3 papers
math.NA2026
Parametric Sensitivity of POD Reduced-Order Models for Semilinear Evolution Equations with Applications to G-Equations
Shengbo Ma, Luhao Xue, Zhiwen Zhang
Proper Orthogonal Decomposition (POD) provides low-dimensional surrogate models of evolution equations from solution snapshots. In parameterized problems, however, a basis computed…
math.OC2026
Optimization on Affine-Transversal Hilbert Submanifolds: Part I -- Theoretical Foundations
Yongcun Song, Luhao Xue, Xiaoming Yuan +1
In this paper, we establish the theoretical foundations for the generic optimization problem in a Hilbert space whose feasible set is an affine-transversal Hilbert submanifold give…
math.NT2023
Eisenstein series part of the primitive representations for even rank quadratic forms
Ben Kane, Luhao Xue
In this paper, we first investigate the relationship between the number of primitive representations of by quadratic forms and the number of non-primitive ones. We hence obtain…