Colloquium/Seminar

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Event(s) on February 2015


  • Tuesday, 3rd February, 2015

    Title: Sharpness q-Index for regularization parameter selection of image restoration and gaussian noise estimation
    Speaker: Ms. CUI Lei , Department of Mathematics, Hong Kong Baptist University, Hong Kong
    Time/Place: 10:00
    FSC1014, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We propose a new approach to select regularization parameter for image restoration models by a new metric: sharpness q-index. We exhibit several theoretical demonstrations about the properties of the new metric and its application to parameter selection for image restoration with different kinds of blur and noise. We show that the selected parameter for our constrained optimization model can estimate precisely the variance of added gaussian noise. And through our experimentations, we show that our method can achieve a competitive performance for image deconvolution comparing with other state-of-the-art methods.


  • Wednesday, 4th February, 2015

    Title: Global small solution to incompreesible MHD system
    Speaker: Dr. Xu Li, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, China
    Time/Place: 16:00  -  17:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, we consider the global wellposedness of both 2-D and 3-D incompressible magneto-hydrodynamical (MHD) system with small and smooth initial data. It is a coupled system between the Navier-Stokes equations and a transport equation with an universal nonlinear coupling structure. The main difficulty of the proof lies in exploring the dissipative mechanism of the system due to the fact that there is a transport equation in the system. To achieve this and to avoid the difficulty of propagating anisotropic regularity for the transport equation, we first reformulate the MHD system in the Lagrangian coordinates. Then we employ anisotropic Littlewood-Paley analysis to establish the key $L^1$ in time estimates to the velocity and the gradient of the pressure in the Lagrangian coordinate. With this estimate, we prove the global wellposedness of the Lagrangian system with smooth and small initial data by using the energy method. The global wellposedness of the original MHD system then follows by a suitable change of variables together with a continuous argument.


  • Thursday, 5th February, 2015

    Title: Several Advances in Nonlinear Programming
    Speaker: Prof. DAI Yu-Hong, Institute of Computational Mathematics, Chinese Academy of Sciences, China
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Nonlinear programming has received significant attentions since the proposition of the quasi-Newton method in the middle of last century. In this talk, I shall address several recent advances in nonlinear programming by myself and collaborators. They are related to nonlinear conjugate gradient method, quasi-Newton method and interior point method.


  • Friday, 6th February, 2015

    Title: 微積分和無限的文化
    Speaker: 林群, 中國科學院, China
    Time/Place: 11:30  -  12:30 (Preceded by Reception at 11:00am)
    SPH, HSH Campus, Hong Kong Baptist University
    Abstract: 一尺之棰,日取其半,永世不竭;也可用數學上的無窮等比級數求和來 表達。但是,為什麼無限求和可以變成有限數呢?更嚴格的數學語言需 要用到ε−δ語言。本講座試圖用淺顯的語言和思想去描述並延伸這個 問題。從無限求和我們甚至可以聯系到一個追求真理的哲學公式。


  • Friday, 6th February, 2015

    Title: Some Mysteries of Multiplication, and How to Generate Random Factored Integers
    Speaker: Prof. Richard P. Brent, Mathematical Sciences Institute, Australian National University, Australia
    Time/Place: 14:30  -  16:00
    RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist University
    Abstract: Let M (n) be the number of distinct entries in the multiplication table for integers smaller than n. The order of magnitude of M (n) was established in a series of papers by various authors, starting with Erd ӧs (1950) and ending with Ford (2008), but an asymptotic formula for M (n) is still unknown. After describing some of the history of M (n) I will consider algorithms for computing M (n) exactly for moderate values of n, and Monte Carlo algorithms for estimating M (n) accurately for large n. This leads to consideration of algorithms, due to Bach (1985–88) and Kalai (2003), for generating random factored integers – integers r that are uniformly distributed in a given interval, together with the complete prime factorisation of r. This is joint work with Carl Pomerance.


  • Tuesday, 10th February, 2015

    Title: On Boltzmann and Landau equations in a unified framework
    Speaker: Prof. HE Lingbing, Department of Mathematical Sciences, Tsinghua University, China
    Time/Place: 10:00  -  11:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, we will show some recent progress on sharp bounds for the Boltzmann and Landau collision operators in a unified framework. As applications, e well-posedness for equations and the asymptotics from Boltzmann equation to Landau equation in the so-called grazing collisions limit are established.


  • Thursday, 26th February, 2015

    Title: Second Order BSDEs with Jumps
    Speaker: Dr. Chao ZHOU, Department of Mathematics, National University of Singapore, Singapore
    Time/Place: 14:30  -  15:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We first provide a wellposedness result of second order backward stochastic differential equations with jumps. We then prove a nonlinear Feynman-Kac formula and give a probabilistic representation for some fully nonlinear partial integro-differential equations. This talk is based on joint works with Nabil Kazi-Tani and Dylan Possamai.