contraction semi-group

例句：

1. 1.In the study of mathematical analysis, the concept of a contraction semi-group plays a crucial role.
   在数学分析研究中，收缩半群的概念起着至关重要的作用。
2. 2.The theory of contraction semi-groups has been applied to various fields such as control systems and signal processing.
   收缩半群理论已被应用到控制系统和信号处理等领域。
3. 3.The research on contraction semi-groups is still ongoing, with many open questions that need further exploration.
   收缩半群的研究仍在进行中，有许多尚未解答的开放问题需要进一步探索。