Academic/Professional Qualifications

Ph.D. in Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China, Sep 2004--Jul 2009

B.S. in Mathematics, Nanjing University, China, Sep 2000--Jun 2004

Career History

Visiting Scholar, University of Minnesota, USA, Sep 2019--Sep 2021

Associate Professor, University of Shanghai for Science and Technology, China, Aug 2009--now

Selected Publications (*Corresponding author)：

1. Liu J*, Ni F. Distance invariant method for normalization of indexed differentials. Journal of Symbolic Computation, 2021, 104: 256-275.

2. Liu J, Ni F*, Song S H, et. al. Normalization of indexed differentials by extending Gröbner basis theory. Journal of Systems Science and Complexity, 2022, doi: 10.1007/s11424-021-0302-2.

3. Liu J*, Ni F. An extension of Gröbner basis theory to indexed polynomials without eliminations. Journal of Systems Science and Complexity, 2020, 33: 1708-1718. 

4. Liu J, Ni F*, Du M J, et.al. Upper bounds on the node numbers of hidden layers in MLPs. Neural Network World, 2021, 31 (4), 297-309.

5. Liu J. Block distance invariant method for monoterm canonicalization of Riemann tensor

polynomials. ACM Communications in Computer Algebra, 2019, 53(3): 134-137.

6. Liu J. Normalization in Riemann tensor polynomial ring. Journal of Systems Science and Complexity, 2018, 31(2): 569-580

7. Wang D S*, Liu J*. Integrability aspects of some two-component KdV systems. Applied Mathematics Letters, 2018, 79: 211-219 (ESI Highly Cited Paper, 2019)

8.Wang D S*, Liu J*, Wang L Z. Non-autonomous matter-wave solitons in hybrid atomic 

molecular Bose–Einstein condensates with tunable interactions and harmonic potential. Physics Letters A, 2018, 382: 799-805

9.Liu J, Wang D S*, Yin Y B. Lie symmetry analysis of the inhomogeneous Toda lattice 

equation via semi-discrete exterior calculus. Communications in Theoretical Physics, 2017, 67: 643–647 

10.Liu J. Normalization of indexed differentials based on function distance invariants. CASC 

2017, Lecture Notes in Computer Science, 10490: 285-300 

11.Wang D S, Liu J, Zhang Z F*. Integrability and equivalence relationships of six integrable 

coupled Korteweg–de Vries equations. Mathematical Methods in the Applied Sciences, 2016, 39: 3516-3530

12.Liu J*, Li H B, Zhang L X. A complete classification of canonical forms of a class of 

Riemann tensor indexed expressions and its applications in differential geometry (in Chinese). Scientia Sinica Mathematica, 2013, 43: 399–408

13.Liu J*, Li H B, Cao Y H. Simplification and normalization of indexed differentials involving 

coordinate transformation. Science China Series A, 2009, 52(10): 2266–2286 

Project：

1. National Natural Science Foundation of China (Grant No. 11701370,            Jan 2018-Dec 2020)

2. National Project Cultivation Funding of University of Shanghai for Science and Technology (Grant No. 14XPQ01, Jan 2014-Dec 2014)

3. Research Funding for Shanghai’s Excellent Young University Teachers (Grant No. slg10011, Jan 2011-Dec 2013)

4. The Opening Funding of the Key Laboratory of Mathematics Mechanization of Chinese Academy of Sciences, Jun 2011-Jun 2012

 Probability and Statistics, Logic Theory, Finance, Nonlinear Systems

Member of Computer Mathematics Professional Committee, Chinese Mathematical Society

Deputy Secretary General, Management Engineering Branch of Shanghai College Engineering Education Society

Reviewer, Mathematical Reviews, American Mathematical So