HR job title
- Professor
- Contact Info
- 1 979 845 2927
Zhou, Jianxin Professor
Positions
- Professor, Mathematics, College of Arts and Sciences
My research focuses on applied analysis and scientific computation.
- Overview
- Publications
- Teaching
- Works By Students
- Background
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Overview
Publications
selected publications
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academic article
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Li, Z., Wang, Z., & Zhou, J.
(2017).
A New Augmented Singular Transform and its Partial Newton-Correction Method for Finding More Solutions. Journal of Scientific Computing.
71(2), 634-659.
-
Li, M., & Zhou, J.
(2017).
Finding Gateaux-Saddles by a Local Minimax Method. Numerical Functional Analysis and Optimization.
38(2), 205-223.
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Wang, C., & Zhou, J.
(2015).
A New Approach for Numerically Solving Nonlinear Eigensolution Problems. Journal of Scientific Computing.
64(1), 109-129.
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Xie, Z., Yi, W., & Zhou, J.
(2015).
An augmented singular transform and its partial Newton method for finding new solutions. Journal of Computational and Applied Mathematics.
286, 145-157.
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Chen, X., & Zhou, J.
(2015).
Estimate of Morse index of cooperative elliptic systems and its application to spatial vector solitons. Journal of Computational and Applied Mathematics.
281, 169-181.
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Efendiev, Y., Galvis, J., Presho, M., & Zhou, J.
(2014).
A MULTISCALE ENRICHMENT PROCEDURE FOR NONLINEAR MONOTONE OPERATORS. 48(2), 475-491.
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Wang, C., & Zhou, J.
(2013).
An orthogonal subspace minimization method for finding multiple solutions to the defocusing nonlinear Schrdinger equation with symmetry. Numerical Methods for Partial Differential Equations.
29(5), 1778-1800.
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Le, A. n., Wang, Z., & Zhou, J.
(2013).
Finding Multiple Solutions to Elliptic PDE with Nonlinear Boundary Conditions. Journal of Scientific Computing.
56(3), 591-615.
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Xie, Z., Yuan, Y., & Zhou, J.
(2012).
On Finding Multiple Solutions to a Singularly Perturbed Neumann Problem. SIAM Journal on Scientific Computing.
34(1), a395-a420.
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Yao, X., & Zhou, J.
(2011).
A numerically based investigation on the symmetry breaking and asymptotic behavior of the ground states to the p-Hnon equation. Electronic Journal of Differential Equations.
2011.
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Zhou, J.
(2011).
Global Sequence Convergence of a Local Minimax Method for Finding Multiple Solutions in Banach Spaces. Numerical Functional Analysis and Optimization.
32(12), 1365-1380.
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Chen, X., & Zhou, J.
(2010).
A local min-max-orthogonal method for finding multiple solutions to noncooperative elliptic systems. Mathematics of Computation.
79(272), 2213-2236.
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Chen, X., & Zhou, J.
(2008).
On homotopy continuation method for computing multiple solutions to the Henon equation. Numerical Methods for Partial Differential Equations.
24(3), 728-748.
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Chen, X., Zhou, J., & Yao, X.
(2008).
A numerical method for finding multiple co-existing solutions to nonlinear cooperative systems. Applied Numerical Mathematics.
58(11), 1614-1627.
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Yao, X., & Zhou, J.
(2008).
Numerical Methods for Computing Nonlinear Eigenpairs: Part II. Non-Iso-Homogeneous Cases. SIAM Journal on Scientific Computing.
30(2), 937-956.
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Zhou, J.
(2007).
Optimization with some uncontrollable variables: a min-equilibrium approach. Journal of Industrial and Management Optimization.
3(1), 129-138.
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Yao, X., & Zhou, J.
(2007).
Numerical Methods for Computing Nonlinear Eigenpairs: Part I. Iso-Homogeneous Cases. SIAM Journal on Scientific Computing.
29(4), 1355-1374.
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Yao, X., & Zhou, J.
(2007).
Unified Convergence Results on a Minimax Algorithm for Finding Multiple Critical Points in Banach Spaces. SIAM Journal on Numerical Analysis.
45(3), 1330-1347.
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Chen, G., Ding, Z. H., Hsu, S. B., Kim, M., & Zhou, J. X.
(2006).
Mathematical analysis of a Bohr atom model. Journal of Mathematical Physics.
47(2), 022107-022107.
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Yao, X., & Zhou, J.
(2005).
A local minimax characterization for computing multiple nonsmooth saddle critical points. Mathematical programming.
104(2-3), 749-760.
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Li, Q., & Zhou, J. X.
(2005).
The uniqueness of cross-validation selected smoothing parameters in kernel estimation of nonparametric models. ECONOMETRIC THEORY.
21(5), 1017-1025.
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Zhou, J.
(2005).
Instability analysis of saddle points by a local minimax method. Mathematics of Computation.
74(251), 1391-1411.
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Zhou, J.
(2005).
Saddle critical point analysis and computation. Nonlinear Analysis : Modelling and Control.
63(5-7), 1000-1009.
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Yao, X., & Zhou, J.
(2005).
A Minimax Method for Finding Multiple Critical Points in Banach Spaces and Its Application to Quasi-linear Elliptic PDE. SIAM Journal on Scientific Computing.
26(5), 1796-1809.
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Zhou, J.
(2004).
A local min-orthogonal method for finding multiple saddle points. Journal of Mathematical Analysis and Applications.
291(1), 66-81.
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Wang, Z., & Zhou, J.
(2004).
A Local Minimax-Newton Method for Finding Multiple Saddle Points with Symmetries. SIAM Journal on Numerical Analysis.
42(4), 1745-1759.
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Li, Y., & Zhou, J.
(2003).
Convergence Results of a Local Minimax Method for Finding Multiple Critical Points. SIAM Journal on Scientific Computing.
24(3), 865-885.
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Chen, G., Hsu, S. B., & Zhou, J. X.
(2002).
Nonisotropic spatiotemporal chaotic vibration of the wave equation due to mixing energy transport and a van der Pol boundary condition. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering.
12(3), 535-559.
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Chen, G., Ni, W. M., Perronnet, A., & Zhou, J. X.
(2001).
Algorithms and visualization for solutions of nonlinear elliptic equations part II: Dirichlet, Neumann and Robin boundary conditions and problems in 3D. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering.
11(7), 1781-1799.
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Li, Y., & Zhou, J.
(2001).
A Minimax Method for Finding Multiple Critical Points and Its Applications to Semilinear PDEs. SIAM Journal on Scientific Computing.
23(3), 840-865.
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Chen, G., Zhou, J. X., & Ni, W. M.
(2000).
Algorithms and visualization for solutions of nonlinear elliptic equations. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering.
10(7), 1565-1612.
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Chen, G., Deng, Y. H., Ni, W. M., & Zhou, J. X.
(2000).
Boundary element monotone iteration scheme for semilinear elliptic partial differential equations, part II: Quasimonotone iteration for coupled 2 x 2 systems. Mathematics of Computation.
69(230), 629-652.
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Chen, G. O., Hsu, S. B., Zhou, J. X., Chen, G. R., & Crosta, G.
(1998).
Chaotic vibrations of the one-dimensional wave equation due to a self-excitation boundary condition - Part I: Controlled hysteresis. Transactions of the American Mathematical Society.
350(11), 4265-4311.
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Chen, G., Hsu, S. B., & Zhou, J. X.
(1998).
Snapback repellers as a cause of chaotic vibration of the wave equation with a van der Pol boundary condition and energy injection at the middle of the span. Journal of Mathematical Physics.
39(12), 6459-6489.
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You, P., Ding, Z., & Zhou, J.
(1998).
Optimal Boundary Control of the Stokes Fluids with Point Velocity Observations. SIAM Journal of Control and Optimization.
36(3), 981-1004.
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Chen, G., Hsu, S. B., & Zhou, J. X.
(1998).
Chaotic vibrations of the one-dimensional wave equation due to a self-excitation boundary condition. II. Energy injection, period doubling and homoclinic orbits. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering.
8(3), 423-445.
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Chen, G., Hsu, S. B., & Zhou, J. X.
(1998).
Chaotic vibrations of the one-dimensional wave equation due to a self-excitation boundary condition. III. Natural hysteresis memory effects. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering.
8(3), 447-470.
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Chen, G., Fulling, S. A., & Zhou, J. X.
(1997).
Asymptotic equipartition of energy by nodal points of an eigenfunction. Journal of Mathematical Physics.
38(10), 5350-5360.
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You, P., & Zhou, J.
(1997).
Constrained LQR Problems in Elliptic Distributed Control Systems with Point Observations--- on Convergence Rates. SIAM Journal of Control and Optimization.
35(5), 1739-1754.
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Ding, Z., & Zhou, J.
(1997).
Constrained LQR problems in elliptic distributed control systems with point observations - Convergence results. Applied Mathematics and Optimization.
36(2), 173-201.
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Chen, G. O., Zhou, J. X., & Hsu, S. B.
(1996).
Linear superposition of chaotic and orderly vibrations on two serially connected strings with a Van der Pol joint. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering.
6(8), 1509-1527.
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Deng, Y. H., Chen, G., Ni, W. M., & Zhou, J. X.
(1996).
Boundary element monotone iteration scheme for semilinear elliptic partial differential equations. Mathematics of Computation.
65(215), 943-982.
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Ding, Z., Ji, L., & Zhou, J.
(1996).
Constrained LQR Problems in Elliptic Distributed Control Systems with Point Observations. SIAM Journal of Control and Optimization.
34(1), 264-294.
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Zhou, J. X.
(1995).
On the Existence of Equilibrium for Abstract Economies. Journal of Mathematical Analysis and Applications.
193(3), 839-858.
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Tian, G., & Zhou, J.
(1995).
Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization. Journal of Mathematical Economics.
24(3), 281-303.
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CHEN, G., MORRIS, P. J., & ZHOU, J. X.
(1994).
VISUALIZATION OF SPECIAL EIGENMODE SHAPES OF A VIBRATING ELLIPTIC MEMBRANE. SIAM Review.
36(3), 453-469.
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Zhou, J. X.
(1994).
Extension of the Zorn lemma to general nontransitive binary relations. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS.
80(2), 333-347.
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Baye, M. R., Tian, G., & Zhou, J.
(1993).
Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs. Review of Economic Studies.
60(4), 935-948.
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Tian, G. Q., & Zhou, J. X.
(1993).
Quasi-Variational Inequalities without the Concavity Assumption. Journal of Mathematical Analysis and Applications.
172(1), 289-299.
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Tian, G., & Zhou, J.
(1992).
The maximum Theorem and the existence of Nash equilibrium of (generalized) games without lower semicontinuities. Journal of Mathematical Analysis and Applications.
166(2), 351-364.
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CHEN, G., COLEMAN, M. P., & ZHOU, J. X.
(1991).
ANALYSIS OF VIBRATION EIGENFREQUENCIES OF A THIN PLATE BY THE KELLER-RUBINOW WAVE METHOD .1. CLAMPED BOUNDARY-CONDITIONS WITH RECTANGULAR OR CIRCULAR GEOMETRY. SIAM Journal on Applied Mathematics.
51(4), 967-983.
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ZHOU, J. X., & CHEN, G.
(1991).
THE WAVE METHOD FOR DETERMINING THE ASYMPTOTIC DAMPING RATES OF EIGENMODES .1. THE WAVE-EQUATION ON A RECTANGULAR OR CIRCULAR DOMAIN. SIAM Journal of Control and Optimization.
29(3), 656-677.
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Tian, G., & Zhou, J.
(1991).
Quasi-variational inequalities with non-compact sets. Journal of Mathematical Analysis and Applications.
160(2), 583-595.
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CHEN, G., & ZHOU, J. X.
(1990).
THE WAVE-PROPAGATION METHOD FOR THE ANALYSIS OF BOUNDARY STABILIZATION IN VIBRATING STRUCTURES. SIAM Journal on Applied Mathematics.
50(5), 1254-1283.
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CHEN, G., BRIDGES, T. J., & ZHOU, J.
(1988).
MINIMIZING THE REFLECTION OF WAVES BY SURFACE IMPEDANCE USING BOUNDARY ELEMENTS AND GLOBAL OPTIMIZATION. Wave Motion.
10(3), 239-255.
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ZHOU, J. X., & CHEN, G. N.
(1988).
DIAGONAL CONVEXITY CONDITIONS FOR PROBLEMS IN CONVEX-ANALYSIS AND QUASI-VARIATIONAL INEQUALITIES. Journal of Mathematical Analysis and Applications.
132(1), 213-225.
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CHEN, G., KRANTZ, S. G., RUSSELL, D. L., WAYNE, C. E., WEST, H. H., & ZHOU, J. X.
(1988).
MODELING, ANALYSIS AND TESTING OF DISSIPATIVE BEAM JOINTS - EXPERIMENTS AND DATA SMOOTHING. Mathematical and Computer Modelling.
11(C), 1011-1016.
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CHEN, G., ZHENG, Q., & ZHOU, J. X.
(1986).
MINIMAX METHODS FOR OPEN-LOOP EQUILIBRIA IN N-PERSON DIFFERENTIAL-GAMES .1. LINEAR QUADRATIC GAMES AND CONSTRAINED GAMES. Proceedings of the Royal Society of Edinburgh Section A Mathematics.
103(1-2), 15-34.
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Li, Z., Wang, Z., & Zhou, J.
(2017).
A New Augmented Singular Transform and its Partial Newton-Correction Method for Finding More Solutions. Journal of Scientific Computing.
71(2), 634-659.
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book
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Chen, G., & Zhou, J.
(2010).
BOUNDARY ELEMENT METHODS WITH APPLICATIONS TO NONLINEAR PROBLEMS 2nd edition. Springer Science & Business Media.
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Chen, G., Lasiecka, I., & Zhou, J.
(2001).
Control Of Nonlinear Distributed Parameter Systems. Ed. Chen, Goong.
CRC Press.
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Chen, G., & Zhou, J.
(1993).
Vibration and Damping in Distributed Systems Vol. I: Analysis, Estimation, Attenuation and Design. CRC Press.
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Chen, G., & Zhou, J.
(1993).
Vibration and Damping in Distributed Systems, Volume II: WKB and Wave Methods, Visualization and Experimentation. CRC Press.
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Chen, G., & Zhou, J.
(1992).
Boundary element methods. Academic Press.
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Chen, G., & Zhou, J.
(2010).
BOUNDARY ELEMENT METHODS WITH APPLICATIONS TO NONLINEAR PROBLEMS 2nd edition. Springer Science & Business Media.
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chapter
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Chen, G., Hsu, S. B., & Zhou, J. X.
(2003).
Chaotic vibration of the wave equation with nonlinear feedback boundary control: Progress and open questions. Lecture Notes in Control and Information Sciences.
Chen, G., & Yu, X. (Eds.),
Chaos Control.
(pp. 25-50).
Springer Nature.
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Chen, G., Hsu, S. B., & Zhou, J. X.
(2003).
Chaotic vibration of the wave equation with nonlinear feedback boundary control: Progress and open questions. Lecture Notes in Control and Information Sciences.
Chen, G., & Yu, X. (Eds.),
Chaos Control.
(pp. 25-50).
Springer Nature.
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conference paper
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Chen, G., & Zhou, J.
(1990).
Boundary element method for shape control of distributed parameter elastostatic systems. 161-175.
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Ji, L., & Zhou, J.
(1990).
The boundary element method for boundary control of the linear Stokes flow. IEEE Conference on Decision and Control.
1192-1194.
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Zhou, J.
(1989).
Computations of eigenfunctions and eigenfrequencies of two dimensional vibrating structures by the boundary element method. IEEE Conference on Decision and Control.
2045-2049.
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Chen, G., & Zhou, J.
(1987).
COMPUTING OPTIMAL BOUNDARY CONTROLS OF A PLATE BY THE BOUNDARY ELEMENT METHOD. IEEE Conference on Decision and Control.
992-996.
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Chen, G., & Zhou, J.
(1990).
Boundary element method for shape control of distributed parameter elastostatic systems. 161-175.
Teaching
teaching activities
- MATH304 Linear Algebra Instructor
- MATH308 Differential Equations Instructor
- MATH311 Top In Applied Math I Instructor
- MATH491 Research Instructor
- MATH602 Meth Appl Part Diff Eq Instructor
- MATH651 Optimization I Instructor
- MATH652 Optimization Ii Instructor
- MATH684 Prof Internship Instructor
- MATH685 Directed Studies Instructor
- MATH691 Research Instructor
- MATH691 Research Instructor
Works By Students
chaired theses and dissertations
-
Chen, Xianjin (2009-05). Analysis and computation of multiple unstable solutions to nonlinear elliptic systems.
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Wang, Changchun (2012-07). On Computing Multiple Solutions of Nonlinear PDEs Without Variational Structure.
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Yao, Xudong (2005-11). Minimax methods for finding multiple saddle critical points in Banach spaces and their applications.
Background
education and training
- Ph.D. in Mathematics, Pennsylvania State University - (State College, Pennsylvania, United States) 1986
Contact
first name
- Jianxin
has last name
- Zhou
mailing address
-
Texas A&M University
Mathematics
3368 TAMU
College Station, TX 77843-3368
USA
Other
- j-zhou@tamu.edu