以下为句子列表：
英文: According to the simulation result, the characteristics of tooth profile such as undercut and convexity of pitch curve of the machined gears could be analyzed and judged, so that a sort of Intuitive judgment method was provided for designing and manufactu
中文: 根据仿真图形结果可以分析和判断所加工的非圆齿轮的齿形特征，从而为设计和制造节曲线封闭型外啮合非圆齿轮提供了一种直观的判断方法。
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英文: In the higher mathematics category, routine methods to work out the proof of an inequation are a flexible use of mathematical knowledge like monotonicity of functions, extremum values, maximum and minimum values, convexity function, medium value theorem,
中文: 摘要在高等数学範畴中，灵活运用函数的单调性、极值、最值、凸性函数、以及中值定理与泰勒公式、赫尔德不等式、施瓦兹不等式等数学知识，对不等式问题进行分析、构造与转化，是解决不等式的证明问题的常用方法。
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英文: Non-convexity is in general the main feature of the difficulties for solving these models for wastewater treatment network optimization.
中文: 它们是具有非凸性的复杂非线性数学规划问题，用现有的方法进行求解不能保证得到全局最优解。
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英文: They were as follows: cases located on the convexity of cerebellar hemisphere, 7 in the cerebellar-pontin angle, around the foramen magnum and attached to the transverse sinus. cases died after operation ( .9% ).
中文: 计小脑凸面例,小脑桥脑角7例,枕大孔区例及横窦部例。
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