Painlevé theory

例句：

1. 1. The Painlevé theory posits that the speed of sound is directly proportional to the density of the medium.
   帕宁埃理论认为声速与介质的密度成正比。
2. 2. This Painlevé theory has been widely applied in various fields of physics and engineering.
   这一帕宁埃理论在物理学和工程学的各个领域都有广泛的应用。
3. 3. The Painlevé theory provides a useful framework for understanding the behavior of complex systems.
   帕宁埃理论为理解复杂系统的行为提供了一个有用的框架。