查询词典 codimension

In this chapter, under the penalty functional satisfies the local Lipschitz condition, by using the Ekeland's variational principle and the properties of finite codimension, the Pontryagin's maximum principle of corresponding optimal control problem whose control variable is the harvesting rate and the input rate respectively is obtained.

本章在性能指标泛函满足局部Lipschitz条件下，利用Ekeland变分原理和有限余维的性质，证明了控制变量分别为收获率和输入率的相应控制问题的Pontryagin极大值原理。

The emphasis was placed on the bifurcation problem of impact vibration systems, including codimension one and two bifurcations, flip bifurcations and Hopf bifurcations.

本文着重研究碰撞振动系统的分叉问题，包括余维一分叉、余维二分叉、倍化分叉和Hopf分叉等。

In the first part, for competitive discrete-time dynamical systems on a strongly ordered topological vector space, we prove that any α-or ω-limit set is unordered and lies on some invariant hypersurface with codimension one, which generalizes M.

在第一部分中，对于强序拓扑向量空间上的竞争离散动力系统，我们研究了极限集的序结构和极限集的几何位置，证明了任何α-或ω-极限集是无序的且位于一个完全无序的，余维为1的不变Lipschitz流形上。

Then we use above mentioned theory to study degenerate bifurcations of codimension two in nonlinear oscillator under combined parame-tric and forcing excitation. Thereby stability problems with double zero eigenvalues can be solved.

然后利用上述理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉，从而解决了当解具有两个零特征值时解的稳定性问题。

We use the method of multiple scales to study local bifurcations of this system and obtainbifurcating response equation,transition sets and eight different diagrams of bifurcatingresponse curves.We find that some singular points in bifurcation set are codimension twodegenerate.

首先利用多尺度法研究了这个系统的局部分岔问题，得到了分岔响应方程、局部分岔集和8种分岔响应曲线，并且发现在分岔集上有一些奇点是余维2退化的。

Then we use theory ofnormal form and universal unfolding and Melnikov's and Petrov's methods to studydegenerate bifurcations of codimension three and global bifurcations in the averagedequations.

然后利用规范形理论、普适开折理论、Petrov方法和Melnikov方法研究了平均系统的余维3退化分岔和全局分岔。

Clearance ; vibro-impact ; periodic motion ; stability ; codimension two bifurcation ; chaos

间隙；冲击振动；周期运动；稳定性；余维二分岔；混沌

The existence of saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation is studied clearly, and high codimension bifurcation may emerge for some special parameters.

文中我们全面分析了鞍结分支、Hopf分支和Bogdanov-Takens分支在各种参数条件下的存在性，还发现在一定参数条件下可能出现高余维分支。

First we use the method of multiple scales tostudy local bifurcations of this system and obtain transition sets and bifurcating responsecurves.Then we use theory of normal form and universal unfolding and Melnikov'smethod to study further degenerate bifurcations of codimension two and globalbifurcations.

然后利用规范形理论、普适开折理论和Melnikov方法进一步研究了余维2退化分岔和全局分岔，并且获得了一些有意义的结果，提出了不完全普适开折的问题。

7The local and global bifurcations and degenerate bifurcations of codimension threefor a nonlinear oscillator under combined parametric and forcing excitations are studiedin detail.

7研究了参数激励与强迫激励联合作用下非线性振子的局部分岔、余维3退化分岔和全局分岔。

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。