函数的连续性

Math: any binary relation that is complete, transitive, and continuous can be represented by a continuous real-valued utility function

效用指数，效用函数的存在性：理性是必要条件；连续性是充分条件，效用函数也是连续函数。

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。

This article is mainly discussed the relation between some important concepts and conclusions about the Limit of Sequence, the Limit, Continuity ,Differentiability, Integrability of Function, the Infinite Series , and the Limit, Continuity, Derivativeness,Differentiability of Multivariable Function ,as well as the Multiple Integral, and Integral with parameter .

本文对数列极限，一元函数的极限、连续性、可微性、可积性，无穷级数，多元函数的极限、连续性、可导性、可微性以及重积分，参变量积分中的一些重要概念和结论之间的关系进行了一些探讨，每一个问题都作了适当说明或举出反例，并对一些相关的内容进行了讨论，得到若干结果。

After studying the characteristics of Particle Swarm Optimization,Particle Swarm Optimization is used in wavelet domain to optimize the thresholds,and garrote shrinkage function is used to process wavelet decomposition coefficients,which overcome the shortcoming of discontinuity of hard-threshold and decreased the fixed bias of soft-threshold.

研究粒子群优化算法的特性，将其应用于小波域，对阈值进行寻优，并使用garrote阈值函数量化小波分解系数，而garrote阈值函数既克服了硬阈值函数的不连续性，也减小了软阈值函数存在的恒定偏差。

In Chapter 4, we give a new proof of the local Lipschitz continuity of H-convex functions on the Heisenberg group. For a Carnot group of step two, we obtain a characterization of H-convex functions and prove that H-convex functions are locally Lipschitz continuous.

第四章，我们导出了Heisenberg群上H-凸函数的Lipschitz连续性的一个新证明，对于二阶Carnot群，我们给出了H-凸函数的一个特征并证明了Carnot群上H-凸函数是局部Lipschitz连续函数。

Criteria were derived for functions to be quasiconvex under lower semicontinuity or upper semicontinuity conditions by Mukherjee and Yeddy .

Mukherjee和Yeddy在文献[1]中，分别在函数的下半连续性和上半连续性的条件下，对于函数的各种拟凸性给出了一些判别方法。

And the sufficient and necessary conditions of the monotone set function which is continuous of the empty set and the full set are given.

李军[6]引入了强序连续性概念，证明了单调测度空间上实值函数的Lebesgue定理成立的充要条件是单调集函数具有强序连续性。

The function's uniform continuity is one of the most important theories in the mathematics analysis course.

弄清函数的一致连续性的概念和掌握判断函数一致连续的方法无疑是学好函数一致连续性理论的关键。

In chapter 4, we discuss further some properties of generalized fuzzy inte-grable functions, and prove that not only generalized fuzzy integrable functions have the weak integral absolute continuity, but also sequences of generalized fuzzy integrable functions have uniform weak and absolute continuity.

进一步讨论了广义模糊可积函数的某些性质，证明了在广义三角模S满足(S-1)的条件下，不仅广义模糊可积函数具有弱积分绝对连续性，而且广义模糊可积函数列具有一致弱绝对连续性。

In mathematics the smoothing of a function is often measured with the continuity, or nth deriv-ation, of the function, and the more precise measurement is the Lipschitz exponent of afunction.

函数在某点的光滑程度可用其在这点的连续性和各阶导数描述，但更细致的描述是用函数在这点的Lipschitz指数来刻划的，而函数在一个区间上的光滑性则可以用函数的一致连续和导函数来考察，更精确的是用一致Lipschitz指数来考虑。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。