We determine the form of all semiflows of pairs of weighted quasi-arithmetic means, those over positive dyadic numbers as well as the continuous ones. Then the iterability of such pairs is characterized: necessary and sufficient conditions for a given pair of weighted quasi-arithmetic means to be embeddable into a continuous semiflow are given. In particular, it turns out that surprisingly the existence of a square iterative root in the class of such pairs implies the embeddability.

中文翻译：

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加权拟算术对对到半流中的可嵌入性

我们确定成对的加权半算术均值的所有半流的形式，即正二进数和连续数上的半流。然后表征这种对的可迭代性：给出了给定的一对加权的拟算术装置可嵌入连续半流中的必要和充分条件。尤其是，事实证明，令人惊讶的是，在此类对的类中存在平方迭代根意味着可嵌入性。