We prove that the low dimensions of a class of Moran sets coincide with their Hausdorff dimensions and obtain a formula for the lower dimensions. Subsequently, we consider some homogeneous Cantor sets which belong to Moran sets and give the counterexamples in which their Assouad dimension is not equal to their upper box dimensions and packing dimensions under the case of not satisfying the condition of the smallest compression ratio .

中文翻译：

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一些Moran集的Assouad尺寸和较低尺寸

我们证明一类Moran集的低维与其Hausdorff维一致，并获得了低维的公式。随后，我们考虑属于Moran集的一些齐次Cantor集，并给出了在不满足最小压缩比条件的情况下，其Assouad尺寸不等于其上盒尺寸和包装尺寸的反例。。