Hao Zhi-feng

Superior-in-Status Analysis of Improved Genetic Algorithm for GTSP

Superiority in status relation (≻) can be used to rank the given EAs in terms of convergence capacity. The performance of an EA can be improved if it is modified to be superior in status to its original version. In this paper, the (≻) relation model is applied to analyzing the improvement of generalize-chromosome genetic algorithm (GCGA) for generalized traveling salesman problem (GTSP). Hybrid-chromosome genetic algorithm (HCGA) is superiority to GCGA. The numerical results also indicate that HCGA performs better and more steadied than GCGA in solving several GTSP instances. The case is the application example of the proposed relation model.

Modules Over Double Crossproducts of Skew-Hopf Pairs

The purpose is to study modules of double crossproducts D(X, A) of Skew-Hopf pairs (X, A). A sufficient and necessary condition for M to be D(X, A)-mod is shown. Relations between D (X, A)-mod and quantam Yang-Baxter A-mod or X-mod are revealed.

Free quadratic bialgebra

AbstractIn this paper, we obtain the following main theorem for a free quadratic bialgebraJ:(a)Forp≠0,J is a pointed cosemisimple coalgebra. Forp=0,J is a hyperalgebra.(b)Forp≠0 andq≠0,J has antipodeS iffp·q+2=0 andS(x)=x. Forp=0 orq=0,J has antipode andS(x)=×.(c)All leftJ*-modules are rational. Also, we give some applications in homological theory and algebraicK-theory.