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Boundary blow-up analysis for approximate Dirac-harmonic maps into stationary Lorentzian manifolds
《Science China Mathematics》2025年第3期649-676,共28页Wanjun Ai Lei Liu Miaomiao Zhu 
supported by National Natural Science Foundation of China (Grant No. 12201515);the Natural Science Foundation of Chongqing, China (Grant No. cstc2021jcyj-msxmX1058);the China Scholarship Council (Grant No. 202206995009);supported by National Natural Science Foundation of China (Grant No. 12101255).;supported by Innovation Program of Shanghai Municipal Education Commission (Grant No. 2021-01-07-00-02-E00087);National Natural Science Foundation of China (Grant No. 12171314);Shanghai Frontier Science Center of Modern Analysis。
For a sequence of approximate Dirac-harmonic maps from a Riemannian surface with a smooth boundary into a stationary Lorentzian manifold, we study the boundary blow-up analysis and prove the positive energy identity f...
关键词：Dirac-harmonic maps boundary regularity BLOW-UP Lorentzian manifolds 
Gradient-based algorithms for multi-objective bi-level optimization被引量：1
《Science China Mathematics》2024年第6期1419-1438,共20页Xinmin Yang Wei Yao Haian Yin Shangzhi Zeng Jin Zhang 
supported by the Major Program of National Natural Science Foundation of China(Grant Nos.11991020 and 11991024);supported by National Natural Science Foundation of China(Grant No.12371305);supported by National Natural Science Foundation of China(Grant No.12222106);Guangdong Basic and Applied Basic Research Foundation(Grant No.2022B1515020082);Shenzhen Science and Technology Program(Grant No.RCYX20200714114700072)。
Multi-objective bi-level optimization(MOBLO)addresses nested multi-objective optimization problems common in a range of applications.However,its multi-objective and hierarchical bi-level nature makes it notably comple...
关键词：MULTI-OBJECTIVE bi-level optimization convergence analysis Pareto stationary learning to optimize 
On Leray's problem in an infinitely long pipe with the Navier-slip boundary condition
《Science China Mathematics》2024年第4期819-854,共36页Zijin Li Xinghong Pan Jiaqi Yang 
supported by Natural Science Foundation of Jiangsu Province(Grant No.BK20200803);National Natural Science Foundation of China(Grant No.12001285);supported by National Natural Science Foundation of China(Grant Nos.11801268 and 12031006);supported by National Natural Science Foundation of China(Grant No.12001429)。
The original Leray’s problem concerns the well-posedness of weak solutions to the steady incompressible Navier-Stokes equations in a distorted pipe,which approach the Poiseuille flow subject to the no-slip boundary c...
关键词：stationary Navier-Stokes system Navier-slip boundary condition Leray's problem 
The qualitative behavior for approximate Dirac-harmonic maps into stationary Lorentzian manifolds
《Science China Mathematics》2022年第8期1679-1706,共28页Wanjun Ai Miaomiao Zhu 
supported by the Fundamental Research Funds for the Central Universities(Grant No.SWU119064);supported by Shanghai Frontier Research Institute for Modern Analysis(IMA-Shanghai)and Innovation Program of Shanghai Municipal Education Commission(Grant No.2021-01-07-00-02-E00087)。
For a sequence of approximate Dirac-harmonic maps from a closed spin Riemann surface into a stationary Lorentzian manifold with uniformly bounded energy,we study the blow-up analysis and show that the Lorentzian energ...
关键词：approximate Dirac-harmonic maps blow-up analysis no neck Lorentzian manifolds 
Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation
《Science China Mathematics》2022年第2期291-308,共18页Qian Yang Mingkang Ni 
supported by National Natural Science Foundation of China(Grant No.11871217);the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000)。
A piecewise-smooth second-order singularly perturbed differential equation whose right-hand side is a nonlinear function with a discontinuity on some curve is investigated. This is a new class of problems in the case ...
关键词：reaction-diffusion equation multizonal internal layer asymptotic method piecewise-smooth dynamical system 
Convergence of some finite element iterative methods related to different Reynolds numbers for the 2D/3D stationary incompressible magnetohydrodynamics被引量：3
《Science China Mathematics》2016年第3期589-608,共20页DONG Xiao Jing HE Yin Nian 
National Natural Science Foundation of China (Grant Nos. 11271298 and 11362021)
Based on the finite element method(FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics(MHD) numerically. Tw...
关键词：stationary incompressible magnetohydrodynamics finite element method iterative method twolevel algorithms 
Global existence and stability of a stationary Mach reflection被引量：1
《Science China Mathematics》2015年第1期11-34,共24页CHEN Shu Xing 
supported by National Natural Science Foundation of China(Grant Nos.11031001 and 11101101)
We prove the global existence and stability of a wave structure containing a stationary Mach con- figuration, which occurs when an incident shock front hits a wall with a large incident angle. Our result shows that ti...
关键词：Euler system Mach reflection EXISTENCE STABILITY free boundary problem elliptic-hyperboliccomposcd system 
On the structure of stationary sets
《Science China Mathematics》2007年第5期615-627,共13页Thomas JECH Jindich ZAPLETAL 
the Coalition for National Science Funding (Grant No. 10571168);the GACR (Grant Nos. 201/02/857 and 201-03-0933);the GAAV (Grant No. IAA 100190509);NSF (Grant No.DMS-0071437);visiting appointments at Chinese Academy of Sciences in Beijing and National University of Singapore
We isolate several classes of stationary sets of [κ]ω and investigate implications among them. Under a large cardinal assumption, we prove a structure theorem for stationary sets.
关键词：stationary set projective stationary set stationary reflection principles 03E40 03E65 
Approximation of weak sense stationary stochastic processes from local averages被引量：7
《Science China Mathematics》2007年第4期457-463,共7页Zhan-jie SONG Wen-chang SUN Shou-yuan YANG Guang-wen ZHU 
This work was supported partially by the National Natural Science Foundation of China (Grant Nos. 60472042,10571089 and 60572113),the Liuhui Center for Applied Mathematics, the Program for New Century Excellent Talents in Universitiesthe Research Fund for the Doctoral Program of Higher Education;the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China
We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
关键词：sampling theorem weak sense stationary stochastic processes local averages average sampling 42C15 60G10 94A20 
Ergodic degrees for continuous-time Markov chains被引量：17
《Science China Mathematics》2004年第2期161-174,共14页MAO Yonghua 
This work was supported in part by the'973'Project;the Research Fund for the Doctoral Program of Higher Education(Grant No.20010027007);the National Natural Science Foundation of China(Grant Nos.10121101 and 10301007);the National Natural Science Foundation of China for Distinguished Young Scholars(Grant No.10025105).
This paper studies the existence of the higher orders deviation matrices for continuous time Markov chains by the moments for the hitting times. An estimate of the polynomial convergence rates for the transition matri...
关键词：MARKOV chain  ERGODIC degree  hitting time  CONVERGENCE to stationary. 
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