求解铸件凝固问题的一种新方法

用线性摄动法给出了铸件在表面形状呈正弦变化的有限厚度铸型上凝固的三维热传导问题的数学模型，结合自变量变换法与有限差分法求解了热传导方程的数值解，给出了相变面随时间的变化过程和铸件的温度场分布情况．     

The Impact of Measurement Error on Principal Component Analysis

We investigate the effect of measurement error on principal component analysis in the high‐dimensional setting. The effects of random, additive errors are characterized by the expectation and variance of the changes in the eigenvalues and eigenvectors. The results show that the impact of uncorrelated measurement error on the principal component scores is mainly in terms of increased variability and not bias. In practice, the error‐induced increase in variability is small compared with the original variability for the components corresponding to the largest eigenvalues. This suggests that the impact will be negligible when these component scores are used in classification and regression or for visualizing data. However, the measurement error will contribute to a large variability in component loadings, relative to the loading values, such that interpretation based on the loadings can be difficult. The results are illustrated by simulating additive Gaussian measurement error in microarray expression data from cancer tumours and control tissues.     

Perturbation diagnostics of autocorrelation coefficients in non linear mixed-effects models with AR(1) errors based on M-estimation

In this work we propose and analyze non linear mixed-effects models for longitudinal data, which are widely used in the fields of economics, biopharmaceuticals, agriculture, and so on. A robust method to obtain maximum likelihood estimates for the parameters is presented, as well as perturbation diagnostics of autocorrelation coefficient in non linear models based on robust estimates and influence curvature. The obtained results are illustrated by plasma concentrations data presented in Davidian and Giltinan, which was analyzed under the non robust situation.     

The homotopy perturbation method for the Black–Scholes equation

The homotopy perturbation method is designed to obtain a quick and accurate solution to the Black–Scholes equation and boundary conditions for a European option pricing problem. The problem of pricing a European option can be cast a partial differential equation. The analytical solution of the equation is calculated in the form of a convergent power series with easily computable components.     

Local influence in box-cox transformation for multivariate regression data

The Box-Cox power family of transformations for multivariate regression data is considered. The influence of cases on the maximum likelihood estimators of the transformation parameters is investigated using the local influence approach, An example is given to- illustrate the local influence method and to show the effectiveness of the method.     

Local influence in multivariate regression

The method of local influence is generalized to the multivariate regression. The scheme of perturbations adopted in multivariate regression is similar in spirit to the perturbation of case-weights in univariate regression case. The method developed here is useful for identifying influential observations in multivariate regression as an exploratory or confirmatory data analysis. An illustrative example is given for the effectiveness of the local influence approach in multivariate regression.     

可对称化矩阵特征值的任意扰动

针对可对称化矩阵,研究了可对称化矩阵特征值的任意扰动和实任意扰动。从Schur分解入手,利用矩阵可对角化的性质,通过矩阵等式的恒等变形,得到了可对角化矩阵关于F-范数和Q-范数的任意扰动界。     

弯曲光波导的本地场理论

本文从弯曲光波导的本地正交弯曲坐标系出发,展开MaxweII方程组,并借助于函数变换和普通小参数展开法导出了在o(1/R)近似下的弯曲光波导的修正场本地方程及修正传播常数。以圆光纤为例,讨论了一阶近似本地场形式及基模场在最大值处的场位移。与一些文献作以比较,我们的计算与数值方法相一致。本理论的特点是利用相应直波导的已知场来构造弯曲光波导的本地场,故本理论适应于分析任意截面,亦满足于在弱导条件下的弯曲光波导。     

非自治方程奇摄动问题解的渐近性分析

利用稳定性理论,分析了非线性非自治奇摄动方程εy″=y-ty′-(y′)4,t∈(-1,1)Robin问题边界值对解的渐近性态的影响,得出了边界层存在的位置与渐近解存在的条件.     

Influence analysis on crossover design experiment in bioequivalence studies

Crossover designs are commonly used in bioequivalence studies. However, the results can be affected by some outlying observations, which may lead to the wrong decision on bioequivalence. Therefore, it is essential to investigate the influence of aberrant observations. Chow and Tse in 1990 discussed this issue by considering the methods based on the likelihood distance and estimates distance. Perturbation theory provides a useful tool for the sensitivity analysis on statistical models. Hence, in this paper, we develop the influence functions via the perturbation scheme proposed by Hampel as an alternative approach on the influence analysis for a crossover design experiment. Moreover, the comparisons between the proposed approach and the method proposed by Chow and Tse are investigated. Two real data examples are provided to illustrate the results of these approaches. Our proposed influence functions show excellent performance on the identification of outlier/influential observations and are suitable for use with small sample size crossover designs commonly used in bioequivalence studies. Copyright © 2013 John Wiley & Sons, Ltd.