查询词典 mapping theorem

This paper, by means of Rolle theorem, introduces constant method to demonstrate mean value theorem for differential calculus and attains the corresponding supplementary function of the demonstrating method.

借助于Rolle定理，用待定常数法证明了微分中值定理，得到了该证明方法的辅助函数簇，这种证明方法对解决同类问题有很好的推广应用价值。

In the dissertation, we do a further study in value distribution theorem and normal families theorem of meromorphic function and get some results by using the Nevanlinna's value distribution and the Ahlfors value distribution.

中文摘要：本论文主要运用Nevanlinna值分布理论以及Ahlfors值分布理论在亚纯函数值分布理论和亚纯函数正规族理论两个领域内做了进一步研究，并且相应的得到了几个结果。

The first systematic and fundamental research is did by Modigliani and Miler, they bring out with the famous MM theorem in 1958.Which says capital structure doesn't affect enterprise market value and average capital cost in a condition of perfect market. After that, several economists including Modigliani and Miler themselves put this theory forward with the MM theorem with the consideration of tax, the trade-off theory, the pecking order theory,market for corporate control, these analyses throw lights on the problem from different aspect.

对此做出系统性和开创性研究的是Modigliani和Miler，在1958年提出了资本成本与资本结构无关的MM定理，在此基础上，包括Modigliani和Miller在内的许多经济学家对此进行了探索，他们先后提出了考虑税收的MM定理、权衡理论、优序融资理论、控制权理论，从不同的角度分析了资本结构的优化问题。

This paper study the character and application of the solution of BSDE, the main results include: for the second kind of BSDE, the existence and uniqueness of the solution under non-Lipschitz condition, comparison theorem and stability are established , under weaker condition , the existence of the minimal and maximal solution is proved and the application in stochastic control and utility function is given; for the first kind of BSDE, under weaker condition , the existence of minimal and maximal solution .stability, comparison theorem and application to utility function are proved.

本文研究倒向随机微分方程解的性质及其应用，主要结果有：针对第二类方程，讨论了在非Lipschitz条件下倒向随机微分方程解的存在唯一性，比较定理及稳定性等，在更弱条件下，得到了倒向随机微分方程的最大解和最小解的存在性，在此基础之上，给出了在随机控制及效用函数方面的应用；针对第一类方程，同样在较弱条件下，证明了方程最大、最小解的存在性、稳定性、比较定理及其在效用函数的应用。

This paper study the character and application of the solution of BSDE, the main results include: for the second kind of BSDE, the existence and uniqueness of the solution under non-Lipschitz condition, comparison theorem and stability are established , under weaker condition , the existence of the minimal and maximal solution is proved and the application in stochastic control and utility function is given; for the first kind of BSDE, under weaker condition , the existence of minimal and maximal solution .stability, comparison theorem and application to utilityfunction are proved.

本文研究倒向随机微分方程解的性质及其应用，主要结果有：针对第二类方程，讨论了在非Lipschitz条件下倒向随机微分方程解的存在唯一性，比较定理及稳定性等，在更弱条件下，得到了倒向随机微分方程的最大解和最小解的存在性，在此基础之上，给出了在随机控制及效用函数方面的应用；针对第一类方程，同样在较弱条件下，证明了方程最大、最小解的存在性、稳定性、比较定理及其在效用函数的应用。

A section theorem, a minimax inequality and a generalized fixed point theorem where the underlying space is a product space of two topological vector space s, are given.

给出了两个拓扑向量空间的乘积空间上截口定理，极小极大不等式及一个推广的不动点定理。指出这3个形式不同的结果与Tychonov不动点定理是相互蕴含的。并且用截口定理直接证明了多值映射的一个重合定理

Equilibrium; continuous selection; the fixed point theorem; variational inequality; minimax theorem; H-space

基础科学，数学，数学分析均衡；连续选择；不动点定理；变分不等式；极小极大定理； H-空间

Firstly, the generalization of Fan-Ha section theorem and a general vector variational inequality without convexity assumption and minimax theorem of vector-valued function are obtained. Then, the quasi-montone vector variational inequality problem is concerned. Cx-quasi-monotone operator is defined in topological vector space, inner point of a closed convex set K is introduced, the relation between inner point and relative algebraic interior point is given, an existence result for quasi-monotone vector variational inequality is obtained.

第三章主要研究了向量变分不等式和极小极大定理(来源：3282AB83C论文网www.abclunwen.com)，建立了广义的Fan-Ha截口定理、新的向量变分不等式与极小极大定理，并在拓扑向量空间中定义了C_x-拟单调算子，引入了闭凸集K的inner点，给出了inner点与相对代数内点的关系，利用innK_c代替K的拓扑内部，建立了新的拟单调向量变分不等式。

As a special example, our theorem is also applicable to the case that the reaction function is monotone. And our theorem is consistent to the previous concludes.

作为一个特例，即反应项是拟单调的，我们的构造耦合拟上解和拟下解的方法也适用并且与以前文献的结论一致。

Following that, the theorem of maximum entropy andthe theorem of monotonicity are proved as well as the positivity of entropy.

本文指出了度量模糊变量的不确定性和度量模糊集的不确定性之间的本质差异，表明了定义模糊变量的熵的意义所在。

In other research, chondroitin is being investigated for use in several other conditions.

在其它研究，软骨素被调查用於几个其它情况。

They would make fun of him for having to work.

他们拿他的工作来开玩笑。