Zaijiu Shang

Professor

Email: zaijiu _at_ simis.cn
Research Fields: Geometric Numerical Methods for Dynamical Systems, Hamiltonian Dynamical Systems
Office No.:

BIO

Zaijiu Shang, Professor and Vice Director of Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS). Before joining SIMIS, he served as a full professor, doctoral supervisor, and member of the Academic Committee at the Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences (CAS). He also held the positions of Director of Institute of Mathematics at AMSS, Deputy Director of the National Center for Mathematics and Interdisciplinary Sciences, CAS, and Director of the Mathematics and Physical Sciences Division within the center. Additionally, he was a post teacher at the University of Chinese Academy of Sciences (UCAS). Currently he is members of the Editorial Boards of the journals “Science China Mathematics” and “Acta Math. Appl. Sinica” Etc. He is the Executive Deputy Editor of the journal “Mathematical Advances in Translation”. He is a member of the Panel of Experts of the NSFC major research plan “Basic Theories and Key Technologies for Future Industrial Internet”. Professor Shang’s main research interests include Hamiltonian Dynamical Systems and Geometric Numerical Methods for Dynamical Systems.

Education Experience

  • 1991 Computing Center, Chinese Academy of Sciences Applied Mathematics Ph.D.
  • 1987 Inner Mongolia University Pure Mathematics M.Sc.
  • 1984 Inner Mongolia University Department of Mathematics B.Sc.

Work Experience

  • 2024.10- Shanghai Institute for Mathematics and Interdisciplinary Sciences Professor, Deputy Director
  • 2002.3-2024.10 Academy of Mathematics and Systems Science, Chinese Academy of Sciences Professor.
  • 2023.1– National Center for Mathematics and Interdisciplinary Sciences, CAS Deputy Director/Division of Mathematics and Physical Sciences Head
  • 2015.9–2024.12 University of Chinese Academy of Sciences Post Teacher
    • Core Course: Calculus B
    • Seminar Courses: Ergodic Theory, Mathematical Methods of Classical Mechanics
  • 2012.6-2017.10 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences Director
  • 2003.5-2012.5 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences Deputy Director
  • 1999.1-2002.2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences Associate Professor.
  • 1995.5-1998.12 Institute of Mathematics, Chinese Academy of Sciences. Associate Professor.
  • 1993.8-1995.4 Institute of Mathematics, Chinese Academy of Sciences. Assistant Professor.
  • 1991.8-1993.7 Institute of Mathematics, Chinese Academy of Sciences. Postdoctoral Fellow
  • 1987.8-1988.9 Department of Mathematics, Inner Mongolia University Teaching Assistant

Visiting Experience

  • 1995.10–1996.10 Max Planck Institute for Mathematics, Germany Visiting Scholar
  • 1997.10 Center for Nonlinear Studies, Hong Kong Baptist University Visiting Scholar
  • 1998.06–1998.08, 1999.01 Department of Mathematics, University of Geneva, Switzerland Visiting Associate Professor
  • 2004.06–2004.08 Department of Mathematics, Princeton University, USA Advanced Visiting Scholar
  • 2005.10 Department of Mathematics, University of Tuebingen, Germany Visiting Professor
  • 2009.02–2009.04 Department of Mathematics, The Chinese University of Hong Kong Visiting Professor

Honors and Awards

  • 2022 Science China Mathematics Excellent Service Award1999 Recipient of the State Council Special Government Allowance
  • 1999 Recipient of the State Council Special Government Allowance (a prestigious honor for outstanding contributions in professional fields)
  • 1997 Key contributor (ranked 4th) to the project “Symplectic Geometric Algorithms for Hamiltonian Systems” (Awardee: Feng Kang et al.), which won the First Prize of the National Natural Science Award
  • 1993 Second Prize of the Science and Technology Progress Award by the State Education Commission (Project: Spectral Theory of Differential Operators, ranked 2nd)
  • 1991 Excellence Award of the President’s Scholarship, Chinese Academy of Sciences (Ph.D. dissertation: KAM Theory and Related Topics of Symplectic Geometric Algorithms for Hamiltonian Systems, Advisor: Kang Feng)

Publications

Papers:

  1. Shen, Xinhua; Shang, Zaijiu; Sun, Hongpeng, A preconditioned second-order convex splitting algorithm with a difference of varying convex functions and line search. arXiv:2411.07661, 2024 (submitted)
  2. Li, Mingkun; Shang, Zaijiu; Wang, Peng; Zhang, Hongkun; Fan, Junjie, Universal-basis neural ODE modeling of the discrete Sine-Gordon system. 2024 (submitted)
  3. Shang, Zaijiu; Xu, Yang, The elliptic invariant tori of nearly integrable Hamiltonian system through symplectic algorithms. arXiv:2402.14517, 2024.
  4. Shang, Zaijiu; Xu, Yang, A KAM theorem of symplectic algorithms for nearly integrable Hamiltonian systems. arXiv:2402.14478, 2024.
  5. Sun, Geng; Gan, Siqing; Liu, Hongyu; Shang, Zaijiu，Symmetric-adjoint and symplectic- adjoint Runge-Kutta methods and their applications. Numer. Math. Theory Methods Appl.15(2022), no.2, 304-335.
  6. 尚在久，宋丽娜. 关于辛算法稳定性的若干注记，《计算数学》42 ：4（2020）(纪念 冯康先生百年诞辰) ，405-418.
  7. Li, Xuemei; Shang, Zaijiu, On the existence of invariant tori in non-conservative dynamical systems with degeneracy and finite differentiability. Discrete Contin. Dyn. Syst. 39 (2019), no. 7, 4225-4257.
  8. Li, Xuemei; Shang, Zaijiu, Quasi-periodic solutions for differential equations with an elliptic-type degenerate equilibrium point under small perturbations. J. Dynam. Differential Equations 31 (2019), no. 2, 653-681.
  9. Ding, Zhaodong; Shang, Zaijiu, Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems. Sci. China Math. 61 (2018), no. 9, 1567-1588.
  10. Ding, Zhaodong; Shang, Zaijiu; Xie, Bo, Exponential stability estimate of symplectic integrators for integrable Hamiltonian systems. arXiv:1805.03355 (2018)
  11. Jiang, Ningning; Hua, Junbo; Shang, Zaijiu; Yang, Kehu, A new method for channel availability analysis and the associated policy design for selection of channel sensing order in CRNs. IEEE Trans. Signal Process. 64 (2016), no. 9,2443-2458.
  12. Li, Guimin; Shang, Zaijiu; Yang Kehu, Detection and Leasing of Joint Space and Spectrun Opportunities by Multiple Secondary Network Operators in Cognitive Radio Systems,Journal of Signal Processing Sytems for Signal Image and Video technology, 83(2)(2016), 293-308.
  13. He,Yang; Sun,Yajuan; Shang,Zaijiu, Integrable discretisation of the Lotka-Volterra system. J. Comput. Math. 33 (2015), no. 5, 468-494.
  14. Li, Jingzhi; Liu, Hongyu; Shang, Zaijiu; Sun, Hongpeng, Two single-shot methods for locating multiple electromagnetic scatterers. SIAM J. Appl. Math. 73 (2013), no. 4, 1721- 1746.
  15. Gan, Siqing; Shang, Zaijiu; Sun, Geng, A class of symplectic partitioned Runge-Kutta methods,Appl. Math. Lett.26(2013), no.9, 968-973.
  16. Liu, Hongyu; Shang, Zaijiu; Sun, Hongpeng; Zou, Jun. Singular perturbation of reduced wave equation and scattering from an embedded obstacle. J. Dynam. Differential Equations 24 (2012), no. 4, 803–821.
  17. Ding, Xiaohua; Liu, Hongyu; Shang, Zaijiu; Sun, Geng, Preservation of stability properties near fixed points of linear Hamiltonian systems by symplectic integrators. Appl. Math. Comput. 217 (2011), no. 13, 6105–6114.
  18. Feng, Quandong; Huang, Jingfang; Nie, Ningming; Shang, Zaijiu; Tang. Yifa, Implementing arbitrarily high-order symplectic methods via Krylov deffered correction technique, International Journal of Modeling, Simulation, and Scientific Computing, 1(2)(2010), 277-301.
  19. Shang, Zaijiu, Volume-preserving maps, source-free systems and their local structures. J. Phys. A 39(2006), no. 19, 5601–5615.
  20. Sun, YJ; Shang, ZJ, Structure-preserving algorithms for Birkhoffian systems, Physics Letters A, 336(4-5) (2005), 358-369.
  21. Shang, Zai-jiu, A note on the KAM theorem for symplectic mappings. J. Dynam. Differential Equations 12 (2000), no. 2, 357–383.
  22. Shang, Zaijiu, Resonant and Diophantine step sizes in computing invariant tori of Hamiltonian systems. Nonlinearity 13 (2000), no. 1, 299–308.
  23. Shang, Zaijiu, KAM theorem of symplectic algorithms for Hamiltonian systems. Numer. Math. 83(1999), no. 3, 477–496.
  24. Shang, Zaijiu, Generating functions for volume-preserving mappings with applications I: Basic theory. China/Korea Joint Seminar: Dynamical Systems and Their Applications, 1998. Available from: http://www.mathnet.or.kr/mathnet/kms_tex/60105.pdf.
  25. Shang, Zaijiu, Generating functions for volume-preserving mappings with applications II: An application. China/Korea Joint Seminar: Dynamical Systems and Their Applications, 1998. Available from: http://www.mathnet.or.kr/mathnet/kms_tex/60106.pdf.
  26. 尚在久，关于J-对称微分算子J-自拌扩张的若干注记. 《数学学报》39：3（1996）.
  27. Feng, Kang; Shang, Zaijiu, Volume-preserving algorithms for source-free dynamical systems. Numer. Math. 71 (1995), no. 4, 451–463.
  28. Shang, Zaijiu, Generating functions for volume-preserving mappings and Hamilton-Jacobi equations for source-free dynamical systems. Sci.China Ser. A 37 (1994), no. 10, 1172–1188.
  29. Shang, Zaijiu, Construction of volume-preserving difference schemes for source- free systems via generating functions. J. Comput. Math. 12 (1994), no. 3, 265–272.
  30. Shang, Zaijiu, Remarks on volume-preserving algorithms for source-free dynamical systems. Proc. of Conference on Scientific and Engineering Computing for Young Chinese Scientists, August 17-21,1993, Beijing. Eds. Jun-zhi Cui, Zhong-ci Shi, Dao-liu Wang, National Defense Industry Press, Beijing, China.
  31. 尚在久，李文明. 关于J-对称微分算子的若干问题. 《内蒙古大学学报》（自然科学版）22：3（1991）.
  32. Shang, Zaijiu, On J-selfadjoint extensions of J-symmetric ordinary differential operators. J. Differential Equations 73 (1988), no. 1, 153–177.
  33. 尚在久, 朱瑞英. (-∞,+∞)上对称常微分算子的自拌域，《内蒙古大学学报》（自然科学版）17：1（1986）pp. 17-28.

Preprints:

  1. Cheng, Xu; Liu, Jiaqi; Shang, Zaijiu, A class of generalized Nesterov’s accelerated gradient method from dynamical perspective. Preprint, January 2025.
  2. Li, Mingkun; Shang, Zaijiu, Lagrangian immersion and generalized Hamilton-Jacobi equation. Preprint, April 2025.

Books and Chapters：

  1. Chapter 13, KAM theorem of symplectic algorithms, in the monograph “Symplectic Geometric Algorithms for Hamiltonian Systems, by Kang Feng and Mengzhao Qin, Zhejiang Science and Technology Publishing House in Hangzhou and Springer-Verlag in Heidelberg, 2010”
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