| THE
UNIVERSITY OF HONG KONG |
DEPARTMENT OF MATHEMATICS
| Researcher : Bai Z |
| List of Research Outputs |
| Bai Z., Golub G.H. and Ng K.P., Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems, SIAM Journal on Matrix Analysis and Applications. 2003, 24: 603-626. |
| Bai Z. and Ng K.P., Preconditioners for Nonsymmetric Block-Toeplitz-Like-Plus-Diagonal Linear System , Numer. Math.. 2003, 96: 197-220. |
| Researcher : Bertaccini D |
| List of Research Outputs |
| Bertaccini D. and Ng K.P., Band-Toeplitz Preconditioned GMRES Iterations for Time-dependent PDEs, BIT. 2003, 43: 901-914. |
| Bertaccini D. and Ng K.P., Omega-Circulant Preconditioners for Time-Dependent Integrators, CALCOLO. 2003, 40: 71-90. |
| Researcher : Chan JT |
| Project Title: | The linear preserver problem |
| Investigator(s): | Dr. Chan J.T., Prof. Li C.K. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 09/2003 |
| Abstract: |
| To investigate linear mappings on an operator algebra that leave invariant a certain set or function of the algebra. |
| Project Title: | The linear preserver problem |
| Investigator(s): | Dr. Chan J.T., Prof. Li C.K. |
| Department: | Mathematics |
| Source(s) of Funding: | RGC Projects (Block Grant Funded) |
| Start Date: | 09/2003 |
| Abstract: |
| To investigate linear mappings on an operator algebra that leave invariant a certain set or function of the algebra. |
| Researcher : Chan PK |
| List of Research Outputs |
| Chan P.K., Ching W.K. and Yung S.P., Optimal Strategies in Equity Securities and Derivatives, Journal of Applied Mathematics and Computations. 2004, 151: 615-643. |
| Researcher : Chan YL |
| List of Research Outputs |
| Chan Y.L., Ching W.K., Ng K.P. and Huang J.Z., An Optimization Algorithm for Clustering Using Weighted Dissimilarity Measures, Pattern Recognition. 2004, 37: 943-952. |
| Researcher : Cheung WS |
| Project Title: | Canonical metrics, uniformization of complex manifolds, rigidity of holomorphic tangent bundles: generalizations of a theorem of K.H. Look |
| Investigator(s): | Dr. Cheung W.S., Prof. Wong B. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 11/2000 |
| Abstract: |
| To characterize those bounded domains in a complex manifold which cover a compact complex manifold; to study the inverse of the following recent result in the rigidity problem of deformation of holomorphic vector bundles on a compact Kahler manifold: if the tangent bundle of a compact complex surface M of general type does not admit a non-trivial trace-free deformation, then M is covered by the euclidean ball. |
| Project Title: | On multi-dimensional integral inequalities |
| Investigator(s): | Dr. Cheung W.S. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 02/2002 |
| Completion Date: | 10/2003 |
| Abstract: |
| To investigate, improve, and generalize existing integral inequalities like Opial's inequality, Poincare' inequality, Sobolev inequality and the like which are fundamental for the study of both qualitative and quantitative properties of solutions of differential and integral equations; to develop specific integral inequalities so that they can be applied to solve certain calculus of variations problems which cannot be solved effectively by classical approach. |
| Project Title: | On multi-dimensional integral inequalities and applications |
| Investigator(s): | Dr. Cheung W.S., Prof. Pecaric J. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 12/2003 |
| Abstract: |
| To develop new integral inequalities of the Opial-type, Poincare-type, Wirtinger-type, Gronwall-Bellman-type, Hardy-type, etc., which are useful in nonlinear analysis and approximations; to establish discrete analogues of the above-mentioned integral inequalities; to qualitative analysis of solutions of differential and difference equations. |
| Project Title: | On multi-dimensional integral inequalities and applications |
| Investigator(s): | Dr. Cheung W.S., Prof. Pecaric J. |
| Department: | Mathematics |
| Source(s) of Funding: | RGC Projects (Block Grant Funded) |
| Start Date: | 12/2003 |
| Abstract: |
| To develop new integral inequalities of the Opial-type, Poincare-type, Wirtinger-type, Gronwall-Bellman-type, Hardy-type, etc., which are useful in nonlinear analysis and approximations; to establish discrete analogues of the above-mentioned integral inequalities; to qualitative analysis of solutions of differential and difference equations. |
| Project Title: | Sufficient conditions for the existence of positive solutions of boundary value problems |
| Investigator(s): | Dr. Cheung W.S. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 02/2004 |
| Abstract: |
| To study quasi-linear BVP and discrete multi-point BVP. |
| List of Research Outputs |
| Cheung W.S., Some Discrete Nonlinear Inequalities and Applications to Boundary Value Problems for Difference Equations, Journal of Difference Equations and Applications. 2004, 10, No.2: 213-223. |
| Cheung W.S., Wong B. and Yau S.S.T., Some Remarks on the Local Moduli of Tangent Bundles over Complex Surfaces, American Journal of Mathematics. 2003, 125: 1029-1035. |
| Researcher : Ching WK |
| Project Title: | Models and numerical algorithms for some problems in transportation research |
| Investigator(s): | Dr. Ching W.K. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 11/2001 |
| Completion Date: | 10/2003 |
| Abstract: |
| To study traffic demand estimation in a transportation network; to model and solve inventory replenishmnt in a supply chain. |
| Project Title: | Models and numerical algorithms for queuing and manufacturing systems |
| Investigator(s): | Dr. Ching W.K., Prof. Chan R.H.F. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 09/2002 |
| Abstract: |
| Markovian models are widely used in modelling and analysing queuing and manufacturing systems. This research project aims at developing: 1) models for complex manufacturing systems and queuing systems; and 2) fast numerical algorithms for solving linear systems arising from the captured applications. |
| Project Title: | Logistic models for manufacturing and re-manufacturing systems |
| Investigator(s): | Dr. Ching W.K. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 11/2002 |
| Completion Date: | 10/2004 |
| Abstract: |
| To focus on modelling two types of manufacturing systems: Re-manufacturing systems and Flexible Manufacturing Systems (FMSs); to develop fast algorithms for solving the formulated models |
| Project Title: | Higher-order hidden markov models and their applications |
| Investigator(s): | Dr. Ching W.K. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 11/2003 |
| Abstract: |
| To develop higher-order Hidden Markov Models (HHMMs) and fast numerical methods for solving the parameters of HHMMs, and applies to the classifications of customers in marketing analysis and the modelling of DNA sequences. |
| List of Research Outputs |
| Chan P.K., Ching W.K. and Yung S.P., Optimal Strategies in Equity Securities and Derivatives, Journal of Applied Mathematics and Computations. 2004, 151: 615-643. |
| Chan Y.L., Ching W.K., Ng K.P. and Huang J.Z., An Optimization Algorithm for Clustering Using Weighted Dissimilarity Measures, Pattern Recognition. 2004, 37: 943-952. |
| Ching W.K. and Ng K.P., Building Simple Hidden Markov Models, International Journal of Mathematical Education in Science and Engineering. 2004, 35: 295-299. |
| Ching W.K., Ng K.P. and Wong K.K., Hidden Markov Models and Its Applications to Customer Relationship Management, IMA Journal of Management Mathematics. 2004, 15: 13-24. |
| Ching W.K., Ng K.P. and Fung S.L., Higher-order Hidden Markov Models with Applications to DNA Sequences, IDEAL, Lecture Notes in Computer Science. Springer, 2003, 535-539. |
| Ching W.K., Fung S.L. and Ng K.P., Higher-order Markov Chain Models for Categorical Data Sequences, International Journal of Naval Research Logistics. 2004, 51: 557-574. |
| Ching W.K., Ng K.P. and Wong K.K., Higher-order Markov Decision Process and Its Applications in Customer Lifetime Values, The 32nd International Conference on Computers and Industrial Engineering. Limerick, Ireland, 2003, 2: 821-826. |
| Ching W.K., Iterative Methods for Queuing Systems with Batch Arrivals and Negative Customers, BIT. 2003, 43: 285-296. |
| Ching W.K., Scholtes S. and Zhang S., Numerical Algorithms for Estimating Traffic Between Zones in a Network, Engineering Optimisation. 2004, 36: 379-400. |
| Ching W.K., Chung S.K. and Ng T.W., On Modeling SARS in Hong Kong, International Journal of Applied Mathematics. 2003, 13, no.1: 1-7. |
| Lin F., Ching W.K. and Ng K.P., Accurate and Fast Inversion Methods for Triangular Toeplitz Matrices, Theoretical Computer Science. 2004, 315: 511-523. |
| Lin F., Ching W.K. and Ng K.P., Discrete Wavelet Transforms for Toeplitz Matrices, Linear Algebra and Its Applications. 2003, 370: 269-285. |
| Ng K.P., Ching W.K., Sze N.K. and Yau C.K., Super-resolution Image Reconstruction from Blurred Observation by Multisensor, International Journal of Imaging Systems and Technology. 2003, 13: 153-160. |
| Researcher : Chu SCK |
| Project Title: | Heuristic solution comparisons of exact modelling for fixed-length duties generation |
| Investigator(s): | Dr. Chu S.C.K. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 11/2003 |
| Abstract: |
| To ensure computational robustness for the intrinsically high complexity of such integer optimization; to further study and develop parallel heuristic approaches that compare well with exact solutions of known cases, and beyond. |
| List of Research Outputs |
| Chu S.C.K., Associate editor of the IMA Journal of Management Mathematics. 2003. |
| Chu S.C.K., Generating Shift Crew-Duties, Proceedings of the 6th International Conference on Multi Objective Programming and Goal Programming (MOPGP'04). Hammamet, Tunisia, 2004, 12pp. |
| Chu S.C.K., Optimization Modeling of Fixed-Length Duties, Proceedings of the 32nd International Conference on Computers and Industrial Engineering. Limerick, Ireland, 2003, 737-742. |
| Researcher : Chung SK |
| List of Research Outputs |
| Ching W.K., Chung S.K. and Ng T.W., On Modeling SARS in Hong Kong, International Journal of Applied Mathematics. 2003, 13, no.1: 1-7. |
| Researcher : Fung SL |
| List of Research Outputs |
| Ching W.K., Ng K.P. and Fung S.L., Higher-order Hidden Markov Models with Applications to DNA Sequences, IDEAL, Lecture Notes in Computer Science. Springer, 2003, 535-539. |
| Ching W.K., Fung S.L. and Ng K.P., Higher-order Markov Chain Models for Categorical Data Sequences, International Journal of Naval Research Logistics. 2004, 51: 557-574. |
| Researcher : Golub GH |
| List of Research Outputs |
| Bai Z., Golub G.H. and Ng K.P., Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems, SIAM Journal on Matrix Analysis and Applications. 2003, 24: 603-626. |
| Researcher : Hwang J |
| List of Research Outputs |
| Hwang J. and Mok N., Automorphism groups of the spaces of minimal rational curves on Fano manifolds of Picard Number 1, Journal of Algebraic Geometry. University Press, Inc., 2004, 13: 663-673. |
| Hwang J. and Mok N., Deformation rigidity of the 20-dimensional F4-homogeneous space associated to a short root, In: V.L. Popov, Algebraic Transformation Groups and Algebraic Varieties. Berlin-Heidelberg-New York, Springer-Verlag, 2004, 37-58. |
| Researcher : Lai TL |
| List of Research Outputs |
| Lai T.L., Limit Theorems for Moving Averages, Probability, Finance and Insurance. Singapore, World Scientific, 2004, 1-14. |
| Researcher : Lau YK |
| List of Research Outputs |
| Lau Y.K., An estimate for symmetric square L-functions on weight aspect, Archiv der Mathematik. Springer, 2003, 81: 169-174. |
| Lau Y.K., On the error term in an asymptotic formula for the symmetric square L-function, Proceedings of the American Mathematical Society. 2004, 132: 317-323. |
| Researcher : Li G |
| List of Research Outputs |
| Deng X.T., Li G., Zang W. and Zhou Y., A 2-Approximation Algorithm for Path Coloring on a Restricted Class of Trees of Rings, Journal of Algorithms. CA, USA, Elsevier, 2003, 47: 1-13. |
| Researcher : Li Y |
| List of Research Outputs |
| Li Y. and Zang W., The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers, Journal of Combinatorial Optimization. MA, USA, Kluwer Academic Publishers, 2003, 7: 353-359. |
| Researcher : Lin F |
| List of Research Outputs |
| Lin F., Ching W.K. and Ng K.P., Accurate and Fast Inversion Methods for Triangular Toeplitz Matrices, Theoretical Computer Science. 2004, 315: 511-523. |
| Lin F., Ching W.K. and Ng K.P., Discrete Wavelet Transforms for Toeplitz Matrices, Linear Algebra and Its Applications. 2003, 370: 269-285. |
| Lin F. and Ng K.P., Super-Resolution Image Reconstruction with Estimation of Low-Resolution Frames, International Journal of Applied Mathematics. 2003, 13: 84-99. |
| Researcher : Liu MC |
| List of Research Outputs |
| Liu M.C., Cochrane T. and Zheng Z., Upper bound on n-dimensional Kloosterman sums, Journal of Number Theory. 2004, 106: 259-274. |
| Researcher : Lu J |
| Project Title: | Poisson Morse theory |
| Investigator(s): | Dr. Lu J.H. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 01/2003 |
| Abstract: |
| To further study on Poisson Morse Theory, which can provide new ways to study topology and make connections between Poisson geometry and topology. |
| Project Title: | Poisson structures associated to real semi-simple Lie groups |
| Investigator(s): | Dr. Lu J.H. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 09/2003 |
| Abstract: |
| To advance Poisson geometry, we try to achieve this goal by relating Poisson geometry with Lie theory. More precisely, we will study a class of examples of Poisson structures that are connected to interesting problems in Lie theory. The Poisson geometric considerations of these examples will shed lights on the Lie theoretical problems associated to them, and the input from Lie theory will motivate new constructions in Poisson geometry. |
| Project Title: | Poisson structures associated to real semi-simple Lie groups |
| Investigator(s): | Dr. Lu J.H. |
| Department: | Mathematics |
| Source(s) of Funding: | RGC Projects (Block Grant Funded) |
| Start Date: | 09/2003 |
| Abstract: |
| To advance Poisson geometry, we try to achieve this goal by relating Poisson geometry with Lie theory. More precisely, we will study a class of examples of Poisson structures that are connected to interesting problems in Lie theory. The Poisson geometric considerations of these examples will shed lights on the Lie theoretical problems associated to them, and the input from Lie theory will motivate new constructions in Poisson geometry. |
| List of Research Outputs |
| Foth P. and Lu J., Poisson structures on flad manifolds associated to real forms, Comptes Rendus des Rencontres Mathmatiques de Glanon. Glanon, France, 2003, 8 pages. |
| Lu J., Editor of Pacific Journal of Mathematics. 2004. |
| Researcher : Makar-Limanov L |
| List of Research Outputs |
| Yu J., Makar-Limanov L., van Rossum P. and Shpilrain V., The stable equivalence and cancellation problems, Comment. Math. Helv. 2004, 79, no.2: 341-349. |
| Researcher : Mikhalev AA |
| List of Research Outputs |
| Yu J., Shpilrain V. and Mikhalev A.A., Combinatorial Methods: Free groups, Polynomials, and Free Algebras. New York, Springer-Verlag, 2003. |
| Researcher : Mok N |
| Project Title: | Geometry of varieties of minimal rational tangents |
| Investigator(s): | Prof. Mok N. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 12/2001 |
| Abstract: |
| To study the implications of projective-geometric properties of VMRTs on the structure of the Lie algebra of holomorphic vector fields on X with an application to proviing deformation rigidity for all rational homogenenous manifolds of Picard number 1; to develop a notion of holonomy as we vary over VMRTs on a minimal rational curve, with a first objective of characterizing rational homogeneous manifolds of Picard number 1 in terms of their generic VMRTs; to study the geometry of the tangent map tx: Ux ® Cx Ì PTx at generic points with an aim to proving local rigidity of generically finite maps onto any Fano manifold of Picard number 1. |
| Project Title: | Bounded holomorphic functions and rigidity problems |
| Investigator(s): | Prof. Mok N. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 12/2002 |
| Abstract: |
| The project attempts to understand the rigidity problems on quotients of bounded domains by means of bounded holomorphic functions, often in relation to Carattheodory metrics. The link between rigidity and bounded holomorphic functions open up a new directionn of research on bounded domains both from the geometric and from the function-theorectic perspectives. |
| Project Title: | Holomorphic local isometries between bounded symmetric domains and related problems |
| Investigator(s): | Prof. Mok N. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 12/2003 |
| Abstract: |
| To prove that any holomorphic local isometric embedding between bounded symmetric domains extends to a global totally-geodesic embedding; to prove that any holomorphic measure-preserving local map from an irreducible bounded symmetric domain to a Cartesian product of copies of D must be totally geodesic; to consider generalizations and ramifications of approaches and solutions to the preceding problems, e.g., to formulate and establish a non-equidimensional analogue of Fefferman's Theorem on the smooth extension of biholomorphisms between strictly pseudoconvex domains. |
| Project Title: | Holomorphic local isometries between bounded symmetric domains and related problems |
| Investigator(s): | Prof. Mok N. |
| Department: | Mathematics |
| Source(s) of Funding: | RGC Projects (Block Grant Funded) |
| Start Date: | 12/2003 |
| Abstract: |
| To prove that any holomorphic local isometric embedding between bounded symmetric domains extends to a global totally-geodesic embedding; to prove that any holomorphic measure-preserving local map from an irreducible bounded symmetric domain to a Cartesian product of copies of D must be totally geodesic; to consider generalizations and ramifications of approaches and solutions to the preceding problems, e.g., to formulate and establish a non-equidimensional analogue of Fefferman's Theorem on the smooth extension of biholomorphisms between strictly pseudoconvex domains. |
| List of Research Outputs |
| Hwang J. and Mok N., Automorphism groups of the spaces of minimal rational curves on Fano manifolds of Picard Number 1, Journal of Algebraic Geometry. University Press, Inc., 2004, 13: 663-673. |
| Hwang J. and Mok N., Deformation rigidity of the 20-dimensional F4-homogeneous space associated to a short root, In: V.L. Popov, Algebraic Transformation Groups and Algebraic Varieties. Berlin-Heidelberg-New York, Springer-Verlag, 2004, 37-58. |
| Mok N., Extremal bounded holomorphic functions and an embedding theorem for arithmetic varieties of rank ³ 2, Inventiones Mathematicae. Berlin-Heidelberg-New York, Springer-Verlag, 2004, 101: 31 pages. |
| Mok N., Inventiones Mathematicae. Berlin-Heidelberg-New York, Springer-Verlag, 2003. |
| Mok N., Mathematische Annalen. Berlin-Heidelberg-New York, Springer-Verlag, 2003. |
| Mok N., Negativity of curvature on spaces parametrizing Hodge decompositions of reduced first cohomology groups, Contemporary Mathematics. Providence, Rhode Island, USA, American Mathematical Society, 2003, 332: 219-234. |
| Researcher : Ng KP |
| Project Title: | Iterative methods for Toeplitz Weighted Least Squares problems |
| Investigator(s): | Dr. Ng K.P. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 12/2000 |
| Completion Date: | 12/2003 |
| Abstract: |
| To extend the circulant preconditioner idea to Toeplitz weighted least squares problems. The project will focus on designing good transform based preconditioners that incorporate the Toeplitz-like structure of the weighted least sqares problems. |
| Project Title: | On Successive-overrelaxation acceleration of the hermitian and skew-hermitian splitting iterations |
| Investigator(s): | Dr. Ng K.P. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 11/2002 |
| Abstract: |
| To generalize the technique for constructing the Hermitian/skew-Hermitian splitting (HSS) iteration method for solving large sparse non-Hermitian positive definite system of linear equations to the normal/skew-Hermitian (NS) splitting obtaining a class of normal/skew-Hermitian splitting (NSS) iteration methods; to study a successive overrelaxation (SOR) acceleration scheme for the NSS iteration. |
| Project Title: | Hermitian and skew-hermitian splitting methods for non-hermitian positive definite systems |
| Investigator(s): | Dr. Ng K.P. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 12/2002 |
| Abstract: |
| This research proposal is centered on the development of efficient iterative methods for the large sparse non-Hermitian positive definite system of linear equations based on the Hermitian and skew-Hermitian splitting of the coefficient matrix. |
| Project Title: | Intelligent classification technologies for documents |
| Investigator(s): | Dr. Ng K.P., Dr. Ching W.K., Dr. Huang J.Z. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 09/2003 |
| Abstract: |
| To develop and implement new technologies to increase the classificaton accuracy of even growing documents in Chinese and mixed languages. |
| Project Title: | Analysis of half-quadratic regularization and applications to magnetic resonance imaging |
| Investigator(s): | Dr. Ng K.P., Dr. Deriche R., Dr. Kornprobst P., Dr. Nikolova M. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 12/2003 |
| Abstract: |
| To develop and analyze efficient algorithms to speed up the calculation of the solution in restoration; to analyze the convergence rate of the half-quadratic minimization method and examine the conditions required for the construction of the equivalent objective function; to implement, test and compare different edge-preserving functions and apply and analyze our method to constrained regulization problems. |
| Project Title: | Analysis of half-quadratic regularization and applications to magnetic resonance imaging |
| Investigator(s): | Dr. Ng K.P., Dr. Deriche R., Dr. Kornprobst P., Dr. Nikolova M. |
| Department: | Mathematics |
| Source(s) of Funding: | RGC Projects (Block Grant Funded) |
| Start Date: | 12/2003 |
| Abstract: |
| To develop and analyze efficient algorithms to speed up the calculation of the solution in restoration; to analyze the convergence rate of the half-quadratic minimization method and examine the conditions required for the construction of the equivalent objective function; to implement, test and compare different edge-preserving functions and apply and analyze our method to constrained regulization problems. |
| List of Research Outputs |
| Bai Z., Golub G.H. and Ng K.P., Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems, SIAM Journal on Matrix Analysis and Applications. 2003, 24: 603-626. |
| Bai Z. and Ng K.P., Preconditioners for Nonsymmetric Block-Toeplitz-Like-Plus-Diagonal Linear System , Numer. Math.. 2003, 96: 197-220. |
| Bertaccini D. and Ng K.P., Band-Toeplitz Preconditioned GMRES Iterations for Time-dependent PDEs, BIT. 2003, 43: 901-914. |
| Bertaccini D. and Ng K.P., Omega-Circulant Preconditioners for Time-Dependent Integrators, CALCOLO. 2003, 40: 71-90. |
| Chan Y.L., Ching W.K., Ng K.P. and Huang J.Z., An Optimization Algorithm for Clustering Using Weighted Dissimilarity Measures, Pattern Recognition. 2004, 37: 943-952. |
| Ching W.K. and Ng K.P., Building Simple Hidden Markov Models, International Journal of Mathematical Education in Science and Engineering. 2004, 35: 295-299. |
| Ching W.K., Ng K.P. and Wong K.K., Hidden Markov Models and Its Applications to Customer Relationship Management, IMA Journal of Management Mathematics. 2004, 15: 13-24. |
| Ching W.K., Ng K.P. and Fung S.L., Higher-order Hidden Markov Models with Applications to DNA Sequences, IDEAL, Lecture Notes in Computer Science. Springer, 2003, 535-539. |
| Ching W.K., Fung S.L. and Ng K.P., Higher-order Markov Chain Models for Categorical Data Sequences, International Journal of Naval Research Logistics. 2004, 51: 557-574. |
| Ching W.K., Ng K.P. and Wong K.K., Higher-order Markov Decision Process and Its Applications in Customer Lifetime Values, The 32nd International Conference on Computers and Industrial Engineering. Limerick, Ireland, 2003, 2: 821-826. |
| Ho K.F., Beling C.D., Fung S.H.Y., Cheng V.K.W., Ng K.P. and Yip A.M., Deconvolution of positron annihilation coincidence Doppler broadening spectra using an iterative projected Newton method with non-negativity constraints, Review of Scientific Instruments. New York, American Institute of Physics, 2003, 74: 4779-4787. |
| Ho K.F., Ching A.H.M., Cheng V.K.W., Beling C.D., Fung S.H.Y. and Ng K.P., Optimized coincidence Doppler broadening spectroscopy using deconvolution algorithms, Materials Science Forum. Switzerland, Trans Tech Publications, 2004, 445-446: 477-479. |
| Ho K.F., Ching A.H.M., Beling C.D., Fung S.H.Y., Ng K.P., Biasini M., Ferro G. and Gong M., Positron-electron autocorrelation function study of E-center in silicon, Journal of Applied Physics. New York, American Institute of Physics, 2003, 94: 5549-5555. |
| Huang Z. and Ng K.P., A Note on K-Modes Clustering, Journal of Classification. 2003, 20: 257-261. |
| Lam E.Y.M. and Ng K.P., Restoration of images with optical aberrations and quantization in a transform domain, Computational Imaging II. 2004, 5299: 93-100. |
| Lin F., Ching W.K. and Ng K.P., Accurate and Fast Inversion Methods for Triangular Toeplitz Matrices, Theoretical Computer Science. 2004, 315: 511-523. |
| Lin F., Ching W.K. and Ng K.P., Discrete Wavelet Transforms for Toeplitz Matrices, Linear Algebra and Its Applications. 2003, 370: 269-285. |
| Lin F. and Ng K.P., Super-Resolution Image Reconstruction with Estimation of Low-Resolution Frames, International Journal of Applied Mathematics. 2003, 13: 84-99. |
| Ng K.P., Circulant and Skew-Circulant Splitting Methods for Toeplitz Systems, Journal of Computational Applied Math.. 2003, 159: 101-108. |
| Ng K.P., Qin X. and Sun H., Recursive-Based PCG Methods for Toeplitz Systems with Nonnegative Generating Functions, SIAM Journal on Scientific Computing. 2003, 24: 1507-1529. |
| Ng K.P., Ching W.K., Sze N.K. and Yau C.K., Super-resolution Image Reconstruction from Blurred Observation by Multisensor, International Journal of Imaging Systems and Technology. 2003, 13: 153-160. |
| Ngan Y.T., Pang G.K.H., Ng K.P. and Yung S.P., Defect Detection on Patterned Jacquard Fabrics, IEEE International Workshop on 32nd Applied Imagery Pattern Recognition, 15-17 Oct, 2003. 163-168. |
| Yip Y.L., Ng K.P. and Cheung D.W.L., A Review on Projected Clustering Algorithms, International Journal of Applied Mathematics. 2003, 13: 24-35. |
| Researcher : Ng TW |
| Project Title: | Factorization and complex dynamics of meromorphic functions and related topics |
| Investigator(s): | Dr. Ng T.W., Dr. Beardon A.F., Prof. Yang C.C. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 10/2002 |
| Abstract: |
| To extend the proposer's studies and accomplishments by utilizing more powerful analytic and geometric tools to explore existing and related research resaults, as well as applying these results to some related research fields such as complex dynamics, functional and differential equations and sharing value problems of meromorphic functions. |
| Project Title: | Factorization and complex dynamics of meromorphic functions and related topics |
| Investigator(s): | Dr. Ng T.W., Dr. Beardon A.F., Prof. Yang C.C. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 10/2002 |
| Abstract: |
| To extend the proposer's studies and accomplishments by utilizing more powerful analytic and geometric tools to explore existing and related research resaults, as well as applying these results to some related research fields such as complex dynamics, functional and differential equations and sharing value problems of meromorphic functions. |
| Project Title: | Factorization and complex dynamics of meromorphic functions and related topics |
| Investigator(s): | Dr. Ng T.W., Dr. Beardon A.F., Prof. Yang C.C. |
| Department: | Mathematics |
| Source(s) of Funding: | RGC Projects (Block Grant Funded) |
| Start Date: | 10/2002 |
| Abstract: |
| To extend the proposer's studies and accomplishments by utilizing more powerful analytic and geometric tools to explore existing and related research resaults, as well as applying these results to some related research fields such as complex dynamics, functional and differential equations and sharing value problems of meromorphic functions. |
| Project Title: | A double epidemic model for SARS propagation |
| Investigator(s): | Dr. Ng T.W., Prof. Danchin A.L.M., Dr. Turinici G. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 11/2003 |
| Abstract: |
| To explore the consequences of a situation where two overlapping epidemics interfere with each other; to explore the possible situation where viruses A and B would be of totally different origin, but would cause an overlapping immune response of the host. |
| List of Research Outputs |
| Ching W.K., Chung S.K. and Ng T.W., On Modeling SARS in Hong Kong, International Journal of Applied Mathematics. 2003, 13, no.1: 1-7. |
| Guo H., Zheng J. and Ng T.W., On a new singular direction of meromorphic functions, Bull Austral. Math. Soc.. 2004, 69, no.2: 277-287. |
| Ng T.W., Turinici G. and Danchin A., A Double Epidemic Model for the SARS Propagation, BMC Infections Diseases. 2003, 3:19. |
| Ng T.W., Smale's mean value conjecture for odd polynomials, Journal of the Australian Mathematical Society. 2003, 75, no.3: 409-411. |
| Researcher : Shpilrain V |
| List of Research Outputs |
| Yu J. and Shpilrain V., Birational morphisms of the plane, Proc. Amer. Math. Soc. 2004, 132, no.9: 2511-2515. |
| Yu J., Shpilrain V. and Mikhalev A.A., Combinatorial Methods: Free groups, Polynomials, and Free Algebras. New York, Springer-Verlag, 2003. |
| Yu J., Makar-Limanov L., van Rossum P. and Shpilrain V., The stable equivalence and cancellation problems, Comment. Math. Helv. 2004, 79, no.2: 341-349. |
| Researcher : Siu MK |
| List of Research Outputs |
| Siu M.K., Learning and teaching of analysis in the mid 20th century: A semi-personal observation, In: D. Coray, F. Furinghetti, H. Gispert, B.R. Hodgson, G. Schubring, One Hundred Years of L'Enseignement Mathématique: Moments of Mathematics Education in the Twentieth Century. Genève, L'Enseignement Mathématique, 2003, 179-190. |
| Researcher : Sun H |
| List of Research Outputs |
| Ng K.P., Qin X. and Sun H., Recursive-Based PCG Methods for Toeplitz Systems with Nonnegative Generating Functions, SIAM Journal on Scientific Computing. 2003, 24: 1507-1529. |
| Researcher : Sun X |
| Project Title: | Logarithmic projective flat connection for generalized q functions |
| Investigator(s): | Dr. Sun X.T. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 09/2002 |
| Abstract: |
| To define a reasonable conformal field theory in algebraic geometry. Two basic problems have to be solved. One is to prove that when the curve moves in its moduli space, the associated vector spaces form a vector bundle and there is a logarithmic projective flat connection on this vector bundle. Another problem is to prove that any generalized theta function associated to a singular curve can be obtained from generalized q functions associated to a smooth curve, normalization of the singular curve. |
| Project Title: | Topological aspects of degeneration of moduli spaces of vector bundles |
| Investigator(s): | Dr. Sun X.T., Prof. Mok N. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 09/2003 |
| Abstract: |
| not available |
| Project Title: | Topological aspects of degeneration of moduli spaces of vector bundles |
| Investigator(s): | Dr. Sun X.T., Prof. Mok N. |
| Department: | Mathematics |
| Source(s) of Funding: | RGC Projects (Block Grant Funded) |
| Start Date: | 09/2003 |
| Abstract: |
| not available |
| List of Research Outputs |
| Sun X., Moduli spaces of SL(r)-bundles on singular irreducible curves, Asian Journal of Mathematics. 2003, 7: 609-626. |
| Researcher : Sze NK |
| List of Research Outputs |
| Ng K.P., Ching W.K., Sze N.K. and Yau C.K., Super-resolution Image Reconstruction from Blurred Observation by Multisensor, International Journal of Imaging Systems and Technology. 2003, 13: 153-160. |
| Researcher : Tsang KM |
| Project Title: | Waring Goldbach Type problems for low degrees |
| Investigator(s): | Dr. Tsang K.M., Prof. Liu J.Y., Dr. Ren X.M. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 10/2003 |
| Abstract: |
| not available |
| Project Title: | Waring Goldbach Type problems for low degrees |
| Investigator(s): | Dr. Tsang K.M., Prof. Liu J.Y., Dr. Ren X.M. |
| Department: | Mathematics |
| Source(s) of Funding: | RGC Projects (Block Grant Funded) |
| Start Date: | 10/2003 |
| Abstract: |
| not available |
| Researcher : Umirbayev U |
| List of Research Outputs |
| Yu J. and Umirbayev U., The strong Nagata conjecture, Proc. Natl. Acad. Sci. USA. 2004, 101, no.13: 4352-4355. |
| Researcher : Wang J |
| List of Research Outputs |
| Wang J., Xu G. and Yung S.P., Exponential Stability of Variable Coefficients Rayleigh Beams under Boundary Feedback Controls, Systems and Control Letters. 2004, 51/1: 33-50. |
| Researcher : Wong B |
| List of Research Outputs |
| Cheung W.S., Wong B. and Yau S.S.T., Some Remarks on the Local Moduli of Tangent Bundles over Complex Surfaces, American Journal of Mathematics. 2003, 125: 1029-1035. |
| Researcher : Wong KK |
| List of Research Outputs |
| Ching W.K., Ng K.P. and Wong K.K., Hidden Markov Models and Its Applications to Customer Relationship Management, IMA Journal of Management Mathematics. 2004, 15: 13-24. |
| Ching W.K., Ng K.P. and Wong K.K., Higher-order Markov Decision Process and Its Applications in Customer Lifetime Values, The 32nd International Conference on Computers and Industrial Engineering. Limerick, Ireland, 2003, 2: 821-826. |
| Researcher : Xu G |
| List of Research Outputs |
| Feng D.X., Xu G. and Yung S.P., Riesz Basis Property of the Generalized Eigenvector System of A Timoshenko Beam, IMA J. Math. Control Inf. 2004, 21, Issue 1: 65-83. |
| Wang J., Xu G. and Yung S.P., Exponential Stability of Variable Coefficients Rayleigh Beams under Boundary Feedback Controls, Systems and Control Letters. 2004, 51/1: 33-50. |
| Xu G. and Yung S.P., Stabilization of Timoshenko Beam by Means of Pointwise Controls, ESAIM: Control, Optimisation and Calculus of Variations. 2003, 9: 579-600. |
| Researcher : Yau CK |
| List of Research Outputs |
| Ng K.P., Ching W.K., Sze N.K. and Yau C.K., Super-resolution Image Reconstruction from Blurred Observation by Multisensor, International Journal of Imaging Systems and Technology. 2003, 13: 153-160. |
| Researcher : Yu J |
| Project Title: | Stably equivalence problem for free algebras |
| Investigator(s): | Dr. Yu J.T. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 12/2001 |
| Completion Date: | 12/2004 |
| Abstract: |
| To study stably equivalence problem for free algebras by combinatorial and computational methods including Tietze Transformation, Universal Differential Calculus, and Standard (Groebner) Basis. |
| Project Title: | Small cancellation method for polynomial algebras |
| Investigator(s): | Dr. Yu J.T. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 12/2003 |
| Abstract: |
| not available |
| Project Title: | Small cancellation method for polynomial algebras |
| Investigator(s): | Dr. Yu J.T. |
| Department: | Mathematics |
| Source(s) of Funding: | RGC Projects (Block Grant Funded) |
| Start Date: | 12/2003 |
| Abstract: |
| not available |
| List of Research Outputs |
| Yu J. and Shpilrain V., Birational morphisms of the plane, Proc. Amer. Math. Soc. 2004, 132, no.9: 2511-2515. |
| Yu J., Shpilrain V. and Mikhalev A.A., Combinatorial Methods: Free groups, Polynomials, and Free Algebras. New York, Springer-Verlag, 2003. |
| Yu J., Editor of International Journal of Mathematics: Algebra and Game Theory. 2004. |
| Yu J., Makar-Limanov L., van Rossum P. and Shpilrain V., The stable equivalence and cancellation problems, Comment. Math. Helv. 2004, 79, no.2: 341-349. |
| Yu J. and Umirbayev U., The strong Nagata conjecture, Proc. Natl. Acad. Sci. USA. 2004, 101, no.13: 4352-4355. |
| Researcher : Yung SP |
| Project Title: | Boundary feedback stabilizing systems: a Riesz Basis approach |
| Investigator(s): | Dr. Yung S.P. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 09/2002 |
| Abstract: |
| Feedback is a technique that uses information gathered from sensors attached to a device to construct stabilizing controls. This project is to solve the feedback stabilizing problem through a systematic investigation of a so-called "Riesz Basis Property". |
| Project Title: | Fast pyramid algorithms for solving differential equations |
| Investigator(s): | Dr. Yung S.P., Dr. Ching W.K., Dr. Ng K.P. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 01/2003 |
| Completion Date: | 12/2003 |
| Abstract: |
| To find fast pyramid algorithms to solve differential as well as integral equations. The significance of this research comes form the fact that there are a lot of engineering problems formulated in the form of differential equations, which in turns can be converted into integral equations. Finding a fast algorithm to solve them become vital and it is our intention to design pyramid algorithms, which have worked so well for wavelet applications, to achieve this task. |
| Project Title: | Controllability of boundary feedback beam problems |
| Investigator(s): | Dr. Yung S.P. |
| Department: | Mathematics |
| Source(s) of Funding: | RGC Projects (Block Grant Funded) |
| Start Date: | 07/2003 |
| Abstract: |
| To extend the method of moments that determines controllabilities on problems related to beams (including strings, Euler-Bernoulli, Rayleigh, Timoskenko beams) and carry over the obtained results to other elastic problems (such as coupled beams and hybrid problems). |
| Project Title: | Generating wavelet filters via lifting schemes |
| Investigator(s): | Dr. Yung S.P. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 11/2003 |
| Abstract: |
| To develop the theoretical background of generating wavelet filters that are pertinent for specific applications via lifting schemes. |
| List of Research Outputs |
| Chan P.K., Ching W.K. and Yung S.P., Optimal Strategies in Equity Securities and Derivatives, Journal of Applied Mathematics and Computations. 2004, 151: 615-643. |
| Feng D.X., Xu G. and Yung S.P., Riesz Basis Property of the Generalized Eigenvector System of A Timoshenko Beam, IMA J. Math. Control Inf. 2004, 21, Issue 1: 65-83. |
| Lai T.L., Yang H. and Yung S.P., Probability, Finance and Insurance. Singapore, World Scientific, 2004. |
| Ngan Y.T., Pang G.K.H., Ng K.P. and Yung S.P., Defect Detection on Patterned Jacquard Fabrics, IEEE International Workshop on 32nd Applied Imagery Pattern Recognition, 15-17 Oct, 2003. 163-168. |
| Wang J., Xu G. and Yung S.P., Exponential Stability of Variable Coefficients Rayleigh Beams under Boundary Feedback Controls, Systems and Control Letters. 2004, 51/1: 33-50. |
| Xu G. and Yung S.P., Stabilization of Timoshenko Beam by Means of Pointwise Controls, ESAIM: Control, Optimisation and Calculus of Variations. 2003, 9: 579-600. |
| Researcher : Zang W |
| Project Title: | Obstructions to some combinatorial properties |
| Investigator(s): | Dr. Zang W. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 09/2001 |
| Abstract: |
| To characterize the graphs with the min-max relation on cycle (resp. odd cycle) packing and covering in terms of forbidden subgraphs, and give polynomial-time algorithms for the corresponding cycle packing and covering problems; to design combinatorial polynomial-time algorithm for the minimum weighted colorings of certain perfect graphs; in particular, solve the minimum-weighted coloring problem on claw-free perfect graphs, which was posed by Hsu and Nemhauser as an open problem in 1984; to prove Chvatal's conjecture concerning obstructions to the intersection property for maximal cliques and maximal stable sets in graphs, and characterize the finite posets with the min-max relation on fibres and nontrivial miximal antichains; to derive bounds for some Ramsey numbes and Turan numbers involving bipartite graphs. |
| Project Title: | The independent set problem and its application |
| Investigator(s): | Dr. Zang W. |
| Department: | Mathematics |
| Source(s) of Funding: | Block Grant Earmarked for Research |
| Start Date: | 01/2003 |
| Abstract: |
| To investigate the independent set problem in different settings using various algorithmic ideas such as linear programming, dynamic programming, decomposition method, and probabilistic method. |
| Project Title: | Optimization: integrality and duality |
| Investigator(s): | Dr. Zang W. |
| Department: | Mathematics |
| Source(s) of Funding: | Hong Kong Research Grants Council Competitive Earmarked Research Grants |
| Start Date: | 08/2003 |
| Abstract: |
| To establish the dual version of Toft's conjecture on nowhere-zero 3-flows, confirm the Keedwell-Cameron conjecture by proving a 4-flow theorem, and attack Tutte's 3-, 4-, and 5-flow conjectures; to study various packing and covering problems in combinatorics and optimization (my focus will be on the circuit packing problem and its dual on matroids; to investigate the edge-coloring problem on multigraphs and the circular arc coloring problem, and design approximation algorithms for these problems based on the corresponding fractional optimal values. |
| Project Title: | Optimization: integrality and duality |
| Investigator(s): | Dr. Zang W. |
| Department: | Mathematics |
| Source(s) of Funding: | RGC Projects (Block Grant Funded) |
| Start Date: | 08/2003 |
| Abstract: |
| To establish the dual version of Toft's conjecture on nowhere-zero 3-flows, confirm the Keedwell-Cameron conjecture by proving a 4-flow theorem, and attack Tutte's 3-, 4-, and 5-flow conjectures; to study various packing and covering problems in combinatorics and optimization (my focus will be on the circuit packing problem and its dual on matroids; to investigate the edge-coloring problem on multigraphs and the circular arc coloring problem, and design approximation algorithms for these problems based on the corresponding fractional optimal values. |
| List of Research Outputs |
| Chen B., Deng X.T. and Zang W., On-line Scheduling a Batch Processing System to Minimize Total Weighted Job Completion Time, Journal of Combinatorial Optimization. MA, USA, Kluwer Academic Publishers, 2004, 8: 85-95. |
| Deng X.T., Li G., Zang W. and Zhou Y., A 2-Approximation Algorithm for Path Coloring on a Restricted Class of Trees of Rings, Journal of Algorithms. CA, USA, Elsevier, 2003, 47: 1-13. |
| Li Y. and Zang W., The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers, Journal of Combinatorial Optimization. MA, USA, Kluwer Academic Publishers, 2003, 7: 353-359. |
| Liu G. and Zang W., f-Factors in Bipartite (mf)-Graphs, Discrete Applied Mathematics. Amsterdam, Netherlands, North-Holland, 2004, 136: 45-54. |
| Researcher : Zhang S |
| List of Research Outputs |
| Ching W.K., Scholtes S. and Zhang S., Numerical Algorithms for Estimating Traffic Between Zones in a Network, Engineering Optimisation. 2004, 36: 379-400. |
| Researcher : Zheng J |
| List of Research Outputs |
| Guo H., Zheng J. and Ng T.W., On a new singular direction of meromorphic functions, Bull Austral. Math. Soc.. 2004, 69, no.2: 277-287. |