函数

We prove the equivalent conditions of completely monotone function, we also discuss the relationship of positive definite function, semi-positive definite function and completely monotone function when the function take values in a commutitive von Neumann algebras.

我们证明了完全单调函数的几个等价条件，并且讨论了取值于交换von Neumann代数的正定函数，半正定函数及完全单调函数之间的关系。

In this paper, complex valued harmonic conjugate function is defined, Cauchy Riemann equations of complex valued harmonic functions are considered.

定义了复调和函数的共轭复调和函数，给出了复调和函数的Cauchy—Rie－mann方程，同时讨论了它们与解析函数之间的关

The continuity and differentiability for composite function are the important content in advanced mathematics.

对高等数学中复合函数的连续性条件进行了弱化改进，得到了类似复合函数连续及在x0处极限存在的充分条件，对复合函数的可微性条件进行改进，得到了复合函数可微以及在x0处存在左右导数的充分条件。

These results show the corresponding relationship between the composite function and interior function and outer function.

本文讨论复合函数的性质，对复合函数在极限、连续性、可导性、可积性、有界性、奇偶性、周期性、单调性、极值等方面的性质进行了总结和进一步的探讨，得到一系列结果，这些结果描述了复合函数与其内外函数之间在相应性质上的关系。

To solve the third problem, the definition of T-revision function and RT-computation model are proposed, and it is proved that with the increase of revision time, T-revision function converges to revision function and T-revision function is computable.

作为对第3个问题的解决，作者提出了T-修正函数的定义和RT-计算模型，证明了随修正时间的增长，T-修正函数逼近修正函数，且T-修正函数是可计算的。

To solve the third problem, we present the definition of T-revision function and RT-computation model, prove that T-revision function converges to revision function with the increase of revision time and Trevision function is computable.

作为对第3个问题的解决，作者提出了T－修正函数的定义和RT－计算模型，证明了随修正时间的增长，T－修正函数逼近修正函数，且T－修正函数是可计算的。

Finally, the optimization warehousing allocation policy is achieved by digital simulation, which shows that expecting revenue is concave function of surplus capacity, and is also concave function of booking leading time, the opportunity costs is a non-increase function of surplus capacity, and is also is a non- increase function of booking leading time.

论文按照随机背包问题思路建立了考虑第三方仓储能力分配动态随机规划模型，对模型性质进行了分析，得到了基于阈值的舱位预订动态控制策略，并通过数值仿真，得知期望收益是剩余仓储能力的凹函数，是时间的凹函数；机会成本是剩余仓储能力的非增函数，是时间的非增函数。

Inequality proof of various ways, they were: use derivative testify inequality nature, Includes using functional monotonicity and extreme value, the function and the concave and convex inequality, proving is concave and convex function in the original definition of equivalent definitions and a lemma is proposed on the basis of relevant concave and convex function of several theorems about inequality, and briefly discusses how to use the definitions and theorems in proof of inequality.

不等式的证明方法多种多样，它们分别是：用导数性质证明不等式；包括利用函数单调性，极值与最值，函数凹凸性证明不等式，其中在给出凹凸函数原始定义等价的解析定义和一个引理的基础上提出有关凹凸函数关于不等式的几个定理，并简要阐述了利用定义和定理在证明不等式中的运用。

The convex function develeped so many years that convex functionals are now a class of very universal functionals.The kinetic energy in the classical is the most natural convex function.Others like entropy and so on are convex functions.The economic core is closely connected with the convex function.The western economic core question is the optimized question.The optimized theory has something to do with the convex function and the concave function.

凸函数的发展经年已相当完善其应用非常广泛，在古典力学中的动能，就是最自然直接的凸函数，其他如熵……等均是，连经济学的核心都与之有极密切相关，西方经济学的核心问题是最优化问题，最优化理论又与凸函数与凹函数密切相关。

In order to get the principle of cell distribution in buffer, the local rate function is obtained, which can be expressed in detail with the help of DuBoisReymond equation and conditional integral. This gives us the system's rate function.

为了能够分析缓存器中分组信息变化的规律，论文首先给出了主干系统的本地速率函数，利用变量积分的DuBois-Reymond方程，给出了本地速率函数所满足的微分方程，在条件积分的约束下求得本地速率函数表达式，由此求得系统的速率函数。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。