Regularity and free boundary regularity for the  Laplacian in Lipschitz and  domains.

Lewis, John L.; Nyström, Kaj

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We give the Thom polynomials for the singularities $I_{2, 2}$ associated with maps $(ℂ^{•}, 0) \to (ℂ^{• + k}, 0)$ with parameter $k \geq 0$ . Our computations combine the characterization of Thom polynomials via the “method of restriction equations” of Rimanyi et al. with the techniques of Schur functions.

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Greedy and lazy representations in negative base systems

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We consider positional numeration systems with negative real base $- β$ , where $β > 1$ , and study the extremal representations in these systems, called here the greedy and lazy representations. We give algorithms for determination of minimal and maximal $(- β)$ -representation with respect to the alternate order. We also show that both extremal representations can be obtained as representations in the positive base $β^{2}$ with a non-integer alphabet. This enables us to characterize digit sequences admissible...