The Cauchy Problem of the Nonlinear Schr■dinger Equations in R~(1 1)

In this paper,we consider the local and global solution for the nonlinear Schrdinger equationwith data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data.Thetechniques to be used are adapted from the Strichartz type estimate,Kato's smoothing effect and the maximalfunction(in time)estimate for the free Schrdinger operator.     

A note on initial value problem for the generalized Tricomi equation in a mixed-type domain

In this paper, we study the well-posedness of initial value problem for n-dimensional gener-alized Tricomi equation in the mixed-type domain {(t,x):t∈[1,+∞),x∈Rn} with the initial data given on the line t=1 in Hadamard's sense. By taking partial Fourier transformation, we obtain the explicit expression of the solution in terms of two integral operators and further establish the global estimate of such a solution for a class of initial data and source term. Finally, we establish the global solution in time direction for a semilinear problem used the estimate.     

The Global Well-posedness for the 2D Leray-α MHD Equations with Zero Magnetic Diffusivity

By means of Fourier frequency localization and Bony's paraproduct decomposition,we study the global existence and the uniqueness of the 2D Leray-α Magneta-hydrodynamics model with zero magnetic diffusivity for the general initial data.In view of the profits bring by the α model,then using the energy estimate in the frequency space and the Logarithmic Sobolev inequality,we obtain the estimate ∫t0||?u|| L_∞ ds which is crucial to get the global existence for the general initial data.     

A new method of spectral decomposition of covariance matrix in mixed effects models and its applications

For the mixed effects models with balanced data, a new ordering of design matrices of random effects is defined, and then a simple formula of the spectral decomposition of covariance matrix is obtained. To compare with the two methods in literature, the decomposition can not only give the actual number of all distinct eigenvalues and their expression, but also show clearly the relationship between the design matrices of random effects and the decomposition. These results can be applied to the problems for testifying the analysis of the variance estimate being a minimum variance unbiased under all random effects models and some mixed effects models with balanced data, for finding the explicit solution of maximum likelihood equations for the general mixed effects model and for showing the relationship between the spectral decomposition estimate and the analysis of variance estimate.     

A moving average Cholesky factor model in joint mean-covariance modeling for longitudinal data

Modeling the mean and covariance simultaneously is a common strategy to efciently estimate the mean parameters when applying generalized estimating equation techniques to longitudinal data.In this article,using generalized estimation equation techniques,we propose a new kind of regression models for parameterizing covariance structures.Using a novel Cholesky factor,the entries in this decomposition have moving average and log innovation interpretation and are modeled as linear functions of covariates.The resulting estimators for the regression coefcients in both the mean and the covariance are shown to be consistent and asymptotically normally distributed.Simulation studies and a real data analysis show that the proposed approach yields highly efcient estimators for the parameters in the mean,and provides parsimonious estimation for the covariance structure.     

On the Error Estimate of the Harmonic B_z Algorithm in MREIT from Noisy Magnetic Flux Field

Magnetic resonance electrical impedance tomography(MREIT, for short) is a new medical imaging technique developed recently to visualize the cross-section conductivity of biologic tissues. A new MREIT image reconstruction method called harmonic Bz algorithm was proposed in 2002 with the measurement of Bz that is a single component of an induced magnetic flux density subject to an injection current. The key idea is to solve a nonlinear integral equation by some iteration process. This paper deals with the convergence analysis as well as the error estimate for noisy input data Bz, which is the practical situation for MREIT. By analyzing the iteration process containing the Laplacian operation on the input magnetic field rigorously, the authors give the error estimate for the iterative solution in terms of the noisy level δ and the regularizing scheme for determiningΔBz approximately from the noisy input data. The regularizing scheme for computing the Laplacian from noisy input data is proposed with error analysis. Our results provide both the theoretical basis and the implementable scheme for evaluating the reconstruction accuracy using harmonic Bz algorithm with practical measurement data containing noise.     

Global well-posedness for the 2D critical dissipative quasi-geostrophic equation

We study the initial value problem for the 2D critical dissipative quasi-geostrophic equation. We prove the global existence for small data in the scale invariant Besov spaces Bp,12/p,1≤p≤∞. In particular, for p=∞, our result does not impose any regularity on the initial data. Our proofs are based on an exponential decay estimate of the semigroup e-tk(-Δ)αand the use of space-time Besov spaces.     

GENERALIZED PARETO DISTRIBUTION FIT TO MEDICAL INSURANCE CLAIMS DATA

How to choose an optimal threshold is a key problem in the generalized Pareto distribution （GPD） model. This paper attains the exact threshold by testing for GPD,and shows that GPD model allows the actuary to easily estimate high quantiles and the probable maximum loss from the medical insurance claims data.     

Cotorsion Dimension of Weak Crossed Products

Let H be a finite-dimensional weak Hopf algebra over a field κ and A an associative algebra, and A#_σH a weak crossed product. In this paper, a spectral sequence for Ext is constructed which yields an estimate for cotorsion dimension of A#_σH in terms of the corresponding data for H and A.     

Some properties for the estimators in linear mixed models

Linear mixed models (LMMs) have become an important statistical method for analyzing cluster or longitudinal data. In most cases, it is assumed that the distributions of the random effects and the errors are normal. This paper removes this restrictions and replace them by the moment conditions. We show that the least square estimators of fixed effects are consistent and asymptotically normal in general LMMs. A closed-form estimator of the covariance matrix for the random effect is constructed and its consistent is shown. Based on this, the consistent estimate for the error variance is also obtained. A simulation study and a real data analysis show that the procedure is effective.     

Measurement error in proportional hazards models for survival data with long-term survivors

This work studies a proportional hazards model for survival data with "long-term survivors",in which covariates are subject to linear measurement error.It is well known that the naive estimators from both partial and full likelihood methods are inconsistent under this measurement error model.For measurement error models,methods of unbiased estimating function and corrected likelihood have been proposed in the literature.In this paper,we apply the corrected partial and full likelihood approaches to estimate the model and obtain statistical inference from survival data with long-term survivors.The asymptotic properties of the estimators are established.Simulation results illustrate that the proposed approaches provide useful tools for the models considered.     

C^1 C^2 INTERPOLATION OF SCATTERED DATA POINTS

In this paper an error in [4] is pointed out and a method for constructing surface interpolating scattered data points is presented, The main feature of the method in this paper is that the surface so constructed is polynomial, which makes the construction simple and the calculation easy.     

一类退化抛物方程高初始能量下解的有限时刻爆破及整体存在性（英文）

We consider the initial-boundary value problem for finitely degenerate parabolic equation. We first give sufficient conditions for the blow-up and global existence of the parabolic equation at high initial energy level. Then, we establish the existence of solutions blowing up in finite time with initial data at arbitrary energy level. Finally, we estimate the upper bound of the blow-up time under certain conditions.     

Harmonic Measures and Numerical Computation of Cauchy Problems for Laplace Equations*

It is well known that the Cauchy problem for Laplace equations is an ill-posed problem in Hadamard’s sense. Small deviations in Cauchy data may lead to large errors in the solutions. It is observed that if a bound is imposed on the solution, there exists a conditional stability estimate. This gives a reasonable way to construct stable algorithms.However, it is impossible to have good results at all points in the domain. Although numerical methods for Cauchy problems for Laplace equations have been widely studied for quite a long time, there are still some unclear points, for example, how to evaluate the numerical solutions, which means whether they can approximate the Cauchy data well and keep the bound of the solution, and at which points the numerical results are reliable? In this paper, the authors will prove the conditional stability estimate which is quantitatively related to harmonic measures. The harmonic measure can be used as an indicate function to pointwisely evaluate the numerical result, which further enables us to find a reliable subdomain where the local convergence rate is higher than a certain order.     

Jackknife empirical likelihood test for the equality of degrees of freedom in t-copulas

It has been argued that fitting a t-copula to financial data is superior to a normal copula. To overcome the shortcoming that a t-copula only has one parameter for the degrees of freedom, the t-copula with multiple parameters of degrees of freedom has been proposed in the literature, which generalizes both the t-copulas and the grouped t-copulas. Like the inference for a t-copula, a computationally efficient inference procedure is to first estimate the correlation matrix via Kendall's τ and then to estimate the parameters of degrees of freedom via pseudo maximum likelihood estimation. This paper proposes a jackknife empirical likelihood test for testing the equality of some parameters of degrees of freedom based on this two-step inference procedure, and shows that the Wilks theorem holds.     

Hierarchically penalized additive hazards model with diverging number of parameters

In many applications,covariates can be naturally grouped.For example,for gene expression data analysis,genes belonging to the same pathway might be viewed as a group.This paper studies variable selection problem for censored survival data in the additive hazards model when covariates are grouped.A hierarchical regularization method is proposed to simultaneously estimate parameters and select important variables at both the group level and the within-group level.For the situations in which the number of parameters tends to∞as the sample size increases,we establish an oracle property and asymptotic normality property of the proposed estimators.Numerical results indicate that the hierarchically penalized method performs better than some existing methods such as lasso,smoothly clipped absolute deviation(SCAD)and adaptive lasso.     

Joint modelling of location and scale parameters of the skew-normal distribution

Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.     

ON THE DECAY AND SCATTERING FOR THE KLEIN-GORDON-HARTREE EQUATION WITH RADIAL DATA

In this paper,we study the decay estimate and scattering theory for the Klein-Gordon-Hartree equation with radial data in space dimension d≥3.By means of a compactness strategy and two Morawetz-type estimates which come from the linear and nonlinear parts of the equation,respectively,we obtain the corresponding theory for energy subcritical and critical cases.The exponent range of the decay estimates is extended to 0<γ≤4 and γ相似文献   

Quantile regression for right-censored and length-biased data

Length-biased data arise in many important fields, including epidemiological cohort studies, cancer screening trials and labor economics. Analysis of such data has attracted much attention in the literature. In this paper we propose a quantile regression approach for analyzing right-censored and length-biased data. We derive an inverse probability weighted estimating equation corresponding to the quantile regression to correct the bias due to length-bias sampling and informative censoring. This method can easily handle informative censoring induced by length-biased sampling. This is an appealing feature of our proposed method since it is generally difficult to obtain unbiased estimates of risk factors in the presence of length-bias and informative censoring. We establish the consistency and asymptotic distribution of the proposed estimator using empirical process techniques. A resampling method is adopted to estimate the variance of the estimator. We conduct simulation studies to evaluate its finite sample performance and use a real data set to illustrate the application of the proposed method.     

高阶抛物不等式组的Liouville型定理及其应用

In this paper, we establish a Liouville-type theorem for a system of higher-order parabolic inequalities by using the method of test functions and an integral estimate. As an application, we observe the Fujita blow-up phenomena for the corresponding parabolic system, which in particular fills up the gap in the recent result of Pang et. al. （Existence and nonexistence of global solutions for a higher-order semilinear parabolic system, Indiana Univ. Math. J., 55（2006）, 1113-1134）. Moreover, the importance of this observation is that we do not impose any regularity assumption on the initial data.