Efficient high-capacity quantum secret sharing with two-photon entanglement

An efficient high-capacity quantum secret sharing scheme is proposed following some ideas in quantum dense coding with two-photon entanglement. The message sender, Alice prepares and measures the two-photon entangled states, and the two agents, Bob and Charlie code their information on their photons with four local unitary operations, which makes this scheme more convenient for the agents than others. This scheme has a high intrinsic efficiency for qubits and a high capacity.Comment: 5 pages, no figures. A inappreciable error is correcte

On fermionic representation of the framed topological vertex

The Gromov-Witten invariants of \mathbb{C}^3 with branes is encoded in the topological vertex which has a very complicated combinatorial expression. A simple formula for the topological vertex was proposed by Aganagic et al in the fermionic picture. We will propose a similar formula for the framed topological vertex and prove it in the case when there are one or two branes.Comment: An acknowledgement adde

A Class of Second Order Difference Approximation for Solving Space Fractional Diffusion Equations

A class of second order approximations, called the weighted and shifted Gr\"{u}nwald difference operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional diffusion equations in one and two dimensions. The stability and convergence of our difference schemes for space fractional diffusion equations with constant coefficients in one and two dimensions are theoretically established. Several numerical examples are implemented to testify the efficiency of the numerical schemes and confirm the convergence order, and the numerical results for variable coefficients problem are also presented.Comment: 24 Page