中文摘要：

对按膨胀规律A-ABA和B-BBB生成的有限长度Cantor型人工DNA序列，采用统计方法研究了序列的净位移及其标准偏差、重标极差函数及其Hurst指数，并将结果与一维随机二元序列进行了对比，直接论证了Cantor序列具有关联、标度不变及自相似等性质．从Anderson紧束缚模型出发，采用重整化群方法研究了该序列的电子输运特性．研究表明具有好的输运效率的扩展态能在较宽的能量区间上存在，随着序列长度的增加，扩展态的能量区间变得更为细碎，但具有好的透射性的电子态数量只是略有减少，共振能态可以在较长的序列中存在，推测为Cantor序列中存在有较强关联的结果．不同长度Cantor序列的Lyapunov指数的相似性进一步证明了Cantor序列中存在有自相似性及标度不变性．

英文摘要：

For the Cantor-styled artificial DNA sequence constructed by following the inflation rule A→ABA and →BBB, using the one-dimensional random walk model and Hurst analysis, we calculate numerically the displacement and its standard deviation, the rescaled range function and the Hurst exponent. The results are compared with those of onedimensional random binary sequence. We show that Cantor-styled DNA sequence presents correlated behavior, scaling invariability, and self-similarity. In addition, according to the renormalization-group method, we study the charge transfer properties of Cantor-styled DNA sequence, including localization length, charge transmission coefficient and Lyapunov exponent. We find that some resonant peaks can survive in relatively long Cantor-styled DNA sequences, which also implies that there are long-range correlations in Cantor-styled DNA sequences.