尚在久

教授

Email: zaijiu _at_ simis.cn
研究领域：动力系统几何算法、 哈密尔顿动力系统
办公室：

BIO

尚在久，上海数学与交叉学科研究院教授（与复旦大学双聘）、副院长。曾任中国科学院数学与系统科学研究院研究员、博士生导师、学术委员会委员、数学研究所所长，中国科学院国家数学与交叉科学中心副主任兼数学与物质科学交叉研究院部主任，中国科学院大学岗位教师。现承担《中国科学：数学》（中、英文版）、《应用数学学报》（中、英文版）等期刊编委，《数学译林》常务副主编，国家自然科学基金委员会重大研究计划“未来工业互联网的基础理论和关键技术”指导专家组成员。尚在久的主要研究领域为动力系统几何算法、哈密尔顿动力系统。

教育经历

  • 1991 中科院计算中心 应用数学 博士
  • 1987 内蒙古大学 基础数学 硕士
  • 1984 内蒙古大学 数学系 学士

工作经历

  • 2024.10- 上海数学与交叉学科研究院 教授 副院长
  • 2002.3-2024.10 中科院数学与系统科学研究院 研究员.
  • 2023.1– 中科院国家数学与交叉科学中心 副主任兼数学与物质科学研究部主任
  • 2015.9–2024.12 中国科学院大学 岗位教师
    • 基础课：微积分B
    • 研讨课：遍历论、经典力学的数学方法
  • 2012.6-2017.10 中科院数学与系统科学研究院数学研究所 所长
  • 2003.5-2012.5 中科院数学与系统科学研究院数学研究所 副所长
  • 1999.1-2002.2 中科院数学与系统科学研究院 副研究员.
  • 1995.5-1998.12 中国科学院数学研究所 副研究员.
  • 1993.8-1995.4 中国科学院数学研究所 助理研究员.
  • 1991.8-1993.7 中国科学院数学研究所 博士后
  • 1987.8-1988.9 内蒙古大学数学系 助教

Visiting Experience

  • 1995.10–1996.10 德国马普数学研究所 访问学者
  • 1997.10 香港浸会大学非线性研究中心 访问学者
  • 1998.06–1998.08, 1999.01 瑞士日内瓦大学数学系 访问副教授
  • 2004.06–2004.08 美国普林斯顿大学数学系 高级访问学者
  • 2005.10 德国Tuebingen大学数学系 访问教授
  • 2009.02–2009.04 香港中文大学数学系 访问教授

荣誉和获奖

  • 2022年《中国科学：数学》优秀服务奖
  • 1999年享受国务院政府特殊津贴
  • 1997年国家自然科学奖一等奖项目“哈密尔顿系统的辛几何算法”（获奖人：冯康等） 的主要成员之一（排名第四）
  • 1993年国家教委科技进步奖二等奖（获奖项目：微分算子谱理论，排名第二）
  • 1991年中科院院长奖学金优秀奖（博士论文：哈密尔顿系统辛几何算法的 KAM 定理及其相关方面的研究，指导教师：冯康）

论著

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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