本文讨论了一类含有有限多条切换线的平面 Filippov 系统极限环在扰动下的保持性。假设该类平面 Filippov 系统的未扰系统含有一个极限环且它分别与每一条切换线横截相交一次，作者应用Diliberto 定理和由此引出的变分引理导出了极限环的特征指标的计算公式，并利用该公式讨论了系统极限环的稳定性及其在扰动下保持的条件。

In this paper we discuss the persistence of the limit cycle in a class of planar Filippov systems with multiple switching lines .The authors assume that the unperturbed system of the planar Filippov systems has a limit cycle that crosses every switching line transversally exactly once .By using Diliberto Theorem and Variation Lemma we derived the formula for the characteristic exponent .Then we give a condition for the stability and persistence of the limit cycle .

对于一类六次一致等时系统，给出原点为中心的充要条件，并证明从细焦点至多可分支出3个极限环；对于一类七次一致等时系统，给出原点为中心的充要条件，并证明从细焦点至多可分支出4个极限环。

For a class of six order rigid systems,the necessary and sufficient conditions for the origin to be center are given.And the maximal number of limit cycles bifurcating from the weak focus is proved to be 3 .For a class of seven order rigid systems,the necessary and sufficient conditions for the origin to be center are given.And the maximal number of limit cycles bifurcating from the weak focus is proved to be 4.

根据常微分方程定性及分支理论，对一类两种群均具有非常数收获率的、且具HollingⅡ类功能反应函数的、基于食饵种群的非线性密度制约的食饵-捕食系统进行定性分析，得出该系统平衡点的性态和极限环存在与否的条件，还分析了多极限环的情形。

Using qualitative and bifurcation theory of ordinary differential equations, in this paper, a Holling II prey-predator system was investigated based on the nonlinear density dependent prey and the two species with variant harvest rate. The behavior of the equilibrium-point of the system and the conditions where its limit cycle exists or not, was obtained.

钢管混凝土中由于膨胀剂的加入补偿收缩作用明显,并产生一定的膨胀应力,使核心混凝土与钢管壁紧密结合。在钢管的紧箍力下,核心混凝土处于三向受压状态,能与钢管协同工作,从而提高钢管混凝土构件的极限承载力。本文对膨胀剂掺量分别为0,4%,8%,12%的钢管混凝土试件轴压下环向应力和承载能力进行试验研究。结果表明:膨胀剂掺量的增加会导致钢管壁环向应力增大从而降低轴压下钢管的承载力,并非膨胀剂掺量越多钢管混凝土极限承载力越大,掺量为4%时钢管极限承载力最高;将钢管混凝土极限承载力计算公式应用于掺膨胀剂钢管混凝土计算结果偏小,会造成原材料的浪费。

Due to the addition of expansive agent,the compensating shrinkage of concrete-filled steel tube is obvious and certain expansion stress is produced,which makes the core concrete and steel tube wall integrate closely. In the steel pipe hoop stress,the kernel concrete was in the state of triaxial compression and could work with the steel tube,which improved the ultimate bearing capacity of construction member of concrete-filled steel tube. This paper adjusted the additive amount of expansive agent,and implemented experimental study of circumferential stress and bearing capacity in axial compression of concrete-filled steel tube members when additive amount of expansive agent was 0,4%,8%,12% respectively. Test results showed that the increase of expansion agent could make tube wall circumferential stress increase and the bearing capacity of steel tube decrease in axial compression,the ultimate bearing capacity of concrete-filled steel tube does not increase with additive amount of expansi

本文研究一类（n＋1）次多项式系统极限环的存在性及无穷远奇点的类型。根据微分方程几何理论计算焦点量，考虑了系统的中心焦点问题，利用旋转向量场与广义Li′enard系统理论，获得了系统极限环存在的充分条件。同时利用Poincar′e变换，分析了系统无穷远奇点的类型。这些工作突破了已有结论关于系统阶数的局限性，因而具有更广泛的应用范围。

In this paper, we investigate the existence of limit cycles and the types of critical points at infinity for a class of (n+1)-th polynomial systems. According to the geo-metrical theory of differential equation, by computing the focal values, the problem of center and focus is considered. By applying the theories of rotated vector field and generalized Li′enard system, a series of su?cient conditions are developed to guarantee the existence of limit cycles, and the types of critical points at infinity are also discussed by Poincar′e transformation. These works improve the results of the differential system. Therefore, it has wide range of application for accompany systems.