1)  generalized function

1.
The duality property of several kinds of generalized functions;

2.
This article using AHP to determine the weighting of index,using generalized function to nondimensionalize the value of index,then calcalute the systematic evaluation index.

3.
First, by comparing with the definition of ordinary function, the definition of the general function and the equality of two generalized functions are introduced.
冲激(偶)函数类性质历来是《信号与系统》教学中的难点,也是学生不易理解的内容,为此,教学策略采用"三步走"的方法:首先与普通函数定义方法相比较引出广义函数定义和"两广义函数相等"的概念,继而用高等数学的微积分知识证明冲激(偶)函数类的"抽样"性质,最后以前两者为基础证明冲激偶函数的"筛选"性质。
2)  generalized functions

1.
The theoretical proof is based on the theory of Schwartz generalized functions.

2.
Utilizing perturbation method, stochastic equations are changed to be a series of deterministic equations, In the meantime stochastic boundary conditions become deterministic boundary conditions considering characters of generalized functions.

3.
On the basis of the classical valuation method of generalized functions, the set value of a generalized function has been defined by the equivalent value mode and the uniform convergence method.

3)  distribution [英][,dɪstrɪ'bju:ʃn]  [美]['dɪstrə'bjuʃən]

1.
Pan-Linear Distributions and Its Differentiation;

2.
In this paper,we present first a class of distributions multiobjective programming model (short for DMPM) which is in prospect of applying.

3.
For the purpose of expanding use scope of wavelet transform, this paper discusses wavelets transform under the framework of distribution and gives some conclutions of wavelets transform in S space.

4)  distribution function

1.
For iviting and requesting from the chief editor of this journal, this paper is written for replying to some readers challenge on those papers published on this journal in the past, and their contents are about the issue of distribution function δ(x).

5)  general function

6)  Generalized AND-OR function

 广义函数generalized function，distribution   古典函数概念的推广。关于广义函数的研究构成了泛函分析中有着广泛应用的一个重要分支。历史上第一个广义函数是由物理学家P.A.M.狄拉克引进的，他因为陈述量子力学中某些量的关系时需要引入了“函数”δ（x）：当x≠0时，δ（x）＝0，但。按20世纪前所形成的数学概念是无法理解这样奇怪的函数的。然而物理学上一切点量，如点质量、点电荷、偶极子、瞬时打击力、瞬时源等物理量用它来描述不仅方便、物理含义清楚，而且当它被当作普通函数参加运算，如对它进行微分和傅里叶变换，将它参与微分方程求解等所得到的数学结论和物理结论是吻合的。这就迫使人们要为这类怪函数确立严格的数学基础。最初理解的方式之一是把这种怪函数设想成直线上某种分布所相应的“密度”函数。所以广义函数又称为分布，广义函数论又称分布理论。用分布的观念为这些怪函数建立基础虽然很直观，但对于复杂情况就又显得繁琐而不很明确。后来随着泛函分析的发展，L.施瓦尔茨（1945）用泛函分析观点为广义函数建立了一整套严格的理论，接着I.M.盖尔范德对广义函数论又作了重要发展。从此，广义函数被广泛地应用于数学、物理、力学以及分析数学的其他各个分支，例如微分方程、随机过程、流形理论等等，它还被应用到群的表示理论，特别是它有力地促进了偏微分方程近30年来的发展。