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HKBU-NSYSU Workshop on Computational and Applied Mathematics

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HKBU-NSYSU Workshop on Computational and Applied Mathematics

HKBU-NSYSU Workshop on Computational and Applied Mathematics

    浸會中山計算與應用數學研討會

    Date: April 9-10, 2007 Co-organised by: Department of Mathematics, Hong Kong Baptist University

    Department of Applied Mathematics, National Sun Yat-sen University

    Program

    April 9, 2007 (Monday) Place;Room 4009-1, Dept. of Applied Mathematics, National Sun Yat-sen University

    Time Speaker Title Session I: Computation

    08:50~09:00 Opening Session

    09:00~09:30 Recent Development in Scientific Computing 湯濤 Tao TANG

    The Numerical Analysis of Pantograph-type Volterra 布魯耐爾 海曼 09:30~10:00 Functional Integral Equations Hermann BRUNNER

    10:00~10:30 Tea Break

    Trefftz, Collocation and Other Boundary Methods -- 10:30~11:00 呂宗澤 Tzon-Tzer LU A Comparison

    Fully Conservative Characteristic Methods for 11:00~11:30 黃杰森 Chien-Sen HUANG Transport Problems

    Point Sources Identification Problem for Heat 11:30~12:00 凌立雲 Leevan LING Equations

    Future Exchange and Collaboration 12:00~14:00 Lunch and Discussion 辦學經驗與交流合作座談

    Inverse Filtering, Wavelet and TV Denoising for 14:00~14:30 吳國寶 Kwok Po NG Image Restoration Problems

    Iterative Methods for Solving Constrained Linear 14:30~15:00 徐洪坤 Hong-Kun XU Inverse Problems 15:00~15:30 Tea Break

    Session II: Combinatorics

    Edge-magic Labeling Matrices of the Composition of 15:30~16:00 邵慰慈 Wai Chee SHIU Paths with Null Graphs 16:00~16:30 The Orientable Hull and Geodetic Numbers董立 Li-Da TONG

    16:30~17:00 Tea Break

    On the Bandwidth and Cyclic Bandwidth Problems 17:00~17:30 陳偉康 Wai Hong CHAN of Graphs

    Construction of Graphs with Given Circular Flow 17:30~18:00 潘志實 Zhi-Shi PAN Number

    18:00~19:00 Dinner晚宴 (英國領事館)

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2/9

    HKBU-NSYSU Workshop on Computational and Applied Mathematics

    浸會中山計算與應用數學研討會

    Date: April 9-10, 2007

    Co-organised by: Department of Mathematics, Hong Kong Baptist University

    Department of Applied Mathematics, National Sun Yat-sen University

    Program

    April 10, 2007 (Tuesday) Place;Room 4009-1, Dept. of Applied Mathematics, National Sun Yat-sen University

    Time Speaker Title Session III: Statistics

    Testing the Non-unity of Rate Ratio under Inverse 09:00~09:30 鄧文禮 Man Lai TANG Sampling

    Monitoring Risk Factors of Heart Rate Variability for 09:30~10:00 郭美惠 Mei-Hui GUO VICU Patients

    10:00~10:30 Campus Tour

    10:30~11:00 Tea Break

    Future Exchange and Collaboration 11:00~12:30 Discussion and Lunch 辦學經驗與交流合作座談

    3/9

Talk 1

    Prof. Tao TANG 湯濤 教授

     Dept of Mathematics, Hong Kong Baptist University

    http://www.math.hkbu.edu.hk/~ttang

Title: Recent Development in Scientific Computing

Abstract:

    Scientific Computing deals with the development of efficient and reliable algorithms for computations with floating-point numbers on computers, as well as the underlying theory related to the accuracy and stability of the algorithms. With the advance of modern high-performance computers, and in particular computers with parallel architecture, the implementation aspects have come to play a very useful role. Moreover, as the computational problems increase in size and complexity, the interplay between the mathematical modeling, the numerical algorithms, and the computer implementation becomes increasingly important. In this talk, the history of the scientific computing research will be reviewed and its current development will be introduced. The applications of scientific computing in several important areas such as computational fluid dynamics, scientific visualization and simulation of physical processes will be also discussed.

Talk 2

    Prof. Hermann BRUNNER 布魯耐爾 海曼 教授

    Dept of Mathematics, Hong Kong Baptist University

    Department of Mathematics and Statistics Memorial University of Newfoundland,

    St. John's, NL, Canada

    http://www.math.hkbu.edu.hk/~hbrunner

Title: The numerical analysis of pantograph-type Volterra functional integral equations

Abstract:

    The years 1971 and 1992/93 saw, respectively, the introduction of the pantograph equation, y’(t)= ay(t) + by (qt) (0 widely known that the very first studies of functional (integral) equations with proportional delay arguments date back to the work of Volterra (1897/1913), Picard (1907), Lalesco (1908/1911), and Andreoli (1913/1914). While most of the theory of such functional equations is now well understood, this is not true for their numerical analysis.

    In this talk I will present a survey of some recent advances in the quantitative and qualitative numerical analysis of pantograph-type integral and integro-differential equations. The focus of the presentation will not be so much on the (super-) convergence and numerical stability results as on the underlying analytical and computational difficulties inherent in these \innocent-looking" delay equations. It will also become apparent that many related questions remain unanswered: in particu-lar, it is not known under which conditions collocation methods on uniform meshes yield uniformly convergent solutions to the oldest of these functional integral equations, namely Volterra's first-kind equation of 1897. All this means that many challenging problems are waiting to be solved, especially in the numerical analysis of pantograph-type equations with nonlinear vanishing delays.

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Talk 3

    Prof. Tzon-Tzer LU 呂宗澤 教授

    Department of Applied Mathematics, National Sun Yat-sen University

    http://www.math.nsysu.edu.tw/faculty/ttlu.html

Title: Trefftz, Collocation and Other Boundary Methods -- A Comparison

Abstract:

    We will survey the algorithms of the collocation method (CM), the Trefftz method (TM) and the collocation Trefftz method (CTM), and summarize the coupling techniques for the exterior and interior boundary conditions, which include the CTM (i.e., the indirect Trefftz method), the very original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Moreover, the error analysis is briefly addressed, and new numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm, and provides the most accurate solution with the best numerical stability.

Talk 4

    Prof. Chien-Sen HUANG 黃杰森 教授

    Department of Applied Mathematics, National Sun Yat-sen University

    http://www.math.nsysu.edu.tw/faculty/huangcs.html

Title: Fully conservative characteristic methods for transport problems

Abstract:

    We consider the problem of simulating the macro-scale transport of inert (tracer) particles in a fluid. The system is generally modeled by a system of two equations, one for the bulk fluid velocity, and the other for the transport of the tracer. The latter equation is called an advection-diffusion equation. In the simplest but widely applicable case where the equation is linear, we may have contact discontinuities, but not shocks. In the absence of diffusion, tracer particles simply transport along the characteristic curves of the hyperbolic part of the transport equation, i.e., along streamlines. Characteristic methods exploit this fact numerically to provide accurate and numerically efficient approximation schemes. If single points are approximately transported, local mass balance errors result, degrading the accuracy of the method. If the mass in an entire region of space is transported, mass may be conserved locally. However, since the shape of the region distorts in time, it must be approximated in numerical implementation, and its volume may be incorrect. This results in inaccurate concentration densities, which has a surprisingly detrimental effect on the accuracy of the method. We present a simple modification of the method that conserves both mass and volume of the transported tracer fluid regions. The techniques are illustrated in several numerical examples involving flow in porous media (groundwater aquifers or petroleum reservoirs). A convergence theory is presented.

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Talk 5

    Dr. Leevan Ling 凌立雉 教授

    Dept of Mathematics, Hong Kong Baptist University

    http://www.math.hkbu.edu.hk/~lling

Title: Point Sources Identification Problem for Heat Equations

Abstract:

    We considered a point source identification problem from observation data. We aim to identify the unknown source number and locations along with unknown strengths. We show that if the regularization parameter is chosen properly, the numerical procedures will converge to a sequence of moment equations involving our target unknowns. A reconstruction scheme is proposed on the basis of the developed theoretical results.

Talk 6

    Prof. Kwok Po Ng 吳國寶 教授

    Department of Mathematics, Hong Kong Baptist University

    http://www.math.hkbu.edu.hk/~mng

Title: Inverse Filtering, Wavelet and TV Denoising for Image Restoration Problems

Abstract:

    In this talk, I will review image restoration methods, and propose a new approach based on inverse filtering (deblurring), wavelet and TV denoising for image restoration methods. Numerical examples are given to illustrate the effectiveness of the proposed method.

Talk 7

    Prof. Hong-Kun XU 徐洪坤 教授

    Department of Applied Mathematics, National Sun Yat-sen University

    http://www.math.nsysu.edu.tw/faculty/xuhk.html

Title: Iterative Methods for Solving Constrained Linear Inverse Problems

Abstract:

    Due to inaccuracies of observations the linear model Tfh is ill-posed ; thus regularization is

    necessary. In this talk we shall report some recent results on iterative methods for solving the regularized minimization problem :

    2minimize gTf;J(f),

    where J is a continuous convex function defined on some closed covex subset C of a Hilbert space. A wide range of inverse problems arising in image reconstructions can be formulated in this way. The feature is that at each iteration, the involving operator is nonexpansive. As a result, iterative technieques of nonexpansive mappings apply, from which weak convergence of the iterative methods follow immediately. In some occasions strong convergence also holds.

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Talk 8

    Dr. Wai Chee Shiu 邵慰慈 教授

    Department of Mathematics, Hong Kong Baptist University

    http://www.math.hkbu.edu.hk/~wcshiu

    Title: Edge-magic Labeling Matrices of the Composition of Paths with Null Graphs

Abstract:

    Given two graphs G and H, the composition of G with H is the graph with vertex set V(G)V(H)in which (u,v) is adjacent to (u,v) if and only if uuE(G) or uu andvvE(H). In 1122121212

    this talk, we shall construct some matrices with some special row sums, column sums or diagonal

    PNsums. By using these matrices we obtain an edge-magic labeling of the composition of with . nn

    PNAlso we obtain an edge-magic labeling of the composition of with for odd mk with m3mmk

    and . k1

Talk 9

    Dr. Li-Da Tong 董立大 教授

    Department of Applied Mathematics, National Sun Yat-sen University

    http://www.math.nsysu.edu.tw/faculty/ldtong.html

Title: The orientable hull and geodetic numbers

Abstract:

    For every pair of vertices u,v in an oriented graph, a u-v geodesic is a shortest directed path from u

    to v. For an oriented graph D, let I[u,v] denoted the set of all vertices lying on a u-v geodesic or a D

    v-u geodesic. And for S V(D, let I [S] denoted the union of all I[u,v] for all u,v S. If S is a DD

    convex set then I[S]=S. Let [S] denoted the smallest convex set containing S. The geodetic DD

    number g(D) of an oriented graph D is the minimum cardinality of a set S with I[S]=V(D). The D

    hull number h(D) of a digraph D is the minimum cardinality of a set S with [S]=V(D). For a Dconnected graph G, let O(G) be the set of all orientations of G, define g(G)= min{g(D):DO(G) },

    ++ g (G)=max{ g(D):DO(G) }, h(G)= min{ h(D):D O(G) }, and h(G)= max{ h(D):DO(G) }.

    +++By the definitions, h(G)g(G) and h(G) g(G). In the paper, we prove that g(G)< h(G) for graph G of order at least 3 and show that, for any nonnegative integers a and b, there exists a ++connected graph G such that g(G)-h(G)=a and g(G)-h(G)=b.

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Talk 10

    Dr. Daricks Chan 陳偉康 教授

    Dept of Mathematics, Hong Kong Baptist University

    http://www.math.hkbu.edu.hk/~dchan

Title: On the Bandwidth and Cyclic Bandwidth Problems of Graphs

Abstract:

    The bandwidth minimization problem arises from a wide application area including sparse matrix computation, coding theory, data structure and the circuit layout of VLSI designs. In this talk, I will revisit the results on the bandwidth problem obtained in the past few decades including the bandwidth in some specific types of graphs, and the change of bandwidth of graphs under elementary operations. An analogous problem is the cyclic bandwidth problem of graphs. I will also introduce a necessary and sufficient condition to characterize graphs with equal bandwidth and cyclic bandwidth.

Talk 11

    Dr. Zhi-shi Pan 潘志實 教授

    Department of Applied Mathematics, National Sun Yat-sen University

    E-mail: panzs@math.nsysu.edu.tw

Title: Construction of graphs with given circular flow number

Abstract: ;

    r2Suppose is a real number. A proper r-flow of a directed multi-graph is a G(V,E)

    mapping such that (i) for every edge , ; (ii) for every vertex f:E(1f(e)r1eE

    ,f(e)f(e)0. The circular flow number of a graph is the least r for vVG;eE(v)eE(v)

    which an orientation of admits a proper r-flow. The well-known -flow conjecture is G5

    equivalent to the statement that every bridgeless graph has circular flow number at most . In this 5

    2paper, we prove that for any rational number r between and , there exists a graph with 5G

    circular flow number r.

    8/9

Talk 12

    Dr. Man Lai Tang 鄧文禮 教授

    Dept of Mathematics, Hong Kong Baptist University

    http://www.math.hkbu.edu.hk/~mltang

Title: Testing the non-unity of rate ratio under inverse sampling

Abstract:

    Inverse sampling is considered to be a more appropriate sampling scheme than the usual binomial sampling scheme when subjects arrive sequentially, when the underlying response of interest is acute, and when maximum likelihood estimators of some epidemiologic indices are undefined. In this article, we study various statistics for testing non-unity rate ratios in case-control studies under inverse sampling. These include the Wald, unconditional score, likelihood ratio and conditional score statistics. Three methods (the asymptotic, conditional exact, and Mid-P methods) are adopted for P-value calculation. We evaluate the performance of different combinations of test statistics and P-value methods in terms of their empirical sizes and powers via Monte Carlo simulation. In general, asymptotic score and conditional score tests are preferable for their actual type I error rates, are well controlled around the pre-chosen nominal level, and their powers are comparatively the largest. The exact version of Wald test is recommended if one wants to control the actual type I error rate at or below the pre-chosen nominal level. If larger power is expected and fluctuation of sizes around the pre-chosen nominal level are allowed, then the Mid-P version of Wald test is a desirable alternative. We illustrate the methodologies with a real example from a heart disease study.

Talk 13

     教授Prof. Mei-Hui Guo 郭美惠

    Department of Applied Mathematics, National Sun Yat-sen University

    http://www.math.nsysu.edu.tw/faculty/guomh.html

Title: Monitoring Risk Factors of Heart Rate Variability for VICU Patients

Abstract:

    In the literature, two important risk factors related to heart rate variability are discovered. The first risk factor is the ratio of low frequency (LF) to high frequency (HF) spectrum power, which is found to be useful in measuring sympathetic/parasympathetic balance. The second risk factor is related to low variability of heart rates. Continuous monitoring of these two risk factors has the potential to early detect physiological deterioration of patients. An recent finding also shows that heart rate data possess self-similar property, in the first part we compare different estimates of the self-similar parameter and establish the EWRMS and EWMV control charts monitoring low heart rate variability. In the second part, we propose a new LF/HF power ratio statistics and establish the control charts to monitor alterations of the LF/HF power ratio. The results are applied to monitor the ratio statistics and heart rate variability for patients after operation in vascular intensive care units(VICU).

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