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Batch process control, fault detection and diagnosis and the theory of multivariate statistics are studied in this thesis. The main purpose of this thesis is to put forward the approach of batch process monitoring and fault diagnosis based on the theory of multivariate statistic and its applications.

本文对间歇过程控制、故障监测与诊断和多元统计分析的研究现状，进行了系统的分析和评述，由此提出自己的研究内容和技术路线，着重完善间歇过程监控与故障诊断的方法，并提出了新方法。

In this paper, we mainly discuss some preliminary studies about statistical diagnostics for one kind of restricted multivariate linear regression model. At first, we give the parameters estimation of this model. After that, the problem of outlier test is considered by giving the equivalence relations of estimators and statistics in multivariate case deletion model and mean shift outlier model under the restricted condition.

本文主要讨论的是一种带线性约束的多元线性回归模型（这里的多元是指多个因变量对多个自变量的情形），重点在与统计诊断方面的一些初步研究，首先给出带有线性约束的多元线性回归模型的参数估计，其次讨论了该模型的异常点检验问题，主要介绍了常见的数据删除模型及均值漂移模型，并证明了此两种模型统计量之间的等价性。

The statistical difference of proinsulin rather than HOMA index was found among the patients of various Gensini's score group (Gensini's score was examined as a categorical variable classified by tertile values) and significantly stenosed vessels group by means of the results of analysis of covariate variance after adjusting for age, sex and body mass index (p＜0.05), and the partial correlation coefficient between proinsulin level and Gensini's score, the number of significantly stenosed vessels after adjusting for age, sex and body mass index was 0.3156 (P＜0.01) and 0.2752 (P＜0.05) respectively. Multivariate linear regression analysis indicated that the level of proinsulin was positively correlated with the Gensini's score (P＜0.01). The results of multivariate stepwise Logistic indicated that the proinsulin was the independent risk factor for the coronary heart disease, and the odds ratio (95％ confidence interval) was 2.268 (1.253～4.105)(P=0.007), however, the HOMA was refused by the final model.

年龄、性别与体重指数为控制变量的协方差分析结果显示，胰岛素原的水平在不同的Gensini评分组、冠状动脉病变血管数分组中分布有统计学差异(P＜0.05)，偏相关分析示胰岛素原的含量与Gensini评分与病变血管数显著正相关，其偏相关系数分别为0.3156(P＜0.01)与0.2752(P＜0.05)，而HOMA指数与两种评分的相关未有统计学意义；多因素线性逐步回归分析结果示胰岛素原水平与Gensini评分独立正相关(P＜0.01)；多因素Logistic回归分析显示，胰岛素原的水平为冠心病的独立的危险因素，其OR值及其95％可信区间为2.268(1.253～4.105)(P＜0.01)，HOMA指数未进入模型。

The control request and the principle of flotation column were analyzed and elaborated emphatically. The design method of the multivariate inputs/multivariate outputs is adopted. The control system selects the controx2000 configuration software and PLC as a exploitation implement.

分析和阐述了浮选柱监控系统的控制要求和原理，采用多变量输入/多变量输出的设计思路，选用开物2000工业组态软件和PLC作为开发工具。

The representiveness of training samples for multivariate calibration has been discussed and the concept of weighted sampling has been introduced to multivariate calibration.

本论文主要包括以下几个方面的工作：1。

Multivariate hypergeometric functions, multivariate Jacobi polynomials and h-harmonic polynomials connected with root systems and Coxeter groups are introduced.

多元超几何函数，多元Jacobi多项式和h与根系考克斯特集团有关的调和多项式介绍。

Some methods of deciding the extreme values for the monadic functions and two-place functions were applied to decide the extreme values for the multivariate functions and then some effective methods of deciding the extreme values for the multivariate functions were presented.

将一元函数和二元函数极值的部分判别方法推广到多元函数极值的判别，提出了判定多元函数极值的几个方法。

The research of the crisis prediction in foreign country has begun early. It is developed extensively since 1960s. Their research in the field maturated, including the single variable model, the multivariate discriminate model, the multivariate regression model and the neural network model.

国外对财务危机预警的研究很早就有，自上个世纪60年代以来，财务危机预警得到广泛发展，从最开始的单变量模型到多元判别模型、多元回归模型等，到现今的神经网络模型，他们对财务危机预警的研究已经比较成熟。

Copula-EVT model is an exploration to risk management using multivariate estreme thory. Copula is a function which links the multivariate distributions to given marginals.

Copula-EVT模型是对利用多维极值理论研究金融风险的一种探讨，Copula函数是把多个随机变量的联合分布与它们各自的边缘分布相连接的一个函数。

First, we introduce and discuss the various methods of multivariate polynomial interpolation in the literature. Based on this study, we state multivariate Lagrange interpolation over again from algebraic geometry viewpoint:Given different interpolation nodes A1,A2 .....,An in the affine n-dimensional space Kn, and accordingly function values fi(i = 1,..., m), the question is how to find a polynomial p K[x1, x2,...,xn] satisfying the interpolation conditions:where X=(x1,X2,....,xn). Similarly with univariate problem, we have provedTheorem If the monomial ordering is given, a minimal ordering polynomial satisfying conditions (1) is uniquely exsisted.Such a polynomial can be computed by the Lagrange-Hermite interpolation algorithm introduced in chapter 2. Another statement for Lagrange interpolation problem is:Given monomials 1 ,2 ,.....,m from low degree to high one with respect to the ordering, some arbitrary values fi(i= 1,..., m), find a polynomial p, such thatIf there uniquely exists such an interpolation polynomial p{X, the interpolation problem is called properly posed.

文中首先对现有的多元多项式插值方法作了一个介绍和评述，在此基础上我们从代数几何观点重新讨论了多元Lagrange插值问题：给定n维仿射空间K~n中两两互异的点A_1，A_2，…，A_m，在结点A_i处给定函数值f_i(i=1，…，m)，构造多项式p∈K[X_1，X_2，…，X_n]，满足Lagrange插值条件：p=f_i，i=1，…，m (1)其中X=(X_1，X_2，…，X_n)，与一元情形相似地，本文证明了定理满足插值条件(1)的多项式存在，并且按&序&最低的多项式是唯一的，上述多项式可利用第二章介绍的Lagrange-Hermite插值算法求出，Lagrange插值另一种描述是：按序从低到高给定单项式ω_1，ω_2，…，ω_m，对任意给定的f_1，f_2，…，f_m，构造多项式p，满足插值条件：p=sum from i=1 to m=Ai=f_i，i=1，…，m (2)如果插值多项式p存在且唯一，则称插值问题适定。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。