,	(419) 530-2970 bou@math.utoledo.edu

Dr. Biao Ou

Work History	2006–current Department of Mathematics, Univ. of Toledo Professor
	1999–2006 Department of Mathematics, Univ. of Toledo Associate Professor
	1993–1999 Department of Mathematics, Univ. of Toledo Assistant Professor
	1987–1993 Department of Mathematics, Univ. of Minnesota Graduate Assistant
	1982–1986 Zhejiang University Hangzhou, P.R. China Teaching and Researching Associate
Education	Ph.D., 1993, University of Minnesota. M.S., 1986, Zhejiang University, P.R. China. B.S., 1982, Zhejiang University, P.R. China.
Math Interests	Computer Recognition of People’s Handwriting, Singular Integral Equations, Conformal Geometry, Crystal Twinning, Stable Configurations in Liquid Crystals, Potential Flows in Space, the Sobolev Trace Imbedding Theorem and the Moving Planes, Surfaces of Constant Mean Curvatures, Free Boundaries, Crystal Precipitation.
Fellowships	Research Fellow, Nankai Mathematics Institute, Tianjing, P.R. China, 1985. Research Fellow, Institute for Mathematics and Its Applications, Minneapolis/St. Paul, 1995.
Courses Taught	Calculus Linear Algebra (sometimes with Maple and Matlab). Differential Equations (Textbooks: Ordinary Differential Equations by Birkhoff and Rota, Partial Differential Equations by John and by Laurence C. Evans). Advanced Applied Mathematics (Textbook: Advanced Engineering Mathematics by Kreyszig). Numerical Analysis (Textbook: Numerical Analysis by Burden and Faires). Mathematical Methods of Physics (Textbook: Mathematical Methods for Physicists by Arfken and Weber).

Publications

Curvature function in the recognition of people’s handwriting. Submitted. (with Wenxiong Chen and Congming Li) Alternative proofs on the radial symmetry and monotonicity of positive regular solutions to a singular integral equation. Submitted. (with Wenxiong Chen and Congming Li) Classification of solutions for an integral equation. Communications on Pure and Applied Mathematics. 59 (2006), 330-343. (with Wenxiong Chen and Congming Li) Classification of solutions to a system of integral equations. Communications on Partial Differential Equations. 30 (1-3) (2005), 59-65. (with Wenxiong Chen and Congming Li) Qualitative properties of solutions for an integral equation. Discrete and Continuous Dynamical systems. 12 (2) (2005), 347—354. (with Guozhen Lu) A Poincaré inequality on R^n and its application to potential fluid flows. Communications in Applied Nonlinear Analysis. 12 (1) (2005), 1--24. An equality for the curvature function of a simple and closed curve on the plane. International Journal of Mathematics and Mathematical Sciences. 49 (1) (2003). 3115-3122. Examinations on a 3-dimensional differentiable vector field that equals its own curl. Communications on Pure and Applied Analysis, 2 (2) (2003), 251-157. A Uniqueness theorem for harmonic functions on the upper-half plane. Conformal Geometry and Dynamics, 4(2000), 120-125. A Remark on a singular integral equation. Houston Journal of Mathematics, 25 (1) (1999), 181–184. On a kinematic compatibility equation related to elastic stress-free joints and crystal twins. Journal of Elasticity, 45 (1996), 73–89. Positive harmonic functions on the upper-half space satisfying a nonlinear boundary condition, Differential and Integral Equations, 19 (3 & 4) (1996), 1157–1164. Global solutions to a free boundary problem. Communications in Partial Differential Equations, 19 (3 & 4) (1994), 369–397. An irrotational and incompressible flow around a body in space. Journal of Partial Differential Equations, 7 (1994), 160–170. (J. of PDE is an English journal published in P.R. China.) (with Guangchang Dong) Subsonic flows around a body in space. Communications in Partial Differential Equations, 18 (1 & 2) (1993), 355-379. (with David Kinderlehrer and Noel Walkington) The elementary defects of the Oseen-Frank energy for a liquid crystal. C.R.Acad.Sci.Paris, Series I, 316 (1993), 465-470. Uniqueness of x/|x| as a stable configuration in liquid crystals. The Journal of Geometric Analysis, 2(2) (1992), 183-194. (with David Kinderlehrer) Second variation of liquid crystal energy at x/|x|. Proceedings of Royal Society in London, A, 436 (1992), 475-484. (with Avner Friedman and David Ross) Crystal Precipitation with discrete initial data. Journal of Mathematical Analysis and Applications, 137(2) (1989), 576-590. (with Avner Friedman) A model of crystal precipitation. Journal of Mathematical Analysis and Applications, 137(2) (1989), 550-575.