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this article discusses the integral theorem of mean the promoted question, mainly has two aspects: On the one hand in analyzes in the teaching material under the first integral theorem of mean condition, had proven lies between the value spot to have to be possible to obtain in the open-interval, further discusses this knot promotes to the generalized Riemann integral, and further proved the conclusion also establishes to the promoted first integral theorem of mean; Promotes on the one hand in addition the integral theorem of mean to in the curve and the curved surface, and has proven the curvilinear integral theorem of mean and the surface integral theorem of mean.

本文讨论积分中值定理的推广问题，主要有二个方面：一方面在分析教材中第一积分中值定理的条件下，证明了介值点必可在开区间内取得，进一步将这个结论推广到广义Riemann积分，并进一步证明结论对推广的第一积分中值定理也成立；另一方面，将积分中值定理推广到曲线和曲面中，并证明了曲线积分中值定理和曲面积分中值定理。

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。

In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.

在巴拿赫空间理论中，Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一，分隔性定理是Hahn-Banach定理的重要应用，本文利用"超平面"的方法，改进了一个分隔性定理的证明；另外，本文利用邻域的"平移"方法，给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。

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

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。

The thesis will introduce, respectively, relevant concepts of residue theorem and its promotion and application in two parts In the basic concepts of chapter II, the definition, classification and relationship between function zero and pole of the isolated singular point are given to lead out relevant definition, theorem and solving method, while the core content of this paper is promotion and application of residue theorem, including calculation of integration by using residues, application in diagonal theorem and argument theorem, application in electromagnetism and theorem promotion and relevant application of extension theorems

本文将从两大部分分别引入和浅析了留数定理的相关概念及其推广和应用在第二章的基本概念部分中，给出了孤立奇点的定义和分类、函数零点与极点的关系，从而引出留数定理的相关定义与定理及其求法而本文的核心内容也就是留数定理的推广和应用，包括运用留数来计算积分、体现在对角定理与辐角定理中的应用、在电磁学中的应用及其定理的推广和推广定理的相关应用

In the paper the separate theorem of convex set with weak topology σ(L ∞,L 1) is proved, and the topological characterization about No Free Lunch with Vanishing Risk Condition is given, from it, the equivalency between exist of equivalent martingale measures and NFLVR is proved, this is the first fundamental theorem of asset pricing.

资产定价的第一基本定理是数量金融学中核心的定理之一，本文证明了在 L∞的弱*拓扑σ(L∞，L1)中的凸集分离定理，并在此定理的基础上给出了没有无风险免费午餐的拓扑描述，证明了市场公平性与没有无风险免费午餐条件的等价性，从而重新证明了资产定价的第一基本定理。

In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.

在巴拿赫空间理论中，Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一，分隔性定理是Hahn-Banach定理的重要应用，本文利用&超平面&的方法，改进了一个分隔性定理的证明；另外，本文利用邻域的&平移&方法，给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。

Generalized reciprocal theorems of non-coupled and coupled system s, which are valid for two deformed bodies with different constitutive relations are established by generalizing the idea of Betti s reciprocal theorem.

推广Betti倒易定理的概念，建立了非耦联系统和耦联系统的广义倒易定理，它们适用于具有不同本构关系的两个变形体·当该两变形体的本构关系相同且为线弹性时，该非耦联系统的广义倒易定理即成为Betti倒易定理·同时，应用该两个广义倒易定理于弹性力学中的模拟计

When the constitutive relations of the two deformed bodies are all alike and linear elastic, the generalized reciprocal theorem of non-coupled system s just becomes Betti s.

推广Betti倒易定理的概念，建立了非耦联系统和耦联系统的广义倒易定理，它们适用于具有不同本构关系的两个变形体·当该两变形体的本构关系相同且为线弹性时，该非耦联系统的广义倒易定理即成为Betti倒易定理·同时，应用该两个广义倒易定理于弹性力学中的模拟计

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