本文第一章介绍可积系统的哈密顿方法。
In chapter one, we give a brief introduction to the Hamiltonian method of integrable system.
对于其中的可积系统，往往是双线性形式。
性质不具有有限可积性。
可积局部鞅有正则修正。
The local martingales of Llog +L-integrals possess cadlag modifications.
研究迹映射的几个性质：保测度，可积，可反。
Some properties of trace map are studied, such as exemple measure-preserving, integrable and reversible.
特别地，许多可积方程都自然地产生于曲线和曲面运动。
In particular, many integrable equations arise naturally from motions of curves and surfaces.
另外，利用马格式求得了上面已知可积系之一的非等谱流。
In addition, the nonisospectral flows of one of the above known hierarchies are given by the use of Ma scheme.
不作旋转波近似， 破缺可积性的因素，主要来自虚光场项。
In NRWA, the main factor which will deslroy the non classical effects is the virtual photon term.
作为应用，利用屠格式得到了TC方程族的一个新的可积耦合。
As the applications, a new integrable coupling of TC hierarchy by using the Tu scheme.
对于二阶变系数线性微分方程来说，这也是可积的一个充分条件。
It is also a sufficient condition for second order linear differential equation with varied coefficient to be integrable.
如极限收敛，停时定理等很多方面都与一致可积性有着重要联系。
There are many results with important relations to it , such as the covergance theorem and stopping time .
本文研究的内容主要包括两个方面：可积方程族的生成和可积耦合。
The major contents in this paper include: the formulation of integrable hierarchies and the integrable couplings.
这些结果能被用来研究共轭调和函数的可积性并且估计它们的积分。
These results can be used to study the integrability of conjugate harmonic functions and estimate the integrals for them.
提出一阶非线性常微分方程新的可积型，且给出其通解的参数形式。
Proposed a new form of non-linear first-order ordinary differential equation, meanwhile, it shows the parameter form of universal solution.
结果推广了该问题可积的一些原有结果，并给出了通解的参数表示式。
Results Original integrable results of this problem are generalized and parametric expression of the general solution is given.
微商非线性薛定谔方程(DNLSE)是有众多物理应用的可积方程。
The derivative nonlinear Schrodinger equation (DNLSE) is an integrable equation of many physical applications.
本文建立了两类可积函数的积分第一中值定理的推广形式，推广了已有结论。
Two kinds of generalizations of the first mean value theorem of integral for integrable functions with different properties are established in the paper, the results extend the previous conclusions.
但是，本文指出并论证了下述结论：黎曼可积函数的连续函数必定黎曼可积。
This paper has drawn and proved the conclusion that continuous function of Riemann integrable function is certainly Riemann integrable.
第一章是本文综述部分，简要介绍了近可积系统的前沿现状和本文所做工作。
Chapter 1, we briefly introduce the near integrable systems and ist developments and the main results in this paper.
采用将圆电流磁矢势表达式中一部分展成级数，使被积函数变成可积分的函数。
A part of results on magnetic vector potential of circular loop are expanded, so the integral function is transformed to integrable series.
分析了诸多积分概念的共性，抽象出黎曼积分的定义，给出了黎曼可积的条件。
This paper sums up the common character of the concept of many integrals, abstracts the concept of Riemann integral and gives the integral conditions of the Riemann integral.
描述了一类平面2r机械臂的模型，利用哈密顿系统理论证明了该系统的可积性。
A 2r Planar Robot Manipulator system is described, whose integrability is proved by the theory of Hamilton system.
对二阶变系数非线性微分方程的常系数化给出两个使其可积的条件，并举例论证。
The two conditions of the second order nonlinear differential equation with variable coefficient are given and expounded with examples.
其次，运用2+1维的零曲率方程和屠格式得到了一类2+1维的多分量的可积系。
Secondly, a type of (2+1)-dimensional multi-component integrable hierarchy is obtained with the help of a (2+1)-dimensional zero-curvature equation and Tu scheme.
文章利用达布和理论，讨论了黎曼积分的可积性问题，给出了一个可积的充分必要条件。
Based on Darboux theory, this paper discussed the integrability of the Riemann Integral and provides a necessary and sufficient condition for integrability.
分析了证明拓扑空间有限可积性的一般方法及所依据的定理，并对一些具体的性质加以证明。
This paper analyses the general method of proving the productive property and the theorems on which it bases.
利用可积系统的方法研究3维球空间中的常中曲率(CMC)曲面，并给出了曲面的谱变换。
It is studied that the CMC surfaces in the sphere space of dimension 3 by means of integrable system and its spectral transformation is given.
给出一类特殊阿贝尔方程新的可积条件，实现了计算机对该类方程可积性及其精确解的自动判定。
A new integrable condition in a kind of special Abel equation is given in this paper. We can realize the special Abel equation integrability and accurate solution by computer.
给出一类特殊阿贝尔方程新的可积条件，实现了计算机对该类方程可积性及其精确解的自动判定。
A new integrable condition in a kind of special Abel equation is given in this paper. We can realize the special Abel equation integrability and accurate solution by computer.
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