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Ming-Jun Lai |
| Mail: |
Department of Mathematics
University of Georgia
Athens, GA 30602-7403
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| Phone: | (706) 542-2065
| | Fax: | (706) 542-2573
| | E-mail: | mjlai at math.uga.edu
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I'm a professor of the Department of
Mathematics at The University
of Georgia.
Research Profiles:
- I have studied the theory and applications of
multivariate splines
for twenty years. One of the reasons that I am so interested in this topic
for so long is
that multivariate splines are a fundamental tool in Numerical Analysis,
Scientific Computation, and Applied Mathematics. I mainly study the
approximation properties of multivariate splines, construction of
locally supported spline functions, computation with multivariate splines
and applications of multivariate splines.
Some typical papers are
On the Approximation Power of Bivariate Splines
, C^r Clough-Tocher Macro-Elements , and
Spherical Splines for Scattered Data Fitting .
They have various applications in
Computer Aided Geometric Design,
Fluid Flow Simulation , and in
Geodetic Applications.
- Larry Schumaker and I wrote a monograph on
"Spline Functions on Triangulations"
which is recently published by Cambridge University Press.
-
An application of multivariate splines for Fluid Flow Simulation
won me a research medal from
the University of Georgia in 2002.
The main representative paper
is Bivariate Splines for Fluid Flows .
- I have also studied
Wavelets Analysis and Its Applications for Image
Processing for about ten years. My interest is to construct various
compactly supported
orthonormal wavelets ,
orthonormal multi-wavelets ,
biorthogonal wavelets , tight
wavelet frames , pre-wavelets, Riesz basis,
and pre-Riesz basis in the
multivariate setting. I am also interested in
wavelet applications in image processing .
Teaching Profiles:
- I have taught many courses for undergraduate students and
graduate students. For graduate students, I mainly teach Advances
in Numerical Analysis including
Numerical Linear Algebra,
Numerical Approximation,
Numerical Solution of PDE's, and
Wavelets Analysis.
- Nine Ph.D's were graduated under my supervision. They are
Dr. Wenjie He,
Dr. Xiangming Xu,
Dr. Gerard Awanou,
Dr. V. Baramidze and
Dr. K. Nam.
Dr. Wenjie He is already an associate professor at Univ. of Missouri,
St. Louis. The research
work which forms a part of Dr. Awanou's dissertation won him
a best student paper award.
V. Baramidze obtained a
GRADUATE STUDENT EXCELLENCE IN RESEARCH AWARD
from the University of Georgia. Dr. J. Zhou and Dr. O. Cho are
graduated in the summer, 2006 and
Dr. H. P. Liu and Dr. J. B. Wu graduated in the Summer, 2007.
- I encouraged and helped Bree Ettinger to work as an intern at
Boeing company in summer, 2004 and Jeremy Praissman to work as an intern
at NASA Langley Research Center in summer, 2007.
Service Profiles:
I have been members of various departmental, college level and
university level committees.
Finally, my personal profiles:
I came from Hangzhou, Zhejiang, China.
I am very proud of
Hangzhou,
because it is one of the most beautiful cities in China. Seeing is believing.