 x v1 x when 0 0 1 0 we succeed in proving that t x is still an asymptotic profile of v t x and this answers partially the open problem left by k nishihara

regression analysis of data from a cluster sample abstract for the case of different regression relationships in different subgroups of a finite population only part of which are sampled the extended least squares estimator of any weighted average of the distinct coefficients is derived under assumptions relating only to the first two moments of the distribution of the coefficients under these assumptions the estimator is shown to be the best linear unbiased estimator while under further distributional assumptions it is also the bayesian estimator for a quadratic loss function for the case of unknown variances a method for estimating them from the sample is proposed the empirical estimator thus obtained is shown to perform well by a simulation comparison with the optimal estimator and with other proposed empirical estimators

best predictive small area estimation we derive the best predictive estimator bpe of the fixed parameters under two well known small area models the fay herriot model and the nested error regression model this leads to a new prediction procedure called observed best prediction obp which is different from the empirical best linear unbiased prediction eblup we show that bpe is more reasonable than the traditional estimators derived from estimation considerations such as maximum likelihood ml and restricted maximum likelihood reml if the main interest is estimation of small area means which is a mixed model prediction problem we use both theoretical derivations and empirical studies to demonstrate that the obp can significantly outperform eblup in terms of the mean squared prediction error mspe if the underlying model is misspecified on the other hand when the underlying model is correctly specified the overall predictive performance of the obp is very similar to that of the eblup if the number of small areas is large a

an optimal estimate for the difference of solutions of two abstract evolution equations abstractikehata and nishihara have established that the difference between any solution u of alinearly damped abstract wave equation and a certain solution v of a related abstract heatequation decays at least like t 1 logt 12 e as time tends to in nity they conjectured that thedecayisinfactliket 1 weproveherethevalidityofthisconjecturebyrelyingonthespectraltheorem for unbounded self adjoint operators we also establish the optimality of thisestimate for the wave equation in an exterior domain r 2003 elsevier science usa all rights reserved msc primary34d05 secondary35l90keywords abstract heatequation abstract waveequation diffusionphenomenon 1 introductionthe main objective of this work is to establish an estimate of the differencebetween the solution u of the abstract dissipative wave equationu 00 u 0 au 0 u 0 u 0 u 0 0 u 1 1 1 and the solution v of the abstract heat equationv 0 av 0 v 0 u 0 u 1 1 2 article in press corresponding author e mail address haraux ann jussieu fr a haraux 0022 0396 03 seefrontmatterr 2003 elsevierscience usa allrights reserved doi 10 1016 s0022 0396 03 00057 3

singularity formation for the 1d compressible euler equations with variable damping coefficient abstract in this paper we consider some blow up problems for the 1d euler equations with time and space dependent damping we investigate sufficient conditions on initial data and the rate of spatial or time like decay of the coefficient of damping for the occurrence of the finite time blow up in particular our sufficient conditions ensure that the derivative blow up occurs in finite time with the solution itself and the pressure bounded our method is based on simple estimates with riemann invariant furthermore we give sharp lower and upper estimates of the lifespan of solutions when initial data are small perturbations of constant states

simple incorporation of interactions into additive models summary often the functional form of covariate effects in an additive model varies across groups defined by levels of a categorical variable this structure represents a factor by curve interaction this article presents penalized spline models that incorporate factor by curve interactions into additive models a mixed model formulation for penalized splines allows for straightforward model fitting and smoothing parameter selection we illustrate the proposed model by applying it to pollen ragweed data in which seasonal trends vary by year

the lp lq estimates of solutions to one dimensional damped wave equations and their application to the compressible flow through porous media we first obtain the lp lq estimates of solutions to the cauchy problem for one dimensional damped wave equation vtt vxx vt 0 v vt t 0 v0 v1 x x t r r corresponding to that for the parabolic equation t xx 0 t 0 v0 v1 x the estimates are shown by v t e t 2v0 t v0 t 2lp ct 121q 1p 1 v0 v1 lq t 1 etc for 1 q p to show the explicit formula of the damped wave equation will be used to apply the estimates to nonlinear problems is the second aim we will treat the system of a compressible flow through porous media the solution is expected to behave as the diffusion wave which is the solution to the porous media equation due to the darcy law when the initial data has the same constant state at a sharp lp convergence rate for p 2 has been recently obtained by nishihara proc roy soc edinburgh sect a 133a 2003 1 20 by choosing a suitably located diffusion wave we will show the l1 convergence applying

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

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

optimal decay error estimates for the hyperbolic parabolic singular perturbation of a degenerate nonlinear equation abstract we consider a degenerate hyperbolic equation of kirchhoff type with a small parameter e in front of the second order time derivative in a recent paper under a suitable assumption on initial data we proved decay error estimates for the difference between solutions of the hyperbolic problem and the corresponding solutions of the limit parabolic problem these estimates show in the same time that the difference tends to zero both as e 0 and as t in particular in that case the difference decays faster than the two terms separately in this paper we consider the complementary assumption on initial data and we show that now the optimal decay error estimates involve a decay rate which is slower than the decay rate of the two terms in both cases the improvement or deterioration of decay rates depends on the smallest frequency represented in the fourier components of initial data

l p convergence rates of solutions for n dimensional quasilinear damped wave equation we realize the asymptotic profile for the solutions to the n dimensional quasilinear damped wave equation in the divergence form is the solution of the corresponding linear parabolic equation with special initial data and we further show the lp 1 p infinity in particular p 1 convergence rates to this linear asymptotic profile c 2013 elsevier inc all rights reserved

global attractor for a class of kirchhoff models the paper studies the longtime behavior of solutions to the initial boundary value problem ibvp for a class of kirchhoff models arising in elastoplastic flow utt div u m 1 u ut 2u h ut g u f x by combining the decomposition idea with the operate technique it proves that under rather mild conditions the dynamical system associated with above mentioned ibvp possesses in different phase spaces a global attractor which is connected respectively for application the fact shows that for the concerned elastoplastic flow the permanent regime global attractor can be observed when the excitation starts from any bounded set in phase space

convergence to strong nonlinear diffusion waves for solutions of p system with damping this paper is concerned with the p system with frictional damping and our main purpose is two fold first we show that for a certain class of given large initial data nu 0 x u 0 x the cauchy problem 1 1 1 2 admits a unique global smooth solution nu t x u t x and such a solution tends time asymptotically at the optimal l p 2 less than or equal to p less than or equal to infinity decay rates to the corresponding nonlinear diffusion wave over bar t x u over bar t x governed by the classical darcy s law provided that the corresponding prescribed initial error function v 0 x u 0 x ties in h 3 x h 2 r boolean and l 1 x l 1 r compared with former results in this direction obtained by l hsiao and t p liu 1992 comm math phys 143 599 605 k nishihara 1996 j differential equations 131 171 188 and k nishihara w k wang and t yang 2000 j differential equations 161 191 218 our main novelty lies in the facts that the nonlinear diffusion wave over bar t x u over bar t x need not to be weak and v 0 x u 0 x can be chosen arbitrarily large secondly we show that the nonlinear diffusion waves over bar t x u over bar t x are nonlinear stable provided that the strength or the nonlinear diffusion waves is weak and that the initial disturbance v 0 x u 0 x satisfies the assumption that parallel tov 0xx x parallel to l infinity parallel tou 0x x parallel to l infinity is sufficiently small we also show that the smallness assumption imposed oil the strength of the diffusion waves is a necessary condition to guarantee the nonlinear stability result and compared with the corresponding results obtained by l hsiao and t p liu 1992 comm math phys 143 599 605 the smallness conditions we imposed on the initial disturbance are much more weaker c 2001 academic press

lp convergence rate to nonlinear diffusion waves for p system with damping abstract in this paper we study the p system with frictional damping and show that the solutions time asymptotically tend to the nonlinear diffusion waves governed by the classical darcy s law by introducing an approximate green function we obtain the optimal l p 2 p convergence rate of the solution which is a perturbation of the nonlinear diffusion wave to the hyperbolic system

restricted likelihood ratio lack of fit tests using mixed spline models penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non linearity in the smooth function estimates this motivates the study of lack of fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values for this one sided testing problem a further complication is that the variance component belongs to the boundary of the parameter space under the null hypothesis conditions are obtained on the design of the regression spline models under which asymptotic distribution theory applies and finite sample approximations to the asymptotic distribution are provided test statistics are studied for simple as well as multiple regression models

data driven selection of the spline dimension in penalized spline regression a number of criteria exist to select the penalty in penalized spline regression but the selection of the number of spline basis functions has received much less attention in the literature we propose a likelihood based criterion to select the number of basis functions in penalized spline regression the criterion is easy to apply and we describe its theoretical and practical properties

decomposition of prediction error abstract the problem considered is that of predicting the value of an unobservable random variable w from the value of an observable random vector y this problem is considered under each of four states of knowledge about the joint distribution of w and y ranging from complete knowledge to no knowledge a point predictor or predictors are presented for each case prediction error is decomposed so that each component reflects an absence of information under certain conditions these components are uncorrelated and have zero means an exact or approximate expression is given for the variance of each component

cauchy problem for a class of nonlinear dispersive wave equations arising in elasto plastic flow abstract the paper studies the existence both locally and globally in time stability decay estimates and blowup of solutions to the cauchy problem for a class of nonlinear dispersive wave equations arising in elasto plastic flow under the assumption that the nonlinear term of the equations is of polynomial growth order say it proves that when 1 the cauchy problem admits a unique local solution which is stable and can be continued to a global solution under rather mild conditions when 5 and the initial data is small enough the cauchy problem admits a unique global solution and its norm in l 1 p r decays at the rate 1 t p 2 2 p for 2 p 10 and if the initial energy is negative then under a suitable condition on the nonlinear term the local solutions of the cauchy problem blow up in finite time

the undecidability of the second order unification problem abstract it is shown that there is no effective procedure for determining whether or not two terms of the language of second order logic have a common instance

mean squared error of empirical predictor the term empirical predictor refers to a two stage predictor of a linear combination of fixed and random effects in the first stage a predictor is obtained but it involves unknown parameters thus in the second stage the unknown parameters are replaced by their estimators in this paper we consider mean squared errors mse of empirical predictors under a general setup where ml or reml estimators are used for the second stage we obtain second order approximation to the mse as well as an estimator of the mse correct to the same order the general results are applied to mixed linear models to obtain a second order approximation to the mse of the empirical best linear unbiased predictor eblup of a linear mixed effect and an estimator of the mse of eblup whose bias is correct to second order the general mixed linear model includes the mixed anova model and the longitudinal model as special cases

diffusion phenomenon in hilbert spaces and applications abstract we prove an abstract version of the striking diffusion phenomenon that offers a strong connection between the asymptotic behavior of abstract parabolic and dissipative hyperbolic equations an important aspect of our approach is that we use in a natural way spectral analysis without involving complicated resolvent estimates our proof of the diffusion phenomenon does not use the individual behavior of solutions instead we show that only their difference matters we estimate the hilbert norm of the difference in terms of the hilbert norm of solutions to the parabolic problems which allows us to transfer the decay from the parabolic to the hyperbolic problem the application of these estimates to operators with markov property combined with a weighted nash inequality yields explicit and sharp decay rates for hyperbolic problems with variable x dependent coefficients in exterior domains our method provides new insight in this area of extensive research which was not well understood until now

asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping we consider the asymptotic behavior of the solution of quasilinear hyperbolic equation with linear dampingvtt a vx x vt 0 x t r 0 subsequent to k nishihara j differential equations131 1996 171 188 in that article the system with dampingvt ux 0 ut p v x u p v 0 was treated and the convergence rates to the diffusion wave by l hsiao and t p liu comm math phys 143 1992 599 605 and l hsiao and t p liu chinese ann math ser b14 1993 465 480 were improved for initial data v0 u0 x satisfying v0 u0 v0 0 and v0 x v0 dx 0 this system is reduced to the quasilinear hyperbolic equation with linear dampingvtt p v0 vx p v0 x vt 0 and the decay rates v t l o t 1 2 vx t l o t 1 vt t l o t 3 2 were obtained provided that v vt t 0 h3 h2 is small and inl1 l1 from these decay rates vis expected to behave as a solution to the parabolic equation the aims of this paper are to seek the asymptotic profile x t satisfying t l o t 1 2 x t l o t 1 t t l o t 3 2 and to show that the solution of satisfies v t l o t 1 v x t l o t 3 2 v t t l o t 2 the proof is based on the elementary energy method and the green function method for the parabolic equation

the undecidability of simultaneous rigid e unification abstract simultaneous rigid e unification was introduced in 1987 by gallier raatz and snyder it is used in the area of automated reasoning with equality in extension procedures like the tableau method or the connection method many articles in this area assumed the existence of an algorithm for the simultaneous rigid e unification problem there were several faulty proofs of the decidability of this problem in this paper we prove that simultaneous rigid e unification is undecidable as a consequence we obtain the undecidability of the fragment of intuitionistic logic with equality

global existence asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term abstract the paper studies the global existence asymptotic behavior and blowup of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative term it proves that under rather mild conditions on nonlinear terms and initial data the above mentioned problem admits a global weak solution and the solution decays exponentially to zero as t respectively in the states of large initial data and small initial energy in particular in the case of space dimension n 1 the weak solution is regularized to be a unique generalized solution and if the conditions guaranteeing the global existence of weak solutions are not valid then under the opposite conditions the solutions of above mentioned problem blow up in finite time and an example is given

asymptotic behavior of solutions to bipolar euler poisson equations with time dependent damping abstract in this paper we study the one dimensional euler poisson equations of bipolar hydrodynamic model for semiconductor device with time dependent damping effect j 1 t for 1 1 where the damping effect is time gradually degenerate for 0 and time gradually enhancing for 0 such a damping effect makes the hydrodynamic system possess the nonlinear diffusion phenomena time asymptotic weakly or strongly based on technical observation and by using the time weighted energy method where the weights are artfully chosen we prove that the system admits a unique global smooth solution which time asymptotically converges to the corresponding diffusion wave when the initial perturbation around the diffusion wave is small enough the convergence rates are specified in the algebraic forms o t 3 4 1 and o t 1 according to different values of in 1 1 7 and 1 7 1 respectively where 1 7 is the critical point and the convergence rate at the critical point is o t 6 7 ln t all these convergence rates obtained in different cases are optimal in the sense when the initial perturbations are l 2 integrable particularly when 1 7 the convergence rate is the fastest namely the asymptotic profile of the original system at the critical point is the best

existence and nonexistence of time global solutions to damped wave equation on half line on the half line r 0 infinity the initial boundary value problems with null dirichlet boundary for both the semilinear heat equation and damped wave equation are considered the critical exponent p c n k of semilinear term for the existence and nonexistence about the semilinear heat equation on the halved space d n d k r k rn k is given by p c n k 1 2 n k j appl math phys 39 1988 135 149 arch rational mech anal 109 1990 63 71 since the damped wave equation is expected to be close to the heat equation j differential equations 191 2003 445 469 math z 244 2003 631 649 the critical exponent for the semilinear damped wave equation is expected to be same as that of the semilinear heat equation however there is no blow up result on the halved space for the damped wave equation in this paper the exponent pc l 1 2 is shown to be critical for the existence and nonexistence of time global solution to both the semilinear heat equation and damped wave equation on the half line r together with the derivation of the blow up time for the proof the explicit formulas of solutions are used in a similar fashion to those in li and zhou discrete continuous dynamic systems 1 1995 503 520 c 2005 elsevier ltd all rights reserved

large time behavior and lp lq estimate of solutions of 2 dimensional nonlinear damped wave equations abstract we show the asymptotic behavior of the solution to the cauchy problem of the two dimensional damped wave equation it is shown that the solution of the linear damped wave equation asymptotically decompose into a solution of the heat and wave equations and the difference of those solutions satisfies the lp lq type estimate this is a two dimensional generalization of the three dimensional result due to nishihara math z 244 2003 631 to show this we use the fourier transform and observe that the evolution operators of the damped wave equation can be approximated by the solutions of the heat and wave equations by using the lp lq estimate we also discuss the asymptotic behavior of the semilinear problem of the damped wave equation with the power nonlinearity u u our result covers the whole super critical case 1 where the 1 is well known as the fujita exponent when n 2

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

non parametric small area estimation using penalized spline regression the paper proposes a small area estimation approach that combines small area random effects with a smooth non parametrically specified trend by using penalized splines as the representation for the non parametric trend it is possible to express the non parametric small area estimation problem as a mixed effect model regression the resulting model is readily fitted by using existing model fitting approaches such as restricted maximum likelihood we present theoretical results on the prediction mean squared error of the estimator proposed and on likelihood ratio tests for random effects and we propose a simple non parametric bootstrap approach for model inference and estimation of the small area prediction mean squared error the applicability of the method is demonstrated on a survey of lakes in north eastern usa

exact likelihood ratio tests for penalised splines summary penalised spline based additive models allow a simple mixed model representation where the variance components control departures from linear models the smoothing parameter is the ratio of the random coefficient and error variances and tests for linear regression reduce to tests for zero random coefficient variances we propose exact likelihood and restricted likelihood ratio tests for testing polynomial regression versus a general alternative modelled by penalised splines their spectral decompositions are used as the basis of fast simulation algorithms we derive the asymptotic local power properties of the tests under weak conditions in particular we characterise the local alternatives that are detected with asymptotic probability one confidence intervals for the smoothing parameter are obtained by inverting the tests for a fixed smoothing parameter versus a general alternative we discuss f and r tests and show that ignoring the variability in the smoothing parameter estimator can have a dramatic effect on their null distributions the powers of several known tests are investigated and a small set of tests with good power properties is identified the restricted likelihood ratio test is among the best in terms of power

existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping abstract this paper concerns with the cauchy problem for the damped nonlinear hyperbolic system u t t u u t v p t x r 1 r n v t t v v t u q t x r 1 r n u 0 x u 0 x u t 0 x u 1 x x r n v 0 x v 0 x v t 0 x v 1 x x r n where p q 1 and satisfy p q 1 we shall prove that if max 1 p p q 1 1 q p q 1 n 2 for n 1 or 3 then the solution with small initial data exists globally in time and satisfies the decay estimates u t c 1 t and v t c 1 t for some positive constants and while if max 1 p p q 1 1 q p q 1 n 2 for n 1 then every solution with initial data having positive average value does not exist globally

lp lq estimates of solutions to the damped wave equation in 3 dimensional space and their application it has been asserted that the damped wave equation has the diffusive structure as t in this paper we consider the cauchy problem in 3 dimensional space for the linear damped wave equation and the corresponding parabolic equation and obtain the lp lq estimates of the difference of each solution which represent the assertion precisely explicit formulas of the solutions are analyzed for the proof the second aim is to apply the lp lq estimates to the semilinear damped wave equation with power nonlinearity if the power is larger than the fujita exponent then the time global existence of small weak solution is proved and its optimal decay order is obtained

energy decay for linear dissipative wave equations in exterior domains abstract in earlier works 2 12 we have shown the uniform decay of the local energy of the damped wave equation in exterior domain when the damper is spatially localized near captive rays in order to have uniform decay of the total energy the damper has also to act at space infinity in this work we establish uniform decay of both the local and global energies the rates of decay turn out to be the same as those for the heat equation which shows that an effective damper at space infinity strengthens the parabolic structure in the equation

diffusion phenomenon for linear dissipative wave equations in an exterior domain abstract under the general condition of the initial data we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain in order to derive the diffusion phenomenon for dissipative wave equations the time integral method which was developed by ikehata and matsuyama sci math japon 55 2002 33 plays an effective role

nonlinear diffusion waves for hyperbolic p system with nonlinear damping abstract this paper is concerned with the p system of hyperbolic conservation laws with nonlinear damping when the constant states are small the solutions of the cauchy problem for the damped p system globally exist and converge to their corresponding nonlinear diffusion waves which are the solutions of the corresponding nonlinear parabolic equation given by the darcy s law the optimal convergence rates are also obtained in order to overcome the difficulty caused by the nonlinear damping a couple of correction functions have been technically constructed the approach adopted is the elementary energy method together with the technique of approximating green function on the other hand when the constant states are large the solutions of the cauchy problem for the p system will blow up at a finite time

wave equations with strong damping in hilbert spaces abstract we study the cauchy problem for abstract dissipative equations in hilbert spaces generalizing wave equations with strong damping terms in r n or exterior domains our main result is a generalized diffusion phenomenon the long time asymptotics of strongly damped wave equations is a combination of solutions of diffusion and wave equations in particular we obtain sharp decay estimates the proofs rely on the energy method in the fourier space and its generalization based on the spectral theorem for self adjoint operators

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

diffusion phenomena for partially dissipative hyperbolic systems abstract we consider a partially dissipative hyperbolic system with time dependent coefficients and show that under natural assumptions its solutions behave like solutions to a parabolic problem modulo terms of faster decay this generalises the well known diffusion phenomenon for damped waves and gives some further insights into the structure of dissipative hyperbolic systems

higher order asymptotic expansion of solutions to abstract linear hyperbolic equations the paper concerned with higher order asymptotic expansion of solutions to the cauchy problem of abstract hyperbolic equations of the form u au u 0 in a hilbert space where a is a nonnegative selfadjoint operator the result says that by assuming a suitable regularity of initial data asymptotic profiles of arbitrary order are explicitly written by using the c 0 semigroup e ta generated by a to prove this a kind of maximal regularity for e ta is used

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

global and blow up solutions for a system of nonlinear hyperbolic equations with dissipative terms abstract in this paper we study a nonlinear hyperbolic system with strong damping firstly by use of the successive approximation method and a series of classical estimates we prove the local existence and uniqueness of weak solution secondly via some inequalities applying the potential method and the concave method we discuss the asymptotic and blow up behavior of weak solution with different conditions

lp convergence rate to diffusion waves for p system with relaxation in this paper we consider the asymptotic behavior of solution for the cauchy problem for p system with relaxation vt ux 0 ut p v x 1 f v u e with initial data v u x 0 v0 x u0 x v0 u as x i by applying the elementary energy method and the green function method for the parabolic equation we obtain the l p convergence rate to the diffusion waves for the cauchy