- 更多网络例句与凸等价关系相关的网络例句 [注：此内容来源于网络，仅供参考]
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At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational, basic, differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.
本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式，给出了这几个不等式的一些应用实例，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。
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At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational ,basic , differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality and Minkowski inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.
本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式和闵可夫斯基不等式以及这几个不等式的应用，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。
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It also provided the conditions for the existence of large cores of symmetric games. It proved the equivalence relation of convex games and monotonic symmetric games.
本章还给出了对称对策的广义核心存在的条件，证明了凸对策与单调对称对策的等价关系。
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Firstly, some analyses for the quadratic approximation to a quasiconvex function are presented. In particular, it is pointed out that their quasiconvexities are not equivalent.
本文对算法中的拟凸的二次近似作一些分析，相出了它的不等价性并分析了解序列中的 Minkowski凸体的关系。
- 更多网络解释与凸等价关系相关的网络解释 [注：此内容来源于网络，仅供参考]
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convex domain：凸域
convex curve 凸曲线 | convex domain 凸域 | convex equivalence relation 凸等价关系
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convex equivalence relation：凸等价关系
convex domain 凸域 | convex equivalence relation 凸等价关系 | convex function 凸函数