证明性的

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。

We study the recursive structure of the twisted-cube connected network sufficiently, and prove that the twisted-cube connected network is an n regular graph with connectivity n: point out that the twisted-cube connected network is a cube-free network, which is an essential distinction with the hypercube and other variations of the hypercube; prove that the diameter of n dimensional twisted-cube connected network is [ (n+1)/2] , which is almost the half of hypercube's.

首先对其结构的递归性进行充分地研究，证明它是连通度为n的n正则图；指出扭立方体连接网络无立方体子图，这是扭立方体连接网络与超立方体及其其它变种的本质差别；证明了n维扭立方体连接网络的直径为[（n+1）/2]，它几乎是超立方体直径的一半；最后，给出超立方体及其变种的等价定义，并对它们的结构递归性、网络参数和拓扑性质等作了简单的分析、综合和比较。

Are also given by constructing Lyapunov function. Finally, by applying the energy methods, Sobolev embedding theorems and bootstrap arguments, the global existence of nonnegative classical solutions to equations with homogeneous Neumann boundary value condition is proved when the space dimension is at most 5. Under certain conditions for the coefficients of the reaction functions, the convergence of the solutions is established for the system with large diffusion coefficients by constructing Lyapunov function.

的正平衡点全局渐近稳定的充分条件；最后，当空间维数不超过5时，应用能量估计、Sobolev嵌入定理和bootstrap技巧证明在齐次Neumann边值条件下非负古典解的整体存在性，并通过构造Lyapunov函数给出当反应函数的系数满足一定条件、扩散系数较大时该模型解的收敛性。

By their capacity for the immortal deed, by their ability to leave nonperishable traces behind, men, their individual mortality notwithstanding, attain an immortality of their own and prove themselves to be of a "divine"nature.

这样，通过它们，必死者能够在一个万物不死而惟独自己要死的宇宙中发现自己的位置，通过自己的行动能力以及留下不朽痕迹的能力，人，尽管有其个人的必死性，却依然获得了自己的不朽性，证明自己具有"神圣"本质。

In the first part, firstly, we introduce the nonstandard analysis theory simply. Using the axioms in nonstandard analysis, the nonstandard model is axiomatic approached, and the existence of nonstandard model and the consistence of axioms in nonstandard analysis are proved by the construction of nonstandard model. Secondly, some properties of nonstandard model are discussed, such as transitivity, Boolean properties, etc. Finally, Loeb measure spaceY,L

在第一部分里，首先对非标准分析理论进行了简单的概述，通过用非标准理论中的公理，给出了非标准模型，进而利用非标准模型的构造，证明了非标准模型的存在性和非标准模型中公理的一致性；其次，讨论了非标准模型的一些简单性质，如传递性，布尔代数运算性质等；最后，在内测度空间Y，

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 local decision space partitioning is given in the sense of maximum Bhattacharyya distance criterion. The optimality and the non-triviality of the partitioning scheme are proved. The reasonability of using Bhattacharyya distance as partitioning criterion is analyzed. The simulation results show that the partitioning method based on Bhattacharyya distance criterion is superior to that based on J-diversity criterion.

研究了基于 Bhattacharyya 距离准则的决策空间优化划分问题，求出了在 Bhattacharyya 距离最大意义下的决策空间划分方法，证明了这种决策空间划分方法的最优性和非退化性，分析了选择 Bhattacharyya 距离作为划分准则的合理性，并进行了计算机仿真比较，结果表明基于 Bhattacharyya 距离准则的决策空间优化划分优于基于最大 J-散度准则的决策空间划分。

Under some proper conditions we prove the existence of optimal controls in the class of Lipschitz functions, and obtain an optimality condition looks somehow like Pontryagin's maximum principle for a smooth optimal control function.

在适当的假设条件下，我们证明了状态方程解的存在唯一性和最优控制的存在性；并且根据最有控制函数的光滑性进一步对最优化存在的必要条件进行分析。

In chapter 1, regression models with censored data, LSE for censored regression models and LAD estimation for models with fixed censoring point are introduced. Then, we state our main results for LAD estimator of nonlinear regression models with randomly censored data, including consistency, boundedness in probability and asymptotic normality. The proofs of our main theorems are given in detail. In chapter 2, we state the main difficulty of obtaining numerical solution for censored LAD estimation, and recall the history of studies on this problem including some anterior algorithms.

在第一章，首先介绍删失线性回归模型的基本概念和性质，并对已有的估计方法，如最小二乘估计、固定点删失的最小一乘估计等做了简单的回顾；然后，把固定点删失线性回归模型的最小一乘估计方法推广到了随机删失、非线性模型的情形，并得到了估计量的一些渐近性质，如相合性、渐近正态性等；最后，给出主要结果的详细证明过程。

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