关于无偏估计的若干问题

通过理论分析和实例讨论有关无偏估计的若干问题：无偏估计不一定存在;无偏估计一般不唯一;在均方误差意义下,无偏估计不一定优于有偏估计;均方误差最小的估计是最小方差无偏估计,但反之不然。     

LOCAL A PRIORI AND A POSTERIORI ERROR ESTIMATE OF TQC9 ELEMENT FOR THE BIHARMONIC EQUATION

In this paper, local a priori, local a posteriori and global a posteriori error estimates are obtained for TQC9 element for the biharmonic equation. An adaptive algorithm is given based on the a posteriori error estimates.     

A MIXED FINITE ELEMENT METHOD ON A STAGGERED MESH FOR NAVIER-STOKES EQUATIONS

In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral Q1 × Q1 - P0 element approximation for the Navier-Stokes equations. First-order error estimates are obtained for both the velocity and the pressure. Numerical examples are presented to illustrate the effectiveness of the proposed method.     

基于指数每日最高最低值预测的一种新方法

金融市场中有各种各样的指数,在做投资决策时需要对这些指数进行预测。在我国沪深300指数是第一个全面反映沪市、深市综合走势的指数,也是目前作为股指期货标的物的唯一指数,本文构建模型对沪深300指数日最高和最低值进行预测。文中分别使用普通误差修正模型(VECM)和基于广义异方差(GARCH)模型进行分向量估计的VECM对2005年4月8日至2010年3月19日的沪深300指数价格最高、最低值序列进行实证分析,做出相关预测,并利用相对误差对结果进行评价。结果表明,用基于GARCH模型的VECM获得的预测结果相对误差更小,预测也更加精确。     

L~1空间带弱奇异核的第二类Fredholm积分方程解法探究

针对带有弱奇异核的第二类Fredholm积分方程数值解法问题,介绍了两种方法.一种方法是直接用L~1空间中的离散化方法求其数值解;另一种方法是将弱奇异核通过迭代变为连续核,再用L~1空间中的离散化方法求其数值解,且通过对具体算例作图分析,从而得出直接用L~1空间中离散化方法更好.     

Efficient statistical inference for partially nonlinear errors-in-variables models

In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.     

EQ 1 rot nonconforming finite element method for nonlinear dual phase lagging heat conduction equations

EQ rot 1 nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O(h2 ) one order higher than its interpolation error O(h), the superclose results of order O(h2 ) in broken H1 -norm are obtained. At the same time, the global superconvergence in broken H1 -norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O(h4 ) is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQ rot 1 element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.     

STABILITY OF DISPLACEMENT TO THE SECOND FUNDAMENTAL PROBLEM IN PLANE ELASTICITY

In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density happen, we discuss the stability of the second fundamental problem in plane elasticity when the smooth perturbation for the boundary of the elastic domain （unit disk） and the Sobolev type perturbation for the displacement happen. And the error estimate of the displacement between the second fundamental problem and its perturbed problem is obtained.     

择优RBF神经网络下切削率的优化

本文通过择优RBF(径向基函数,Radial Basis Function)神经网络对影响切削加工过程的切削参数进行建模,对切除率进行拟合预测;提出松弛误差作为衡量网络精度的指标,使RBF选择最优的分布密度,从而有效提高RBF神经网络的拟合预测能力;并将择优RBF的拟合和预测结果与BP的相应结果进行了比较,结果显示择优RBF神经网络的拟合和预测精度大大优于BP神经网络.