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1·Are Infinite Dimensional Spheres Invertible?

无限维球面可逆吗？

2·In a highly developed alien society, the habitats are almost infinite dimensional space.

在一个高度发达的外星文明中，有着近乎无限维度的生存空间。

3·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。

4·In this paper, we expound a main distinction between finite dimensional space and infinite dimensional space.

本文阐述了有限维与无限维线性空间的主要差别。

5·In an infinite dimensional space there always exist two subspaces whose vector sum is different from their span.

在一无限空间中恒存在两个子空间，其矢量和与其张成空间不同。

6·This is helpful for us to understand the evolution rules of states for the infinite dimensional dynamical systems.

这有助于我们理解和认识无穷维动力系统的状态的演化规律。

7·Lattice systems and nonlinear wave equations are two kinds of very important infinite dimensional dynamical systems.

格点系统与非线性波动方程是两类很重要的无穷维系统。

8·In this paper, the necessary and sufficient conditions of controllability on a infinite dimensional semilinear system are given.

本文给出无穷维半线性系统能控的充分必要条件及其应用。

9·In this paper the problem of the controllability of a class of infinite dimensional linear systems with control energy constraint is discussed.

本文讨论控制器能量受限下一类无限维线性系统的精确零能控性问题，得到了这类能控性的充分必要条件。

10·In this doctoral dissertation, we mainly consider the long-time behaviors for the solutions of infinite dimensional dissipative dynamical systems in unbounded domains.

在这篇博士学位论文中，我们主要考虑无界域上的无穷维耗散动力系统的解的长时间行为。