定理

At first, we establish some new KKM type theorems involving admissible set-valued mappings and the set-valued mapping with compactly local intersection property in FC-spaces. As applications, some new coincidence theorems and fixed point theorems are proved in FC-spaces.

首先，在FC-空间中得到了涉及容许类集值映射和具有紧局部交性质的更为一般的KKM 型定理，作为应用，在FC-空间中证明了一些新的重合点定理和不动点定理。

The proof of some propositions on points collinear in elementary geometry with vector mothod;2. The last we proof points of intersection being collinear .

文章首先证明了巴卜斯定理的特殊情况，然后利用此特殊情况及巴卜斯定理作了四个推广应用，最后将巴卜斯定理的原来三点共线推广到了六点共线，再推广到12n(n-1)个交点共线。

In part 1, we explore some properties of solution y of a backward stochastic differential equation, such as comparison theorem, reverse comparison theorem and uniqueness theorem of generator.

第一部分研究了倒向随机微分方程的解中y的性质，其中包括解的比较定理，逆比较定理，生成元的唯一性定理。

In the first charpter,response variable is generalized to q dimensions, we propose the concept of QMLE and quasi function in nonlinear models, then under mild conditions, we prove that there exists the solution_n with probability 1 for sufficiently large n, and obtain the strong consistency, some results of asymptotic normality, meanwhile consistent estimator of σ~2 for QMLE for heterosedastic nonlinear models is presented.

在第一章中，我们首先将响应变量由一维推广到了多维，得出了非线性模型的极大拟似然估计的定义和拟似然方程，然后在一定的条件下，证明了当样本量n充分大时，拟似然方程以概率1有解？？_n且收敛于参数的真值(即定理1.2)，并且给出了极大拟似然估计的渐近正态性(即定理1.3，1.4)，最后考虑了异方差非线性模型的离差参数σ~2的相合估计(即定理1.5)。

In the proof,sufficient conditions are proved mainly by properties of K function and continuity of Lyapunov function:in necessary proof,we separately structure Lyapunov functions which satisfy the conditions of the theorems, such that the results establish.

在定理的证明中充分性主要利用K类函数严格单调递增和Lyapunov函数的连续性；必要性的证明中，分别构造Lyapunov函数，满足定理的条件，使得定理的结论成立。

Helling and Jorgensen established the algebraic convergence theorem,limit theorem and convergence theorem in plane,respectively.

Helling、Jorgensen分别建立了平面Mobius群列的极限定理、代数收敛性定理和收敛性定理等等。

In Chapter 3,we discuss theconvergence of Newton's method for nonlinear inclusion problems with values in aclosed convex cone,using the new theory developed by Wang Xinghua,we generalizeRobinson's Kantorovich theorem for this problem to a more widely function classes,inthe same time our results take Smale theorem as a special case.

在第三章，我们利用王兴华最近提出的理论框架研究在闭凸锥中取值的非线性包含问题的Newton方法，将Robinson在特殊Lipshitz条件下建立的Kantorovich型收敛性定理推广至满足中心Lipshitz条件的函数类，我们建立的一般的收敛性定理同时将Smale型收敛性定理包容其中。

All notions and results in Section 2 of reference [1] are generalized and a counterexample is given to illustrate that Theorem 2.6 of [1] is incorrect.

摘要推广了文[1]第二部分中的所有概念和所有定理（即定理2.2、2.4、2.5、2.7、2.9、2.11和2.12），并通过举反例说明文[1]中的定理2.6是错误的。

In chapter 5,we persue the ctiticality and complexity of thecritical sets.We describe carefully the Whitney's example in 1935.Meantime,we introduce some rsults about the critical sets and thecritical value sets,in particular,on W-sets and C-sets.And usingthe Lebesgue density theorem and the Vitali covering lemma weprove a rank zero theorem with Hausdorff measures.Finally wegive some examples to prove our results are sharp in the sense thatthe numbers k,m,n,s,〓,etc.,in the hypothesescan not be improved.

第五章研究临界点集的临界性和复杂性，并详细地描绘了Whit-ney在1935年的例子，同时也介绍了关于临界点集和临界值集的一些结果，尤其是W-集和C-集的一些结果，并利用Lebesgue密度定理和Vitali覆盖引理证明了一个与Hausdorff测度相关的秩零定理，最后举例证明我们的结果在定理的假设中的那些数字如k，m，n，s，a，r+/等不能被改进的情况下是最佳的。

This article is applying the second theorem of dimension to dimensionless the different potential function of Schrodinger equation.

量纲Ⅱ定理是物理学中处理量纲问题的一个重要定理，应用量纲Ⅱ定理对不同势函数薛定谔方程无量纲化。

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。