The curvature measurement of the human eyeball

The curvature of the cornea in the ophthalmology field is essential data, especially for humans when they are being tested for wearing contact lenses, or for patients undergoing refractive surgery by either knife or laser. It is extremely difficult to measure the curvature of the eye precisely because the measurement of the cornea, using a contact tool, is not possible. In this paper, we propose a method to measure the curvature using lens aberration theory and an image processing technique. We project a circular grating, known as a Placido disc, on to the cornea. The reflective image does not have equal divisions and this distortion value contains the curvature information.     

A linear negative multinomial model

A linear model is defined for logarithmic and linear functions of negative multinomial frequency counts. A closed-form estimator of the model parameters, estimator covariance matrix, and general Wald test are derived under the assumption of negative multinomial sampling.     

国产航空有机玻璃(PMMA)的压缩应力-应变行为研究——Ⅱ.力学性能特征参数分析

讨论从加卸载循环的应力-应变表征曲线提取得到的各材料力学性能,尤其是关于屈服和塑性变形的特征参数。包括加卸载弹性模量E_L~T,E_u~T;屈服点的表征参数:屈服应力σ_s~T,屈服应变ε_s~N,屈服应变能U_s;热激活塑性变形的表征参数:活化体积V_τ和活化能ΔH。讨论这些参数对温度和应变率的依赖关系,寻求由这些特征参数作表述,或是存在于这些参数之间的经验关系或规律。     

Minimaxity of a preliminary test estimator for the mean of normal distribution

Summary The problem is to estimate the mean of the normal distribution under the situation where there is vague information that the mean might be equal to zero. A minimax property of the preliminary test estimator obtained by the use of AIC (Akaike information Criterion) procedure is proved under a loss function based on the Kullback-Leibler information measure.     

Principal components in the nonnormal case: The test of equality of Q roots

The limiting distribution of the likelihood ratio statistic W_q for testing the hypothesis of equality of q characteristic roots of a covariance matrix is studied in the case of nonnormal populations. It is shown, both theoretically and empirically, that the limiting distribution of W_q is not robust to departures from normality and that W_q cannot be used for nonnormal populations with long tails. For the class of elliptical populations the limiting distribution of W_q can be expressed in close form. A corrected test statistic, W_q^*, is proposed that can be used in principal component analysis when sampling from elliptical populations.     

关于级数敛散性的积分判别法的一个新证明及其推广

给出了现行的数学分析 ,微积分与高等数学的教材中的数值级数敛散性的积分判别法的一个新证明 ,获得了这个判别法的一个推广 ,由此得到一批渐近公式与命题     

多层连锁不平衡的齐一性检验

In this article, using the likelihood score theory extended to nuisance parameters we derive a new homogeneity score test for comparing linage disequilibrium across several strata. Power and sample size formulae are also obtained.     

2-氟-6-氯甲苯氨氧化法制备2-氟-6-氯苯腈初探

以2—氟—6—氯甲苯(CFT)为原料，采用氨氧化法一步制得了2—氟—6—氯苯睛．通过实验筛选到以钒、磷为主要成分的5组分F52号催化剂．使用该催化剂进行2—氟—6—氯甲苯氨氧化反应的最佳工艺条件：温度为380℃，反应物摩尔比n(CFT)：n(NH3)：n(空气)＝1：6：25．在此条件下，2—氟—6—氯甲苯的转化率为98．99％，2—氟—6—氯苯睛的产率(摩尔)为71．47％，选择性为72．20％．经气相色谱分析，产品纯度高于99％．     

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??A single distribution-free (nonparametric) Phase II exponentially weighted moving average (EWMA) chart based on the Cucconi statistic, referred to as the EWMA-Cucconi (EC) chart, is considered here for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous process. A comparison with some other existing nonparametric EWMA charts is presented in terms of the average, the standard deviation and some percentiles of the run length distribution. Numerical results based on Monte Carlo analysis show that the EC chart provides quite a satisfactory performance. The effect of the Phase I (reference) sample size on the IC performance of the EC chart is studied in detail. The application of the EC chart is illustrated by two real data examples.