中文摘要：

定义了光滑函数芽的弱有限决定性与弱无限决定性，对于右等价群及其两类子群，给出函数芽是弱决定的充要条件，并且证明了这三类弱有限决定性或弱无限决定性是等价的．

英文摘要：

In this paper, germs are defined, and of subgroups are studie Besides,it proves that equivalent. e weak finite determinacy and weak infinite determinacy of smooth function- e weak determinacy with respect to right-equivalence group and its two kinds Some necessary and sufficient conditions for the weak determinacy are given. ese three kinds of weak finite determinacy or weak infinite determinacy are