讨论了有限积空间上积映射的APOTP并证明无限积空间上移位映射具有APOTP。

We also discuss the APOTP of the product map on the finite product space and show that the shift map on infinite product space has the APOT p.

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研究迹映射的几个性质：保测度，可积，可反。

Some properties of trace map are studied, such as exemple measure-preserving, integrable and reversible.

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利用树的结构给出了X到Y的映射YZ，Sn以及矩阵积和式per（A）的一种计算方法和高效率计算机鼓轮的设计方法。

In this paper the authors give a kind of useful method that the structure of tree is applied in calculating permutation Sn, mapping YZ and permanent per(A) and designing high-efficient computer cam.

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