以下为句子列表：
英文: Based on one dimension flow theory and Lagrange method, the correlation of speeding rate of particles under gas flow drag with the size of particles and the length of Laval nozzle used for the gas and solid two-phase separation test apparatus was studied.
中文: 摘要采用一元流动理论和拉格朗日方法，研究了用于气、固两相分离试验装置的缩放喷管内，被气流拖曳的颗粒加速率与颗粒大小和缩放喷管长度的关系。
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英文: Based on the Rolle mid-value theorem, by using determinant method, the Lagrange mid-value theorem and Cauchy mid-value theorem are obtained, and some new results are discovered.
中文: 本文从罗尔中值定理出发，这用行列式理论，不仅证明了拉格朗日中值定理和柯西中值定理，还发现了一些新的结论。
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英文: Enforce essential boundary conditions using Lagrange multipliers.
中文: 用拉氏乘子加强本征边界条件。
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英文: Lagrange and Cauchy differential mean value theorem on open interval are obtained based on generalized Roll's theorem, which make it more expedient to study general character of function defined on open interval by means of derivative.
中文: 摘要基于推广的罗尔中值定理，得到有限开区间上的拉格朗日中值定理及柯西中值定理，使得利用导数研究开区间上函数的整体性态更为方便。
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英文: Lagrange believed that a mathematician did not thoroughly understand his work until he had made it so clear that he could go out and explain it to the first person he met on the street.
中文: 拉格朗日认为，一个数学家，只有当他走出去，对他在街上遇到的第一个人清楚地解释自己的工作时，他才算完全理解了自己的工作。
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