次极限

In the fifth section, we obtain some sufficient conditions under which a class of a planar quintic system has at most two limit cycles by transforming it into Abel equation.

第五章讨论了一类可化为Abel方程的五次多项式系统的极限环的个数，得到此类平面五次多项式系统至多存在两个极限环的充分条件。

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。

Research results show that: 1 The FLSD is basically path independent whether is for steel or for aluminium; 2 Shape of the forming limit curve in stress space is sensitive to the type of material model used in transformation form FLD to FLSD; 3 the anisotropy of sheet metal has considerable influence on the FLSD; 4 The application of the FLSD in sheet metal processes optimization was considered to be effective and more precise.

钢板和铝板应该分别采用不同的材料模型进行转换。3）板料各向异性性能对板料成形极限有影响，在使用FLSD时应该考虑板料的各向异性情况；4）FLSD在应用于多道次成形零件的有限元分析时，由于其具有的与加载路径无关的特点，因此比通常用的FLD更加准确可靠。本课题的研究为以后在板料成形仿真中，使用应力成形极限曲线代替应变成形极限曲线，提供了理论和试验依据。

The uncertain relationship between the double limit and the quadratic limit is explained and the determination methods to the nonexistence of the odd function's limit are given.

本文阐明二重极限与二次极限的不确定关系，给出齐次函数的极限不存在的判定方法。

The second chapter is the main part of this paper, in which the formulation of the Riemann boundary value problem of non-normal type on the real axis, the solution method of homogeneous problem, the relation between the two kinds of different derivatives and the inhomogeneous problem will be thoroughly given. In this paper, the solution and the solvability of the Riemann boundary value problem of non-normal type on the real axis will be given. Furthermore, it is shown that the twokinds of derivatives of the function Ψ are existing and equivalent in the case ofthe solution about the original problem, therefore, we get uniformly Hermite interpolatory polynomial. The relation between the two kinds of different derivativesof the function Ψ are similar for smooth closed contours by means of the same proof.

第二章是本文的主要部分，分别给出了实轴上一类非正则型Riemann边值问题的提法、齐次问题的解法、两种导数的关系及非齐次问题的求解，本文运用杜金元教授[11]的方法获得了实轴上非正则型Riemann边值问题的封闭解及可解性条件，且在问题可解的情况下论证了函数Ψ的非切向极限导数和Peano导数存在且相等，从而获得了统一的Hermite插值多项式，同样关于封闭曲线上非正则型Riemann边值问题，采用本文论证方法证得了函数Ψ的非切向极限导数和Peano导数存在且相等，从而较好地统一了[10]、[11]中的Hermite插值多项式。

Using the recursive formula and computer algebra system-Mathematica, the first six singular point values at infinity of the system are given.

对一类三次系统给出了计算无穷远点奇点量的递推公式，并在计算机上用计算机代数系统Mathematica推导出该系统无穷远点的前6个奇点量，进而导出了无穷远点成为中心和最高阶细焦点的条件，在此基础上得到了一个三次系统在无穷远点分支出6个极限环的实例，指出了极限环的精确位置。

In chapter 3,we dig out two families of invariant quartic curves of a quadratic system.

第五章讨论向量场具有对称中心的二次系统，利用系统的不变双曲线及不变四次曲线，我们确定了一个对应极限环（1.1）分布的二维参数区域，其边界的构成为如下几种常见的极限环分枝：霍夫分析，庞加莱分枝，同宿分枝和异宿分枝。

If there is not reflexive dependent relation among the head literals of the all k free clauses occurred in the program, then the k—th limit is its supported model.

如果G中含k个自由子句，并且这k个子句头中出现的文字不含自反依赖关系，则它的k次极限就是其支持模型。

Recently, Professor Liu Wen and his associates study the strong law of large numbers for Markov chain fields on trees. But for the nonhomogeneous Markov chain fields ,they only study the even-odd Markov chain and non-symmetric Markov chain. However, this article goes in the normal nonhono-geneous Markov chain fields and gets a class of limit theorems for the functions of two variables of finite nonhomogeneous Markov chain fields. Some limit theorems on the frequences of states and ordered state couples are obtained by several corollaries.

最近刘文教授及其合作者对树上的马氏链场的极限定理作了研究，对于非齐次马氏链场，仅对其中的奇偶马氏链场和非对称马氏链场作了研究，本文讨论了一般的非齐次马氏链场的极限性质，得到了关于Caylay树上有限非齐次马氏链场二元泛函的一类极限定理，作为推论得到了关于状态与状态序偶出现频率的极限定理。

It, therefore, suggested that using NIRS, energy metabolic level in local working muscles and anaerobic threshold could be determined, as well as athletes aerobic capacity during submaximal exercise could be evaluated.

结果表明，采用近红外线光谱技术无损伤测定局部工作肌群的代谢水平，评定运动员在次极限运动时有氧工作能力是可行的，它为无损伤测定无氧阈提供了一种新的途径。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。