单调函数

It shows that all properties of fuzzy number and fuzzy-valued function which relating to distance can be obtained by this family of standard bounded monotone function.

进而，模糊数空间和模糊值函数空间上的与距离相关的所有性质都可以在一类单调函数类上得到。

Monotone functions; functions of bounded variation and Borel measures; absolute continuity; differentiation and integration; convex functions; semicontinuity; Borel sets; properties of the Cantor set.

单调函数；囿变函数；绝对连续性；微分和积分；凸函数；半连续性；博雷尔集类；康托集的性质

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 chapter 2 the strong deviation theorems for functions of series of discrete random variables are given. Here we construct a moment generating function and a convergent martingale .

本文第二章用矩母函数构造一收敛鞅，利用截尾法和单调函数的性质，证明了离散型随机变量序列泛函的强偏差定理。

According to the structured element representation theorem of fuzzy number and fuzzy-valued function, we obtained one-to-one isometric mapping from the family of standard bounded monotone function with same monotonic formal on [-1, 1] to the fuzzy number space, and proved they are homeomorphic.

在模糊值函数的模糊结构元表述理论的基础上，利用[-1，1]上同序标准单调函数类上的距离诱导出模糊值函数空间上的距离，证明了模糊实数空间与[-1，1]上同序单调函数类同胚。

It is easy to see that the composite of two monotone mappings is also monotone.

容易看出两个单调函数的复合也是单调的。

Also, it is proved to be monotonic function.

通过引入一个无量纲参数——单位水面宽度，对梯形明渠正常水深的基本方程进行恒等变形，得到了求解单位水面宽度的超越函数，并证明该方程为单调函数。

The Legendre transformation generated by uis 〓where uis a convex-monotone function,〓 is the normal mapping of u.

引进函数u的Legendre变换〓（3）这里u为凸单调函数，〓为u确定的法映射。

The new algorithm uses the particle aggregation quality to judge that if the particles in the swarm are congregative so much,then apply the differential evolution to mutate the self prevenient best position of each particle,in order to realize the aim of preserving the varieties of the swarm.

该算法对于单调函数、严格凸或单峰函数，能在初始时很快向最优值行进，但在最优值附近收敛较慢。对于多峰函数，则更容易出现所谓&早熟&现象，即局部收敛[3]。粒子群算法出现&早熟&现象的主要原因是缺乏种群多样性。

Then the above results are extended to the general form of quasi monotone decomposition. In conclusion, we give the necessary and sufficient conditi...

最后将上述结果推广到布尔函数拟单调分解的一般形式，给出一个布尔函数可以分解成 k个单调函数的逻辑组合的充分必要条件。

What are your goals and strategies for growth?

你的成长目标和策略是什么？

And unto the angel of the church in Sardis write; These things saith he that hath the seven irits of God, and the seven star I know thy works, that thou hast a name that thou livest, and art dead.

3：1 你要写信给撒狄教会的使者，说，那有神的七灵和七星的，说，我知道你的行为，按名你是活的，其实是死的。