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Automated geometric theorem proving, as a byproduct of the completion of geometric theorems, is further developed into automated quantitative description of geometric relations. The recovery of the geometric meaning of this quantitative description leads to a natural extension of the geometric theorem.

几何定理的机器证明作为几何定理完全化的副产品，被发展成几何定理的关系定量化，这种量化的几何还原就是几何定理的自然推广。

In the third chapter, first, we introduce the factorization technique in some theorems.

本文研究了一类非线性色散波方程的奇异行波解。

For the computation of the minimal covers of a family of sets, we propose several theorems to describe the principle, and develop corresponding algorithm elaborately.

而对于族集最小覆盖集的计算问题，本文则提出了若干个定理刻画了其计算方法的原理并予以正确性证明，并精心设计了相应的算法。

For the calculus of set valued functions,some convergence theorems about thePettis-Aumann integral,such as Fatou's Lemma,are mainly investigated;theproperties of the parametric Pettis-Aumann integral are gotten.

在集值映射的微积分方面，本文着重讨论了Pettis-Aumann积分的一些收敛定理，如Fatou引理等，并研究了含参变量Pettis-Aumann积分的一些性质。

Fermat s little theorem is one of the important theorems in number theory,but there has been little discussion in geometric field about it.

费马小定理是数论中的一个重要定理，但对其几何意义的论述几乎没有，给出了费马小定理的几何意义。

Advanced course covering topics selected from: semimartingale theory, stochastic integrals, homogeneous chaos expansions, stochastic differential equations, Malliavin calculus, infinite dimensional processes, functional central limit theorems, Feynman-Kac formula, Feynman integral.

随机分析：高级课程，包括：半鞅理论，随机积分，齐次混沌展开，随机差分方程， Malliavin 微积分，，有限维过程，泛函中心极限理论， Feynman-Kac公式， Feynman积分，过滤理论的应用，无限粒子系统，量子力学，神经学中的随机模型。

This paper talks about these two theorems around the finiteness conjecture and mainly gives detailed proofs for them.

本文将围绕有限性猜测仔细来讨论这两个定理，主要是详细补出了这两个定理的证明。

In this paper, by using fixed point theorems of strict set contraction mapping, we study two kinds of boundary value problems for compact type conditions in Banach spaces.

中文摘要：本文利用严格集压缩映象的不动点定理分别讨论了紧型条件下的两类Banach空间边值问题。

Using the fixed point theorem and degree theory, we give two existence theorems to the system under some conditions.

讨论了一类二、四阶耦合常微分方程组正解的存在性，利用不动点定理和度理论，在一定条件下得到了该方程组正解的两个存在性定理。

We establish some existence theorems for systems of vector equilibrium problems with_+-conditions by using the Kakutani-Fan-Glicksberg fixed point theorem.

运用经典的Kakutani-Fan-Glicksberg不动点定理证明了一类具_+-条件的向量均衡系统问题解的存在性。

So it was last week in Selma , alabama.

上星期在亚拉巴马州塞尔马市发生的事件也是这样一个转折点。

The group also spearheads various social programs in China.

该组织还带头参与中国的各种社会活动。