We compute the ring structure of Floer cohomology groups of Lagrangian torus fibers in some toric Fano manifolds continuing the study of [CO]. Related <i>A</i>-formulas hold for a transversal choice of chains. Two different computations are provided: a direct calculation using the classification of holomorphic discs by Oh and the author in [CO], and another method by using an <i>analogue of divisor equation</i> in Gromov-Witten invariants to the case of discs. Floer cohomology rings are shown to be isomorphic to Clifford algebras, whose quadratic forms are given by the Hessians of functions <i>W</i>, which turn out to be the superpotentials of Landau-Ginzburg mirrors. In the case of , this proves the prediction made by Hori, Kapustin and Li by B-model calculations via physical arguments. The latter method also provides correspondence between higher derivatives of the superpotential of LG mirror with

We consider the numerical solution of the time-fractional diffusion-wave equation on two-dimensional and three-dimensional unbounded spatial domains. Introduce an artificial boundary and find the exact and approximate artificial boundary conditions for the given problem, which lead to a bounded computational domain. Using the exact or approximating boundary conditions on the artificial boundary, the original problem is reduced to an initial-boundary-value problem on the bounded computational domain which is respectively equivalent to or approximates the original problem. Finite difference methods are used to solve the reduced problems on the bounded computational domain and the stability of these finite difference methods are proved. The numerical results demonstrate that the method given in this paper is effective and feasible.

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The goal of this paper is to prove the well-posedness for the governing equations which are used for cylindrical cloaking simulation. A new time-domain finite element scheme is developed to solve the governing equations. Numerical results demonstrating the cloaking phenomenon with the cylindrical cloak are presented. We finally extend the analysis and simulation to an elliptical cloak model.