定理

Theorem A.If the density function fhas the first derivative andlogfis a concave function,the MLE of〓for the two-sample location modelPL uniquely exists.

定理A。若密度函数f具有一阶导数并且logf是严格的凹函数，则对于双子样位置参数模型在PL的限制下，〓的MLE唯一存在。

Theorem C.If the density function fhas the second derivative andlogfis a concave function,the MLE of〓for two-sample scale model PSuniquely exists.

定理C。若密度函数f具有二阶导数并且logf是严格凹函数，则对于双子样尺度参数模型在PS条件限制下，〓的MLE唯一存在。

Thereinto the concavity and convexity of functions is important condition in minimax theory.

其中函数的凹凸性是极大极小定理的重要条件。

Sometimes different combinations in the concavity and convexity of functions may construct a new theorem.

函数凹凸性的不同组合往往可以构成一个新的极大极小定理。

In Chapter 1,some elementary knowledge was introduced,such as theBernstein-Bezier representation for polynomials,conform triangulation,theconditions of convexity for Bézier spline surfaces,the funtional andgeometric continuity condition for neibour Bézier surface patches etc.,specially,based on the Liu-Ding-Yuan Theorem for geometric continuity,some simple and practical conditions were obtained.

第一章介绍一些基本知识，如多项式的Bernstein-Bézier表示，相容三角剖分的定义，Bézier三角样条曲面保凸的条件，相邻Bézier曲面片函数连续和几何连续的条件等，特别地，在刘鼎元关于几何连续条件的一般定理的基础上，导出了几个较简单的实用的一阶几何连续条件。

However, Hacking convincingly argues that the theorem of convergence of opinions is not about the convergence of a posterior probability Pre, but about the convergence of a conditional probability Pr.

然而，哈金有说服力地表明，意见收敛定理证明的是条件概率Pr的收敛，而不是验后概率Pre的收敛。

On the other hand, an iterative hard shrinkage algorithm is obtained by using the generalized conditional gradient method, as well as convergent theorems for Solutions and stopping criterion.

此外，利用广义条件梯度法得到了迭代硬阈值算法，并给出了解的收敛性定理和停止准则。

The the probabilistic forecasting method of the error between the sample mean and expectation value of the random variable utilizing the central limit theory was researched, then the mathematical formula for the relation between sampling size and variance coefficient of loss of load probability was analyzed. Furthermore, the formulas for the relation between confidence intervals of variance coefficient and sampling size are deduced.

基于中心极限定理深入研究随机变量的样本均值与期望值之间误差的概率预测方法，在此基础上分析失负荷概率(loss of load probability，LOLP)指标的方差系数和样本容量之间的关系表达式，导出方差系数给定时的样本容量置信区间公式及样本容量给定时的方差系数置信区间公式。

On the base of this model, we give the method based on execution graph that is used to analyze the confluence and the condition that guarantees that the set of rules is confluent.

在此模型的基础上，提出了基于执行图的汇流性分析方法，给出了路径汇流和边汇流的定理，并提出了保证规则集汇流的条件。

For the case that the eigenstrains is in the form of linear function of Cartesian coordinates of the points of the inhomogeneity, the solution for the stress and strain fields is analytically derived based on the polynomial conservation theorem, the complex function method and conformal transformation together with the principle of minimum strain energy.

对于夹杂的特征应变为线性分布的情况，基于多项式保守定理，运用复解析函数法、保角变换和最小势能原理，获得了问题的封闭形式的解析解。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。