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Then we study holomorphic vector bundles with trivial pull-back on nonprimary Hopf manifolds, of which the fundamental group is 〓, get the filtrable property and the Structure Theorem.

然后我们研究了具有Abel基本群〓的非主Hopf流形上具有平凡拉回的全纯向量丛E，得到其可滤性以及结构定理。

We establish an asymptotic Lipschitz homotopy invariance theorem for these K-homology groups and K-theory groups. We show that the asymptotic index maps are isomorphisms for the asymptotically scaleable spaces, which include Euclidean cones, simply connected complete Riemannian manifolds with nonpositive curvature.

我们证明了这些K-同调群和K-理论群具有渐近Lipschitz同伦不变性；对于渐近可标度的几何空间（包括欧氏锥、单连通非正曲率完备黎曼流形等），证明了渐近指标映射为同构。

In this paper,we determine J_~(2~k+2v)by constructing ingeniously indecomposable manifolds M,which can be generators in MO_*,and defining appropriate(Z_2)~k-action on M.

在本文中，我们通过巧妙地构造流形M，使其所在的上协边类不可分解，从而可以作为上协边环MO_*的生成元，并在M上定义适当的(Z_2)~k作用使其不动点集F具有常余维数r，决定了未定向上协边环MO_*的理想J_~(2~k+2v)。

The idea of coarse geometry is motivated by the heat equation approach to the index theorem on noncompact manifolds.

用粗几何的观念研究非紧空间上的指标问题，这种想法来源于指标定理的热方程方法的启发。

These results make it possible to analyze the control systems on infinite dimensional manifolds.

这些结果使得在无穷维流形上进行控制系统的分析成为可能。

The method is a com- bination of the theory of normally hyperbolic invariant manifolds and an appropriate continuation method.

我们将在第四章利用法向双曲不变流形理论和Kopell，Chicone的延拓方法，来证明2个自由度的非哈密顿扰动系统的2维共振不变环面的存在性定理。

By virtue of the invariant manifolds and conservative property of Hamiltonian system, we construct a"switching algorithm"to compute the periodic solution of equation (4) when the dispersion distribution σ is periodic and piecewise constant function.

4运用不变流形的分析方法和哈氏系统的守恒性质，给出了当色散分布σ为周期的分片常数情形计算方程(4)的周期轨的一个"开关算法"。

The work of Simgroup on invariant manifolds and dynamical systems theory in the late 1980?

在星际组不变流形和理论工作的动力系统在80年代后期？

We obtain these theorems on the isometry groupsof pinched Hadamard manifolds under Condition A.

特别是在三维双曲情形，条件A等是自然满足的，因此我们所得到的代数收敛性定理、极限定理和收敛性定理与平面上的经典情形一致。

The Laplacian on Riemannian manifolds is an essential linear operator, and it is also the main object to be studied of Geometric A...

Riemann流形上的Laplace算子是一个重要的线性算子，也是流形上几何分析研究的主要对象之一。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。