以下为句子列表：
英文: Based on the solution set, the optimal approximation to a given matrix is constructed, and the necessary and sufficient conditions for the solvability of the problem are given and the expression for the solution is provided.
中文: 讨论了用双中心矩阵反问题的解构造给定矩阵的最佳逼近问题，给出该问题有解的充分必要条件和解的表达式。
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英文: In this article the authors consider Canchy problem for quasilinear hyperbolic systems in 3-step completely reducible type, and the global smooth resolvability is obtained.
中文: 摘要本文对三步完全可化约拟线性双曲型方程组的整体经典解进行讨论，得到了整体经典解的存在性。
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英文: Its limited resource is well known; the other low solvability in water.
中文: 这主要有两个原因：首先，它的资源极为有限；其次，它的水溶性较差。
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英文: Some solvability conditions of periodic solutions are obtained for a class of first order superquadratic non-autonomous Hamiltonian systems in light of the minimax methods of critical point theory.
中文: 摘要运用临界点理论中的极小、极大方法得到一类超二次哈密顿系统的周期解的存在性的存在性定理。
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英文: The amount of catalyst can be reduced by selecting nice solvability catalyst, cutting down the remnant carboxyl amount of esterification and elevating polycondensation temperature.
中文: 选择溶解性能好的催化剂，降低酯化残存羧基量，提高缩聚温度，可减少催化剂用量。
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