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• Theory of the Frequency Principle for General Deep Neural Networks

  Tao Luo, Zheng Ma, Zhi-Qin John Xu, Yaoyu Zhang

  2021-08-31

  44683 3662 Pages:484-507

• Embedding Principle in Depth for the Loss Landscape Analysis of Deep Neural Networks

  Zhiwei Bai, Tao Luo, Zhi-Qin John Xu, Yaoyu Zhang

  2024-05-20

  21368 1902 Pages:350-389

• A Variational Discretization Method for Mean Curvature Flows by the Onsager Principle

  Yihe Liu, Xianmin Xu

  2025-02-11

  11325 1075 Pages:63-95

• Unconditionally Maximum-Principle-Preserving Parametric Integrating Factor Two-Step Runge-Kutta Schemes for Parabolic Sine-Gordon Equations

  Hong Zhang, Xu Qian, Jun Xia, Songhe Song

  2023-01-09

  33429 3721 Pages:177-224

• Linear Maximum Bound Principle Preserving Finite Difference Schemes for the Convective Allen-Cahn Equation

  Jingwei Li, Kun Wang, Lili Ju

  2026-01-28

  49 37

• An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions

  Li Chen, Ruo Li, Feng Yang

  2020-09-25

  39966 3539 Pages:491-517

• Stochastic Runge-Kutta Methods for Preserving Maximum Bound Principle of Semilinear Parabolic Equations. Part II: Sinc Quadrature Rule

  Yabing Sun, Weidong Zhao

  2025-02-11

  11067 987 Pages:176-206

• A New $\mathcal{L}1$-TFPM Scheme for the Singularly Perturbed Subdiffusion Equations

  Wang Kong, Zhongyi Huang

  2025-02-11

  11349 1065 Pages:1-30

• Stochastic Runge-Kutta Methods for Preserving Maximum Bound Principle of Semilinear Parabolic Equations. Part I: Gaussian Quadrature Rule

  Yabing Sun, Weidong Zhao

  2024-05-20

  21660 1840 Pages:390-420

• A Survey of Optimal Control Problems Evolved on Riemannian Manifolds

  Li Deng, Xu Zhang

  2022-08-31

  34671 3155 Pages:351-382

• Implicit Bias in Understanding Deep Learning for Solving PDEs Beyond Ritz-Galerkin Method

  Jihong Wang, Zhi-Qin John Xu, Jiwei Zhang, Yaoyu Zhang

  2022-05-30

  38329 3254 Pages:299-317

• Boundary Condition for Dislocation Dynamic Simulation in BCC Crystal

  Shuyang Dai, Fengru Wang, Yang Xiang, Jerry Zhijian Yang, Cheng Yuan

  2021-02-26

  41365 4343 Pages:175-194

• A Mathematical Perspective on Corruption’s Effect on Productivity and Service Efficiency with Cost-Effective Control Strategies

  N. S. Tibane, O. D. Makinde, R. L. Monaledi

  2026-01-21

  84 92 Pages:433-460

• Optical Wave Turbulence: The Conformal Symmetry Transformations of Statistics of the Quantum Fluids of Light

  V. N. Grebenev

  2026-01-25

  736 74 Pages:62-85

• Computational Imaging of Small-Amplitude Biperiodic Surfaces with Negative Index Material

  Yuliang Wang

  2025-02-11

  11185 1077 Pages:148-175

• A Nonlinear Eigenvalue Problem Associated with the Sum-of-Rayleigh-Quotients Maximization

  Lei-Hong Zhang, Rui Chang

  2021-05-13

  42683 3910 Pages:313-335