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Then,the thesis improved the results of Qiu Gandi about meromorphic function and its derivative sharing values.

其次,本文对与其导函数分担公共值的亚纯函数的唯一性问题进行了分析和讨论,推广了邱凎俤的相关结果。

In chapter one, we state a few usual notations, definitions and basic results in value distribution theory of meromorphic function and unicity.

第一章,我们给出本文所要用到的一些基础知识;亚纯函数值分布理论方面的基础知识及一些常用的记号,复分析和唯一性里的一些基本结果。

Uniqueness of meromorphic function is derived from the five-value and four-value theorems in Nevanlinna Theory.

亚纯函数唯一性理论起源于Nevanlinna五值定理和四值定理。

In chapter three, we study the uniqueness of meromorphic function and its derivative, and obtain the following result: There exists a set S with 6(4) elements such that any nonconstant meromorphic function f and its derivative f' satisfying E=E must be identical.

在第三章中,我们讨论了涉及导函数的唯一性问题,得到了下述结果:存在一个集合 S含有 6(4)元素,对于任意一个非常数亚纯函数f 及其导函数 f',若 E=E,则f=f'。

Using the value distribution theory, the author studied the uniqueness of meromorphic function concerning multiple value .

应用值分布理论,在涉及重值情况下进一步研究了亚纯函数唯一性理论中Gross 。F提出的一个问题,获得如下结果:设集合S ={ω∈C|P =aω7- 42ω2 +70bω- 30b2 =0 },其中a ,b为不等于零的常数,ab5≠ 2。

Meromorphic function, Sharing value, Uniqueness

亚纯函数,分担值,唯一性

The object of this thesis is to study the uniqueness problems of meromorphic func-tions and meromorphic mapping s in several complex variables.

本文以多复变数的亚纯函数与亚纯映射的唯一性问题为研究对象。

Based on the study of the relation between meromorphic mapping and moving targets,a new truncated second main theorem is proved for meromorphic mapping in several complex variables with moving targets.

通过对亚纯映射与小映射之间关系的研究,给出了一个涉及小映射的亚纯映射精简密指量形式的第二基本定理,并由此得到相应的亚纯映射唯一性定理。

Pronounce to replace an English to translate to have a few advantages with the Chinese language:A, simple go easily, so easily popular;Two, the Chinese language pronounce to translate to be advantageous to the only sex which promises a business enterprise particularly more than the English;Three, the blindness may conflict with the taboo of a certain consumption community place country after translating the meaningful English phrase, resulting in bad result, but adoption to foreigner the milli- nonsense Chinese language pronounce but can avoid this kind of phenomenon availably.

用汉语拼音来取代英译有几个好处:一、简便易行,所以容易流行;二、汉语拼音比英译更有利于保证企业专名的唯一性;三、盲目译成有意义的英文词后可能会与某个消费群体所在国的禁忌发生冲突,造成不良后果,而采用对外国人来说毫无意义的汉语拼音却可以有效地避免这种现象。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先,第二章在非Lipschitz条件下,研究了第二类方程的解的存在唯一性问题,在此基础上,又证明了解的稳定性;第三章在非Lipschitz条件下,证明了第二类BSDE解的比较定理,并在此基础上,利用单调迭代的方法,构造性证明了最大、最小解的存在性;第四章在以上的一些理论基础之上,得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果,主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的,得到了最优控制和动态规划的一些结果,在这一章的最后还讨论了相应的效用函数的性质,如,效用函数的单调性、凹性以及风险规避性等;第五章,针对第一类倒向随机微分方程,运用单调迭代方法,证明了最大和最小解的存在性,并研究了解的其它性质及在效用函数上的应用。

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