DEPARTMENT OF MATHEMATICS
| Researcher : Ao SI |
| List of Research Outputs |
| Ao S.I., Ng K.P. and Ching W.K., Modeling Gene Expression Network with PCA-NN on Continuous Inputs and Outputs Basis, Current Trends in High Performance Computing and Its Applications.Proceedings of the International Conference on High Performance Computing and Applications. Springer, 2005, 209-214. |
| Researcher : Bai Z |
| List of Research Outputs |
| Bai Z., Ng K.P. and Pan J., Alternating splitting waveform relaxation method and its successive overrelaxation acceleration, Applied Mathematics and Computation. 2005, 49, no.2-3: 157-170. |
| Pan J., Bai Z. and Ng K.P., Two-step waveform relaxation methods for implicit linear initial value problems, Numer. Linear Algebra Appl. . 2005, 12, no.2-3: 293-304. |
| Researcher : Belov A |
| List of Research Outputs |
| Yu J., Belov A. and Makar-Limanov L., On generalized cancellation problem, Journal of Algebra. 2004, 281, no.1: 161-166. |
| Researcher : Bertaccini D |
| List of Research Outputs |
| Bertaccini D., Wen Y. and Ng K.P., The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form, Numer. Linear Algebra Appl.. 2005, 12, no.2-3: 315-325. |
| Researcher : Cai J |
| List of Research Outputs |
| Wei Y., Cai J. and Ng K.P., Computing Moore-Penrose inverses of Toeplitz matrices by Newton's iteration, Mathematical and Computer Modelling. 2004, 40, no.1-2: 181-191. |
| Researcher : Chan JT |
| Project Title: | The linear preserver problem |
| Investigator(s): | Chan JT, Li C.K. |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| 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): | Chan JT, Li C.K. |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 09/2003 |
| Abstract: |
| To investigate linear mappings on an operator algebra that leave invariant a certain set or function of the algebra. |
| List of Research Outputs |
| Chan J.T., Li C.K. and Sze N.S., Isometries for unitarily invariant norms, Linear Algebra and Its Applications. 2005, 399: 53-70. |
| Researcher : Cheung WS |
| Project Title: | Bounded domains in n-dimensional complex spaces |
| Investigator(s): | Cheung WS, Wong B. |
| Department: | Mathematics |
| Source(s) of Funding: | Other Funding Scheme |
| Start Date: | 09/1991 |
| Abstract: |
| To study the behaviour and properties of certain intrinsic measures on bounded domains in an n-dimensional euclidean space. |
| Project Title: | Canonical metrics, uniformization of complex manifolds, rigidity of holomorphic tangent bundles: generalizations of a theorem of K.H. Look |
| Investigator(s): | Cheung WS, Wong B. |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| 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 and applications |
| Investigator(s): | Cheung WS, Pecaric J. |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| 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): | Cheung WS, Pecaric J. |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| 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): | Cheung WS |
| Department: | Mathematics |
| Source(s) of Funding: | Seed Funding Programme for Basic Research |
| Start Date: | 02/2004 |
| Completion Date: | 07/2005 |
| Abstract: |
| To study quasi-linear BVP and discrete multi-point BVP. |
| Project Title: | Complete Monotonicity of Special Functions Involving the Gamma, Digamma, and Polygamma Functions |
| Investigator(s): | Cheung WS |
| Department: | Mathematics |
| Source(s) of Funding: | Seed Funding Programme for Basic Research |
| Start Date: | 02/2005 |
| Abstract: |
| Please refer to attachment. |
| List of Research Outputs |
| Changjian Z., Cheung W.S. and Bencze M., On Reverse Hilbert Type Inequalities, Studia Univ. "Babes-Bolyai'' Mathematica. 2004, XLIX, No.4: 53-60. |
| Chen C.P., Cheung W.S. and Qi F., Note on Weighted Carleman-Type Inequality, International Journal of Mathematics and Mathematical Sciences. 2005, 2005, No.3: 475-481. |
| Cheung W.S., An Exterior-Differential-Systems Approach of the Calculus of Variations, 2005 Southeast Asian Conference in Mathematics, Tamsui, Taiwan, 4/2005. Tamsui, Taiwan, 2005. |
| Cheung W.S., Editor of Australian Journal of Mathematical Analysis and Applications. 2005. |
| Cheung W.S., Editor of Journal of Inequalities in Pure and Applied Mathematics. 2005. |
| Cheung W.S., Editor of the Bulletin of Southeast Asian Mathematical Society. 2005. |
| Cheung W.S., Lin Y.T., Tseng S. and Strecker G.E., On a Weak Form of the Blumberg Property, In: W. Gähler and G. Preuss, Categorical Structures and Their Applications. New Jersey, World Scientific, 2004, 41-49. |
| Cheung W.S. and Ren J., On the Existence of Periodic Solutions for p-Laplacian Generalized Liénard Equation, Nonlinear Analysis. 2005, 60, No.1: 65-75. |
| Cheung W.S. and Ren J., Periodic Solutions for p-Laplacian Liénard Equation with a Deviating Argument, Nonlinear Analysis. 2004, 59, No.1-2: 107-120. |
| Cheung W.S. and Ren J., Positive Solutions for Discrete Three-Point Boundary Value Problems, Australian Journal of Mathematical Analysis and Applications. 2004, 1, No.2, Art. 9: 7pp. |
| Cheung W.S. and Ren J., Positive Solutions for m-point Boundary Value Problems, Journal of Mathematical Analysis and Applications. 2005, 303: 565-575. |
| Cheung W.S., Reviewer of Zentralblatt Math. V.1050, No. 49001. 2004, 1050, no.49001. |
| Cheung W.S., Reviewer of Zentralblatt Math. V.1054, No. 49020. 2005, 1054, no.49020. |
| Cheung W.S., Reviewer of Zentralblatt Math. V.1056, No. 49032. 2005, 1056, no.49032. |
| Cheung W.S., Reviewer of Zentralblatt Math. V.1057, No. 58008. 2005, 1057, no.58008. |
| Cheung W.S., Some Discrete Nonlinear Inequalities and Applications to Boundary Value Problems, International Conference in Discrete Mathematics with Applications to Information Science and Related Topics, Chongqing, China, 10/2004. Chongqing, China, 2004. |
| Cheung W.S., Some Discrete Nonlinear Inequalities and Applications to Boundary Value Problems, Proceedings of the 8th International Conference on Difference Equations and Applications (Brno, 2003). 2005, 83-90. |
| Cheung W.S. and Ren J., Twin Positive Solutions for Quasi-linear Multi-Point Boundary Value Problems, Nonlinear Analysis. 2005, 62, No.1: 167-177. |
| Researcher : Ching WK |
| Project Title: | Models and numerical algorithms for queuing and manufacturing systems |
| Investigator(s): | Ching WK, Chan R.H.F. |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| 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): | Ching WK |
| Department: | Mathematics |
| Source(s) of Funding: | Small Project Funding |
| 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): | Ching WK |
| Department: | Mathematics |
| Source(s) of Funding: | Small Project Funding |
| 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. |
| Project Title: | Models and Algorithms for Multivariate Markov Chains |
| Investigator(s): | Ching WK |
| Department: | Mathematics |
| Source(s) of Funding: | Incentive Award for RGC CERG Fundable But Not Funded Projects |
| Start Date: | 07/2004 |
| Abstract: |
| Refer to hard copy |
| Project Title: | Higher dimensional Markov Chain Models for biological data sequences |
| Investigator(s): | Ching WK |
| Department: | Mathematics |
| Source(s) of Funding: | Seed Funding Programme for Basic Research |
| Start Date: | 05/2005 |
| Abstract: |
| refer to hard copy proposal |
| List of Research Outputs |
| Ao S.I., Ng K.P. and Ching W.K., Modeling Gene Expression Network with PCA-NN on Continuous Inputs and Outputs Basis, Current Trends in High Performance Computing and Its Applications.Proceedings of the International Conference on High Performance Computing and Applications. Springer, 2005, 209-214. |
| Chan R., Ching W.K., Luk F. and Ng M., Invited Editor of Vol. 12, Nos. 2-3 of Numerical Linear Algebra with Applications, In: Raymond H. Chan, Wai-Ki Ching, Franklin Luk and Michael Ng, UK, John Wiley & Son, 2005, 12(2-3): 87-336. |
| Ching W.K., Ng K.P. and Yuen W.O., A Hybrid Algorithm for Solving the Page Rank, Current Trends in High Performance Computing and Its Applications.Proceedings of the International Conference on High Performance Computing and Applications. Springer, 2005, 257-264. |
| Ching W.K., A Note on the Paper: Optimizing Web Servers Using Page Rank Prefetching for Clustered Accesses, Information Sciences. 2005, 169, no.3-4: 245-247. |
| Ching W.K. and Tai A.H.L., A Quantity-time-based Dispatching Policy for a VMI System, Lecture Notes in Computer Science. Springer, 2005, 3483: 342-349. |
| Ching W.K., Fung S.L. and Ng K.P., Building Genetic Networks in Gene Expression Patterns, Lecture Notes in Computer Science. Springer, 2004, 3177: 17-24. |
| Ching W.K., Building Genetic Networks with Multivariate Markov Chains, The 50th National Institute for Basic Biology Conference,Structure and Dynamics of Complex Biological Networks,Okazaki, Japan. 2005. |
| Ching W.K., Fung S.L. and Ng K.P., Building Higher-order Markov Chain Models with EXCEL, International Journal of Mathematical Education in Science and Technology. 2004, 35: 921-932. |
| Ching W.K., Ng K.P., Wong K.K. and Atlman E., Customer Lifetime Value: A Stochastic Programming Approach, Journal of Operational Research Society. 2004, 55: 860-868. |
| Ching W.K., Ng K.P. and Zhang S., On Computation with Higher-order Markov Chain, Current Trends in High Performance Computing and Its Applications.Proceedings of the International Conference on High Performance Computing and Applications. Springer, 2005, 15-24. |
| Ching W.K., On Hybrid Algorithm for Solving Stochastic Matrix, Workshop on Applied Numerical Linear Algebra, Department of Mathematics, Fudan University, Shanghai, China. 2004. |
| Ching W.K., Ng K.P., Sze N.K. and Yau C.K., Super-resolution image reconstruction using multisensors, Numer. Linear Algebra Appl.. 2005, 12, no.2-3: 271-281. |
| Fu H., Ng K.P., Nikolova M., Barlow J. and Ching W.K., Fast Algorithms for l1 Norm/Mixed l1 and l2 Norms for Image Restoration, Lecture Notes in Computer Science. Springer, 2005, 3483: 843-851. |
| Lin F., Ching W.K. and Ng K.P., Fast inversion of triangular Toeplitz matrices, Theoret. Comput. Sci.. 2004, 315, no.2-3: 511-523. |
| Lin F. and Ching W.K., Inverse Toeplitz Preconditioners for Hermitian Toeplitz Systems, Numerical Linear Algebra with Applications. 2005, 12, no.2-3: 221-229. |
| Lin F., Ching W.K. and Ng K.P., Preconditioning regularized least squares problems arising from high-resolution image reconstruction from low-resolution frames, Linear Algebra and Its Applications. 2004, 391: 149-168. |
| Lu L., Ching W.K. and Ng K.P., Exact algorithms for singular tridiagonal systems with applications to Markov chains, Applied Mathematics and Computation. 2004, 159, no.1: 275-289. |
| So M.C., Ching W.K. and Ng K.P., Customer Migration, Campaign Budgeting, Revenue Estimation: The Elasticity of Markov Decision Process on Customer Lifetime Value, Electronic International Journal of Advanced Modeling and Optimization. 2004, 6(2): 65-80. |
| Wen Y., Ng K.P., Ching W.K. and Liu H., A note on the stability of Toeplitz matrix inversion formulas, Applied Mathematics Letters. 2004, 17, no.8: 903-907. |
| Wen Y., Ng K.P. and Ching W.K., High-Resolution Image Reconstruction from the Low-Resolution Rotated and Translated Image Frames, International Journal of Imaging Systems and Technology. 2004, 14: 75-83. |
| Wen Y., Ng K.P. and Ching W.K., Preconditioner Based on Gohberg-Semumcul Formula forPositive Definitive Toeplitz Systems, Proceedings of ICNAAM. Wiley-VCH, 2004, 473-476. |
| Yuen W.O., Ching W.K. and Ng K.P., A Hybrid Algorithm for Queueing Systems, CALCOLO. 2004, 41: 139-151. |
| Researcher : Chu SCK |
| Project Title: | Heuristic solution comparisons of exact modelling for fixed-length duties generation |
| Investigator(s): | Chu SCK |
| Department: | Mathematics |
| Source(s) of Funding: | Small Project Funding |
| 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. 2004. |
| Chu S.C.K. and Lam S.S., Best OR Paper Award, Best OR Paper Award of the IIE Annual Conference - Industrial Engineering Research Conference 2005 (IERC 2005), Atlanta, GA, USA (14-18 May 2005). 2005. |
| Chu S.C.K. and Yuen C.S.Y., Effective Heuristics vs GP for Shift Duties Generation, Proceedings of the International Workshop on Multi-Criteria Decision Making, Ustron, Poland, 2-6 April 2005. 14pp. |
| Chu S.C.K. and Lam S.S., Optimization Modeling DSS for Least Cost IDD Route Planning, [Winner of IIE Annual Conference Best OR Paper Award]Proceedings of the Institute of Industrial Engineers AnnualConference - 2005 Industrial Engineering Research Conference (IERC 2005), Atlanta, GA, USA, 14-18 May 2005. 6 pp. |
| Chu S.C.K. and Ho J.K., Topological and Optimization Modelling for Internet Data of Online Auction Markets, Proceedings of the 27th International Conference on Information Technology Interfaces (ITI2005), Cavtat/Dubrovnik, Croatia, 20-23 June 2005 . 2005, 5 pp. |
| Researcher : Eyssidieux PP |
| List of Research Outputs |
| Eyssidieux P.P. and Mok N., On the validity of failure of gap rigidity for certain pairs of bounded symmetric domains, Asian Journal of Mathematics. 2004, 8, no.4: 773-794. |
| Researcher : Fu H |
| List of Research Outputs |
| Fu H., Ng K.P., Nikolova M., Barlow J. and Ching W.K., Fast Algorithms for l1 Norm/Mixed l1 and l2 Norms for Image Restoration, Lecture Notes in Computer Science. Springer, 2005, 3483: 843-851. |
| Researcher : Fung SL |
| List of Research Outputs |
| Ching W.K., Fung S.L. and Ng K.P., Building Genetic Networks in Gene Expression Patterns, Lecture Notes in Computer Science. Springer, 2004, 3177: 17-24. |
| Ching W.K., Fung S.L. and Ng K.P., Building Higher-order Markov Chain Models with EXCEL, International Journal of Mathematical Education in Science and Technology. 2004, 35: 921-932. |
| Researcher : Hwang J |
| List of Research Outputs |
| Hwang J. and Mok N., Birationality of the tangent map for minimal rational curves, Asian Journal of Mathematics. 2004, 8, no. 1: 51-63. |
| Hwang J. and Mok N., Prolongations of infinitesimal linear automorphisms of projective varieties and rigidity of rational homogeneous spaces of Picard number 1 under Kähler deformation, Invent. Math.. 2005, 160: 591-645. |
| Researcher : Ji L |
| List of Research Outputs |
| Ji L. and Lu J., New realizations of the maximal Satake compactification ofRiemannian symmetric spaces, Letters in Mathematical Physics. 2004, 69 (1-3): 139-145. |
| Researcher : Lam CM |
| List of Research Outputs |
| Yu J. and Lam C.M., Tame and wild coordinates of Z[x,y], Journal of Algebra. 2004, 279, no.2: 425-436. |
| Researcher : Lau YK |
| List of Research Outputs |
| Lau Y.K., Mean square estimate for twisted automorphic L-functions on weight aspect, The Quarterly Journal of Mathematics. Oxford University Press, 2005, 56, No. 2: 223-237. |
| Lau Y.K. and Tsang K.M., Moments of the Probability Density Functions of Error Terms in Divisor Problems, Proceedings of the American Mathematical Society. 2005, 133: 1283-1290. |
| Lau Y.K. and Tsang K.M., Moments over Short Intervals, Archiv der Mathematik. Springer, 2005, 84: 249-257. |
| Researcher : Li CK |
| List of Research Outputs |
| Chan J.T., Li C.K. and Sze N.S., Isometries for unitarily invariant norms, Linear Algebra and Its Applications. 2005, 399: 53-70. |
| Researcher : Li G |
| List of Research Outputs |
| Deng X.T., Li G. and Zang W., Proof of Chvátal's conjecture on maximal stable sets and maximal cliques in graphs, Journal of Combinatorial Theory Series B. CA, USA, Academic Press, 2004, 91: 301-325. |
| Researcher : Lin F |
| List of Research Outputs |
| Lin F., Ching W.K. and Ng K.P., Fast inversion of triangular Toeplitz matrices, Theoret. Comput. Sci.. 2004, 315, no.2-3: 511-523. |
| Lin F. and Ching W.K., Inverse Toeplitz Preconditioners for Hermitian Toeplitz Systems, Numerical Linear Algebra with Applications. 2005, 12, no.2-3: 221-229. |
| Lin F., Ching W.K. and Ng K.P., Preconditioning regularized least squares problems arising from high-resolution image reconstruction from low-resolution frames, Linear Algebra and Its Applications. 2004, 391: 149-168. |
| Researcher : Liu H |
| List of Research Outputs |
| Wen Y., Ng K.P., Ching W.K. and Liu H., A note on the stability of Toeplitz matrix inversion formulas, Applied Mathematics Letters. 2004, 17, no.8: 903-907. |
| Researcher : Liu J |
| List of Research Outputs |
| Liu J. and Tsang K.M., Small Prime Solutions of Ternary Linear Equations, Acta Arithematica. 2005, 118: 79-100. |
| Researcher : Lu J |
| Project Title: | Poisson Morse theory |
| Investigator(s): | Lu J |
| Department: | Mathematics |
| Source(s) of Funding: | Seed Funding for New Staff |
| 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): | Lu J |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| 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): | Lu J |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| 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 Geometry and Spherical Varieties |
| Investigator(s): | Lu J |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 01/2005 |
| Abstract: |
| To study: (1) the geometry of the Poisson structures of the spherical subvarieties of L; (2) the degeneration of a family of spherical varieties that naturally occur in our study of the variety L. Spherical varieties are important for representation theory and for algebraic geometry. There has been active research on spherial varieties, and particularly on their embedding theory and cohomology theories. |
| Project Title: | Poisson Geometry and Spherical Varieties |
| Investigator(s): | Lu J |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| Start Date: | 01/2005 |
| Abstract: |
| Refer to hard copy |
| Project Title: | Poisson structures and tropical geometry |
| Investigator(s): | Lu J |
| Department: | Mathematics |
| Source(s) of Funding: | Seed Funding Programme for Basic Research |
| Start Date: | 01/2005 |
| Abstract: |
| The objectives of the project is to study large limits of Poisson varieties in the language of tropical geometry. |
| List of Research Outputs |
| Evens S. and Lu J., Thompson's conjecture for real semi-simple Lie groups, In: Marsden, Jerrold E.; Ratiu, Tudor S., Progress in Mathematics. Birkhauser, 2004, 232: 121-147. |
| Foth P. and Lu J., A Poisson structure on compact symmetric spaces, Communications in Mathematical Physics. 2004, 251 (3): 557-566. |
| Ji L. and Lu J., New realizations of the maximal Satake compactification ofRiemannian symmetric spaces, Letters in Mathematical Physics. 2004, 69 (1-3): 139-145. |
| Lu J., Editor of Pacific Journal of Mathematics. 2005. |
| Lu J. and Yakimov M.T., On a class of double cosets in reductive algebraic groups, International Mathematics Research Notices. 2005, 13: 761-797. |
| Researcher : Lu L |
| List of Research Outputs |
| Lu L., Ching W.K. and Ng K.P., Exact algorithms for singular tridiagonal systems with applications to Markov chains, Applied Mathematics and Computation. 2004, 159, no.1: 275-289. |
| Lu L. and Ng K.P., Localization of Perron roots, Linear Algebra and Its Applications. 2004, 392: 103-117. |
| Lu L. and Ng K.P., On sufficient and necessary conditions for the Jacobi matrix inverse eigenvalue problem, Numer. Math.. 2004, 98, no.1: 167-176. |
| Researcher : Makar-Limanov L |
| List of Research Outputs |
| Yu J., Belov A. and Makar-Limanov L., On generalized cancellation problem, Journal of Algebra. 2004, 281, no.1: 161-166. |
| Researcher : Mok N |
| Project Title: | Geometry of varieties of minimal rational tangents |
| Investigator(s): | Mok N |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 12/2001 |
| Completion Date: | 08/2004 |
| 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 [tau]x: Ux [rarr] Cx [subset] 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): | Mok N |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| 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: | Topological aspects of degeneration of moduli spaces of vector bundles |
| Investigator(s): | Mok N, Sun X |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 09/2003 |
| Abstract: |
| For a given projective smooth curve Y, let U(Y, r, d) be the moduli space of semistable bundles of rank r and degree d on Y (r and d are coprime). One of the open problems about the topology of moduli spaces of bundles on curves is to compute Chern-classes of U(Y, r, d) using degeneration method: (1) Degenerate the curve Y into an irreducible curve X with only one node, and construct a degeneration of U(Y, r, d), which is a moduli space G(X) of stable bundles on some semistable curves. (2) Find the relationship between G(X) and U(C, 2, d), where C is the normalization of X and g(C)=g(Y-1), so that one can reduce the problem of genus g(Y)=g to a problem of genus g1. (1) is established, but (2) remains open. Instead of studying the relationship between G(X) and U(C, r, d) in the category of algebraic varieties, we propose to study the relationship in the category of topological spaces. |
| Project Title: | Holomorphic local isometries between bounded symmetric domains and related problems |
| Investigator(s): | Mok N |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| 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): | Mok N |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| 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: | Geometric problems on complex hyperbolic space forms and their subvarieties |
| Investigator(s): | Mok N |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 01/2005 |
| Abstract: |
| To find obstructions to holomorphically fibering or foliating compact complex hyperbolic space forms and their complex submanifolds; to study holomorphic mappings from compact complex hyperbolic space forms into Kähler manifolds of constant holomorphic sectional curvature; to tackle the compact case of Oort's conjecture asserting that there are no Shimura varieties on the Siegel modular variety lying on the locus of Jacobians of curves of sufficiently high genus: to study the geometry of complex-analytic subvarieties of complex hyperbolic space forms with respect to the holomorphic projective structure of the latter manifolds. |
| Project Title: | Geometric problems on complex hyperbolic space forms and their subvarieties |
| Investigator(s): | Mok N |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| Start Date: | 01/2005 |
| Abstract: |
| Refer to hard copy |
| List of Research Outputs |
| Eyssidieux P.P. and Mok N., On the validity of failure of gap rigidity for certain pairs of bounded symmetric domains, Asian Journal of Mathematics. 2004, 8, no.4: 773-794. |
| Hwang J. and Mok N., Birationality of the tangent map for minimal rational curves, Asian Journal of Mathematics. 2004, 8, no. 1: 51-63. |
| Hwang J. and Mok N., Prolongations of infinitesimal linear automorphisms of projective varieties and rigidity of rational homogeneous spaces of Picard number 1 under Kähler deformation, Invent. Math.. 2005, 160: 591-645. |
| Mok N., Editor of Inventiones Mathematicae. Berlin-Heidelberg-New York, Springer-Verlag, 2004. |
| Mok N., Editor of Mathematische Annalen. Berlin-Heidelberg-New York, Springer-Verlag, 2004. |
| Mok N., On holomorphic immersions into Kähler manifolds of constant holomorphic sectional curvature, Science in China Ser. A Mathematics. 2005, 48 Supp.: 123-145. |
| Researcher : Ng KP |
| Project Title: | On Successive-overrelaxation acceleration of the hermitian and skew-hermitian splitting iterations |
| Investigator(s): | Ng KP |
| Department: | Mathematics |
| Source(s) of Funding: | Small Project Funding |
| Start Date: | 11/2002 |
| Completion Date: | 10/2004 |
| 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): | Ng KP |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 12/2002 |
| Completion Date: | 08/2005 |
| 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): | Ng KP, Ching WK, Huang JZ |
| Department: | Mathematics |
| Source(s) of Funding: | Seed Funding Programme for Applied Research |
| Start Date: | 09/2003 |
| Completion Date: | 08/2004 |
| 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): | Ng KP, Nikolova M., Kornprobst P., Deriche R. |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| Start Date: | 12/2003 |
| Completion Date: | 08/2005 |
| 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): | Ng KP, Nikolova M., Kornprobst P., Deriche R. |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 12/2003 |
| Completion Date: | 08/2005 |
| 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: | Minimization of L1 norm/mixed L1 and L2 norms for image restoration |
| Investigator(s): | Ng KP |
| Department: | Mathematics |
| Source(s) of Funding: | Small Project Funding |
| Start Date: | 11/2004 |
| Abstract: |
| To formulate the solution to a convex programming problem, and solved by the interior point method; to investigate how to solve a structured linear system efficiently at each step of interior point method. |
| Project Title: | New Preconditioners for Toeplitz-Related Systems |
| Investigator(s): | Ng KP, Benzi M. |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 12/2004 |
| Completion Date: | 08/2005 |
| Abstract: |
| To find a general approach of constructing high-quality factorization-type preconditioners inexpensively for Toeplitz-related systems with large displacement rank; to develop and analyze factorized inverse preconditioners for Toeplitz-related systems. Spectral analysis of the preconditioned matrices will be studied; to implement and test the factorization-type preconditioners for the reconstruction of high-resolution image from low-resolution image sequence, and for the nonlinear image restoration. |
| Project Title: | Fast Methods to Minimize Classes of Nonsmooth Cost-functions used in Image Restoration |
| Investigator(s): | Ng KP, Nikolova M., Ching WK, Yung SP |
| Department: | Mathematics |
| Source(s) of Funding: | France/Hong Kong Joint Research Scheme - Travel Grants |
| Start Date: | 01/2005 |
| Completion Date: | 08/2005 |
| Abstract: |
| To take a benefit from the special form of the cost-function in order to construct an equivalent minimization problem which is composed out of a quadratic function and a set of linear constraints, containing equalities and inequalities. To examine serveral alternative approaches such as projected gradient methods[18] or interior point methods [34,35]. To explore the possibilities to construct adapted preconditionners in order to accelerate the convergence speed. |
| Project Title: | New Preconditioners for Toeplitz-Related Systems |
| Investigator(s): | Ng KP |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| Start Date: | 01/2005 |
| Completion Date: | 08/2005 |
| Abstract: |
| Refer to hard copy |
| List of Research Outputs |
| Ao S.I., Ng K.P. and Ching W.K., Modeling Gene Expression Network with PCA-NN on Continuous Inputs and Outputs Basis, Current Trends in High Performance Computing and Its Applications.Proceedings of the International Conference on High Performance Computing and Applications. Springer, 2005, 209-214. |
| Bai Z., Ng K.P. and Pan J., Alternating splitting waveform relaxation method and its successive overrelaxation acceleration, Applied Mathematics and Computation. 2005, 49, no.2-3: 157-170. |
| Bertaccini D., Wen Y. and Ng K.P., The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form, Numer. Linear Algebra Appl.. 2005, 12, no.2-3: 315-325. |
| Ching W.K., Ng K.P. and Yuen W.O., A Hybrid Algorithm for Solving the Page Rank, Current Trends in High Performance Computing and Its Applications.Proceedings of the International Conference on High Performance Computing and Applications. Springer, 2005, 257-264. |
| Ching W.K., Fung S.L. and Ng K.P., Building Genetic Networks in Gene Expression Patterns, Lecture Notes in Computer Science. Springer, 2004, 3177: 17-24. |
| Ching W.K., Fung S.L. and Ng K.P., Building Higher-order Markov Chain Models with EXCEL, International Journal of Mathematical Education in Science and Technology. 2004, 35: 921-932. |
| Ching W.K., Ng K.P., Wong K.K. and Atlman E., Customer Lifetime Value: A Stochastic Programming Approach, Journal of Operational Research Society. 2004, 55: 860-868. |
| Ching W.K., Ng K.P. and Zhang S., On Computation with Higher-order Markov Chain, Current Trends in High Performance Computing and Its Applications.Proceedings of the International Conference on High Performance Computing and Applications. Springer, 2005, 15-24. |
| Ching W.K., Ng K.P., Sze N.K. and Yau C.K., Super-resolution image reconstruction using multisensors, Numer. Linear Algebra Appl.. 2005, 12, no.2-3: 271-281. |
| Fu H., Ng K.P., Nikolova M., Barlow J. and Ching W.K., Fast Algorithms for l1 Norm/Mixed l1 and l2 Norms for Image Restoration, Lecture Notes in Computer Science. Springer, 2005, 3483: 843-851. |
| Lin F., Ching W.K. and Ng K.P., Fast inversion of triangular Toeplitz matrices, Theoret. Comput. Sci.. 2004, 315, no.2-3: 511-523. |
| Lin F., Ching W.K. and Ng K.P., Preconditioning regularized least squares problems arising from high-resolution image reconstruction from low-resolution frames, Linear Algebra and Its Applications. 2004, 391: 149-168. |
| Lu L., Ching W.K. and Ng K.P., Exact algorithms for singular tridiagonal systems with applications to Markov chains, Applied Mathematics and Computation. 2004, 159, no.1: 275-289. |
| Lu L. and Ng K.P., Localization of Perron roots, Linear Algebra and Its Applications. 2004, 392: 103-117. |
| Lu L. and Ng K.P., On sufficient and necessary conditions for the Jacobi matrix inverse eigenvalue problem, Numer. Math.. 2004, 98, no.1: 167-176. |
| Ng K.P. and Kwan C., Image restoration by cosine transform-based iterative regularization, Applied Mathematics and Computation. 2005, 160, no.2: 499-515. |
| Ng K.P., Iterative methods for Toeplitz systems, Numerical Mathematics and Scientific Computation. Oxford University Press, New York, 2004, xiv+350 pp. |
| Ng K.P., Serra-Capizzano S. and Tablino-Possio C., Numerical behaviour of multigrid methods for symmetric sinc-Galerkin systems, Numer. Linear Algebra Appl.. 2005, 12, no.2-3: 261-269. |
| Ng K.P., Sze C.K. and Yung S.P., Wavelet Algorithms for De-blurring Models, International Journal of Imaging Systems and Technology. 2004, 14: 113-121. |
| Ngan Y.T., Pang G.K.H., Ng K.P. and Yung S.P., Wavelet Based Methods on Patterned Fabric Defect Detection, Pattern Recognition. 2005, 38, Issuce 4: 559-576. |
| Pan J., Bai Z. and Ng K.P., Two-step waveform relaxation methods for implicit linear initial value problems, Numer. Linear Algebra Appl. . 2005, 12, no.2-3: 293-304. |
| So M.C., Ching W.K. and Ng K.P., Customer Migration, Campaign Budgeting, Revenue Estimation: The Elasticity of Markov Decision Process on Customer Lifetime Value, Electronic International Journal of Advanced Modeling and Optimization. 2004, 6(2): 65-80. |
| Wei Y., Cai J. and Ng K.P., Computing Moore-Penrose inverses of Toeplitz matrices by Newton's iteration, Mathematical and Computer Modelling. 2004, 40, no.1-2: 181-191. |
| Wei Y. and Ng K.P., Displacement structure of group inverses, Numer. Linear Algebra Appl.. 2005, 12, no.2-3: 103-110. |
| Wei Y. and Ng K.P., Weighted Tikhonov filter matrices for ill-posed problems, Applied Mathematics and Computation. 2004, 149, no.2: 411-422. |
| Wen Y., Ng K.P., Ching W.K. and Liu H., A note on the stability of Toeplitz matrix inversion formulas, Applied Mathematics Letters. 2004, 17, no.8: 903-907. |
| Wen Y., Ng K.P. and Ching W.K., High-Resolution Image Reconstruction from the Low-Resolution Rotated and Translated Image Frames, International Journal of Imaging Systems and Technology. 2004, 14: 75-83. |
| Wen Y., Ng K.P. and Ching W.K., Preconditioner Based on Gohberg-Semumcul Formula forPositive Definitive Toeplitz Systems, Proceedings of ICNAAM. Wiley-VCH, 2004, 473-476. |
| Yuen W.O., Ching W.K. and Ng K.P., A Hybrid Algorithm for Queueing Systems, CALCOLO. 2004, 41: 139-151. |
| Researcher : Ng TW |
| Project Title: | Factorization and complex dynamics of meromorphic functions and related topics |
| Investigator(s): | Ng TW |
| Department: | Mathematics |
| Source(s) of Funding: | Seed Funding for New Staff |
| 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): | Ng TW, Beardon A.F., Yang CC |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 10/2003 |
| 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): | Ng TW |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| Start Date: | 10/2003 |
| 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): | Ng TW, Danchin ALM, Turinici G. |
| Department: | Mathematics |
| Source(s) of Funding: | Small Project Funding |
| 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. |
| Project Title: | D-companion matrices and geometry of polynomials |
| Investigator(s): | Ng TW, Cheung WS |
| Department: | Mathematics |
| Source(s) of Funding: | Small Project Funding |
| Start Date: | 11/2004 |
| Abstract: |
| To introduce a new type of companion matrices, D - companion matrices. By using these D - companion matrices we are able to apply matrix theory directly to the study of geometry of polynomials. |
| List of Research Outputs |
| Beardon A.F., Carne T.K., Minda D. and Ng T.W., Random iteration of analytic maps, Ergodic Theory and Dynamical Systems. 2004, 24, no.3: 659-675. |
| Ng T.W., D-companion matrices and geometry of polynomials, Computational methods and function theory 2005, University of Joensunn, Finland. 2005. |
| Ng T.W., D-companion matrices and geometry of polynomials, Hong Kong Mathematical Society Annual Meeting, HKUST. 2005. |
| Ng T.W., D-companion matrices and geometry of polynomials, International Conference on Analysis and its Applications, Nanjing University. 2004. |
| Ng T.W., Random iteration of analytic maps, 2004 Beijing-international Conference on Several Complex Variables, Capital Normal University, Beijing. 2004. |
| Ng T.W., Residual Julia sets of meromorphic functions , Conference on Riemann surfaces and Klelinian groups, Research Institute for Mathematical Sciences, Kyoto University. 2004. |
| Ng T.W., 博弈高手 － 淺論約翰 ·納殊的諾貝爾獎得獎理論, 2004. |
| Researcher : Nikolova M |
| List of Research Outputs |
| Fu H., Ng K.P., Nikolova M., Barlow J. and Ching W.K., Fast Algorithms for l1 Norm/Mixed l1 and l2 Norms for Image Restoration, Lecture Notes in Computer Science. Springer, 2005, 3483: 843-851. |
| Researcher : Pan J |
| List of Research Outputs |
| Bai Z., Ng K.P. and Pan J., Alternating splitting waveform relaxation method and its successive overrelaxation acceleration, Applied Mathematics and Computation. 2005, 49, no.2-3: 157-170. |
| Pan J., Bai Z. and Ng K.P., Two-step waveform relaxation methods for implicit linear initial value problems, Numer. Linear Algebra Appl. . 2005, 12, no.2-3: 293-304. |
| Researcher : Qi F |
| List of Research Outputs |
| Chen C.P., Cheung W.S. and Qi F., Note on Weighted Carleman-Type Inequality, International Journal of Mathematics and Mathematical Sciences. 2005, 2005, No.3: 475-481. |
| Researcher : Ren J |
| List of Research Outputs |
| Cheung W.S. and Ren J., On the Existence of Periodic Solutions for p-Laplacian Generalized Liénard Equation, Nonlinear Analysis. 2005, 60, No.1: 65-75. |
| Cheung W.S. and Ren J., Periodic Solutions for p-Laplacian Liénard Equation with a Deviating Argument, Nonlinear Analysis. 2004, 59, No.1-2: 107-120. |
| Cheung W.S. and Ren J., Positive Solutions for Discrete Three-Point Boundary Value Problems, Australian Journal of Mathematical Analysis and Applications. 2004, 1, No.2, Art. 9: 7pp. |
| Cheung W.S. and Ren J., Positive Solutions for m-point Boundary Value Problems, Journal of Mathematical Analysis and Applications. 2005, 303: 565-575. |
| Cheung W.S. and Ren J., Twin Positive Solutions for Quasi-linear Multi-Point Boundary Value Problems, Nonlinear Analysis. 2005, 62, No.1: 167-177. |
| Researcher : Ren X |
| List of Research Outputs |
| Ren X. and Tsang K.M., On Roth's theorem concerning a cube and three cubes of primes, Quarterly J. Math. (Oxford). 2004, 55 (3): 357-374. |
| Ren X. and Tsang K.M., On Waring-Goldbach-type problem for fourth powers, Journal of Number Theory. 2004, 108: 90-110. |
| Researcher : Shpilrain V |
| List of Research Outputs |
| Gutierrez J., Shpilrain V. and Yu J., Affine algebraic geometry. Papers from the Special Session at the 1st Joint AMS-RSME Meeting held in Seville, June 18-21, 2003. Edited by Jaime Gutierrez, Vladimir Shpilrain and Jie-Tai Yu, International Journal of Mathematics: Game Theory and Algebra. American Mathematical Society, 2005. |
| Researcher : Siu MK |
| Project Title: | Mathematical thinking and history of mathematics |
| Investigator(s): | Siu MK |
| Department: | Mathematics |
| Source(s) of Funding: | Other Funding Scheme |
| Start Date: | 01/1987 |
| Completion Date: | 06/2005 |
| Abstract: |
| Inspired by Leibniz' saying that "the art of discovery be promoted and its method known through illustrious examples', an attempt is made to develop undergraduate teaching material out of selected excerpts from memoirs of great mathematicians in the past, with emphasis on mathematical concepts involved, especially their evolution, and important aspects of mathematical thinking. |
| Project Title: | Autocorrelation properties of binary sequences and arrays |
| Investigator(s): | Siu MK |
| Department: | Mathematics |
| Source(s) of Funding: | Other Funding Scheme |
| Start Date: | 02/1987 |
| Completion Date: | 06/2005 |
| Abstract: |
| Binary sequences and arrays find important applications in communication science and electrical engineering. In particular, their autocorrelation properties are of interest, and such study is intimately related to various other topics in combinatorial mathematics and abstract algebra. As the subject is vast, the study has a more specific (short-term) objective, viz. to study sequences with special form of auto-correlation function (periodic or aperiodic), especially their two-dimensional analogues. |
| Project Title: | The role of proof in mathematics |
| Investigator(s): | Siu MK |
| Department: | Mathematics |
| Source(s) of Funding: | Other Funding Scheme |
| Start Date: | 01/1988 |
| Completion Date: | 06/2005 |
| Abstract: |
| The project attempts to answer such questions as: what role does proof play in mathematics? Rigour vs. intuition? What sort of proof will enhance understanding? How should proof be treated in the teaching of mathematics? Is proof a way to discover new results or a mere verification? etc. |
| List of Research Outputs |
| Siu M.K., 杵臼關節.阿基米德.多面體, Ball-and-Socket, Archimedes, Polyhedra. Hong Kong, HKU Faculty of Science and Department of Mathematics, 2004, 30 pages. |
| Siu M.K. and Tzanakis C., History of mathematics in classroom teaching -- Appetizer? main course? or dessert?, Mediterranean Journal for Research in Mathematics Education (Guest Editor). Cyprus Mathematical Society, 2004, 3, No.1-2. |
| Siu M.K., Official curriculum in mathematics in ancient China: How did candidates study for the examination?, In: J. Cai, L. Fan, S. Li, N.Y. Wong, How Chinese Learn Mathematics: Perspectives from Insiders, . World Scientific, Singapore, 2004, 157-185. |
| Researcher : So MC |
| List of Research Outputs |
| So M.C., Ching W.K. and Ng K.P., Customer Migration, Campaign Budgeting, Revenue Estimation: The Elasticity of Markov Decision Process on Customer Lifetime Value, Electronic International Journal of Advanced Modeling and Optimization. 2004, 6(2): 65-80. |
| Researcher : Sun X |
| Project Title: | Logarithmic projective flat connection for generalized [theta] functions |
| Investigator(s): | Sun X |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 09/2002 |
| Completion Date: | 08/2004 |
| 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 [theta] 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): | Sun X, Mok N |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| Start Date: | 09/2003 |
| Abstract: |
| Refer to hard copy |
| Researcher : Sze CK |
| List of Research Outputs |
| Ng K.P., Sze C.K. and Yung S.P., Wavelet Algorithms for De-blurring Models, International Journal of Imaging Systems and Technology. 2004, 14: 113-121. |
| Researcher : Sze NK |
| List of Research Outputs |
| Ching W.K., Ng K.P., Sze N.K. and Yau C.K., Super-resolution image reconstruction using multisensors, Numer. Linear Algebra Appl.. 2005, 12, no.2-3: 271-281. |
| Researcher : Sze NS |
| List of Research Outputs |
| Chan J.T., Li C.K. and Sze N.S., Isometries for unitarily invariant norms, Linear Algebra and Its Applications. 2005, 399: 53-70. |
| Researcher : Tai AHL |
| List of Research Outputs |
| Ching W.K. and Tai A.H.L., A Quantity-time-based Dispatching Policy for a VMI System, Lecture Notes in Computer Science. Springer, 2005, 3483: 342-349. |
| Researcher : Tsang KM |
| Project Title: | Waring Goldbach Type problems for low degrees |
| Investigator(s): | Tsang KM, Ren X, Liu J.Y. |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| Start Date: | 10/2003 |
| Abstract: |
| Refer to hard copy |
| Project Title: | Waring Goldbach Type problems for low degrees |
| Investigator(s): | Tsang KM, Ren X, Liu J.Y. |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 10/2003 |
| Abstract: |
| Refer to hard copy |
| Project Title: | Error Terms in the Summatory Formula for certain Arithmetical Functions |
| Investigator(s): | Tsang KM, Lau YK |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 01/2005 |
| Abstract: |
| To study the higher power moments and the distribution function of D(x) over short intervals of the form [X,X + U] where U is of order lower than X; to extend the above study to a general class of arithmetical functions, whose associated Dirichlet series satisfy certain function equations; to try to obtain the third (or possibly the fourth) power moment as well as the distribution for the error term in the sphere problem. Will also attempt the same for the lattice points problem in ellipoids. |
| Project Title: | Error Terms in the Summatory Formula for certain Arithmetical Functions |
| Investigator(s): | Tsang KM |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| Start Date: | 01/2005 |
| Abstract: |
| Refer to hard copy |
| List of Research Outputs |
| Lau Y.K. and Tsang K.M., Moments of the Probability Density Functions of Error Terms in Divisor Problems, Proceedings of the American Mathematical Society. 2005, 133: 1283-1290. |
| Lau Y.K. and Tsang K.M., Moments over Short Intervals, Archiv der Mathematik. Springer, 2005, 84: 249-257. |
| Liu J. and Tsang K.M., Small Prime Solutions of Ternary Linear Equations, Acta Arithematica. 2005, 118: 79-100. |
| Ren X. and Tsang K.M., On Roth's theorem concerning a cube and three cubes of primes, Quarterly J. Math. (Oxford). 2004, 55 (3): 357-374. |
| Ren X. and Tsang K.M., On Waring-Goldbach-type problem for fourth powers, Journal of Number Theory. 2004, 108: 90-110. |
| Researcher : Tseng S |
| List of Research Outputs |
| Cheung W.S., Lin Y.T., Tseng S. and Strecker G.E., On a Weak Form of the Blumberg Property, In: W. Gähler and G. Preuss, Categorical Structures and Their Applications. New Jersey, World Scientific, 2004, 41-49. |
| Researcher : Wang J |
| List of Research Outputs |
| Vu Q.P., Wang J., Xu G.Q. and Yung S.P., Spectral Analysis and System of Fundamental Solutions for Timoshenko Beams, Applied Mathematics Letters. 2005, 18: 127-134. |
| Wang J., Xu G.Q. and Yung S.P., Riesz Basis Property, Exponential Stability of Variable Coefficient Euler-Bernoulli Beams with Indefinite Damping, IMA Journal of Applied Mathematics. 2005, 1-19. |
| Researcher : Wei Y |
| List of Research Outputs |
| Wei Y., Cai J. and Ng K.P., Computing Moore-Penrose inverses of Toeplitz matrices by Newton's iteration, Mathematical and Computer Modelling. 2004, 40, no.1-2: 181-191. |
| Wei Y. and Ng K.P., Displacement structure of group inverses, Numer. Linear Algebra Appl.. 2005, 12, no.2-3: 103-110. |
| Wei Y. and Ng K.P., Weighted Tikhonov filter matrices for ill-posed problems, Applied Mathematics and Computation. 2004, 149, no.2: 411-422. |
| Researcher : Wen Y |
| List of Research Outputs |
| Bertaccini D., Wen Y. and Ng K.P., The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form, Numer. Linear Algebra Appl.. 2005, 12, no.2-3: 315-325. |
| Wen Y., Ng K.P., Ching W.K. and Liu H., A note on the stability of Toeplitz matrix inversion formulas, Applied Mathematics Letters. 2004, 17, no.8: 903-907. |
| Wen Y., Ng K.P. and Ching W.K., High-Resolution Image Reconstruction from the Low-Resolution Rotated and Translated Image Frames, International Journal of Imaging Systems and Technology. 2004, 14: 75-83. |
| Wen Y., Ng K.P. and Ching W.K., Preconditioner Based on Gohberg-Semumcul Formula forPositive Definitive Toeplitz Systems, Proceedings of ICNAAM. Wiley-VCH, 2004, 473-476. |
| Researcher : Wong KK |
| List of Research Outputs |
| Ching W.K., Ng K.P., Wong K.K. and Atlman E., Customer Lifetime Value: A Stochastic Programming Approach, Journal of Operational Research Society. 2004, 55: 860-868. |
| Researcher : Yakimov MT |
| List of Research Outputs |
| Lu J. and Yakimov M.T., On a class of double cosets in reductive algebraic groups, International Mathematics Research Notices. 2005, 13: 761-797. |
| Researcher : Yau CK |
| List of Research Outputs |
| Ching W.K., Ng K.P., Sze N.K. and Yau C.K., Super-resolution image reconstruction using multisensors, Numer. Linear Algebra Appl.. 2005, 12, no.2-3: 271-281. |
| Researcher : Yu J |
| Project Title: | Stably equivalence problem for free algebras |
| Investigator(s): | Yu J |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| 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): | Yu J |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| Start Date: | 12/2003 |
| Abstract: |
| Refer to hard copy |
| Project Title: | Small cancellation method for polynomial algebras |
| Investigator(s): | Yu J |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 12/2003 |
| Abstract: |
| Refer to hard copy |
| List of Research Outputs |
| Gutierrez J., Shpilrain V. and Yu J., Affine algebraic geometry. Papers from the Special Session at the 1st Joint AMS-RSME Meeting held in Seville, June 18-21, 2003. Edited by Jaime Gutierrez, Vladimir Shpilrain and Jie-Tai Yu, International Journal of Mathematics: Game Theory and Algebra. American Mathematical Society, 2005. |
| Yu J., Editor of International Journal of Mathematics: Game Theory and Algebra . 2005. |
| Yu J., Editor of Serdica. Mathematical Journal. 2004. |
| Yu J., Belov A. and Makar-Limanov L., On generalized cancellation problem, Journal of Algebra. 2004, 281, no.1: 161-166. |
| Yu J. and Lam C.M., Tame and wild coordinates of Z[x,y], Journal of Algebra. 2004, 279, no.2: 425-436. |
| Yu J., Test polynomials, retracts, and the Jacobian conjecture, Affine algebraic geometry. Providence, RI, Amer. Math. Soc., 2005, 369: 253-259. |
| Researcher : Yuen CSY |
| List of Research Outputs |
| Chu S.C.K. and Yuen C.S.Y., Effective Heuristics vs GP for Shift Duties Generation, Proceedings of the International Workshop on Multi-Criteria Decision Making, Ustron, Poland, 2-6 April 2005. 14pp. |
| Researcher : Yuen WO |
| List of Research Outputs |
| Ching W.K., Ng K.P. and Yuen W.O., A Hybrid Algorithm for Solving the Page Rank, Current Trends in High Performance Computing and Its Applications.Proceedings of the International Conference on High Performance Computing and Applications. Springer, 2005, 257-264. |
| Yuen W.O., Ching W.K. and Ng K.P., A Hybrid Algorithm for Queueing Systems, CALCOLO. 2004, 41: 139-151. |
| Researcher : Yung SP |
| Project Title: | Boundary feedback stabilizing systems: a Riesz Basis approach |
| Investigator(s): | Yung SP |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| 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: | Controllability of boundary feedback beam problems |
| Investigator(s): | Yung SP |
| Department: | Mathematics |
| Source(s) of Funding: | Incentive Award for RGC CERG Fundable But Not Funded Projects |
| 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): | Yung SP |
| Department: | Mathematics |
| Source(s) of Funding: | Small Project Funding |
| Start Date: | 11/2003 |
| Abstract: |
| To develop the theoretical background of generating wavelet filters that are pertinent for specific applications via lifting schemes. |
| Project Title: | A Spectral Study of Coupled-Beam Problems and Its Applications |
| Investigator(s): | Yung SP |
| Department: | Mathematics |
| Source(s) of Funding: | Incentive Award for RGC CERG Fundable But Not Funded Projects |
| Start Date: | 07/2004 |
| Abstract: |
| Refer to hard copy |
| Project Title: | Method of Moments and its Applications |
| Investigator(s): | Yung SP |
| Department: | Mathematics |
| Source(s) of Funding: | Seed Funding Programme for Basic Research |
| Start Date: | 12/2004 |
| Abstract: |
| We intend to study in-depth the method of moments and explore its applications. The obtained results will be used as foundation to support the re-submission of the RGC `fundable but not funded' project (HKU7053/03P). |
| List of Research Outputs |
| Ng K.P., Sze C.K. and Yung S.P., Wavelet Algorithms for De-blurring Models, International Journal of Imaging Systems and Technology. 2004, 14: 113-121. |
| Ngan Y.T., Pang G.K.H., Ng K.P. and Yung S.P., Wavelet Based Methods on Patterned Fabric Defect Detection, Pattern Recognition. 2005, 38, Issuce 4: 559-576. |
| Vu Q.P., Wang J., Xu G.Q. and Yung S.P., Spectral Analysis and System of Fundamental Solutions for Timoshenko Beams, Applied Mathematics Letters. 2005, 18: 127-134. |
| Wang J., Xu G.Q. and Yung S.P., Riesz Basis Property, Exponential Stability of Variable Coefficient Euler-Bernoulli Beams with Indefinite Damping, IMA Journal of Applied Mathematics. 2005, 1-19. |
| Xu G.Q. and Yung S.P., The Expansion of Semigroup and Criterion of Riesz Basis, Journal of Differential Equations. 2005, 210 no.1: 1-24. |
| Xu G.Q. and Yung S.P., The Exponential Decay Rate for A Timoshenko Beam with Boundary Damping, Journal of Optimization Theory and Applications. 2004, 123 no.3: 669-693. |
| Researcher : Zang W |
| Project Title: | The independent set problem and its application |
| Investigator(s): | Zang W |
| Department: | Mathematics |
| Source(s) of Funding: | Seed Funding Programme for Basic 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): | Zang W |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| 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): | Zang W |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| 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: | Bonds, Cycles, and Ring Networks |
| Investigator(s): | Zang W, Yu X.X. |
| Department: | Mathematics |
| Source(s) of Funding: | Competitive Earmarked Research Grants (CERG) |
| Start Date: | 09/2004 |
| Abstract: |
| To characterize all quadruples (G;X,Y,Z), where G=(V,E) is a multigraph and X,Y,Z are three even-sized subsets of V, for which G has a bond (i.e. a minimal nonempty edge cut) [S, V-S] such that S contains an odd number of vertices from each of X,Y, and Z; to investigate Nash-Williams' conjecture which asserts that every 4 connected toroidal graph contains a Hamiltonian cycle, and the following Seymour-Thomas conjecture: there exist a constant c>0 and a function f(t).0 such that, for any integer t>2, the length of longest cycle in any 3-connected graph G=(V,E) with no K(3,t)-minors (where K(3,t) stands for the 3 by t complete bipartite graph) is at least f(t)[V]∧c(our focus will be on the latter); to describe all graphs with the min-max relation on packing and covering odd cycles (vertex version) in terms of forbidden structures; to study will wavelength allocation problem on trees, rings, and trees of rings, which are three important topologies of optical networks in practice. |
| Project Title: | Bonds, Cycles, and Ring Networks |
| Investigator(s): | Zang W |
| Department: | Mathematics |
| Source(s) of Funding: | Merit Award for RGC CERG Funded Projects |
| Start Date: | 01/2005 |
| Abstract: |
| Refer to hard copy |
| List of Research Outputs |
| Chen X., Hu Z. and Zang W., Perfect Circular Arc Coloring, Journal Of Combinatorial Optimization. The Netherlands, Springer, 2005, 9: 267-280. |
| Deng X.T., Li G. and Zang W., Proof of Chvátal's conjecture on maximal stable sets and maximal cliques in graphs, Journal of Combinatorial Theory Series B. CA, USA, Academic Press, 2004, 91: 301-325. |
| Li X. and Zang W., A Combinatorial Algorithm for Minimum Weighted Colorings of Claw-freePerfect Graphs, Journal of Combinatorial Optimization. The Netherlands, Springer, 2005, 9: 331-347. |
| Luo R., Zang W. and Zhang C., Nowhere-zero 4-flows, simultaneous edge-colorings, and critical partial Latin squares, Combinatorica. Budapest, Hungary, Springer, 2004, 24: 641-659. |
| Thomas R., Yu X. and Zang W., Hamilton Paths in Toroidal Graphs, Journal of Combinatorial Theory Series B. CA, USA, Academic Press, 2005, 94: 214-236. |
| Zang W., Min-Max Theorems on Packing and Covering Cycles in Graphs, First National Conference on Combinatorics and Graph Theory, Xinjiang, China. 2004. |
| Researcher : Zhang C |
| List of Research Outputs |
| Luo R., Zang W. and Zhang C., Nowhere-zero 4-flows, simultaneous edge-colorings, and critical partial Latin squares, Combinatorica. Budapest, Hungary, Springer, 2004, 24: 641-659. |
| Researcher : Zhang S |
| List of Research Outputs |
| Ching W.K., Ng K.P. and Zhang S., On Computation with Higher-order Markov Chain, Current Trends in High Performance Computing and Its Applications.Proceedings of the International Conference on High Performance Computing and Applications. Springer, 2005, 15-24. |