吴小宁^*

（  无锡市委办公室，无锡 214131；  ）

摘要： 利用加乘系运算可对实数域中的初等函数进行更精细的分类. 至多2级函数具有更独特的单调性以及更好判断的积分散敛性. 把初等加乘系运算改造成初等加乘系化变后, 还可在一般的复直线上观察到最初出现在实数集上的现象. 如果限定在正整数集上, 任意泛加乘系化变构成的单变都具有初等单变在复直线上的类似性质.
关键词： 化变论, 广义乘, 超运算, 初等函数, 单变

WU Xiaoning^*

（  Wuxi municipal party committee office, Wuxi 214131；  ）

Abstract： Based on additive-multiplicative-operations, the elementary functions in real number field can be classified more detailedly. At most 2-grade functions have more uniqu monotonicity and better character of convergence and divergence for infinite integral. After turning elementary additive-multiplicative-operations to elementary additive-multiplicative-huabians, a particular phenomenon in real number set can be reconstructed in arbitrary complex line. Within positive integer set, any alone-bian formed by extensive additive-multiplicative-huabian has the character similar to elementary alone-bian in complex line.
Keywords： huabian theory, general multiplication, hyperoperation, elementary function, alone-bian

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