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Event(s) on January 2016
- Monday, 4th January, 2016
Title: Hardy Spaces and Elliptic Boundary Value Problems Speaker: Prof. Der-Chen Chang, Department of Mathematics and Statistics, Georgetown University, USA Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: The first part of this talk with discuss estimates of elliptic boundary value problems in Hardy spaces. More precisely, let Omega be a bound domain in R^n with smooth boundary. Consider the following elliptic boundary valued problem: Delta u = f in Omega Xu = g on partial Omega Here X is a transversal vector field to the boundary. This includes the regular Dirichlet and Neumann problem. The first part of this talk, we first introduce suitable Hardy spaces H^p(Omega) and BMO space BMO(Omega) on a "suitable" domain Omega in R^n. Then we shall show that ||(partial^2 u) / (partial x_j partial x_k)|| <= C_p ||f||_{H^p(Omega)} for 0 < p < infty. In the second part of this talk, I will discuss a generalization of a div-curl lemma of Coifman, Lions, Meyer and Semmes (1993) to Hardy spaces that we introduced in the first part of this talk. Then we shall discuss applications of this generalization to partial differential equations. - Tuesday, 12th January, 2016
Title: Linear Algebra Methods in Graph Theory Speaker: Prof Yaoping Hou, College of Mathematics and Computer Science, Hunan Normal University, China 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: Linear algebra is one of the most important courses of undergraduate. The graph is a mathematical abstraction of many real-world situations. It plays an important role in many fields of natural and social science. In this talk, the concepts and methods of linear algebra, such as determinants, eigenvalues and eigenvectors, with applications in solving problems of graph theory are discussed. - Wednesday, 13th January, 2016
Title: Distance Shrinkage and Euclidean Embedding via Regularized Kernel Estimation Speaker: Prof. Ming YUAN, Department of Statistics, University of Wisconsin-Madison, USA Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the so-called regularized kernel estimate. We show that such an estimate can be characterized as simply applying a constant amount of shrinkage to all observed pairwise distances. This fact allows us to establish risk bounds for the estimate implying that the true distances can be estimated consistently in an average sense as the number of objects increases. In addition, such a characterization suggests an efficient algorithm to compute the distance matrix estimator, as an alternative to the usual second order cone programming known not to scale well for large problems. Numerical experiments and an application in visualizing the diversity of Vpu protein sequences from a recent HIV-1 study further demonstrate the practical merits of the proposed method. - Wednesday, 13th January, 2016
Title: The Cauchy problem on large time for surface waves type Boussinesq systems Speaker: Dr. Li XU, The State Key Laboratory of Scientific and Engineering Computing (LSEC), Chinese Academy of Sciences, China Time/Place: 15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: We consider the well-posedness on time intervals of order 1/ϵ for the Cauchy problem associated to two-dimensional dispersive systems of Boussinesq type which model weakly nonlinear long wave surface waves. This achieves their full rigorous justification as asymptotic models to the full Euler equations with free surface. - Thursday, 14th January, 2016
Title: Some matrix invariants on a threshold graph Speaker: Prof. Yaoping HOU, College of Mathematics and Computer Science, Hunan Normal University, China Time/Place: 16:30 - 17:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: A graph is called a threshold graph (or degree maximal graph) if it can be obtained from a single vertex by iterating the operations of adding a new vertex that is either connected to no other vertex (an isolated vertex ) or connected to every other vertex (a cone vertex). In this talk, we will report some matrix invariants (such as energy, generalized inverse, the Smith normal form) on a threshold graph. - Tuesday, 19th January, 2016
Title: A Uniform Analysis of Combinatorial Markov Chains via Speaker: Dr. Amy PANG, Laboratoire de Combinatoire et d’Informatique Mathématique, Université du Québecà Montréal, Canada Time/Place: 11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Markov chains are a basic tool of simulation and optimisation in applied mathematics and scientific computing. One simple, widely-used chain is the move-to-front rule for dynamic storage allocation: suppose one repeatedly makes independent requests for a random file amongst a list, searching for the neccessary file from the front of the list at each request. One method of reducing the average search time is to return each requested file to the front, so that frequently-requested files are more likely to be near the front. To investigate whether this scheme is efficient, one wishes to calculate the likely order of the files in the long run (the stationary distribution), and how many requests it takes to put the system into this long run state (the convergence rate). We illustrate how a new connection to Hopf algebras can shed light on these two important questions for many similar chains on lists all at once, as well as for analogous processes on trees, graphs and numerous other objects. - Friday, 22nd January, 2016
Title: The incompressible limit in $L^p$ type critical spaces Speaker: Dr. He Lingbing, Department of Mathematical Sciences, Tsinghua University, China Time/Place: 15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: This talk aims at justifying the low Mach number convergence to the incompressible Navier-Stokes equations for viscous compressible flows in the emph{ill-prepared data} case. The fluid domain is either the whole space, or the torus. A number of works have been dedicated to this classical issue, all of them being, to our knowledge, related to $L^2$ spaces and to energy type arguments. In the present work, we investigate the low Mach number convergence in the $L^p$ type critical regularity framework. More precisely, in the barotropic case, the divergence-free part of the initial velocity field just has to be bounded in the critical Besov space $dot B^{d/p-1}_{p,r}capdot B^{-1}_{infty,1}$ for some suitable $(p,r)in[2,4]times[1,+infty].$ We still require $L^2$ type bounds on the low frequencies of the potential part of the velocity and on the density, though, an assumption which seems to be unavoidable in the ill-prepared data framework, because of acoustic waves. - Monday, 25th January, 2016
Title: Numerical methods to fractional Laplace equation Speaker: Ms. Yuan Huifang, Department of Mathematics, Hong Kong Baptist University, Hong Kong Time/Place:
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: The fractional Laplacian $(-Delta)^{alpha/2}$ is a non-local operator which depends on the parameter $alpha$ and recovers the usual Laplacian operator as $alpha to 2$.Here we will discuss what has been done to solve the fractional Laplacian equation numerically. Firstly, we introduce a finite difference-quadrature method proposed by Huang. Then we try to solve it by spectral method, and the key is to find a proper set of basis. To do this, we first show recent progress in the field of spectral methods for fractional differential equations. Our aim is to mimic this procedure and propose a properbasis for the unbounded domain using Hermite polynomials. - Wednesday, 27th January, 2016
Title: HKBU MATH 45th Anniversary Distinguished Lecture - A Parallel Line Search Subspace Correction Method for Composite Convex Optimization Speaker: Prof. Ya-xiang Yuan, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China Time/Place: 16:30 - 17:30 (Preceded by Reception at 4:00pm)
SCT909, Science Tower, HSH Campus, Hong Kong Baptist UniversityAbstract: In this talk, we investigate a parallel subspace correction framework for composite convex optimization. The variables are first divided into a few blocks based on certain rules. At each iteration, the algorithms solve a suitable subproblem on each block simultaneously, construct a search direction by combining their solutions on all blocks, then identify a new point along this direction using a step size satisfying the Armijo line search condition. They are called PSCLN and PSCLO, respectively, depending on whether there are overlapping regions between two immediately adjacent blocks of variables. Their convergence is established under mild assumptions. We compare PSCLN and PSCLO with the parallel version of the fast iterative thresholding algorithm and the fixed-point continuation method using the Barzilar-Borwein step size and the greedy coordinate block descent method for solving the L1-regularized minimization problems. Our numerical results show that PSCLN and PSCLO can run fast and return solutions no worse than those from the state-of-the-art algorithms. It is also observed that the overlapping domain decomposition scheme is helpful when the data of the problem has certain special structures. - Friday, 29th January, 2016
Title: An over-determined problem for confocal ellipsoids and Speaker: Prof. Hyeonbae Kang, Department of Mathematics, Inha University, Korea Time/Place: 15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: A neutral inclusion is a structure whose presence does not perturb uniform fields. Its usefulness in composites was first discovered by Hashine in 1960s. Recently interest in neutral inclusions has been revived in relation to enhancement of cloaking. I will talk about recent development in the neutral inclusion problem including an overdetermined problem for confocal ellipsoids. I will also discuss on some related problems.