Proves the standard observable package is insufficient for quantitative trace rates in NS one-component degeneration and states a conditional dichotomy on relaxed Schur visibility versus an NS-realizable left-singular cascade.
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Improved minimax bounds in expectation and high-probability for discrete distribution estimation under l_infty norm, with fully empirical risk bounds and identification of worst-case extremal distribution.
Develops and analyzes single- and double-layer potential operators for doubly-periodic harmonic functions on finitely-connected tori, proves compactness and boundary limits, constructs the null space for multiply-connected cases, and demonstrates spectral convergence for Dirichlet, Neumann, and Stek
The paper establishes a coarse-grained resolution inequality Psi(r) <= 4 Psi^ell(r) + 4 Omega^ell(r) and a fixed-chain depletion theorem for combined pressure-flux work in the Navier-Stokes CKN setting.
A sharp-interface VOF method for phase-change simulations on unstructured meshes computes evaporation rates from local temperature gradients at geometrically reconstructed interfaces and validates against analytical solutions on Stefan, Sucking, and Scriven problems.
Proves a conditional finite-scale reduction theorem deriving a lower bound on the regularity radius from smallness of the vertical velocity component under multiple structural assumptions for 3D Navier-Stokes.
PAM approximates discontinuous data via Shepard-normalized RBFs, sparse regression, and adaptive refinement to achieve small L1 error while enabling parallel subdomain solves for porous media flow problems.
Causal PDE-Control Models combine causal drivers with PDE control and filtering to deliver interpretable dynamic portfolio rules that outperform benchmarks in Sharpe ratio and turnover on U.S. equity data.
A public GPU workflow for non-Fourier SENSE MRI reconstruction with sensitivity and off-resonance mapping enables fast, accurate imaging from challenging spiral trajectories.
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