• Journal of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.453-467
• /
• 1997

A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.

• Steel and Composite Structures
• /
• v.19 no.3
• /
• pp.569-583
• /
• 2015

Recent years, explosive welding structures have been widely used in many engineering fields. The bonding state detection of explosive welding structures is significant to prevent unscheduled failures and even catastrophic accidents. However, this task still faces challenges due to the complexity of the bonding interface. In this paper, a new method called dual-tree complex wavelet transform based permutation entropy (DTCWT-PE) is proposed to detect bonding state of such structures. Benefiting from the complex analytical wavelet function, the dual-tree complex wavelet transform (DTCWT) has better shift invariance and reduced spectral aliasing compared with the traditional wavelet transform. All those characters are good for characterizing the vibration response signals. Furthermore, as a statistical measure, permutation entropy (PE) quantifies the complexity of non-stationary signals through phase space reconstruction, and thus it can be used as a viable tool to detect the change of bonding state. In order to more accurate identification and detection of bonding state, PE values derived from DTCWT coefficients are proposed to extract the state information from the vibration response signal of explosive welding structure, and then the extracted PE values serve as input vectors of support vector machine (SVM) to identify the bonding state of the structure. The experiments on bonding state detection of explosive welding pipes are presented to illustrate the feasibility and effectiveness of the proposed method.