查询词典 theorems

This paper presents the new bound theorems in structural limit analysis developed on the basis of the generalized variational principle. The approximate limit factors determined from the new bound theorems are closer to the exact limit factor than the ones obtained from the classical bound theorems.

本文给出在极限分析的一般变分原理[1]的基础上发展起来的极限乘子的新的上、下限定理[10]，由这个新的上、下限定理决定的极限乘子的上、下限比经典的上、下限定理给出的更为靠近准确解。

Chapter one has introduced the background and classification of minimax theorems; Chapter two summarizes several proof method of minimax theorems, which are illustrated with examples; Chapter three has explained the development general situation of minimax theorems for a function and for two functions with chapter four respectively, and according to the classification of the theorem, has illustrated some important conclusionses in quantitative minimax theorems, topological minimax theorems and quantitative-topological minimax theorems separately.

第一章介绍了极大极小定理的背景及其分类；第二章总结了极大极小定理的几种证明方法，并举出例子进行说明；第三章和第四章分别阐述了单函数的极大极小定理和两个函数的极大极小定理的发展概况，在第三章中，按照极大极小定理的分类，分别对数量极大极小定理，拓扑极大极小定理和数量拓扑极大极小定理的一些重要结论作了介绍。

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。

Inequality proof of various ways, they were: use derivative testify inequality nature, Includes using functional monotonicity and extreme value, the function and the concave and convex inequality, proving is concave and convex function in the original definition of equivalent definitions and a lemma is proposed on the basis of relevant concave and convex function of several theorems about inequality, and briefly discusses how to use the definitions and theorems in proof of inequality.

不等式的证明方法多种多样，它们分别是：用导数性质证明不等式；包括利用函数单调性，极值与最值，函数凹凸性证明不等式，其中在给出凹凸函数原始定义等价的解析定义和一个引理的基础上提出有关凹凸函数关于不等式的几个定理，并简要阐述了利用定义和定理在证明不等式中的运用。

In chapter three, we prove that there exist solutions to the Ky Fan variation inequality, as the set-valued mappings are defined on spheres in infinite dimensional Banach spaces or odd dimensional Euclidean spaces, following from these theorems, we obtain some fixed point theorems for set-valued mappings defined on a sphere. When G is an approximate compact convex subset of E, or G is a almost quasi-convex set-valued mapping, we prove that there exist solutions to and type generalized Ky Fan variation inequality, following these theorems, we prove several best approximation theorems and coincidence theorems involving two set-valued mappings and two different spaces. In chapter four, we first present a new Simplicial algorithm for computing the Leray - Schauder fixed points, the algorithm can solve the set-valued nonlinear complementarily problem. We give a condition to guarantee the computation proceeding in a bounded region. We present integer-labeling algorithms for computing fixed points of some set-valued mappings, the best approximation points and solutions to a kind of set-valued variation inequalities.

第四章给出了计算定义在非凸集上的非自映射的Leray-Schauder不动点的算法，而现有的不动点算法都是计算凸集的上半连续集值自映射的不动点；给出了保证计算有界的一个充分条件，我们的条件大大弱于Mdrrill条件，我们的算法也可用来计算Eaves不动点；给出了集值非线性互补问题存在解的一个充分条件，此时可利用Leray-Schauder不动点算法来求解；向量标号算法以往是计算集值映射不动点的唯一有效算法，我们给出用整数标号算法计算一类集值映射的Kakutani 不动点的算法；定义在紧凸集上的连续映射不一定有不动点，但一定有最近点，最近点是不动点概念的推广，我们给出了计算最近点的算法；集值映射变分不等式尚无有效的求解算法，我们给出求解一类集值映射变分不等式的算法。

The Remark about Some Theorems of Real Number s Continuity;2. A class of fixed point theorems on a compact hausdorff topological space;3. This article has introduced some common basic natures of prime numbers,and has discussed other non-common natures and theorems of prime numbers.

主要介绍了量纲的基本概念、量纲分析的∏定理及齐次性原则，用两个实例解释了量纲分析在物理中的应用，最后指出了用量纲分析问题时应注意的问题和存在的不

This thesis consists of five chapters. At first, We introduce the study history as well as present situation on KKM theory. Secondly, We discuss the invariability of transfer open valued multimap under the restriction of upper and lower semicontinuity on generalized convex spaces. Then, We obtain new KKM type theorems from the classical KKM theorem by applying upper and lower semicontinuity. We also obtain intersection theorems by applying the KKM type theorems for a multimap from a topological space to another topological space. Further, We obtain Ky-Fan type coincidence theorem by applying known variational results on the KKM type theorems. Finally, We give an application to new theorems.

本文共分五章，首先回顾了KKM理论的研究历史和现状，其次讨论了在一般化凸空间上转移开值映射在上、下半连续映射下的不变性，然后在上、下半连续映射下，以古典的KKM定理为基础得到新的KKM型定理，并利用从一个拓扑空间到另一个拓扑空间的集值映射及KKM型定理得到相交定理，进一步利用已知的KKM型定理的变形结论得到Ky-Fan型重叠定理，最后给出新定理的一个应用。

As a application of the above results, some minimax inequalities and saddle point theorems can be obtained. In addition, fixed point theorems and section theorems, maximal element theorems and the existence theorems of equilibrium for abstract economies can also be discussed.

作为应用，可以得到L-凸空间中极大极小不等式和鞍点定理；进一步，还可以探讨不动点定理和截口定理，极大元定理和抽象经济的平衡存在性等问题。

In chapter one,the backgrounds and current situation of operator theory in Banach space are introduced and the preliminaries of Banach space are given.In chapter two,we study the existence and uniqueness of fixed point for decreasing strict-set-contraction operator in product space.Under the weak continuous condition,we obtain the existence and uniqueness of fixed point for decreasing operator and we give an application of these results; In chapter three,we get several positive fixed point theorems of decreasing operator and the existence and uniqueness theorems of positive fixed point for operator C=A+B,C=D-A in real Banach space where the order is decided by a normal cone; In chapter four,we obtained some existence and uniqueness theorems of fixed point for some mixed monotone operators in semi-ordered Banach space.

在第一章中，主要介绍了半序Banach空间非线性算子的研究历史背景、现状以及半序Banach空间中的预备知识；在第二章中，我们利用半序方法研究了Banach乘积空间中严格集压缩减算子不动点存在唯一性问题，在弱连续的条件下，得到了不动点的存在唯一性和迭代收敛性，同时，给出了它们的一些应用；在第三章中，我们建立了拟弱连续减算子的正不动点定理，并证明了算子C=A+B，C=D-A的正不动点存在唯一性定理；在第四章中，我们得到了半序Banach空间中混合单调算子的不动点存在性及唯一性定理。

The fundamental properties of the system K are studied,and it is pointed out that All theorems of the system L are theorems of the system K.Some important theorems about quantifiers are obtained.Moreover,the following results also are proved that all instances of substitution in the system K of tautologies of the system L are logically valid for any R0 chain,the soundness theorem and strong soundness theorem hold in the system K,i.e.,all theorems ofthe system K also logically valid for any R0 chain.

其次，研究了系统K*的基本性质，指出了系统L*的定理都是系统K*的定理，给出了系统K*与量词有关的一些重要定理，证明了系统L*的重言式在系统K*中的代换实例都是系统K*中关于任何R0链的逻辑有效公式；系统K*的可靠性定理成立，即系统K*中的定理关于任何R0链也是逻辑有效的；系统K*的强可靠性定理也成立，即系统K*在任何理论T下的定理关于任何R0链也是逻辑有效的。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了