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Tag: Applied Mathematics

  • Generic cuspidal points can be localized from eigenvalue loops

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    What the study found The study finds that generic cuspidal points, meaning parameter values where eigenvalues coalesce in smooth complex-valued matrix functions of two parameters, can be analyzed through loops in parameter space. It also states that phase accumulation for eigenvectors can occur around such loops, and that eigenvalue periodicity and phase accumulation may help…

  • Log-Sobolev inequality holds for some Gibbs measures

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    What the study found The authors show that the Gibbs measures for the focusing Schrödinger equation satisfy a log-Sobolev inequality when 2 ≤ p ≤ 4. For p > 4, they establish a lower bound for the Hessian of the effective potential. Why the authors say this matters The study suggests that the log-Sobolev inequality…

  • Multilinear maximal operators on homogeneous curves are bounded

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    What the study found The authors prove a boundedness result for multilinear maximal operators along homogeneous polynomial curves. In the stated setting, the result holds when p1, …, pn are greater than 1 and the exponents satisfy 1/p = sum from j=1 to n of 1/pj. Why the authors say this matters The abstract does…

  • Local Lipschitz regularity proved for minimizers of certain functionals

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    What the study found The authors prove local Lipschitz regularity for minimizers of a class of functionals, meaning the minimizers have locally bounded slopes. They also show, as a byproduct, that a locally Lipschitz minimizer exists for a related class of functionals in which the function f may be nonconvex. Why the authors say this…

  • Improved Omega bound for lattice point discrepancy in bodies of revolution

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    What the study found The study found an improved Omega-bound for the error term in a lattice counting problem for bodies of revolution in three-dimensional space. In this setting, a body of revolution is a shape formed by rotating a curve around an axis. Why the authors say this matters The authors say this strengthens…

  • Radial perturbations give spherical harmonic eigenfunctions in impedance tomography

    Radial perturbations give spherical harmonic eigenfunctions in impedance tomography

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    What the study found The study found that, for rotationally symmetric conductivity perturbations in the unit ball, the eigenfunctions of the linearized electrical impedance tomography operator correspond to spherical harmonics. It also gives an explicit formula for the associated eigenvalues. Why the authors say this matters The authors conclude that the structure they establish is…