以下为句子列表：
英文: By the comparison theorem, a series of properties of the backward-forward differential utility process is gotten, such as time consistence, monotonicity with respect to the terminal value, monotonicity with respect to the consumption and concavity.
中文: 运用比较定理，还证明了正倒向随机微分效用过程的时间一致性、终值单调性、消费单调性和凹性等有关性质。
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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: In this paper, some new concepts are introduced for functional monotonicity and co-coerciveness of set-valued mappings, and variously possible implication relationships are studied among known and new concepts.
中文: 摘要本文介绍几个新的集值映射的函数单调性和馀强制性概念，并讨论它们与已有概念间各种可能的蕴含关系。
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英文: In this thesis, we report recent results on existence for complementarity problems in infinite-dimensional spaces under generalized monotonicity are reported.
中文: 中文摘要在本论文中，报告最近对于在无限微空间上广义单调性算子的互补性问题的存在结果。
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英文: The monotonicity and logarithmically complete monotonicity properties for the Gamma function are obtained.
中文: 摘要伽玛函数的单调性质和对数完全单调性质被获得了。
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