4 papers
Continuity of Weighted Dirac Spectra
Zixuan Qiu, Ruijun Wu
For the weighted Dirac eigenvalue problem, we show that the two-sided weighted spectrum depends continuously on the weight under continuous deformations within a uniformly elliptic…
Windowed Fourier Propagator: A Frequency-Local Neural Operator for Wave Equations in Inhomogeneous Media
Yiyang Cai, Zixuan Qiu, Yunlu Shu +4
Wave equations are fundamental to describing a vast array of physical phenomena, yet their simulation in inhomogeneous media poses a computational challenge due to the highly oscil…
Weighted eigenvalues of Dirac operators: complete continuity and comparison
Zixuan Qiu, Ruijun Wu
We give a min-max characterization of the weighted Dirac eigenvalues, and show that the weighted eigenvalues and eigenspaces of Dirac operators are continuous with respect to weak…
INTEGRALBENCH: Benchmarking LLMs with Definite Integral Problems
Bintao Tang, Xin Yang, Yuhao Wang +3
We present INTEGRALBENCH, a focused benchmark designed to evaluate Large Language Model (LLM) performance on definite integral problems. INTEGRALBENCH provides both symbolic and nu…