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Event(s) on June 2011


  • Wednesday, 1st June, 2011

    Title: Lectures on Algebra (5)
    Speaker: Prof. HSIANG Wuyi, Department of Mathematics, University of California, Berkeley, USA
    Time/Place: 10:00  -  12:00
    ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus, Hong Kong Baptist University
    Abstract: 理性文明 (Civilization of rational mind) 乃是世代相承,精益求精對於大自然的本質的認知。概括地來說,大自然的事物與現象是極為多樣而且變化無窮的﹔但是其內在的本質卻又具有精簡的原理和規律。所以唯有穿透表象,探求本質,才能認知其精簡,而這種由表及裡的基本方法就是定量分析(quantitative analysis)。這也就是為什麼基礎數學在理性文明的全程發展中,一直扮演著重要的角色;代數、幾何與分析則是基礎數學的三大支柱。而代數學的根基在於數的運算,是定量分析,有效能算的基本功。幾何學則是對於我們生活所在的空間本質的認知與深入理解。而分析學則是研究變動事物與現象的“變量數學”,它是代數和幾何的自然結合才發展而得的數學,具基礎理論就是微積分。


  • Wednesday, 1st June, 2011

    Title: Solving Polynomial Systems by the homotopy continuation method (1)
    Speaker: Prof. LI Tien-Yien, Department of Mathematics, Michigan State University, USA
    Time/Place: 14:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Solving polynomial systems is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states, etc.. Elimination theory based methods, most notably the Buchberger algorithm for constructing Gröbner bases, are the classical approach to solving polynomial systems, but their reliance on symbolic manipulation makes those methods seem somewhat limited to relatively small problems. During the last three decades, the homotopy continuation method has been established in the U.S. for finding the full set of isolated solutions to a polynomial system numerically. The method has been developed and successfully implemented, and proved to be a reliable and efficient numerical algorithm. In has become very powerful in many occasions. In this series of talks, we shall elaborate the details of the method and the theory behind it.


  • Thursday, 2nd June, 2011

    Title: Solving Polynomial Systems by the homotopy continuation method (2)
    Speaker: Prof. LI Tien-Yien, Department of Mathematics, Michigan State University, USA
    Time/Place: 14:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Solving polynomial systems is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states, etc.. Elimination theory based methods, most notably the Buchberger algorithm for constructing Gröbner bases, are the classical approach to solving polynomial systems, but their reliance on symbolic manipulation makes those methods seem somewhat limited to relatively small problems. During the last three decades, the homotopy continuation method has been established in the U.S. for finding the full set of isolated solutions to a polynomial system numerically. The method has been developed and successfully implemented, and proved to be a reliable and efficient numerical algorithm. In has become very powerful in many occasions. In this series of talks, we shall elaborate the details of the method and the theory behind it.


  • Friday, 3rd June, 2011

    Title: Is Two Better Than One? An Adaptive-Splitting Exploration into the Quenching Numerical Solution of Singular Reaction-Diffusion Equations on Nonuniform Grids
    Speaker: Prof. Qin Sheng, Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research, Baylor University, USA
    Time/Place: 14:30  -  15:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Let us start with Martin Johnson's famous song played by the Boston rock group Boys Like Girls. But this time, we will focus at the SPLITTING and ADAPTATIONS. Can the parties dance? For this, the quenching numerical solution of degenerate reaction-diffusion equations will be investigated. While spatial derivatives are discretized over symmetric nonuniform grids, a Peaceman-Rachford type splitting integrator is employed to advance solutions of our semidiscretized systems. The temporal steps can be generated adaptively through proper arc-length monitor functions. We will see that the quenching numerical solution acquired preserve key properties of the analytic solution. Weak stability will be proven in the Von Neumann sense under the infinity-norm. Interesting computational examples will be shown to illustrate our conclusions (to be announced).


  • Tuesday, 7th June, 2011

    Title: Lectures on Algebra (7)
    Speaker: Prof. HSIANG Wuyi, Department of Mathematics, University of California, Berkeley, USA
    Time/Place: 10:00  -  12:00
    ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus, Hong Kong Baptist University
    Abstract: 理性文明 (Civilization of rational mind) 乃是世代相承,精益求精對於大自然的本質的認知。概括地來說,大自然的事物與現象是極為多樣而且變化無窮的﹔但是其內在的本質卻又具有精簡的原理和規律。所以唯有穿透表象,探求本質,才能認知其精簡,而這種由表及裡的基本方法就是定量分析(quantitative analysis)。這也就是為什麼基礎數學在理性文明的全程發展中,一直扮演著重要的角色;代數、幾何與分析則是基礎數學的三大支柱。而代數學的根基在於數的運算,是定量分析,有效能算的基本功。幾何學則是對於我們生活所在的空間本質的認知與深入理解。而分析學則是研究變動事物與現象的“變量數學”,它是代數和幾何的自然結合才發展而得的數學,具基礎理論就是微積分。


  • Wednesday, 8th June, 2011

    Title: Lectures on Algebra (8)
    Speaker: Prof. HSIANG Wuyi, Department of Mathematics, University of California, Berkeley, USA
    Time/Place: 10:00  -  12:00
    ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus, Hong Kong Baptist University
    Abstract: 理性文明 (Civilization of rational mind) 乃是世代相承,精益求精對於大自然的本質的認知。概括地來說,大自然的事物與現象是極為多樣而且變化無窮的﹔但是其內在的本質卻又具有精簡的原理和規律。所以唯有穿透表象,探求本質,才能認知其精簡,而這種由表及裡的基本方法就是定量分析(quantitative analysis)。這也就是為什麼基礎數學在理性文明的全程發展中,一直扮演著重要的角色;代數、幾何與分析則是基礎數學的三大支柱。而代數學的根基在於數的運算,是定量分析,有效能算的基本功。幾何學則是對於我們生活所在的空間本質的認知與深入理解。而分析學則是研究變動事物與現象的“變量數學”,它是代數和幾何的自然結合才發展而得的數學,具基礎理論就是微積分。


  • Wednesday, 8th June, 2011

    Title: Solving Polynomial Systems by the homotopy continuation method (3)
    Speaker: Prof. LI Tien-Yien, Department of Mathematics, Michigan State University, USA
    Time/Place: 14:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Solving polynomial systems is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states, etc.. Elimination theory based methods, most notably the Buchberger algorithm for constructing Gröbner bases, are the classical approach to solving polynomial systems, but their reliance on symbolic manipulation makes those methods seem somewhat limited to relatively small problems. During the last three decades, the homotopy continuation method has been established in the U.S. for finding the full set of isolated solutions to a polynomial system numerically. The method has been developed and successfully implemented, and proved to be a reliable and efficient numerical algorithm. In has become very powerful in many occasions. In this series of talks, we shall elaborate the details of the method and the theory behind it.


  • Thursday, 9th June, 2011

    Title: Solving Polynomial Systems by the homotopy continuation method (4)
    Speaker: Prof. LI Tien-Yien, Department of Mathematics, Michigan State University, USA
    Time/Place: 14:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Solving polynomial systems is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states, etc.. Elimination theory based methods, most notably the Buchberger algorithm for constructing Gröbner bases, are the classical approach to solving polynomial systems, but their reliance on symbolic manipulation makes those methods seem somewhat limited to relatively small problems. During the last three decades, the homotopy continuation method has been established in the U.S. for finding the full set of isolated solutions to a polynomial system numerically. The method has been developed and successfully implemented, and proved to be a reliable and efficient numerical algorithm. In has become very powerful in many occasions. In this series of talks, we shall elaborate the details of the method and the theory behind it.


  • Friday, 10th June, 2011

    Title: Solving Polynomial Systems by the homotopy continuation method (5)
    Speaker: Prof. LI Tien-Yien, Department of Mathematics, Michigan State University, USA
    Time/Place: 14:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Solving polynomial systems is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states, etc.. Elimination theory based methods, most notably the Buchberger algorithm for constructing Gröbner bases, are the classical approach to solving polynomial systems, but their reliance on symbolic manipulation makes those methods seem somewhat limited to relatively small problems. During the last three decades, the homotopy continuation method has been established in the U.S. for finding the full set of isolated solutions to a polynomial system numerically. The method has been developed and successfully implemented, and proved to be a reliable and efficient numerical algorithm. In has become very powerful in many occasions. In this series of talks, we shall elaborate the details of the method and the theory behind it.


  • Monday, 13th June, 2011

    Title: Solving Polynomial Systems by the homotopy continuation method (6)
    Speaker: Prof. LI Tien-Yien, Department of Mathematics, Michigan State University, USA
    Time/Place: 14:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Solving polynomial systems is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states, etc.. Elimination theory based methods, most notably the Buchberger algorithm for constructing Gröbner bases, are the classical approach to solving polynomial systems, but their reliance on symbolic manipulation makes those methods seem somewhat limited to relatively small problems. During the last three decades, the homotopy continuation method has been established in the U.S. for finding the full set of isolated solutions to a polynomial system numerically. The method has been developed and successfully implemented, and proved to be a reliable and efficient numerical algorithm. In has become very powerful in many occasions. In this series of talks, we shall elaborate the details of the method and the theory behind it.


  • Thursday, 16th June, 2011

    Title: Lectures on Algebra (9)
    Speaker: Prof. HSIANG Wuyi, Department of Mathematics, University of California, Berkeley, USA
    Time/Place: 10:00  -  12:00
    ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus, Hong Kong Baptist University
    Abstract: 理性文明 (Civilization of rational mind) 乃是世代相承,精益求精對於大自然的本質的認知。概括地來說,大自然的事物與現象是極為多樣而且變化無窮的﹔但是其內在的本質卻又具有精簡的原理和規律。所以唯有穿透表象,探求本質,才能認知其精簡,而這種由表及裡的基本方法就是定量分析(quantitative analysis)。這也就是為什麼基礎數學在理性文明的全程發展中,一直扮演著重要的角色;代數、幾何與分析則是基礎數學的三大支柱。而代數學的根基在於數的運算,是定量分析,有效能算的基本功。幾何學則是對於我們生活所在的空間本質的認知與深入理解。而分析學則是研究變動事物與現象的“變量數學”,它是代數和幾何的自然結合才發展而得的數學,具基礎理論就是微積分。


  • Friday, 17th June, 2011

    Title: Lectures on Algebra (10)
    Speaker: Prof. HSIANG Wuyi, Department of Mathematics, University of California, Berkeley, USA
    Time/Place: 10:00  -  12:00
    ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus, Hong Kong Baptist University
    Abstract: 理性文明 (Civilization of rational mind) 乃是世代相承,精益求精對於大自然的本質的認知。概括地來說,大自然的事物與現象是極為多樣而且變化無窮的﹔但是其內在的本質卻又具有精簡的原理和規律。所以唯有穿透表象,探求本質,才能認知其精簡,而這種由表及裡的基本方法就是定量分析(quantitative analysis)。這也就是為什麼基礎數學在理性文明的全程發展中,一直扮演著重要的角色;代數、幾何與分析則是基礎數學的三大支柱。而代數學的根基在於數的運算,是定量分析,有效能算的基本功。幾何學則是對於我們生活所在的空間本質的認知與深入理解。而分析學則是研究變動事物與現象的“變量數學”,它是代數和幾何的自然結合才發展而得的數學,具基礎理論就是微積分。