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Event(s) on February 2010
- Tuesday, 2nd February, 2010
Title: ICM and JRIAM DLS: Maximum-Principles in Parabolic Finite Element Problems Speaker: Prof. Vidar Thomee, Department of Mathematical Sciences, Chalmers University of Technology, Sweden Time/Place: 11:30 - 12:30 (Preceded by Reception at 11:00am)
OEE601-603, Oen Hall Building (East Wing), HSH Campus, Hong Kong Baptist UniversityAbstract: We consider piecewise linear finite element discretizations of the model initial-boundary value problem for the homogeneous heat equation, and discuss the validity of the associated discrete maximum-principles. We demonstrate that for the spatially semidiscrete standard Galerkin approximation, the maximum-principle is not valid in general. However, as was shown by Fujii in 1973, the maximum-principle holds for the lumped mass modification, when the triangulation is of Delaunay type, and this condition on the triangulation is essentially sharp. We also present some results for the simplest time stepping analogues of these approximations. - Wednesday, 10th February, 2010
Title: Limit Theorems for Studentized Statistics and their Applications Speaker: Prof. Jing Bing Yi, Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong Time/Place: 11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Limit theorems for standardized (or normalized) statistics have been well studied in the probability literature. On the other hand, studentized statistics are more useful in statistical inference, the best known example of which is the Student-t statistic. However, limit theorems for studentized statistics are usually more difficult to establish due to their more complicated structure, or they are obtained under much stronger conditions than their standardized counterparts. In this talk, we argue that quite the opposite is true. First, much stronger conclusions can be obtained for studentized statistics than standardized statistics under the same set of conditions. Second, certain results for standardized statistics can hold also for studentized statistics but under much weaker conditions. The class of statistics under consideration include the samplemean, U-statistics, symmetric statistics, etc. - Tuesday, 23rd February, 2010
Title: Electromagnetic Radiations as a Fluid Flow Speaker: Prof. Dianele Funaro, Dipartimento di Matematica, Universita di Modena e Reggio Emilia, Italy Time/Place: 11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Since the advent of the theory of electromagnetic fields, more than a century ago, waves have been described as a kind of energy flow, governed by suitable transport equations in vector form, namely Maxwell’s equations. In void, the electric and magnetic fields (E and B , respectively) are transversally oriented with respect to the direction of propagation, and their envelope produces a sequence of wave-fronts. This is in agreement with the fact that the energy develops according to the evolution of the vector product E × B , otherwise known as Poynting vector. On the other hand, the dynamical behavior of a compressible non viscous fluid is well described by Euler’s equation, where, in principle, the velocity vector field (denoted by V ) might not be necessarily related to a real material fluid. In particular, one could replace the mass density by a sort of charge density. Therefore, the temptation to describe electromagnetic and velocity fields, through a combination of the respective modeling equations, is well motivated. We are going to present a system of equations in the three independent vector unknowns: (E,B,V ). In pure void, the electric and magnetic fields follow the Faraday’s law together with the Amp`ere’s law, where a current, flowing at velocity V , is supposed to be naturally associated with the wave. In order to close the system, the third relation is the Euler’s equation for V , containing an added forcing term E + V × B , perfectly analogous to that expressing the Lorentz’s law. In this way, the three entities (E,B,V ) turn out to be strictly entangled. Despite the appearance, the new model allows for a very large space of solutions. Moreover, it displays numerous conservation and invariance properties, all deducible from a standard analysis. An interesting invariant subspace of solutions is the one where the third equation is reduced to E + V × B = 0, which means that no acceleration is acting on the wave, and the flow is somehow laminar. For this circumstance, the solutions, called free-waves, perfectly follow the laws of geometrical optics, ruled by the eikonal equation. Together with usual known solutions, free-waves also include solitary electromagnetic waves with compact support almost of any shape, intensity, frequency and polarization. Such a result, never achieved before, reopens the path to a serious discussion on photons, the duality wave-particle and the quantum properties of matter. Far more complicated solutions (not of the free-wave type) are however possible. Since our electromagnetic radiations actually behave as a fluid, they can be constrained to evolve in bounded regions of space, similar for instance to vortex rings. According to the model equations, rotating photons in a vortex structure may carry a charge and deform, via Einstein’s equation, the local geometry of the space-time in order to create a gravitational environment assimilable to the presence of mass. The same metric space is responsible for the stability of such a wave, obliged in this way to develop along self-created geodesics. This leaves us with the conjecture that some stable elementary particles (such as the electron) could be made by rotating photons, an idea that has been put forward by many authors in the past, although with not too much recognition, basically due to the lack of a sufficient theoretical description of electromagnetic phenomena, able to go beyond the classical linear Maxwellian approach. Since now we exactly know what a photon is, additional elements are available for a deeper investigation. - Tuesday, 23rd February, 2010
Title: Optimal Design Techniques for the Health Sciences Speaker: Prof. Wong Weng Kee, Dpeartmetn of Biostatistics, UCLA School of Public Health, USA Time/Place: 15:30 - 16:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Optimal design theory and ideas are increasingly applied to many research areas, including education, biomedical sciences, chemical engineering and bioengineering, health services and food science. In this talk, I present an overview of the optimal design methodology and recent advances in the field. The statistical foundation is briefly reviewed and discussed in the context of practical problems in the biomedical sciences. The emphasis is on applications in the health sciences, with illustrative examples in cancer research, behavioral sciences, health services and cardiology. To promote optimal design ideas, I present a website that allows practitioners to generate a variety of optimal designs easily and freely. After selecting a suitable model from a list of statistical models on the site and an optimality criterion, the practitioner inputs design parameters for his or her problem. The site returns the optimal design and the efficiency of any selected design. I will give demonstrations using problems in the biomedical sciences and hope that the site will facilitate practitioners implement a more informed design that provides improved statistical inference at minimal cost.