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Award ID contains: 2243854

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  1. ; ; ; (, Pure and applied functional analysis)
    A novel basis of discrete analytic polynomials on a rhombic lattice is introduced and the associated convolution product is studied. A class of discrete analytic functions that are rational with respect to this product is also described. 
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    Free, publicly-accessible full text available December 1, 2025
  2. ; ; ; ; ; (, Electronic Research Archive)
    This paper presents a numerical method for solving the inverse problem of reconstructing the shape of periodic structures from scattering data. This inverse problem is motivated by applications in the nondestructive evaluation of photonic crystals. The numerical method belongs to the class of sampling methods that aim to construct an imaging function for the shape of the periodic structure using scattering data. By extending the results of Nguyen, Stahl, and Truong [Inverse Problems, 39:065013, 2023], we studied a simple imaging function that uses half the data required by the numerical method in the cited paper. Additionally, this imaging function is fast, simple to implement, and very robust against noise in the data. Both isotropic and anisotropic cases were investigated, and numerical examples were presented to demonstrate the performance of the numerical method. 
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