The energy band structure of single-layer graphene under one-dimensional electric and magnetic field modulation is theoretically investigated. The criterion for bandgap opening at the Dirac point is analytically deriv...The energy band structure of single-layer graphene under one-dimensional electric and magnetic field modulation is theoretically investigated. The criterion for bandgap opening at the Dirac point is analytically derived with a two-fold degeneracy second-order perturbation method. It is shown that a direct or an indirect bandgap semiconductor could be realized in a single-layer graphene under some specific configurations of the electric and magnetic field arrangement. Due to the bandgap generated in the single-layer graphene, the Klein tunneling observed in pristine graphene is completely suppressed.展开更多
One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deri...One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 60776067 and 10974011)
文摘The energy band structure of single-layer graphene under one-dimensional electric and magnetic field modulation is theoretically investigated. The criterion for bandgap opening at the Dirac point is analytically derived with a two-fold degeneracy second-order perturbation method. It is shown that a direct or an indirect bandgap semiconductor could be realized in a single-layer graphene under some specific configurations of the electric and magnetic field arrangement. Due to the bandgap generated in the single-layer graphene, the Klein tunneling observed in pristine graphene is completely suppressed.
文摘One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.
