Mathematical Modeling
Prof. Hung-Chi Kuo ( Department of Atmospheric Sciences, National Taiwan University )2008 - 10 - 24 (Fri.)
15:30 - 17:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

RELATIONSHIP BETWEEN THE COX, LEHMANN, WEIBULL AND ACCELERATED LIFETIME MODELS
Prof. Qiqing Yu ( State University of New York, Binghamton, USA )2008 - 10 - 24 (Fri.)
13:30 - 15:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)Cox and Oakes (1984) claim that a model satisfies the accelerated lifetime (AL) model and the proportional hazards (PH) model iff it is Weibull. We study the claim and further study the relationship between the PH, AL, Lehmann and Weibull models.

Image Processing and Convex Analysis
Hao-Pin Wu ( Department of Mathematics, National Taiwan University )2008 - 10 - 24 (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.

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 )

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

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.)

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.)

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

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

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.)

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.)

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.)

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.

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.

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.)

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.)

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.

Introduction to HHT
Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )2008 - 10 - 15 (Wed.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Golbarg-Trudinger, second order, Elliptic PDE
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 10 - 14 (Tue.)
18:30 - 20:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)這個seminar的目的是由一群學幾何幾析及偏微分方程的學生組成，主要要學習elliptic PDE的基本理論，歡迎有興趣的同學來參加。

A resent result of Phong on Kähler-Ricci flow
Dr. Jun-Nan Tsai ( Department of Mathematics, National Taiwan University )2008 - 10 - 14 (Tue.)
14:00 - 15:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)It has been an important topic to find a Kähler-Einstein metric (Rc=cg) on a given Kähler manifold X. Several researchers have contributed to this problem. For example, Yau used continuity method to study the case when c=-1, 0 and gave a complete proof, and later his student H.D. Cao used Kähler-Ricci flow to reprove this result. In this talk, I will present Phong’s recent work in the case when c=1 and explain how it is related to Perelman’s new estimate.

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

Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )2008 - 10 - 08 (Wed.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Golbarg-Trudinger, second order, Elliptic PDE
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 10 - 07 (Tue.)
18:30 - 20:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)這個seminar的目的是由一群學幾何幾析及偏微分方程的學生組成，主要要學習elliptic PDE的基本理論，歡迎有興趣的同學來參加。

On the singularities of the Szego projection for ''0,q'' forms
Dr. Chin-Yu Hsiao ( École Polytechnique, France & Göteborgs universitet, Sweden )2008 - 10 - 07 (Tue.)
14:00 - 15:50
308, Mathematics Research Center Building (ori. New Math. Bldg.)In this work we completely study the heat equation method of Menikoff-Sjostrand and apply it to the Kohn Laplacian defined on a compact orientable connected CR manifold. We then get the full asymptotic expansion of the Szego projection for (0,q) forms. This generalizes a result of Boutet de Monvel and Sjostrand for (0,0) forms. Our mail tool is Fourier integral operators with complex valued phase functions of Melin and Sjostrand. We hope that this talk can serve as an introduction to certain micolocal techniques with applications to CR geometry and complex geometry.

Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )008 - 10 - 03 (Fri.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Mathematical Modeling
Prof. Hung-Chi Kuo ( Department of Atmospheric Sciences, National Taiwan University )2008 - 10 - 03 (Fri.)
15:30 - 17:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Two-Scale Convergence and Homogenization of Periodic Structures
Prof. Jiann-Sheng Jiang ( Tung Fang Institute of Technology )2008 - 10 - 03 (Fri.)
12:30 - 14:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Online Learning with Matrix Exponentiated Gradient Updates
Dr. Hsin-Hsiung Huang ( Institute of Statistical Science , Academia Sinica )2008 - 10 - 03 (Fri.)
13:30 - 15:00
404, Freshman Classroom BuildingTsuda, Ratsch and Warmuth (2006) address the problem of learning a symmetric positive definite matrix. They offer kernelized updates which involve a calculation based on matrix logs and matrix exponentials. These updates preserve the symmetry and positive definiteness. On the other hand, Vishwanathan, Schraudolph and Smola (2006) provide an online support vector machine (SVM) that uses the stochastic meta-descent (SMD) algorithm to adapt its step size automatically. Based on their method, we derive updates that allow us to perform the step size adaptation of kernel principal component analysis (PCA). Further, the online kernel PCA is an online SVM framework to loss functions, where its gradient trace parameter is no longer a coefficient vector but an element of the RKHS.

PARTIAL DIFFERENTIAL EQUATIONS-I
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 10 - 02 (Thu.)
09:00 - 12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)