Pontryagin number

例句：

1. 1. The Pontryagin number is a mathematical concept that plays an important role in the study of dynamic systems.
   庞特里亚金数是研究动态系统时的一个数学概念，起着重要作用。
2. 2.In the field of physics, the Pontryagin number is used to describe the stability of a system under different initial conditions.
   在物理学领域，庞特里亚金数被用来描述系统在不同初始条件下的稳定性。
3. 3.The Pontryagin number is also used in optimization problems to find the best solution that minimizes the objective function.
   庞特里亚金数还用于优化问题中，以找到最小化目标函数的最佳解。