Zhongshan LiProfessor, Mathematics Graduate Director Mathematics and Statistics, Neuroscience
Ph.D., Mathematics, May 1990, North Carolina State University
M.Sc., Mathematics, June 1986, Beijing Normal University, China
B.Sc., Mathematics, June 1983, Lanzhou University, China
Combinatorial Matrix Theory, Sign Pattern Matrices, Nonnegative Matrices, Integer Matrices, Oriented Matroids, Convex Polytopes, Boolean Matrices, Matrix Theory Applications, Polynomial and Matrix Equations, Matrix Inequalities, Algebraic Graph Theory, Neural Networks
I grew up in a poor rural area belonging to Lanzhou, Gansu Province, China. While in middle school, I became immensely fascinated by mathematics, and realized that my mathematics textbooks could not satisfy my thirst for knowledge. In a region where a library in unheard of, as a first-generation middle schooler, I had a lot of trouble finding extracurricular study materials, but I thoroughly studied the few good books I could get. In my last year in high school (that was in fact my second year in high school, which consisted of two years only back then), I transferred to a much better high school, Yongdeng County No. 2 High School, and participated in various high school mathematics competitions, culminating in the Top Prize in the Gansu Province Mathematics Competition in 1979. Later that year, I entered Lanzhou University, a leading university in China, and obtained my B.Sc. in mathematics in 1983, at the age of 20. Then I spent three years at Beijing Normal University, graduating with a M.Sc. in Mathematics in 1986. After teaching briefly at Hebei Normal University, I went to North Carolina State University, where I got my Ph.D. in mathematics (with concentration in algebra) in 1990 and published two papers on matrix theory. I have been working at GSU since 1991. Thanks to two influential GSU colleagues and collaborators, Drs. Frank Hall and Carolyn Eschenbach, my main research interests shifted to combinatorial matrix theory. For further biographic information, you may read my mini autobiography on my personal webpage https://math.gsu.edu/zli.
Find all of Zhongshan Li publications on Google Scholar
D. Lin, X. Chen, Z. Li, B. Li, X. Yang, On the existence of the exact solution of quaternion-valued neural networks based on a sequence of approximate solutions,
IEEE Transactions on Neural Networks and Learning Systems, 9 pp. In press. DOI: https://doi.org/10.1109/TNNLS.2021.3129269
L. Zhang, G.-F. Mou, F. Liu, Z. Li, Some bounds of the generalized μ-scrambling indices of primitive digraphs with d loops. J. Inequal. Appl. (2021), Paper No. 128, 13 pp. DOI: https://doi.org/10.1186/s13660-021-02667-y
D. Lin, X. Chen, G. Yu, Z. Li, Y. Xia, Global exponential synchronization via nonlinear feedback control for delayed inertial memristor-based quaternion-valued neural networks with impulses. Appl. Math. Comput. 401 (2021), Paper No. 126093, 19 pp. DOI: https://doi.org/10.1016/j.amc.2021.126093
Y. Xia, X. Chen, D. Lin, Z. Li, Some dynamical behaviors of fractional-order commutative quaternion-valued neural networks via direct method of Lyapunov, IEEE Access 9 (2021), 693-708. DOI: https://doi.org/10.1109/ACCESS.2020.3046842
M. Arav, F.J. Hall, Z. Li, H. van der Holst, Two-connected signed graphs with maximum nullity at most two, Linear Algebra Appl. 611 (2021), 82–93. DOI: https://doi.org/10.1016/j.laa.2020.12.002
B.-L. Yu, Z. Li, S. Xu, On the eventual exponential positivity of some tree sign patterns. Symmetry 13 (2021), 1669. DOI: https://doi.org/10.3390/sym13091669
X. Feng, W. Gao, F.J. Hall, G. Jing, Z. Li, C. Zagrodny, J. Zhou, Rank conditions for sign patterns that allow diagonalizability, Discrete Mathematics 343 (2020), no. 5, 111798, 11 pp. DOI: https://doi.org/10.1016/j.disc.2019.111798
G.F. Mou, T.F. Wang, Z. Li, The bipartite zero forcing set for a full sign pattern matrix, Mathematics 8 (3) (2020), 354, 14 pp. DOI: https://doi.org/10.3390/math8030354
W. Fang, H. Yu, Y. Gao, G. Jing, Z. Li, X. Li, Minimum detour index of cactus graphs. Ars Combinatoria 144 (2019), 293–307.
X. Chen, Q. Song, and Z. Li, Design and analysis of quaternion-valued neural networks for associative memories, IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 48, NO. 12, 2018, 2305-2314. DOI: https://doi.org/10.1109/TSMC.2017.2717866
W. Fang, W. Gao, Y. Gao, F. Gong, G. Jing, Z. Li, Y. Shao, L. Zhang, Minimum ranks of sign patterns and zero–nonzero patterns and point–hyperplane configurations, Linear Algebra and its Applications 558 (2018), 44-62. DOI: https://doi.org/10.1016/j.laa.2018.08.019
X. Chen, L. Li, Z. Li, Robust stability analysis of quaternion-valued neural networks via LMI approach, Advances in Difference Equations 2018 (1), Paper No.131, 20 pages. DOI: https://doi.org/10.1186/s13662-018-1585-z
X. Chen, Q. Song, Z. Li, Z. Zhao, Y. Liu, Stability analysis of continuous-time and discrete-time quaternion-valued neural networks with linear threshold neurons, IEEE Transactions on Neural Networks and Learning Systems 29 (7) (2018), 2769-2781. DOI: https://doi.org/10.1109/TNNLS.2017.2704286
W. Fang, H. Yu, Y. Gao, X. Li, G. Jing, Z. Li, Maximum Balaban index and sum-Balaban index of tricyclic graphs, MATCH Commun. Math. Comput. Chem. 79 (2018), no. 3, 717–742.
Z. Li, F. Zhang, X. Zhang, On the number of vertices of the stochastic tensor polytope, Linear and Multilinear Algebra 65 (2017), no. 10, 2064–2075. DOI: https://doi.org/10.1080/03081087.2017.1310178
W. Gao, Z. Li, Path sign patterns of order n≥5 do not require Hn, Linear Algebra Appl. 532 (2017), 99–126. DOI: https://doi.org/10.1016/j.laa.2017.06.039
X. Chen, Z. Li, Q. Song, J. Hu, Y. Tan, Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties, Neural Networks 91 (2017), 55–65.
X. Chen, Q. Song, Z. Li, Design and analysis of quaternion-valued neural networks for associative memories, IEEE Transactions on Systems, Man, and Cybernetics: Systems PP (99) (2017), 1–10. DOI: https://ieeexplore.ieee.org/document/7970154