We show that every Sturmian word has the property that the distance between consecutive ending positions of cubes occurring in the word is always bounded by $10$ and this bound is optimal, extending a result of Rampersad, who proved that the bound $9$ holds for the Fibonacci word. We then give a general result showing that for every $e \in [1,(5+\sqrt{5})/2)$ there is a natural number $N$, depending only on $e$, such that every Sturmian word has the property that the distance between consecutive ending positions of $e$-powers occurring in the word is uniformly bounded by $N$.

翻译：我们证明每个Sturmian词均具有如下性质：其中出现的立方体的连续结束位置之间的距离始终有界于$10$，且该界是最优的。这一结果推广了Rampersad的结论——他证明了斐波那契词满足上界$9$。随后我们给出一个一般性结论：对于每个$e \in [1,(5+\sqrt{5})/2)$，存在仅依赖于$e$的自然数$N$，使得每个Sturmian词均满足：其中出现的$e$次幂的连续结束位置之间的距离一致有界于$N$。