QI YE

PAPERS: 

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators,
(with G. E. Fasshauer), Numerische Mathematik, Volume 119, Number 3, Pages 585-611, 2011, DOI:10.1007/s00211-011-0391-2, 
Updated the Journal Version, arXiv:1204.6448.

Reproducing Kernels of Sobolev Spaces via a Green Kernel Approach with Differential Operators and Boundary Operators, 
(with G. E. Fasshauer), Advances in Computational Mathematics, 2011, DOI: 10.1007/s10444-011-9264-6, arXiv:1109.5755v1.

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Differential Operators,  
Technical Report of Illinois Institute of Technology 2010, arXiv:1109.0109v1, PDF (Revised Version). 

Solving Support Vector Machines in Reproducing Kernel Banach Spaces with Positive Definite Functions, 
(with G. E. Fasshauer and F. J. Hickernell), in preparation.

Approximation of Stochastic Partial Differential Equations by a Kernel-based Collocation Method, 
(with I. Cialenco and G. E. Fasshauer), International Journal of Computer Mathematics, 
Special Issue: Recent Advances on the Numerical Solutions of Stochastic Partial Differential Equations (SPDEs), 2012, 
DOI: 10.1080/00207160.2012.688111, arXiv:1108.4213v1. 

Kernel-based Collocation Methods versus Galerkin Finite Element Methods for Approximating Elliptic Stochastic Partial Differential Equations, 
(with G. E. Fasshauer), Meshfree Methods for Partial Differential Equations VI, 
Springer series: Lecture Notes in Computational Science and Engineering, to appear, 2012, PDF.

A Kernel-based Collocation Method for Elliptic Partial Differential Equations with Random Coefficients,
(with G. E. Fasshauer), submitted.

Happy Travel on Tall Highway, (with H. Cai, A. Xu and H. Wang), Journal of South China Normal University (Chinese), 2005.6.

Generalization of One Probability Example, Teachers Training and Management (Journal of Shaoguan College, Chinese), 2005, No.2

PROJECTS:

1-Norm Support Vector Machines via Green Kernels, 2011.

Approximation of (Stochastic) Partial Differential Equations by Gaussian Processes via a Reproducing Kernel Approach, 2010-2011.

Approximation of Stable/Unstable Manifolds of Random Dynamical Systems by Support Vector Machine Methods, 2009.

Midwest Numerical Analysis Day (NWNA Day) 2012, May 12-13 2012, Notre Dame, IN, Attended.

Approximation of stochastic partial differential equations by a kernel-based collocation method 
   the Tenth International Conference on Monte Carlo and Quasi-Monte Carlo Methods, Feb 13-17, 2012, Sydney, Australia.

Approximation of stochastic partial differential equations by a kernel-based collocation method 
   2012 Joint Mathematics Meeting: AMS-SIAM Special Session on the Mathematics of Computation, Jan 4-7, 2012, Boston MA.

Approximation of stochastic partial differential equations by a kernel-based collocation method 
   Sixth International Workshop of Meshfree Methods for Partial Differential Equations, Oct 4-6, 2011, Bonn, Germany.

Approximation of Nonlinear Partial Differential Equations by Gaussian Processes via Mat¨Śrn Functions
   7th International Congress on Industrial and Applied Mathematics (ICIAM2011), July 18-22 2011, Vancouver, BC Canada.

Midwest Numerical Analysis Day (NWNA Day) 2011, May 7-8 2011, West Lafayette, IN, Attended.

Approximation of Linear Stochaitic Partial Differential Equations by Gaussian Processes via Mat¨Śrn Functions (Poster)
   Recent Advances in the Numerical Approximation of Stochastic Partial Differential Equations, August 9-13 2010, Chicago, IL.

Approximation of Linear Partial Differential Equations by Gaussian Processes via Mat¨Śrn Functions
   2010 SIAM Annual Meeting, July 12-16 2010, Pittsburgh, PA.

Approximating Stable and Unstable Manifolds of 2D Stochastic Dynamical Systems via Reproducing Kernels
   Midwest Numerical Analysis Day (NWNA Day) 2010, April 24-25 2010, Ames, IA.

A Green Function Approach to (Conditionally) Positive Definite Functions and Reproducing Kernels of Generalized Sobolev spaces
  13th International Conference Approximation Theory, March 7-10 2010, San Antonio, TX.

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach
  2009 Joint Midwest Numerical Analysis Day and SIAM Great Lakes Numerical PDEs Spring Conference, April 17-18 2009, Detroit, MI.

Midwest Numerical Analysis Day (NWNA Day) 2008, May 3 2008, St. Paul, MN, Attended.

Visit to Huazhong University of Science and Technology on December 29-31 2010 (Thanks for the invitation Dr. Xu Sun.)
  Talk: Tutorial of Meshfree Approximation Method, PDF

Visit to Department of Mathematics, University of Iowa on June 21-25 2010 (dicussing with Dr. Kendall E. Atkinson)

Sigma Xi Award in recognition of the outstanding accomplishments in research and scholarship, 2012, Sigma Xi, news

Karl Menger Student Award, 2012, Illinois Institute of Technology, news

Award in recognition of outstanding efforts and accomplishments on behalf of the SIAM Student Chapter at 2011-2012, SIAM, news

NSF travel award from Stanford University to the Tenth International Conference on Monte Carlo and Quasi-Monte Carlo Methods (MCQMC 2012)

Graduate student travel grant to the Joint Mathematics Meetings 2012

Award for 2009 student research poster at Annual Karl Menger Lecture, Illinois Institute of Technology, news

Meritorious Winner of the Mathematical Contest in Modeling (MCM) administered by the Consortium for Mathematics and Its Applications (COMAP), 2005, SIAM

"Zhentai" scholarship for outstanding students, 2005, South China Normal University

Teaching Assistant of Probability and Statistics (Math 474 & 563), Applied Analysis (Math 500), Dynamical Systems (Math 515), 
Computational Mathematics (Math 577)