Character sets of strings

Given a string S over a finite alphabet Σ, the character set (also called the fingerprint) of a substring S^′ of S is the subset CΣ of the symbols occurring in S^′. The study of the character sets of all the substrings of a given string (or a given collection of strings) appears in several domains such as rule induction for natural language processing or comparative genomics. Several computational problems concerning the character sets of a string arise from these applications, especially:

(1) Output all the maximal locations of substrings having a given character set.

(2) Output for each character set C occurring in a given string (or a given collection of strings) all the maximal locations of C.

Denoting by n the total length of the considered string or collection of strings, we solve the first problem in Θ(n) time using Θ(n) space. We present two algorithms solving the second problem. The first one runs in Θ(n²) time using Θ(n) space. The second algorithm has Θ(n|Σ|log|Σ|) time and Θ(n) space complexity and is an adaptation of an algorithm by Amir et al. [A. Amir, A. Apostolico, G.M. Landau, G. Satta, Efficient text fingerprinting via Parikh mapping, J. Discrete Algorithms 26 (2003) 1–13].     

Two connected inverse spectral transforms

We establish a transformation which connects the potentials of the one-dimensional Dirac and Klein-Gordon operators. This transformation links the solutions of the nonlinear evolution equations solvable by means of the two inverse spectral transforms which use the Dirac and Klein-Gordon direct and inverse spectral problems.     

柔性衬底上铝背电极制备及相关特性研究

采用射频磁控溅射技术在聚酰亚胺柔性衬底上制备硅基薄膜太阳能电池用铝背电板,研究了不同溅射功率和工作气压条件对铝电极薄膜性能的影响.利用原子力显微镜分析表征了薄膜的表面形貌和粗糙度,薄膜的电学性能和光学性能分别采用四探针测量仪和紫外可见近红外分光光度计进行分析表征.测试结果表明:随着溅射功率的增加,薄膜表面均方根粗糙度迅...