查询词典 theorems

In chapter 2, we first give a generalized type of the Prigons fixed point theorem and a straightforward proof of it. At the same time, we give a positive answer to an open question about convergency of iterative sequence for generalized contraction which is bring forwarded by Frigon in [3]. Secondly, by using the introduced function φ, we establish some fixed point theorems for the set-valued φ-contraction mappings in gauge spaces. These results unify and generalize the corresponding results of Cain and Nashed [1], Figon [3], Espinola and Kirk[4], Tarafder [5] et al.

第二章，首先给出Frigon不动点定理[3]的推广及其简洁证明，同时对Frigon在文[3]中提出的关于广义压缩迭代序列收敛性的公开问题给出肯定的回答；然后，通过引入φ函数，在度规空间上建立集值φ-压缩映射的不动点定理，统一并推广了Cain和Nashed[1]，Figon[3]，Espinola和Kirk[4]，Tarafder[5]等的相应结果。

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.

我认为，数学的存在是不以我们的意志为转移的，我们的作用是发现它或观测它，那些我们证明的和我们称之为'创造'的定理，仅仅是对我们的观测数据的注解。

Design and implement the experimental systems RM and GRM which are based on Reso-lution and Generalized Resolution respectively. Prove all the theorems in Section A and Section Bin Part Ⅰ of " Principia Mathematica " using RM and GRM respectively, and then compare andanalyze the efficiency of RM and GRM.

设计实现了基于归结和基于广义归结的实验系统RM和GRM，分别用RM和GRM证明了《数学原理》第一部分Section A和Section B中的全部定理(350个)，并对RM和GRM的效率进行了分析比较。

Then wehave two important theorems about the lifting of the group of automorphisms and thelifting of derivations of A are given by the function of uce , then to prove them.

然后，利用uce函数给出了关于A的自同构群的提升和导子的提升的两个重要定理并加以证明。

In chapter I, I mainly describe some theorems for Heisenberg AFMs, and the history of models of putting impurities in pure S=1 Haldane chain which can give any clue to our study.

在第一部分的第一章，我们主要回顾了往S=1的自旋反铁磁链里掺杂历史，介绍了与Heisenberg 反铁磁链相关的一些定理，讲述了一些前人所做的工作，及其提供的理论线索。

The stability problems are analyzed and discussed. The optimal control problem is formulated to determine the necessary conditions for optimality in networks. Three theorems about the properties of the steady state-costate solution in Hamilton function are confirmed leading to the natrual meaning and the optimal policy which can be implemented in practice. In chapter Ⅴ, the methods for nonstationary simulation of computer networks are discussed.

第四章表述了计算机通信网动态特性研究的主要数字方法；提出了排队与随机存取机制、网络链路传输和节点分流的状态空间模型，并作了稳定性研究；应用最优控制理论得到网络最优控制的必要条件，证明了哈密尔顿函数协状态变量的稳定解性质，据此研究分析了网络最优控制的本质意义及实现途径，并给出计算及建模实例。

In Chapter 1, we introduce the definitions of Hausdorff dimension and Hausdorff measure, and some related definitions and theorems.

第一章介绍Hausdorff维数和Hausdorff测度的定义及一些相关的定义和定理。

By using the partition theorem of unity, a continuous selection theorem for a multimap from a compact Hausdorff topological space to a finitely continuous topological spaces (simply, FC-spaces) without any convexity structure was obtained, and from which and Tychonoff fixed point theorem, a collectively fixed point theorem for a family of multimaps on the product space of compact FC-spaces and several collectively fixed point theorems for a family of multimaps on the product space of non-compact FC-spaces were given.

利用单位分解定理得到从紧的Hausdorff拓扑空间到没有任何凸结构的有限连续拓扑空间的集值映射的连续选择定理，并从该结果和Tychonoff不动点定理，得到紧的FC-空间的乘积空间上映射族的集族不动点定理和若干个非紧的FC-空间的乘积空间上的映射族的集族不动点定理，对文献中的相应结果进行了改进和一般化。

As applications of these formulae some pinching theorems for Gaussian curvature of holomorphic curves in G is gained.

利用这些公式，文中得到一些关于G中全纯S^2的Gauss曲率的Pinching定理。

In the last chapter, the covering theorems for normalized holomorphic mappings on bounded starlike circular domains are also obtained.

另外，在本文的最后一章，我们还讨论了有界星形圆形域上正规化全纯映射的掩盖定理。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。