In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules i...In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.展开更多
In this note, we prove that the efficient solution set for a vector optimization problem with a continuous, star cone-quasiconvex objective mapping is connected under the assumption that the ordering cone is a D-cone....In this note, we prove that the efficient solution set for a vector optimization problem with a continuous, star cone-quasiconvex objective mapping is connected under the assumption that the ordering cone is a D-cone. A D-cone includes any closed convex pointed cones in a normed space which admits strictly positive continuous linear functionals.展开更多
In this paper, we investigate the dynamics of a diffusive predator prey model with Holling-II functional response and the additive Allee effect in prey. We show the local and global asymptotical stability of the posit...In this paper, we investigate the dynamics of a diffusive predator prey model with Holling-II functional response and the additive Allee effect in prey. We show the local and global asymptotical stability of the positive equilibrium, and give the conditions of the existence of the Hopf bifurcation. By carrying out global qualitative and bifurcation analysis, it is shown that the weak and strong Allee effects in prey can induce different dynamical behavior in the predator-prey model. Furthermore, we use some numerical simulations to illustrate the dynamics of the model. The results may be helpful for controlling and managing the predator-prey system.展开更多
文摘In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.
基金Supported by the National Natural Science Foundation of China(No.10471032)the Excellent Young Teachers Program of the Ministry of Education of China
文摘In this note, we prove that the efficient solution set for a vector optimization problem with a continuous, star cone-quasiconvex objective mapping is connected under the assumption that the ordering cone is a D-cone. A D-cone includes any closed convex pointed cones in a normed space which admits strictly positive continuous linear functionals.
文摘In this paper, we investigate the dynamics of a diffusive predator prey model with Holling-II functional response and the additive Allee effect in prey. We show the local and global asymptotical stability of the positive equilibrium, and give the conditions of the existence of the Hopf bifurcation. By carrying out global qualitative and bifurcation analysis, it is shown that the weak and strong Allee effects in prey can induce different dynamical behavior in the predator-prey model. Furthermore, we use some numerical simulations to illustrate the dynamics of the model. The results may be helpful for controlling and managing the predator-prey system.
