Research
EDUCATION
1987 PhD, Mathematics, University of California at Los Angeles
1985 M.S, Mathematics, University of California at Los Angeles
1982 B.S, Mathematics, University of Science and Technology of China
PROFESSIONAL APPOINTMENTS
2020- Department Chair
2019-2020 Interim Department Chair
2017-2019 Graduate Coordinator, Math/Stat
1998 Fall Visiting Professor, University of Washington
1997- Professor, Wichita State University
1992-1997 Associate Professor, Wichita State University
1990-1992 Assistant Professor, Wichita State University
1987-1990 Assistant Professor, University of Washington
AREAS OF RESEARCH
Partial Differential Equations, Differential Geometry, Inverse Problems
RESEARCH GRANTS
1990-1998 NSF, Classical Analysis
2004-2008 Research Grant from Fudan University
PhD STUDENTS
Feng Qiu Inverse Problems for Linear and Semilinear Elliptic Partial Differential Equations of the Schrodinger Type, 1998
David Hervas An Inverse Boundary Value Problem for a Quasilinear Elliptic Differential Equation, 2001
Md Ibrahim Kholil Inverse Problems for Quasilinear Elliptic Equations in Anisotropic Medium, 2023
PUBLICATIONS
Some special properties of umbilic submanifolds of Riemannian manifolds with constant curvatures, J. Univ. Sci. Tech. Chin., 14 (2), (1984), 187-194.
Submanifolds with constant mean curvature in spheres, Adv. in Math. (Beijing), 16 (1), (1987), 91-96.
On complete hypersurfaces in R-4 with constant scalar curvature, Chin. Ann. of Math., Ser. A8 (1987), No.1, 1-8.
On compact hypersurfaces in S-4 with constant scalar curvature, Chin. Ann. Of Math., Ser. A8 (1987), No.3, 273-286.
On the uniqueness for a multidimensional hyperbolic inverse problem, Comm. in PDE, 13 (10), (1988), 1189-1208.
On an inverse boundary value problem in two dimensions, Comm. in PDE, 14 (8&9), (1989), 1101-1113.
On the continuous dependence for an inverse initial boundary value problem, J. Math. Anal. and Appl. 150 (1), (1990), 188- 204.
The inverse conductivity problem in two dimensions, J. Diff. Equations, 87 (2), (1990), 227-255.
Generic uniqueness for an inverse boundary value problem, Duke Math. J., 62 (1), (1991), 131-155. (with G. Uhlmann)
Uniqueness for formally determined inverse boundary value problems, Comp. Math. Applic., 22 (4/5), (1991), 67-80.
Generic uniqueness for formally determined inverse problems, Inverse Problems in Engineering Sciences, ICM-90 Satellite Conf. Proc., Springer- Verlag, 145-152. (with G. Uhlmann)
An inverse boundary value problem for Schrodinger operators with vector potentials, (1991), Trans. of AMS, 338 (2),
(1993), 953-969.
An inverse boundary value problem for Maxwell's equations, Archive Rat. Mech. Anal., 119, (1992), 71-93. (with G.
Uhlmann)
Stability estimates for hyperbolic inverse problems with local boundary data, Inverse Problems, 8, (1992), 193-206. (with V.
Isakov)
Inverse scattering for singular potentials in two dimensions, Trans. of AMS, 338 (1), (1993), 363-374. (with G. Uhlmann)
An inverse boundary value problem for Schrodinger operators with vector potentials in two dimensions, Comm. in PDE, 18
(1&2), (1993), 83-124.
Recovery of singularities for formally determined inverse problems, Comm. in Math. Physics, 153, (1993), 431-445. (with G.
Uhlmann)
Inverse boundary value problems for Schrodinger operators, Inverse Problems in Mathematical Physics, Lecture Notes in
Physics, 422, (1993), Springer-Verlag, 216-230.
An inverse boundary value problem for St. Venant-Kirchhoff's materials, Inverse Problems, 10 (1994), 1159-1163. (with G.
Nakamura)
A global identifiability theorem for the Schrodinger equation in magnetic field, Math. Ann., 303 (1995), 377-388. (with G.
Nakamura and G. Uhlmann)
The inverse scattering at fixed energies in two dimensions, Indiana Univ. Math. Journal, 44 (3), (1995), 883-896. (with V.
Isakov)
On a quasilinear inverse boundary value problem, Math. Z, 221 (2), (1996), 293-305.
Electrical impedance tomography in nonlinear materials, Journees “Equations aux Derivees Partielles" (Saint-Jean-de-
Monts, 1996), Exp. No. XIV, 11pp., Ecole Polytech., Palaiseau, 1996. (with G. Uhlmann)
Inverse problems in quasilinear anisotropic medium, Amer. Journal of Math. 19 (40), (1997), 771-797. (with G. Uhlmann)
Inverse boundary value problems for nonlinear elasticity, Inverse Problems in Engineering Sciences, Proc. of IPES, (1999),
Springer-Verlag. (with G. Nakamura)
An inverse boundary value problem for quasilinear elliptic equations. Comm. in PDE, 27 (2002), 11&12, 2449-2490. (with
D. Hervas)
An inverse problem for inhomogeneous conformal Killing field equations, Proc. Amer. Math. Soc. 131 (2003), 1583-1590.
Anisotropic inverse problems in two dimensions, Inverse Problems, 19 (2003) 1001-1010. (with Gunther Uhlmann)
A pinching theorem on submanifolds with parallel mean curvature vectors, Colloquium Mathematicum, 98 (2), (2003), 189-
199.
Inverse boundary value problems for a class of semilinear elliptic equations, Advances in Applied Mathematics, 32 (4),
(2004), 791-800.
Note on exponentially growing solutions to the Schrodinger equations, Communications in Applied Math, 9 (2005), 327-
336.
Conjectures in inverse boundary value problems for quasilinear elliptic equations, CUBO Journal, 7 (3), (2005), 65-73.
Anisotropic inverse problems for quasilinear elliptic equations, Journal of Physics, 12 (2005), 156-164.
Inverse boundary value problems for elliptic equations, Advances in Mathematics and Its Applications, USTC, (2008), 149-
171.
An inverse boundary value problem for semilinear elliptic equations, Electron. J. Diff. Equ., Vol. 2010 (2010), No. 37, 1-5.
A method for searching for prime pairs in the Goldbach conjecture, International J. Math & Comp. 10 (2015), No 2, 115-
126. (with W. Zeng)
A uniqueness theorem for inverse problems in quasilinear anisotropic media, Inverse Problems and Imaging. Vol. 16, No. 6, (2022), 1571–1577. (with M. Kholil)
A uniqueness theorem for inverse problems in quasilinear anisotropic media II, Inverse Problems and Imaging, Vol. 18, No. 1, (2024), 104-112. (with M. Kholil)