43,710 research outputs found

    The matching problem between functional shapes via a BV-penalty term: a Γ\Gamma-convergence result

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    In this paper we study a variant of the matching model between functional shapes introduced in \cite{ABN}. Such a model allows to compare surfaces equipped with a signal and the matching energy is defined by the L2L^2-norm of the signal on the surface and a varifold-type attachment term. In this work we study the problem with fixed geometry which means that we optimize the initial signal (supported on the initial surface) with respect to a target signal supported on a different surface. In particular, we consider a BVBV or H1H^1-penalty for the signal instead of its L2L^2-norm. Several numerical examples are shown in order to prove that the BVBV-penalty improves the quality of the matching. Moreover, we prove a Γ\Gamma-convergence result for the discrete matching energy towards the continuous-one

    Toric systems and mirror symmetry

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    Hille and Perling associate to every cyclic full strongly exceptional sequence of line bundles on a toric weak Fano surface a toric system, which defines a new toric surface. In this note we interprete this construction as an instance of mirror symmetry and extend it to a duality on the set toric weak Fano surfaces equiped with a cyclic full strongly exceptional sequence
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