定理

In the following, we list the main works in our paper:(1) We introduce briefly the concepts of fuzzy mathematics and three fundamental principles—decomposition theorem, representation theorem and extension theorem. We also present the concepts of fuzzy number and some simple properties.

本文主要内容包括以下几个方面：(1)简要地介绍了模糊数学中基本概念和三大基本定理--分解定理，表现定理和扩展定理，模糊数的概念、性质以及比较两个模糊数的方法。

It introduces normal families, including equicontinuity, Arzela's theorem, Montel's and Marty's theorems, Zalcman's lemma; univalent functions, including Koebe's and de Branges' theorems; quasiconformal mappings, including conformal length, extremal length, geometric, analytic and metric definitions, quasiconformal extension, distortion theorem, quasicircle; iteration of rational functions, including fixed points, the Fatou and Julia sets, periodic points, Siegel disks, the Hausdorff measure and dimension, etc.

具体为：正规族，包括等度连续性、Arzela定理、Montel和Marty正规定则、Zalcman引理；单叶函数，包括Koebe定理和de Branges定理；拟共形映照，包括共形模、极值长度、几何、分析和距离定义、拟共形延拓、偏差定理，拟圆周等；有理函数的迭代，包括不动点、Fatou集和Julia集、周期点、Siegel盘、Hausdorff测度和维数，等等。在教学内容上充分体现综合性、前沿性。

Building of the operation rules of curl and divergence for vector field in R 3 space;2. Analysing by mathematics and the concepts of flux and curl , we can get the differential form of gauss s theorems in electrostatic field and ampere s cycle theorem in electrostatic field.

电动力学中的内容一般是从电磁学最基本的实验规律出发，由静电场中的库仑定律得到静电场的高斯定理和环路定理，利用通量与散度、环流与旋度的关系，得到静电场的高斯定理和坏路定理的微分形式。

In chapter two, by studying the properties of self-maps on trees, we obtain five necessary and sufficient conditions for the product self-maps on trees which have the property of equicontinuity on their sets of periodic points, i.e.

第二章通过对树上连续自映射性质的研究，给出了树上乘积自映射在其周期点集上等度连续的五个充要条件，即定理2.3.1，定理2.3.2，定理2.3.3和定理2.3.4。

In this paper, we give a section theorem of Ky Fan type and its equivalent theorem in hyperconvex metric spaces, and as their applications we obtain some minimax theorems and a coincidence theorem.

赵云河 ，张惠丽文章给出了超凸度量空间中的一个Ky Fan型截口定理及其等价定理，作为它们的应用，得到了一些极大极小定理和一个重合定理。

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。

Using variable upper limit integration and Lagrange mean value theorem,this article proves the first mean value theorem under the same condition and give several spread of the first integral mean value theorem .

在条件完全相同的情况下改进积分第一中值定理，并利用变上限积分函数和拉格郎日中值定理证明该定理，并给出积分第一中值定理的几个推广

In this paper, by computing the Laplace of the square of the length of the second fundamental form and introducing a self-adjoint operator and using Stokes Theorem and Hopf Theorem, we obtained some pinching theorems and rigidity theorems for hypersurfaces and submanifolds in hyperbolic space.

本论文通过计算双曲空间中子流形的第二基本形式模长平方的拉普拉斯和引进一个新的自共轭二阶算子，利用Stokes定理和Hopf定理得到了子流形的一些拼挤定理和刚性定理。

In thisthesis, we first extend the vanishing theorem due to Lawson, Simons and Xinto the case of compact submanifolds of a hyperbolic space. Thus, by using thenew vanishing theorem for homology groups, we prove the topological spheretheorem for complete submanifolds in a hyperbolic space. Hence we generalizethe Shiohama-Xu topological sphere theorem.

本文进一步将Lawson-Simons-Xin同调群消没定理拓广到双曲空间中紧致子流形的情形，并运用这一新的同调群消没定理证明了双曲空间中完备子流形的拓扑球面定理，从而推广了Shiohama-Xu的拓扑球面定理。

The paper consists of six chapters. Chapter One is the theoretical background, we review the course of mechanical theorem proving and briefly introduce the main mechanical theorem prover of the last decade, Among them, we stress on the Boyer-Moore theorem prover and its throretical foundation a computational logic. In Chapter Two, we discuss two theorem proving tactics. One is the rippling-out tactic, which is a tactic for manipulating the induction conclusion to enable the induction hypothesis to be used in its proof, because it extremely restricts the search space, so it has high efficiency.

全文共分六章，第一章是理论背景知识，回顾了定理机器证明的历程，并对近十年来的主要定理证明器作了扼要的介绍，其中，着重介绍了计算逻辑及Boyer-Moore定理证明系统；第二章讨论了两种定理证明策略，一种是波动策略，它是一种在证明中通过处理归纳结论来激活归纳假设的策略，由于极大的限制了搜索空间，因此搜索效率高。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新