Professor of Mathematics

Department of Mathematics and Statistics

Georgia State University

Atlanta, GA 30302-4110

Phone: (404) 413-6437

E-mail: zli@gsu.edu

Information about my professional activities can be found in my curriculum vitae.

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 is 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
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.

D. Lin, X. Chen, **Z. L**i, 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.

** **DOI:
https://doi.org/10.1016/j.neunet.2017.04.006

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://doi.org/10.1109/TSMC.2017.2717866

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__ PP (99) (2017), 1–13.

DOI:__ __https://doi.org/10.1109/tnnls.2017.2704286__
__

F.J. Hall, **Z. Li**, C.T. Parnass, M.
Rozložník, Sign patterns of J-orthogonal matrices, __Special
Matrices__ 5 (2017),
225–241. DOI: https://doi-org/10.1515/spma-2017-0016

W. Fang, Y.
Gao, K. Fan, **Z. Li**, The second
largest Balaban index (sum-Balaban index) of unicyclic graphs, __J. Math. Res.
Appl. __37 (2017), no. 4, 391–403.

DOI: https://doi.org/10.3770/j.issn:2095-2651.2017.04.002

W. Gao, **Z. Li** and L. Zhang, Characterization of
star sign patterns that require H_{n}, __Linear Algebra and Its Application s__ 499 (2016), 43–65.

DOI: https://doi.org/10.1016/j.laa.2017.06.039

W. Fang, W.
Gao, Y. Gao, F. Gong, G. Jing, **Z. Li**,
Y. Shao, and L. Zhang, The minimum ranks of nonnegative sign patterns and
convex polytopes, __Czech. Math Journal__ 66 (141) (2016), no. 3,
895–911. DOI: https://doi.org/10.1007/s10587-016-0299-1

M. Arav, F.
Hall, **Z. Li**, H. van der Holst, A
graph minors characterization of signed graphs whose
Colin de Verdière parameter ν is two, __Journal of Combinatorial
Theory, Series B__ 116 (2016), 440–455. DOI: https://doi.org/10.1016/j.jctb.2015.09.007

X. Chen, W.
Fang, W. Gao, Y. Gao, G. Jing, **Z. Li**,
Y. Shao, L. Zhang, Essential sign change numbers of full sign pattern matrices.
__Special Matrices__ 4 (2016), 247–254.

DOI: https://doi.org/10.1515/spma-2016-0023

W. Fang, Y.
Gao, Y. Shao, W. Gao, G. Jing, **Z. Li**,
Maximum Balaban index and sum-Balaban index of bicyclic Graphs, __MATCH
Communications in Math. and in Computer Chemistry__ 75 (2016), 129–156.

W. Fang, Y.
Gao, Y. Shao, W. Gao, G. Jing, **Z. Li**,
The generalized competition indices of primitive minimally strong digraphs, * Linear Algebra and Its Applications*
493 (2016), 206–226. DOI: https://doi.org/10.1016/j.laa.2015.11.036

W. Gao, **Z. Li**, L. Zhang, Sign patterns that
require H_{n} exist for each n≥4, * Linear Algebra and Its Applications*
489 (2016), 15–23. DOI: https://doi.org/10.1016/j.laa.2015.09.050

M. Arav, F.
Hall, **Z. Li**, H. van der Holst, J.H.
Sinkovic, L. Zhang, Minimum ranks of sign patterns via sign vectors and
duality, * Electronic Journal of Linear
Algebra* 30 (2015), 360-371. DOI: https://doi.org/10.13001/1081-3810.3077

M. Fiedler, W.
Gao, F.J. Hall, G. Jing, **Z. Li**, M.
Stroev, Ranks of dense alternating sign matrices and their sign patterns, __Linear
Algebra and Its Applications__ 471 (2015), 109–121.

DOI: https://doi.org/10.1016/j.laa.2014.12.034

J. Luo,
T-Z. Huang, H. Li, **Z. Li**, L. Zhang, Tree sign patterns that allow nilpotence of index
4, __Linear Multilinear Algebra__ 63 (2015), no. 5, 1009–1025.

DOI: https://doi.org/10.1080/03081087.2014.914930

W. Gao, **Z. Li**, and L. Zhang, The minimal
critical sets of refined inertias for 3×3 full sign patterns, __Linear
Algebra and Its Applications__ **458**
(2014), 183–196.

DOI: https://doi.org/10.1016/j.laa.2014.06.009

M. Arav, F.
Hall, **Z. Li**, W. Zhou, and L. Zhang,
The minimum rank of a sign pattern with a 1-separation, __Linear Algebra and
Its Applications__ **448** (2014),
205–216.

DOI: https://doi.org/10.1016/j.laa.2014.01.019

L. Zhang, **Z. Li**, T.Z. Huang, Q.F. Zhu, J. Hua, L.H. Zhang, Periodic,
reducible, powerful ray pattern matrices, __Linear Algebra and Its Applications__ **444** (2014), 81–88.

DOI: https://doi.org/10.1016/j.laa.2013.11.007

L. Zhang, T.Z.
Huang, **Z. Li** and J.Y. Zhang, Several
spectrally arbitrary ray patterns, __Linear and Multilinear Algebra__ **61 **(2013), 543-564. https://doi.org/10.1080/03081087.2012.696247

**Z.
Li**, Y. Gao, M. Arav, F. Gong, W. Gao, F.J. Hall and H. van der Holst, Sign
patterns with minimum rank 2 and upper bounds on minimum ranks, __Linear and
Multilinear Algebra__ **61 **(2013),
895-908. DOI: https://doi.org/10.1080/03081087.2012.716431

M. Arav, F. Hall, **Z. Li** and H. van der Holst, The inertia set of a signed graph, __Linear
Algebra and Its Applications__ **439** (2013), 1506–1529. DOI: https://doi.org/10.1016/j.laa.2013.04.032

X. Feng, T.Z.
Huang, **Z. Li**, J. Luo and Y. Gao,
Sign patterns that allow diagonalizability revisited, __Linear and Multilinear
Algebra 61__
(2013), 1223-1233.

DOI: https://doi.org/10.1080/03081087.2012.746329

F. Hall and **Z.
Li**, Sign pattern matrices, Chapter 42 in L. Hogben (Ed.), __Handbook of
Linear Algebra, 2 ^{nd} edition__, Chapman/Hall CRC Press, 2013. DOI: https://doi.org/10.1201/b16113

Y. Shao, Y. Gao
and **Z. Li**, The *m*-competition indices of symmetric primitive digraphs without loop,
__Electronic Journal of Linear Algebra__ **23** (2012), 457-472.

DOI: https://doi.org/10.13001/1081-3810.1532

X. Feng, **Z. Li** and T.Z. Huang, Is every nonsingular matrix diagonally
equivalent to a matrix with all distinct eigenvalues? __Linear Algebra and Its
Applications__ **436** (2012), 120-125.

L. Zhang, T.Z.
Huang, and **Z. Li**, Primitive
zero-symmetric sign pattern matrices with zero diagonal attaining the maximum
base, __Journal of Applied Math __**2012**
(2012), Article ID 276386, 28 pages, doi
10.1155/2012/276386.

M. Arav, F. Hall,
**Z. Li**, K. Kaphle
and N. Manzagol, Spectrally arbitrary tree sign
patterns of order 4, __Electronic Journal of Linear Algebra__ **20** (2010), 180-197.

M. Arav, F.
Hall, **Z. Li**, A. Merid
and Y. Gao, Sign patterns that require almost unique rank, __Linear Algebra
and Its Applications__ **430** (2009),
7-16.

M. Arav, F.
Hall, **Z. Li** and B. Rao, ZPC matrices
and zero cycles, __International Journal of Combinatorics__ **2009** (2009), 1-5.

M. Arav, F.
Hall, **Z. Li** and B. Rao, Rational
solutions of certain matrix equations, __Linear Algebra and Its Applications__
**430** (2009), 660-663.

M. Arav, F. Hall
and **Z. Li**, A Cauchy-Schwarz
inequality for triples of vectors, __Mathematical Inequalities and
Applications__ **11** (2008), 629-634.

Y. Gao, **Z. Li** and Y. Shao, A note on spectrally arbitrary sign patterns, __JP
Journal of Algebra, Number Theory and Applications__ **11** (2008), 15-35

T. Huang, G. Mou,
G. Tian, **Z. Li**, D. Wang, Subdirect
sums of P (P_{0})-matrices and totally nonnegative matrices, __Linear
Algebra and Its Applications__ **429**
(2008), 1730-1743.

Y. Gao, **Z. Li** and Y Shao,
Sign patterns allowing nilpotence of index 3, __Linear Algebra and Its
Applications__ **424** (2007), 55-70.

F. Hall and **Z. Li**, Sign
pattern matrices, Chapter 33 in L. Hogben (Ed.), __Handbook of Linear Algebra__,
Chapman and Hall/CRC Press, 2007.

M. Arav, F. Hall, S. Koyuncu,** Z. Li** and B. Rao, Rational
realizations of the minimum rank of a sign pattern matrix, __Linear Algebra
and Its Applications 411__
(2005), 111-125.

**Z. Li**, F. Hall and J. Stuart, Reducible powerful
ray pattern matrices, __Linear Algebra and Its Applications__ **399**
(2005), 125-140.

G. Chen, G. Davis, F. Hall, **Z.
Li**, K. Patel, M. Stewart, An interlacing result on normalized Laplacians, __SIAM____
Journal on Discrete Mathematics__ **18** (2004), 353-361.

F. Hall, **Z. Li** and B. Rao, From Boolean to sign
pattern matrices, __Linear Algebra and Its Applications__** 393 **(2004),
233-51.

G. Chen, F.
Hall, **Z. Li **and B. Wei, On ranks of matrices
associated with trees, __Graphs and Combinatorics__ **19 **(2003), 323-334.

F. Hall and **Z.
Li**, Sign Patterns, Inverses and generalized inverses — a brief
survey, __Numerical Mathematics: A Journal of Chinese Universities __**12 **(Supplement)
(2003),

8-11.

G. Chen, F.
Hall, **Z. Li **and B. Wei, On ranks of matrices
associated with trees,

__Graphs and Combinatorics__ **19** (2003), no. 3, 323–334.

**Z. Li** and L. Harris, Sign patterns that require all distinct
eigenvalues, __JP Journal of Algebra and Number Theory and Applications__ **2**
(2) (2002), 161-179.

**Z. Li**,
F. Hall and J. Stuart,** **Irreducible powerful ray pattern matrices**,**
__Linear Algebra and its Applications__* ***342** (2002), 47-58.

F. Hall and **Z. Li**, Inertia sets of sign patterns, __Numerical Mathematics: A
Journal of Chinese Universities__ **10 **(2001), 226-240.

F. Hall, **Z.
Li** and Di Wang,** **Symmetric sign pattern matrices that require unique
inertia**,** __Linear Algebra and Its Applications__ **338** (2001),
153-169.

G. Chen, F. Hall, **Z. Li** and H. Zhou, Isomorphisms
involving reversing arcs of di-graphs, __Journal of Combinatorial Mathematics
and Combinatorial Computing __**36** (2001), 155--160.

C. Eschenbach, F. Hall, R. Hemasinha, S.
Kirkland, **Z. Li**, B. Shader, J.
Stuart and J. Weaver, Properties of almost regular tournaments,* *__American Mathematical Monthly__* ***107** (no.10) (2000), 881-892.

C. Eschenbach, F. Hall and **Z. Li**, Eigenvalue distribution of
certain ray patterns, __Czechoslovak Mathematical Journal__ **50**(125)
(2000), 749-762.

C. Eschenbach, F. Hall, R. Hemasinha, S. Kirkland, **Z. Li**, B. Shader, J. Stuart and J. Weaver, On almost regular
tournament matrices,
__Linear____ Algebra and Its Applications__ **306** (2000), 103--121.

C. Eschenbach and **Z. Li**, Potentially nilpotent sign
pattern matrices, __Linear Algebra and its Applications 299__ (1999),
81-99.

F. Hall and **Z. Li**, Sign patterns of idempotent matrices, __Journal of Korean
Mathematical Society__ **36** (1999), 469-487.

C. Eschenbach, F. Hall, D. Harrell
and **Z. Li**, When
does the inverse have the same sign

pattern as the transpose?, __Czechoslovak Mathematical Journal__ **49**(124) (1999), 255-275.

C. Eschenbach, F. Hall and **Z. Li**, From real to complex sign
pattern matrices,

__Bulletin of the Australian
Mathematical Society 57__
(1998), 159-172.

C. Eschenbach, F. Hall, C. Johnson
and **Z. Li**, The graphs of unambiguous
entries

in the product of two (+,-) sign
patterns, __ Linear Algebra and Its
Applications__

**260** (1997), 95-118.

C. Eschenbach and **Z. Li**, How many negative entries can A^{2 } have?,__
Linear __

__Algebra and Its Applications 254__

**Z. Li**, F. Hall and F. Zhang, Sign patterns of nonnegative normal
matrices, __Linear __

__Algebra and Its Applications__
**254 **(1997), 335-354.

C. Eschenbach, F. Hall and **Z. Li**, Some
sign patterns that allow an inverse pair

B and B^{-1}, __Linear
Algebra and Its Applications 252__(1997), 299-321.

**Z. Li**, F. Hall and C. Eschenbach, The structure of nonnegative
cyclic matrices,

__Linear and Multilinear Algebra__
**41** (1996), 23-33.

**Z. Li**, F. Hall and C. Eschenbach, On the period and base of a sign
pattern matrix,

__Linear Algebra and Its
Applications__** 212** (1994),
101-120.

C. Eschenbach, F. Hall and **Z. Li**, Eigenvalue frequency and
consistent sign

pattern matrices, __Czechoslovak
Mathematical Journal__ **44 **(1994),
461-479.

C. Eschenbach, F. Hall and **Z. Li**, Sign pattern matrices and
generalized inverses,

__Linear Algebra and Its
Applications__ **211 **(1994), 53-66.

**Z. Li**, A determinantal description of GCD-closed sets and k-sets, __Linear
and __

__Multilinear Algebra__ **31 **(1992), 245-250.

**Z. Li**, The determinants of GCD matrices, __Linear Algebra and Its
Applications__

**134 **(1990), 137-143.

I am
a member of the Editorial Board of JP Journal of
Algebra, Number Theory and Applications.

Guest
editor of Mathematics.

Math 2211 Calculus of One Variable I

Math 2212 Calculus of One Variable II

Math 2215 Multivariate Calculus

Math 2420 Discrete Mathematics

Math 2641 Linear Algebra I

Math 3000 Bridge to Higher
Mathematics

Math 4435/6435 Linear Algebra II

Math 4441/6441 Modern Algebra I

Math 4450/6450 Theory of Numbers

Math 4661/6661 Analysis I

Math 4662/6662 Analysis II

Math 8200 Advanced Matrix Analysis

Math 8201 Combinatorial Matrix Theory

Math 8210 Topics in Applied
Matrix Analysis

Math 8220 Abstract Algebra I

Math 8535 Applied Matrix Algebra

Angela and Andrew with Grandpa in Dunhuang, 2008

Ying and Zhongshan at Qinghai Lake, 2009

Ying and Zhongshan in Chengdu, 2008

Ying and Zhongshan in Hangzhou, 2008

Ying and Zhongshan in Shanghai, 2008