Associate Professor Emeritus
Ph.D. in Mathematics, 1976, Brown University. Providence, Rhode Island
Thesis Advisor: Walter A. Strauss
Thesis Title: Time Decay of Two Conservative Equations
B.S., 1969, National Tsinghua University (Taiwan)
Summer Enrichment Program in Mathematics and Technology for Talented Youth
(with Chun-Te Lee, Chun-Che Lee, and Mei-Li Liu) Some notes on the computing of two types of fifth-order Korteweg-de Vries equations. Submitted to Numerical Mathematuics, Theory, Methods and Applications, April 2016.
(with Chun-Te Lee, Chun-Che Lee, and Mei-Li Liu) On the numerical modeling of capillary flow dynamics in a microchannel model using finite element method. Submitted to Journal of Applied Mechanics and Technical Physics, December 2015.
Manuscript in revision
Institute of Mathematics, Academia Sinica, Taipei, Taiwan. May 19-June 14, 2016; June 9-30, 2015; January 4-16, 2013; January 11-20, 2012;
January 3-12, 2011; January 5-12, 2010; March 21-April 18, 2008.
Nonexistence of nontrivial solutions for some nonlinear elliptic equations in Rn. NCTS International Workshop on Geometric Analysis & Subelliptic PDEs, National Taiwan University, Taipei, Taiwan. May 24-26, 2016.
On the Integrability of Nonlinear Evolution Equations: one-spatial dimension and two-spatial dimensions. Mini-Workshop on Analysis and Differential Equations, Academia Sinica, Taipei, Taiwan, January 12-14, 2013.
Special Summer One-week Mini-course
The Applications of Graph Theory in the Network Analysis, School of Journalism and Communication Xiamen University, Xiamen, China. June 30-July 4, 2014.
Fairfax County Elementary and Middle School Science and Engineering Fair Judge. May 7, 2016
Siemens Competition Stage 1 Judge. October 5-9, 2014.
Undergraduate Research Mentor
Graduated Ph. D. students
Edward Bosch (CSI/SCS 2005 Ph. D.). Title of the dissertation 'Perturbed neural network backpropagation learning and adaptive wavelets for dimension reduction for improved classification of high-dimensional datasets'
Blane Laubis (CDS/COS 2009 Ph. D.). Title of the dissertation 'Optimal Investment Allocation in a Jump Diffusion Risk Model with Bond and Stock Investments: An Analysis of Several Examples'
Graduated Master Degree students
Yukiko Yarnall (March 2016): Paper presentation 'Newton's Method under Weak Kantorovich Conditions'
Mahyar Alizadeh (December 2015): Paper presentation 'Kantorovich's Theorem on Newton's Method'
Sakti Anupindi (August 2014): Paper presentation 'Applications of Ekeland Variational Principle'
- (with Manal Badgaish and Padmanabhan Seshaiyer) Nonlinear Dynamics and Analysis of Intracranial Saccular Aneurysms with Growth and Remodeling. Journal of Nonlinear Dynamics, Volume 2016 (2016), Article ID 2869083. http://www.hindawi.com/journals/jndy/2016/2869083/
- Time Decay for the Solutions of a Fourth-Order Nonlinear Schrodinger Equation. Contemporary Mathematics, Volume 581 (2012), pp. 169-174.
- Local Time Decay for a Quasilinear Schrodinger Equation. Methods and Applications of Analysis, Volume 16, No. 3 (2009), pp. 313-320.
- (with Blane Laubis) Optimal Investment Allocation in a Jump Diffusion Risk Model with Investment: A Numerical Analysis of Several Examples. Proceedings (electronic) of 43rd Actuarial Research Conference (2008) http://www.soa.org/news-and-publications/publications/proceedings/arch/arch-2009-iss1.aspx
- Local time decay for a nonlinear beam equation. Methods and Applications of Analysis, Volume 11, No. 1 (2004) pp. 65 - 68.
- (with H. H. Chen) On a Direct Contruction of Inverse Scattering Problems for Integrable Nonlinear Evolution Equations in the Two-spatial Dimension, International Journal of Mathematics and Mathematical Sciences, (2004), No. 58, pp. 3117-3128
- (with H. H. Chen) On the Integrability of Nonlinear Evolution Equations in Two-spatial Dimensions, New Studies in Advanced Mathematics, volume 4, (2003) International Press, pp.659-664
- (with E. H. Bosch) Wavelet-based Dimension Reduction of Hyperspectral Image Classification. with E.H. Bosch, Proceeding of SPIE, Vol. 5093 (2003), pp. 57-69
- On the Symmetries, Constants of Motion, and the Hamiltonian Structure of the Modified Kadomtsev-Petviashvili Equation, Bulletin of the Institute of Mathematics, Academia Sinica, Vol. 19 (1991), pp. 1-9
- (with H. H. Chen) On the Integrability of Nonlinear Evolution Equations. Nonlinaer Semigroups, Partial Differential Equations, and Attractors, edited by T. L. Gill and W. W. Zachary, Lecture Notes in Mathematics, Vol. 1394 (1989) pp. 30-43.
- (with H. H. Chen) Integrability of Nonlinear Wave Equations. Integrability in Dynamical Systems, edited by J. Buchler, J. Ipser, and C. Williams, Annals of the New York Academy of Sciences, 536 (1988) pp. 91-99.
- (with H. H. Chen) Factorization of the Recursion Operators and the Integrability of Nonlinear Evolution Equations"), Topics in Soliton Theory and Exactly Solvable Nonlinear Equations, edited by M. Ablowitz, B. Fuchssteiner, and M. Kruskal (World Scientific Publishing Co., 1987) pp. 97-107.
- (with H. H. Chen) On the Infinite Hierarchies of Symmetries of Symmetries and Constants of Motion for the Kadomtsev-Petviashvili Equation" (with H. H. Chen), Physica D, 26 (1987) 171-180.
- (with H. H. Chen) On the Integrability of Multidimensional Nonlinear Evolution Equations. Journal of Mathematical Physics, 28 (1987) 347-350.
- (with H. H. Chen and Y. C. Lee) On the Direct Construction of the Inverse Scattering Operators of Integrable Nonlinear Hamiltonian Systems. Physica D, 26(1987) 165-170.
- Asymptotic Behavior in Time of the Solutions of a System of Multidimensional Coupled Nonlinear Schrodinger Equations. Tamkang Journal of Mathematics, 17 (1986) 27-30.
- Local Energy Decay for waves Governed by a System of Nonlinear Schrodinger Equations in a Nonuniform Medium. International Journal of Mathematics and Mathematical Sciences, 8 (1985) 621-623.
- (with H. H. Chen and Y. C. Lee) A New Hierachy of Symmetries for the Integrable Nonlinear Evolution Equations. Advances in Nonlinear Waves, Volume II, edited by L. Debnath (Pitman, New York, 1985) pp. 233-239.
- On a Nonlinear Modulated Dispersive Wave. Proceedings of the National Science Council of the Republic of China, 8 (1984) 129-131.
- (with. H. Chen and Y. C. Lee) On a New Hierarchy of Symmetries for the Kadomtsev-Petviashvili Equation. Physica D, 9 (1983) 439-445.
- (with H. H. Chen and Y. C. Lee) On a New Hierarchy of Symmetries for the Benjamin-Ono Equation. Physics Letters A, 91 (1982) 381-383.
- Decay of the Local Energy of a Two-dimensional Wave in a Nonlinear Weakly Negative Dispersive Medium. Physics Letters A, 91 (1982) 278-279.
- (with H. H. Chen) Constraints and Conserved Quantities of the Kadomtsev-Petviashvili Equations. Physics Letters A, 89 (1982) 163-167.
- (with H. L. Hwang, D. C. Liu, and J. J. Loferski) Numerical Analysis of Junction-depth Effect in the Grating-type Si Solar Cell. Journal of Applied Physics, 52 (1981) 1548 - 1551.
- On the Generalized Korteweg-de Vries Equation. Manuscripta Mathematica, 30 (1980) 417-423.
- Superexponential Decay of Solutions of a Semilinear Wave Equation. Journal of Functional Analysis, 31 (1979) 321-332.
- (with Walter Strauss) Decay and Scattering of Solutions of a Nonlinear Schrodinger Equation. Journal of Functional Analysis, 30 (1978) 245-263.
- Asymptotic Behavior in Time of the Solutions of Three Nonlinear Partial Differential Equations. Journal of Differential Equations, 29 (1978) 467-473.