名词
中文翻译：巴拿赫流形
同义词：
['Banach manifold', 'Banach manifold', 'Banach manifold']
例句：
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1. In the studyof differential equations, Banach manifolds play a crucial role in finding solutions to complex problems.
在研究微分方程时，巴拿赫流形在解决复杂问题中起着至关重要的作用。
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2.The theory of Banach manifolds is fundamental to the development of modern control systems.
巴拿赫流形理论是现代控制系统发展的基础。
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3. The research on Banach manifolds has led to significant advances in machine learning and data analysis.
巴拿赫流形的研究为机器学习和数据分析带来了显著的进步。