可积条件

Recursion formulas for quantities at infinity in this system were presented.

同时，计算了一类三次系统的前6个赤道环量，得到了系统在赤道邻域的可积性条件及在赤道附近存在5个极限环的系数条件，给出了一个平面三次系统在赤道附近分支出5个极限环的计算实例，并在不构造Poincare环域的情况下，指出了极限环存在的位置。

On the basis of the coincident relation between a radar signal and a radar ambiguity function, an arbitrary bounded two-dimensional function of intergrable square is presented as a necessary and sufficient condition for radar ambiguity function.

本文基于雷达信号和雷达模糊度函数间的一致关系，提出了任意平方可积的二维有界函数是雷达模糊度函数的充要条件，并且指出它包括了Wilcox提出的离散的可实现条件。

Furthermore, under the assumption that the covariant derivative of the sectionssatisfies the Lipschitz condition with L-average along the geodesic, the estimates of the radiiof convergence balls of Newton\'s method and uniqueness balls of singular points around thesingular points of sections on Riemannian manifolds are given.

当截面的协变导数满足沿着测地线的关于取正值非减可积函数L-平均的Lipschitz条件条件时，本文给出关于截面的Newton法的收敛球半径的估计，及在奇异点附近的关于截面的奇异点的唯一性球的半径的估计。

Under the assumptionthat the covariant derivative of the sections satisfies the Lipschitz condition with L-averagealong the piecewise geodesic, a unified convergence criterion for Newton\'s method and theradii of the uniqueness balls of singular points around the initial points of sections are es-tablished.

本章的主要内容包括以下两个方面：当截面的协变导数满足沿着分段测地线的关于取正值非减可积函数L-平均的Lipschitz条件条件时，本文给出了关于截面的Newton法收敛的统一判据，同时给出了在初始点附近的关于截面的奇异点的唯一性球的半径的估计。

The integrability conditions and coefficient conditions for the appearance of 5 and 6 limit cycles from the neighborhood of the equator are obtained. An example of cubic system with 6 limit cycles bifurcating from the equator is given for the first time.

同时计算出系统的前6个赤道环量，得到了系统在赤道邻域的可积性条件及在赤道附近分支出5个和6个极限环的系数条件，从而首次给出了一个平面三次系统在赤道附近分支出6个极限环的计算实例。

In §2, four met0hods for solving the integrable second order homogeneous linear ordinary differential equation with variable coefficientsy +py'+Qy=0 are given. Thus, the equation can be solved by means of elementary integrals and algebra.

给出了二阶变系数线性方程y＂＋py＇＋Qy＝0在可积的条件下的几种不同的求解方程，从而说明了这种可积的二阶方程不仅能用初等积分法求解而且也可以把它代数化，并使其通解公式化。

This paper discusses the conditions of integrability of the function and study how to use the application of relevant theorem to determine the specific function of the integrability, and other related issues.

本文探讨了函数可积性条件以及如何应用相关定理来判定特殊函数可积性等相关问题。

It expands Lebesgue characteristic of integrable function of Riemann through the definition of gather zero measure and builds up the theory of many integral calculus.

通过定义多维零测度集将可积函数的特征扩展到多维情形，同样统一了多维情形的充分条件，建立了多维情形的可积性理论。

An analytic method to study the periodic motion of double pendulums is presented.

描述了一种平面自由运动的双摆，考虑动量矩和能量守恒的条件，根据刘维尔可积定理可知该系统的可积性。

In this paper, we give explicit constructions and formulations for harmonic maps from R1,1 into classical real semisimple Lie groups by using Darboux transformation. We also discuss pluriharmonic maps from complex manifoldsinto symmetric spaces and Willmore surfaces in Sn. By converting geometric conditions satisfied by these maps into integrable systems, and using the the-ory of integrable systems, we give explicit constructions for pluriharmonic maps from complex manifolds into symmetric spaces and the Willmore surfaces in Sn respectively. Finally, we classify hypersurfaces in Sn+1 with three distinct prin-ciple curvatures and zero Mobius form using the theory of Mobius geometry. The paper consists of four chapters.

本文首先利用Darboux变换的方法给出了从Lorentz平面R~(1，1)到经典实半单Lie群的调和映照的具体构造，并给出其显式表示；其次研究了复流形到对称空间的多重调和映照及球空间S~n中Willmore曲面，将这些映照所满足的几何条件转化为可积系统，然后利用可积系统理论分别给出复流形到对称空间的多重调和映照与S~n中Willmore曲面的构造；最后利用Mōbius几何的理论给出S~(n+1)中具有三个不同主曲率且Mōbius形式为零的超曲面的分类。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。