October 24, 2008
Website  http://140.112.50.155/workshop/Workshop on high resolution image restoration.pdf

Blowup rate estimates for the heat equation with a nonlinear gradient source term
Prof. Jong-Shenq Guo ( Tamkang University )2008 - 10 - 23 (Thu.)
16:00 - 16:50
405, Mathematics Research Center Building (ori. New Math. Bldg.)In this talk, we shall present some recent results on the blowup of solutions of the initial boundary value problem for the heat equation with a nonlinear gradient source term. It is shown that the blowup rate will never match that of the self-similar variables. In the one space dimensional case when assumptions are made on the initial data so that the solution is monotonically increasing in time, the exact blowup rate is found.

Prof. Tai-Peng Tsai ( University of British Columbia, Canada & National Taiwan University )

Tai-Peng Tsai 2008-10-23
13:00:00 - 14:00:00 Scattering and Solution dynamics308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Jong-Shenq Guo 2008-10-23
16:00:00 - 16:50:00 Blowup rate estimates for the heat equation with a nonlinear gradient source term405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )2008 - 10 - 22 (Wed.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Yin-Liang Huang ( Department of Applied Mathematics, National University of Tainan )

Yin-Liang Huang 2008-10-22
13:30:00 - 15:20:00 Discrete Fourier Transform and Its Applications to Numerical PDEs405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Norden Huang 2008-10-22
09:00:00 - 11:00:00 Introduction to HHT308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Tai-Peng Tsai ( University of British Columbia, Canada & National Taiwan University )

On the moduli space of flat bundles over a 2-manifold
Prof. Nan-Kuo Ho ( National Tsing Hua University )2008 - 10 - 21 (Tue.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Tai-Peng Tsai 2008-10-21
13:00:00 - 15:00:00 Scattering and Solution dynamics405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Nan-Kuo Ho 2008-10-21
14:00:00 - 15:00:00 On the moduli space of flat bundles over a 2-manifold308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Yin-Liang Huang ( Department of Applied Mathematics, National University of Tainan )

Yin-Liang Huang 2008-10-20
15:30:00 - 18:20:00 Discrete Fourier Transform and Its Applications to Numerical PDEs104 , Multi-Purpose Classroom Building

Recent developments in minimal model program
Prof. Jung-Kai Alfred Chen ( Department of Mathematics, National Taiwan University )2008 - 10 - 17 (Fri.)
13:30 - 15:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )2008 - 10 - 17 (Fri.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Homogenization Theory for the Elasticity I, II
Prof. Ying-Hong Liu ( Research Center for Applied Sciences, Academia Sinica )2008 - 10 - 17 (Fri.)
12:30 - 14:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)In the second talk, we will focus on the application of homogenization in the elastic wave equation. Illustrate step by step how to obtain the effective properties like elastic constants and the mass density in the case of solid-solid composites from one to three dimensionalities. In addition, we extend the theory to study the case of solid-fluid systems with and without damping by the three-scale analysis. By this method, we can define the effective viscosity and find that the propagating longitudinal mode can be supported in the layered composite material with viscosity in the long wavelength limit.

Mathematical Modeling
Prof. Hung-Chi Kuo ( Department of Atmospheric Sciences, National Taiwan University )2008 - 10 - 17 (Fri.)
15:30 - 17:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

A proposal for quantum minimal model program
Prof. Chin-Lung Wang ( Department of Mathematics, National Taiwan University )2008 - 10 - 17 (Fri.)
15:00 - 16:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Image Processing and Convex Analysis
Hao-Pin Wu ( Department of Mathematics, National Taiwan University )2008 - 10 - 17 (Fri.)
11:10 - 12:10
308, Mathematics Research Center Building (ori. New Math. Bldg.)In these series talks, I will first introduce the inpainting problem and a recently developed framelet-based algorithm1. Next, I will cover some background of convex analysis, including conjugate functions, subdiffer-ential, Moreau envelope, and proximity operators2. In the last part, I will prove the convergence of a foward-backward algorithm for convex functional with nondifferential constraints2.

Hao-Pin Wu 2008-10-17
11:10:00 - 12:10:00 Image Processing and Convex Analysis308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Ying-Hong Liu 2008-10-17
12:30:00 - 14:30:00 Homogenization Theory for the Elasticity I, II308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Hung-Chi Kuo 2008-10-17
15:30:00 - 17:30:00 Mathematical Modeling308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Jung-Kai Chen 2008-10-17
13:30:00 - 15:00:00 Recent developments in minimal model program405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Chin-Lung Wang 2008-10-17
15:00:00 - 16:30:00 A proposal for quantum minimal model program405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Norden Huang 2008-10-17
09:00:00 - 11:00:00 Introduction to HHT308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Quantitative uniqueness for the Stokes Equations
Prof. Ching-Lung Lin ( National Cheng Kung University )2008 - 10 - 16 (Thu.)
15:30 - 16:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)I would like to talk about a recent study on the local behavior of a solution to the Stokes Equations. One of the main results is the bound on the vanishing order of the pair of solution and pressure, which is a quantitative estimate of the strong unique continuation property. Our proofs use Carleman estimates with carefully chosen weights. We will derive optimal three-sphere inequalities and doubling inequalities.

PARTIAL DIFFERENTIAL EQUATIONS-I
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 10 - 16 (Thu.)
09:00 - 12:10
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Ching-Lung Lin 2008-10-16
15:30:00 - 16:30:00 Quantitative uniqueness for the Stokes Equations405 , Mathematics Research Center Building (ori. New Math. Bldg.)