几类强弱缓冲算子的构造方法及其内在联系

基于最基本的缓冲算子x(k)d=∑ni=kωix(i)/∑ni=kωi变形,获得了几类范围大大拓宽的实用缓冲算子的构造方法,并揭示了这几类缓冲算子的内在联系.同时揭示了强化缓冲与弱化缓冲的对应关系,即指数γ由正到0,由0到负的变化,导致缓冲算子由弱(强)化到不变化,由不变化到强(弱)化的过程,揭示了由量变到质变的过程.研究表明,现有的大量缓冲算子都是所构造的缓冲算子的特例,此外还包括许多与常见文献中类型迥然不同的新算子.

The Constructing Methods of Several Kinds of Strengthening and Weakening Buffer Operators and Their Inner Link

Based on the deformation of the most basic buffer operator x（k）d=n∑i-kωix（i）/n∑i-kωi,the constructing methods of several kinds of new practical buffer operators in which the scopes are greatly broadened are given in this paper,and the inner link among these kinds of buffer operators is proposed. At the same time,the corresponding relation between the strengthening buffer and the weakening buffer is revealled. The changes of index γ,from positive to 0 and from 0 to negative,lead to the changes of buffer operators from weakening （strengthening） to invariablenes and from invariablenes to strengthening（weakening）,which shows the process from the quantitative change to the qualitative change. Studies show that a great amount of existing buffer operators are all special cases of these constructed buffer operators. Moreover,it includes a lot of new operators different from the types in common literatures.