improved lower bound的用法和样例：
例句
- Based on the results, we calculate a upper bound or a lower bound of the Hausdorff dimension of some self-affine sets.
利用它们可方便地求出某些自仿集维数的上界或下界。 - Input values outside the range are replaced by the lower bound replacement value, or the upper bound replacement value.
范围之外的输入值将由下界替换值或上界替换值进行替换。
