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Event(s) on December 2009
- 1/12/2009
| 題目: |
The calculation of pure imaginary eigenvalues of large sparse matrices with application to the detection of Hopf Bifurcations |
| 講員: |
Prof. Alastair Spence, University of Bath, UK |
| 時間/地點: |
11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
The detection of a Hopf bifurcation in a large scale dynamical
system that depends on a physical parameter often consists of
attempting to compute pure imaginary eigenvalues of large sparse
matrices.
In this talk we describe a new method that utilises a certain
sum of Kronecker products but in practice requires the solution
of a sequence of Lyapunov equations with low rank right hand
sides. It is this last fact that makes the method feasible for
large systems.
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- 1/12/2009
- 1/12/2009
- 3/12/2009
- 7/12/2009
| 題目: |
Lecture Series on Graph Theory and Combinatorial Algorithms: Computing Inverse Sort Transform and Suffix Array in Linear Complexity |
| 講員: |
Dr. Wai-hong Chan, Department of Mathematics, Hong Kong Baptist University, Hong Kong |
| 時間/地點: |
11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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- 8/12/2009
| 題目: |
One stone two birds--adaptive decompositions for singular partial differential equations and beyond |
| 講員: |
Prof. Qin SHENG, Department of Mathematics, Baylor University, USA |
| 時間/地點: |
14:30 - 15:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
Decomposition, or splitting, finite difference methods have been
playing an important role in the numerical solution of nonsingular
partial differential equations dueto their remarkable efficiency,
simplicity and flexibility in computations as compared with their
peers. Although the numerical strategy is still in its infancy
for solving singular differential equation problems arising from
many applications, explorations of the next generation decomposition
schemes associated with various kinds of adaptations can be found
in many recent publications. In this talk, we will focus on the
latest developments in the area. Key comments will be devoted
to the direct solutions of degenerate singular reaction-diffusion
equations. Our explorations will also be extended to adaptive
and decompositions for optical beam propagation computations
and reconstructions. Simulated results with interesting applications
will be presented.
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- 15/12/2009
| 題目: |
Some divergence-free finite elements in 2D and 3D |
| 講員: |
Prof. ZHANG Shangyou, Department of Mathematical Sciences, University of Delaware, USA |
| 時間/地點: |
11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
The incompressible constraint in fluid dynamics and the nearly
incompressible condition in solid mechanics post a difficulty
in computation, especially in the finite element method. In
1983, Scott and Vogelius showed that the P_k-P_{k-1} element
(approximating the velocity by continuous piecewise-polynomials
of degree k and approximating the pressure by discontinuous piecewise-polynomials
of degree k-1) is stable and consequently of the optimal order
on 2D triangular grids for all k>= 4, provided the grids have
no nearly-singular vertex. For such a combination of mixed elements,
the finite element velocity is divergence free point wise, truly
incompressible. The 3D version of P_k-P_{k-1} problem is still
open. We give some partial answers and present some new divergence-free
elements in this talk.
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- 16/12/2009
| 題目: |
SRCC DLS: Statistics under Uncertaity: A New Challenging Problem in Finance |
| 講員: |
Prof. Shige Peng, Shandong University, China |
| 時間/地點: |
11:00 - 12:30 (Preceded by Reception at 10:30am)
RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist University
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| 摘要: |
To solve risk control problem in finance we face a chanllenging
problem: how to quantitatively measure a risk position while
the distribution uncertainty (or ambuguity) is essentially integrated
into the utilities of financial markets, financial institutions,
locally or globally? It also provides a new opportunity for us
to explore fundamental problems in statistics under probability
and distribution model uncertainty. We present our new law of
large number (LLN) and central limit theorem (CLT) under uncertainty
which bring us to a new frontier of risk data analysis. One typical
problem is how to estimate the robust version of the normal distribution
of which naturally appears from our new CLT? This fascinating
problem involves statistics, probability theory, theoretical
and computational nonlinear PDE of HJB type, ....
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- 22/12/2009
| 題目: |
Estimation and Model Selection in a Class of Semiparametric Models |
| 講員: |
Dr. ZHANG Wenyang, Department of Mathematical Sciences, University of Bath, UK |
| 時間/地點: |
11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
Multiparameter likelihood models with multiple covariates have
a wide range of applications. However, they encounter the ``curse
of dimensionality" problem when the dimension of the covariates
is large. We develop a generalized multiparameter likelihood
model that copes with multiple covariates and adapts to dynamic
structural changes well. It includes some popular models, such
as the partially linear and varying coefficient models, as special
cases. When the model is fixed, a simple and effective two-step
method is developed to estimate both the parametric and the nonparametric
components. The proposed estimator of the parametric component
has the $n^{-1/2}$ convergence rate, and the estimator of the
nonparametric component enjoys an adaptivity property. A data-driven
procedure is suggested to select the bandwidths involved. We
further develop an automatic procedure to identify constant parameters
in the underlying model. A simulation study and an application
to the infant mortality data of China are given to demonstrate
performance of the proposed methods.
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