The Leibniz-Hopf algebra is the free associative algebra with one generator in each positive degree and coproduct given by the Cartan formula. Quasi-symmetric functions are a generalisation of symmetric functions [7],...The Leibniz-Hopf algebra is the free associative algebra with one generator in each positive degree and coproduct given by the Cartan formula. Quasi-symmetric functions are a generalisation of symmetric functions [7],and the algebra of quasi-symmetric functions appear as the dual of the Leibniz-Hopf algebra. The Leibniz-Hopf algebra and its dual are word Hopf algebras and play an important role in combinatorics, algebra and topology. We give some properties of words and consider an another view of proof for the antipode in the dual Leibniz-Hopf algebra.展开更多
In the effective-mass approximation, using a simple two-parameter wave function and a one-dimensional （ID） equivalent potential model, we calculate variationally the binding energy of an exciton bound to a neutral d...In the effective-mass approximation, using a simple two-parameter wave function and a one-dimensional （ID） equivalent potential model, we calculate variationally the binding energy of an exciton bound to a neutral donor （D^0, X） in finite GaAs-AIxGa1-xAs quantum well wires （QWWs）. At the wire width of 25 A, the binding energy has a peak value, which is also at the position of the peak of the exciton binding energy, and the center-of-mass wave functions of excitons reaches the most centralized distribution. In addition, the changing tendency of the average interparticle distance as the wire width is reverse to that of the binding energy.展开更多
文摘The Leibniz-Hopf algebra is the free associative algebra with one generator in each positive degree and coproduct given by the Cartan formula. Quasi-symmetric functions are a generalisation of symmetric functions [7],and the algebra of quasi-symmetric functions appear as the dual of the Leibniz-Hopf algebra. The Leibniz-Hopf algebra and its dual are word Hopf algebras and play an important role in combinatorics, algebra and topology. We give some properties of words and consider an another view of proof for the antipode in the dual Leibniz-Hopf algebra.
基金The project supported by National Natural Science Foundation of China under Grant No. 10574036, and the Natural Science Foundation of Hebei Province of China under Grant No. A2004000140
文摘In the effective-mass approximation, using a simple two-parameter wave function and a one-dimensional （ID） equivalent potential model, we calculate variationally the binding energy of an exciton bound to a neutral donor （D^0, X） in finite GaAs-AIxGa1-xAs quantum well wires （QWWs）. At the wire width of 25 A, the binding energy has a peak value, which is also at the position of the peak of the exciton binding energy, and the center-of-mass wave functions of excitons reaches the most centralized distribution. In addition, the changing tendency of the average interparticle distance as the wire width is reverse to that of the binding energy.
