This paper dealt with the existence of periodic waves for a perturbed quintic BBM equation by using geometric singular perturbation theory. By analyzing the perturbations of the Hamiltonian vector field with a hyperelliptic Hamiltonian of degree six, we proved that periodic wave solutions persist for sufficiently small perturbation parameter. It is also proved that the wave speed c 0 (h) is decreasing on h by analyzing the ratio of Abelian integrals, where h is the energy level value. Moreover, the upper and lower bounds of the limit wave speed are given.
Gentile statistics, which is famous for its advantages in dealing with composite particle systems, is a kind of fractional statistics. Lately, researchers are concentrating on finding real systems that obey Gentile statistics. Five years ago, we discovered that the cyclic hydrocarbon polyenes called N-annulenes in the Hückel model had certain correspondence with Gentile oscillators. According to their rotation and dihedral symmetry, these two systems had the same energy levels and partition functions. In this paper, we give further discussions. We discuss the transformations of wave functions between N-annulenes and Gentile oscillators, the creation and annihilation operators in site pictures of N-annulenes, the coherent state, and the mathematical proofs of the intermediate commutation relations of operators. All of our works prove that N-annulenes in the Hückel model are real Gentile statistical systems and offer a new algebraic method to deal with the problems of electron-electron and electron-phonon interactions.
Industrial design was a highly integrated interdiscipline, which combined the scientific rationality and artistic emotion. Meanwhile, it was under the limitation and influence of many factors, such as environment, social morphology, cultural concepts, economy. Also, it was a creative design activity with the integration of function, form, technology and art. Industrial design was an interdiscipline which combined the artistic innovation and engineering discipline. This paper aimed at the current situation of industrial design education, then based on the analysis of its characteristics and discussed both the necessity of multidisciplinary cross and the interdisciplinary cross integration method of industrial design education in order to cultivate the applied talents who could adapt to the era development for complex industrial design. Thus, it could better promote and adapt to the development of economy, technology and other comprehensive national power in China.
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