以下为句子列表：
英文: Based on the sizeof the set of perturbed minimal points in the variational principle, the differentiability of lower semicontinuous functions is examined by means of approximation of the infconvolution sequence.
中文: 摘要通过函数的下卷积函数列的逼近方法，在变分原理中从扰动最小值点集的“大小”入手，研究了下半连续函数的可微性。
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英文: Experimental results show that this method is highly effective and efficient, and moreover it has no requirements on the differentiability and continuity of the objective function, and consequently does not need to perform complex matrix calculations, so
中文: 结果表明，智能算法简单有效，对目标函数没有可微性和连续性要求，避免了复杂的梯度矩阵计算，适合在复杂的非线性水动力系统辨识中应用。
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英文: Following from the results of sensitivity analysis of standard eigenvalue problems, the differentiability of semisimple multiple eigenvalues of nonsymmetric generalized eigenvalue problems is proved, and the derivatives of semisimple multiple eigenvalues
中文: 摘要以标准特征值问题灵敏度分析的有关结论为基础，证明了单参数非对称广义特征值问题半单重特征值的可微性，给出了特征值导数的表达式和特征向量的级数展开式。
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