28 citations · 80 across the 9 of their papers we have counts for
9 papers
Attention-Guided Fair AI Modeling for Skin Cancer Diagnosis
Mingcheng Zhu, Mingxuan Liu, Han Yuan +4
Artificial intelligence (AI) has shown remarkable promise in dermatology, offering accurate and non-invasive diagnosis of skin cancer. While extensive research has addressed skin t…
Time complexity analysis of quantum difference methods for linear high dimensional and multiscale partial differential equations
Shi Jin, Nana Liu, Yue Yu
We investigate time complexities of finite difference methods for solving the high-dimensional linear heat equation, the high-dimensional linear hyperbolic equation and the multisc…
Unconditionally optimal error estimate of a linearized variable-time-step BDF2 scheme for nonlinear parabolic equations
Chengchao Zhao, Nan Liu, Yuheng Ma +1
In this paper we consider a linearized variable-time-step two-step backward differentiation formula (BDF2) scheme for solving nonlinear parabolic equations. The scheme is construct…
Long-time Asymptotic Behavior of the Fifth-order Modified KdV Equation in Low Regularity Spaces
Nan Liu, Mingjuan Chen, Boling Guo
Based on the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann--Hilbert problems and the Dbar approach, the long-time asymptotic behavior of solutions to…
Long-time asymptotic behavior for an extended modified Korteweg-de Vries equation
Nan Liu, Boling Guo, Deng-Shan Wang +1
We investigate an integrable extended modified Korteweg-de Vries equation on the line with the initial value belonging to the Schwartz space. By performing the nonlinear steepest d…
The Gerdjikov-Ivanov type derivative nonlinear Schrödinger equation: Long-time dynamics of nonzero boundary conditions
Boling Guo, Nan Liu
We consider the Gerdjikov--Ivanov type derivative nonlinear Schrödinger equation \berr \ii q_{t}+q_{xx}-\ii q^2\bar{q}_{x}+\frac{1}{2}(|q|^4-q_0^4)q=0 \eerr on the line. The initia…
Long-time asymptotics for the Hirota equation on the half-line
Boling Guo, Nan Liu
We consider the Hirota equation on the quarter plane with the initial and boundary values belonging to the Schwartz space. The goal of this paper is to study the long-time behavior…
Long-time asymptotics for the Sasa-Satsuma equation via nonlinear steepest descent method
Boling Guo, Nan Liu
We formulate a Riemann-Hilbert problem to solve the Cauchy problem for the Sasa-Satsuma equation on the line, which allows us to give a representation for the solution o…
Initial-boundary value problem and long-time asymptotics for the Kundu--Eckhaus equation on the half-line
Boling Guo, Nan Liu
The initial-boundary value problem for the Kundu--Eckhaus equation on the half-line is considered in this paper by using the Fokas method. We will show that the solution c…