DEPT OF MATHEMATICS



Researcher : Akutsu T
List of Research Outputs

Akutsu T., Hayashida M., Ching W.K. and Ng K.P., On the Complexity of Finding Control Strategies for Boolean Networks, Advances in Bioinformatics and Computational Biology, (Editors: T. Jiang, U. Yang, Y. Chen L. Wong) Proceedings of the 4th Asia Pacific Bioinformatics Conference, 13-16 Feb, 2006, Taiwan. Imperial College Press, 2006, 3: 99-108.
Zhang S., Ng K.P., Ching W.K. and Akutsu T., A Linear Control Model for Gene Intervention in a Genetic Regulatory Network, Proceedings of IEEE International Conference on Granular Computing, Beijing, 25-27 July 2005. 1: 354-358.


Researcher : Bai Z
List of Research Outputs

Bai Z., Ching W.K. and Ng K.P., Special Issue on Scientific Computing, Invited Editor of Vol. 172, of Journal of Applied Mathematics and Computations. Elsevier Publisher, 2006, 172(2): 153-160.


Researcher : Cai H
List of Research Outputs

Cai H., Xu X., Lu J., Lichtman J., Yung S.P. and Wong S., Segment and Track Neurons in 3D by Repulsive Snake Method, Proceedings of 2005 International Symposium on Intelligent Signal Processing and Communication Systems. USA, IEEE, 2005, 529-531.


Researcher : Chan JT
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.


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:
N/A


Project Title:Linear and Non-linear Preserver Problems
Investigator(s):Chan JT
Department:Mathematics
Source(s) of Funding:Merit Award for RGC CERG Funded Projects
Start Date:01/2006
Abstract:
N/A


Project Title:Linear and Non-linear Preserver Problems
Investigator(s):Chan JT, Li CK
Department:Mathematics
Source(s) of Funding:Competitive Earmarked Research Grants (CERG)
Start Date:01/2006
Abstract:
To describe some new preservers, to develop new proof techniques, and further explore the connections between different subjects via the study of preserver problems.


List of Research Outputs



Researcher : Chan YC
List of Research Outputs

Leung A.Y.L. and Chan Y.C., Exploring Necessary and Sufficient Conditions in Dynamic Geometry Environment , In: Frederica Olivero and Rosamund Sutherland, Proceedings of the 7th International Conference on Teachnology in Mathematics Teaching, Bristol, UK. Bristol, UK, University of Bristol, 2005, 1: 117-124.


Researcher : Chen X
List of Research Outputs

Chen X. and Zang W., An Efficient Algorithm for Finding Maximum Cycle Packings in Reducible Flow Graphs, Algorithmica. New York, USA, Springer, 2006, 44: 195-211.


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: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
Completion Date:11/2006
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:Merit Award for RGC CERG Funded Projects
Start Date:12/2003
Abstract:
N/A


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:
To investigate the complete monotonicity and logarithmic complete monotonicity of some special functions involving the gamma, digamma, and polygamma functions.


Project Title:Sufficient conditions for existence of solutions to p-Laplacian differential equations
Investigator(s):Cheung WS
Department:Mathematics
Source(s) of Funding:Merit Award for RGC CERG Funded Projects
Start Date:01/2006
Abstract:
N/A


Project Title:Sufficient conditions for existence of solutions to p-Laplacian differential equations
Investigator(s):Cheung WS
Department:Mathematics
Source(s) of Funding:Competitive Earmarked Research Grants (CERG)
Start Date:01/2006
Abstract:
1) To search for sufficient conditions guaranteeing the existence of solutions of certain types of p-Laplacian BVPs at resonance. 2) To obtain sufficient conditions for the existence of periodic solutions of p-Laplacian functional differential equations, including for example delay Duffing equations, Liénard equation, Rayleigh equations and neutral equations etc., with a p-Laplacian. 3) Also intend to investigate how the existence of periodic solutions relies on the delay of the prescribed functional equations


List of Research Outputs

Changjian Z. and Cheung W.S., On p-Quermass integral Differences Function, Proceedings of Indian Academy of Sciences - Mathematical Sciences. 2006, 116, No.2: 1-11.
Cheung W.S. and Ng T.W., A companion matrix approach to the study of zeros and criticalpoints of a polynomial, Journal of Mathematical Analysis and Its application. 2006, 319: 690-707.
Cheung W.S., Discrete Nonlinear Inequalities and Applications to Difference Equations, 2006 Hawaii International Conference on Statistics, Mathematics, and Related Fields, Hawaii, Jan 2006. 2006.
Cheung W.S., Ma Q. and Pecaric J., Discrete Nonlinear Inequalities and Applications to Difference Equations, Proceedings of the 5th Annual Hawaii International Conference on Statistics, Mathematics & Related Fields, Jan 16-18, 2006. 367-376.
Cheung W.S., Editor of Australian Journal of Mathematical Analysis and Applications. 2006.
Cheung W.S., Editor of Journal of Inequalities in Pure and Applied Mathematics. 2006.
Cheung W.S., Editor of the Bulletin of Southeast Asian Mathematical Society. 2006.
Cheung W.S., Gronwall-Bellman-Ou-Iang-type Inequalities and Applications to BVP, Conference on Differential and Difference Equations and Applications, Florida, USA, 8/2005. Florida, USA, 2005.
Cheung W.S. and Ma Q.H., On Certain New Gronwall-Ou-Iang Type Integral Inequalities in Two Variables and Their Applications, Journal of Inequalities and Applications. 2005, 2005, No.4: 347-361.
Cheung W.S., Zhao D. and Pecaric J., Opial-Type Inequalities for Differential Operators, Proceedings of the 5th Annual Hawaii International Conference on Statistics, Mathematics & Related Fields, Jan 16-18, 2006. 377-383.
Cheung W.S. and Ren J., Periodic Solutions for p-Laplacian Differential Equations with Multiple Deviating Arguments, Nonlinear Analysis. 2005, 62, No.4: 727-742.
Cheung W.S., Reviewer of Zentralblatt Math. V.1068, No. 58008. 2005, 1068, No.58008.
Cheung W.S., Reviewer of Zentralblatt Math. V.1072, No.26020. 2005, 1072, No.26020.
Cheung W.S., Reviewer of Zentralblatt Math. V.1075, No. 15030. 2005, 1075, No.15030.
Cheung W.S., Reviewer of Zentralblatt Math. V.1076, No. 58011. 2005, 1076, No.58011.
Cheung W.S., Reviewer of Zentralblatt Math. V.1078, No.26016. 2006, 1078, No.26016.
Cheung W.S., Reviewer of Zentralblatt Math. V.1078, No.26019. 2006, 1078, No.26019.
Cheung W.S., Reviewer of Zentralblatt Math. V.1078, No.58002. 2006, 1078, No.58002.
Cheung W.S., Reviewer of Zentralblatt Math. V.1078, No.58003. 2006, 1078, No.58003.
Cheung W.S., Reviewer of Zentralblatt Math. V.1084, No.26018. 2006, 1084, No.26018.
Cheung W.S., Reviewer of Zentralblatt Math. V.1085, No.26015. 2006, 1085, No.26015.
Cheung W.S., Reviewer of Zentralblatt Math. V.1085, No.26016. 2006, 1085, No.26016.
Cheung W.S., Some New Nonlinear Inequalities and Applications to Boundary Value Problems, Nonlinear Analysis. 2006, 64, No.9: 2112-2128.
Cheung W.S., Ma Q.H. and Pecaric J., Some New Weighted Hardy-type Inequalities of Vector Valued Functions, Mathematical Inequalities and Applications. 2005, 8, No.2: 199-206.
Tai A.H.L., Ching W.K. and Cheung W.S., On Computing Prestige in a Network with Negative Relations, International Journal of Applied Mathematical Sciences. 2005, 2: 97-104.
Tseng S., Wang P.C., Cheung W.S. and Chen C.J., Integral Inequalities in Higher Dimensional Spaces, Zeitschrift für Analysis und ihre Anwendungen. 2005, 24, No.2: 389-400.


Researcher : Cheung WS
List of Research Outputs

Changjian Z. and Cheung W.S., On p-Quermass integral Differences Function, Proceedings of Indian Academy of Sciences - Mathematical Sciences. 2006, 116, No.2: 1-11.
Cheung W.S. and Ng T.W., A companion matrix approach to the study of zeros and criticalpoints of a polynomial, Journal of Mathematical Analysis and Its application. 2006, 319: 690-707.
Cheung W.S., Discrete Nonlinear Inequalities and Applications to Difference Equations, 2006 Hawaii International Conference on Statistics, Mathematics, and Related Fields, Hawaii, Jan 2006. 2006.
Cheung W.S., Ma Q. and Pecaric J., Discrete Nonlinear Inequalities and Applications to Difference Equations, Proceedings of the 5th Annual Hawaii International Conference on Statistics, Mathematics & Related Fields, Jan 16-18, 2006. 367-376.
Cheung W.S., Editor of Australian Journal of Mathematical Analysis and Applications. 2006.
Cheung W.S., Editor of Journal of Inequalities in Pure and Applied Mathematics. 2006.
Cheung W.S., Editor of the Bulletin of Southeast Asian Mathematical Society. 2006.
Cheung W.S., Gronwall-Bellman-Ou-Iang-type Inequalities and Applications to BVP, Conference on Differential and Difference Equations and Applications, Florida, USA, 8/2005. Florida, USA, 2005.
Cheung W.S. and Ma Q.H., On Certain New Gronwall-Ou-Iang Type Integral Inequalities in Two Variables and Their Applications, Journal of Inequalities and Applications. 2005, 2005, No.4: 347-361.
Cheung W.S., Zhao D. and Pecaric J., Opial-Type Inequalities for Differential Operators, Proceedings of the 5th Annual Hawaii International Conference on Statistics, Mathematics & Related Fields, Jan 16-18, 2006. 377-383.
Cheung W.S. and Ren J., Periodic Solutions for p-Laplacian Differential Equations with Multiple Deviating Arguments, Nonlinear Analysis. 2005, 62, No.4: 727-742.
Cheung W.S., Reviewer of Zentralblatt Math. V.1068, No. 58008. 2005, 1068, No.58008.
Cheung W.S., Reviewer of Zentralblatt Math. V.1072, No.26020. 2005, 1072, No.26020.
Cheung W.S., Reviewer of Zentralblatt Math. V.1075, No. 15030. 2005, 1075, No.15030.
Cheung W.S., Reviewer of Zentralblatt Math. V.1076, No. 58011. 2005, 1076, No.58011.
Cheung W.S., Reviewer of Zentralblatt Math. V.1078, No.26016. 2006, 1078, No.26016.
Cheung W.S., Reviewer of Zentralblatt Math. V.1078, No.26019. 2006, 1078, No.26019.
Cheung W.S., Reviewer of Zentralblatt Math. V.1078, No.58002. 2006, 1078, No.58002.
Cheung W.S., Reviewer of Zentralblatt Math. V.1078, No.58003. 2006, 1078, No.58003.
Cheung W.S., Reviewer of Zentralblatt Math. V.1084, No.26018. 2006, 1084, No.26018.
Cheung W.S., Reviewer of Zentralblatt Math. V.1085, No.26015. 2006, 1085, No.26015.
Cheung W.S., Reviewer of Zentralblatt Math. V.1085, No.26016. 2006, 1085, No.26016.
Cheung W.S., Some New Nonlinear Inequalities and Applications to Boundary Value Problems, Nonlinear Analysis. 2006, 64, No.9: 2112-2128.
Cheung W.S., Ma Q.H. and Pecaric J., Some New Weighted Hardy-type Inequalities of Vector Valued Functions, Mathematical Inequalities and Applications. 2005, 8, No.2: 199-206.
Tai A.H.L., Ching W.K. and Cheung W.S., On Computing Prestige in a Network with Negative Relations, International Journal of Applied Mathematical Sciences. 2005, 2: 97-104.
Tseng S., Wang P.C., Cheung W.S. and Chen C.J., Integral Inequalities in Higher Dimensional Spaces, Zeitschrift für Analysis und ihre Anwendungen. 2005, 24, No.2: 389-400.


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: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
Completion Date:10/2005
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: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:
In this project, we focus on developing higher dimensional Markov chain models for categorical data sequences with applications in the analysis of biological sequences. We will also develop fast numerical methods for solving the model parameters.


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:07/2005
Completion Date:06/2006
Abstract:
N/A


Project Title:A New Hidden Markov Model for Categorical Time Series with Applications
Investigator(s):Ching WK, Li WK
Department:Mathematics
Source(s) of Funding:Small Project Funding
Start Date:02/2006
Abstract:
In this project, we will develop a new hidden Markov model (HMM) for modeling categorical time series. In a traditional HMM, the observable states are affected directly by the hidden states but not vice versa. Here, we will develop a HMM such that the transitions of hidden states depend also on the observable states. Our model can be related to a discrete-state version of the class of the first-order self-exciting threshold autoregressive models for modelling non-linear time series taking numerical values. Efficient estimation methods for the transition probabilities among the hidden states and observable states will also be developed. We will apply the model to practical sales demands data sequences in inventory control.


List of Research Outputs

Akutsu T., Hayashida M., Ching W.K. and Ng K.P., On the Complexity of Finding Control Strategies for Boolean Networks, Advances in Bioinformatics and Computational Biology, (Editors: T. Jiang, U. Yang, Y. Chen L. Wong) Proceedings of the 4th Asia Pacific Bioinformatics Conference, 13-16 Feb, 2006, Taiwan. Imperial College Press, 2006, 3: 99-108.
Bai Z., Ching W.K. and Ng K.P., Special Issue on Scientific Computing, Invited Editor of Vol. 172, of Journal of Applied Mathematics and Computations. Elsevier Publisher, 2006, 172(2): 153-160.
Chan R., Ma K. and Ching W.K., Boundary Value Methods for Solving Transient Solutions of Markovian Queueing Networks, Applied Mathematics and Computation. 2006, 172: 690-700.
Ching W.K. and Lee M., A Random Walk on a Circular Path , International Journal of Mathematical Education in Science and Technology. 2005, 36: 680-683.
Ching W.K., Associate Ediotor of Journal of Applied Mathematics and Decision Sciences. Hindawi Publishing Corporation, 2006.
Ching W.K., Editor-in-Chief of Journal of Mathematical Modelling and Applied Computing. Research India Punlications, 2006.
Ching W.K. and Ng K.P., Markov Chains : Models, Algorithms and Applications, International Series on Operations Research and Management Science. Springer, 2006, 224pp.
Ching W.K., Ng K.P., Fung S.L. and Akutsu T., On Construction of Stochastic Genetic Networks Based on Gene Expression Sequences, International Journal of Neural Systems. 2005, 15: 297-310.
Ching W.K., On Multi-dimensional Markov Chain Models,, The Second International Conference on Structured Matrices, Hong Kong, China.. 2006.
Ching W.K., Yuen W.O., Ng K.P. and Zhang S., Optimal Pulsation Advertising Policy with Wearout Effect: A Linear Programming Approach , IMA Journal of Management Mathematics. 2006, 17: 83-96.
Fung S.L., Ching W.K., Lee Y.F. and Ng K.P., A Recursive Method for Solving Haplotype Frequencies in Multiple Loci Linkage Analysis, Advances in Bioinformatics and Computational Biology, (Editors: T. Jiang, U. Yang, Y. Chen, L. Wong), Proceedings of the 4th Asia Pacific Bioinformatics Conference, 13-16 Feb, 2006, Taiwan. Imperial College Press, 2006, 3: 129-138.
Lin F., Ng K.P. and Ching W.K., Factorized Banded Inverse Preconditioners for Matrices with Toeplitz Structure, SIAM Journal on Scientific Computing. SIAM, 2005, 26: 1852-1870.
Siu T., Ching W.K. and Ng K.P., Extracting Information from Spot Interest Rates and Credit Ratings using Double Higher-Order Hidden Markov Models, Computational Economics. 2005, 26: 251-284.
Siu T., Ching W.K., Ng K.P. and Fung S.L., On Multivariate Credibility Approach for Portfolio Credit Risk Measurement, Quantitative Finance. 2005, 5: 543-556.
Tai A.H.L., Ching W.K. and Chan P.L.Y., Hidden Markov Model for the Detection of Machine Failure (in CD-ROM), Proceeding of the 36th International Conference on Computers and Industrial Engineering, Taiwan, June (2006) . 2006.
Tai A.H.L., Ching W.K. and Cheung W.S., On Computing Prestige in a Network with Negative Relations, International Journal of Applied Mathematical Sciences. 2005, 2: 97-104.
Tai A.H.L. and Ching W.K., On the Use of Renewal Theory in Machine Replacement Models, International Journal of Applied Mathematical Sciences. 2005, 2: 230--239.
Wen Y., Ching W.K., Ng K.P. and Liu H., A Hybrid Algorithm for Spatial and Wavelet Domain Image Restoration, Visual Communications and Image Processing 2005, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE) (Editor(s): Li SP, Pereira F, Shum HY, Tescher AG) . 2005, PTS 1-4 5960: 2004-2011: Part 1-4.
Yuen W.O., Ching W.K. and Ng K.P., A Direct Method for Solving Block-Toeplitz with Near-Circulant-Block Systems with Applications to Hybrid Manufacturing Systems, Numerical Linear Algebra with Applications. 2005, 12: 957-966.
Zhang S., Ng K.P., Ching W.K. and Akutsu T., A Linear Control Model for Gene Intervention in a Genetic Regulatory Network, Proceedings of IEEE International Conference on Granular Computing, Beijing, 25-27 July 2005. 1: 354-358.


Researcher : Chow ASH
List of Research Outputs

Chow A.S.H., A Poisson structure on the complex projective space, HKU Mphil Thesis. 2005.


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
Completion Date:10/2005
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.


Project Title:Topological and Optimization Analysis of Online Auction Markets
Investigator(s):Chu SCK
Department:Mathematics
Source(s) of Funding:Merit Award for RGC CERG Funded Projects
Start Date:01/2006
Abstract:
N/A


Project Title:Topological and Optimization Analysis of Online Auction Markets
Investigator(s):Chu SCK, Ho JK, Lam SS
Department:Mathematics
Source(s) of Funding:Competitive Earmarked Research Grants (CERG)
Start Date:01/2006
Abstract:
The objective of our proposed investigation is to pose the intriguing question of what "shape" a given market is in at a particular moment of development, and to produce models with tools for the answer. The key issues of our work include: (1) To construct a topological model based only on operational data, without any expert knowledge of the specific auction market, or conomic details from the transactions. (2) To identify the dimensions for a topology, using extensive analysis of eBay data to extract the information desired. (3) To propose a graphical model to visualize this topology, also for the purpose of comparing markets at different points of a life cycle. (4) To integrate optimization modelling into this topological analysis to further achieve its maximum resolution of any such buyers/sellers market dichotomy. (4) To construct a topological model based only on operational data, without any expert knowledge of the specific auction market, or economic details from the transactions. (5) To identify the dimensions for a topology, using extensive analysis of eBay data to extract the information desired. (6) To propose a graphical model to visualize this topology, also for the purpose of comparing markets at different points of a life cycle. (7) To integrate optimization modelling into this topological analysis to further achieve its maximum resolution of any such buyers/sellers market dichotomy.


List of Research Outputs

Chu S.C.K., Associate editor of the IMA Journal of Management Mathematics. 2005.
Chu S.C.K., Lam S.S. and Ho J.K., Optimization Modeling DSS for Maximum Resolution Topology of Internet Data, Proceedings of the Institute of Industrial Engineers Annual Conference - 2006 Industrial Engineering Research Conference (IERC 2006), Orlando, FL, USA, 20-24 May 2006. 6 pp.
Ho J.K. and Chu S.C.K., Maximum Resolution Topology for Multi-Attribute Dichotomies, INFORMATICA. 2005, 16, No.4: 557-570.


Researcher : Drensky VS
List of Research Outputs

Yu J. and Drensky V.S., Automorphisms fixing a variable of K<x,y,z>, Journal of Algebra. 2005, 291, no.1: 250-258.


Researcher : Fung SL
List of Research Outputs

Ching W.K., Ng K.P., Fung S.L. and Akutsu T., On Construction of Stochastic Genetic Networks Based on Gene Expression Sequences, International Journal of Neural Systems. 2005, 15: 297-310.
Fung S.L., Ching W.K., Lee Y.F. and Ng K.P., A Recursive Method for Solving Haplotype Frequencies in Multiple Loci Linkage Analysis, Advances in Bioinformatics and Computational Biology, (Editors: T. Jiang, U. Yang, Y. Chen, L. Wong), Proceedings of the 4th Asia Pacific Bioinformatics Conference, 13-16 Feb, 2006, Taiwan. Imperial College Press, 2006, 3: 129-138.
Siu T., Ching W.K., Ng K.P. and Fung S.L., On Multivariate Credibility Approach for Portfolio Credit Risk Measurement, Quantitative Finance. 2005, 5: 543-556.


Researcher : Hayashida M
List of Research Outputs

Akutsu T., Hayashida M., Ching W.K. and Ng K.P., On the Complexity of Finding Control Strategies for Boolean Networks, Advances in Bioinformatics and Computational Biology, (Editors: T. Jiang, U. Yang, Y. Chen L. Wong) Proceedings of the 4th Asia Pacific Bioinformatics Conference, 13-16 Feb, 2006, Taiwan. Imperial College Press, 2006, 3: 99-108.


Researcher : Ho JK
List of Research Outputs

Chu S.C.K., Lam S.S. and Ho J.K., Optimization Modeling DSS for Maximum Resolution Topology of Internet Data, Proceedings of the Institute of Industrial Engineers Annual Conference - 2006 Industrial Engineering Research Conference (IERC 2006), Orlando, FL, USA, 20-24 May 2006. 6 pp.
Ho J.K. and Chu S.C.K., Maximum Resolution Topology for Multi-Attribute Dichotomies, INFORMATICA. 2005, 16, No.4: 557-570.


Researcher : Lau YK
List of Research Outputs

Lau Y.K. and Wu J., A density theorem on automorphic L-functions and some applications, Transactions of the American Mathematical Society. American Mathematical Society, 2006, 358: 441-472.
Lau Y.K. and Tsang K.M., A mean square formula for central values of twisted automorphic L-functions, Acta Arithematica. 2005, 118: 231-262.
Lau Y.K., Reviewer of Zentralblatt Math. V. 1076, No. 11049 . 2006, 1076, No. 11049.
Lau Y.K., Subconvexity estimates for Rankin-Selberg L-functions, Workshop on Number Theory and Applications. 2005.


Researcher : Lee YF
List of Research Outputs

Fung S.L., Ching W.K., Lee Y.F. and Ng K.P., A Recursive Method for Solving Haplotype Frequencies in Multiple Loci Linkage Analysis, Advances in Bioinformatics and Computational Biology, (Editors: T. Jiang, U. Yang, Y. Chen, L. Wong), Proceedings of the 4th Asia Pacific Bioinformatics Conference, 13-16 Feb, 2006, Taiwan. Imperial College Press, 2006, 3: 129-138.


Researcher : Li Y
List of Research Outputs

Li Y. and Zang W., Differential Methods for Finding Independent Sets in Hypergraphs, SIAM Journal on Discrete Mathematics. Philadelphia, USA, SIAM, 2006, 20: 96-104.


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: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 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:
N/A


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.


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:
N/A


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:On intersections of real group orbits and Schubert cells in complex flag varities
Investigator(s):Lu J
Department:Mathematics
Source(s) of Funding:Merit Award for RGC CERG Funded Projects
Start Date:09/2005
Abstract:
N/A


Project Title:On intersections of real group orbits and Schubert cells in complex flag varities
Investigator(s):Lu J
Department:Mathematics
Source(s) of Funding:Competitive Earmarked Research Grants (CERG)
Start Date:09/2005
Abstract:
The objective of this project is to understand the intersections of some very important submanifolds of a complex flag variety, namely that of a Schubert cell and an orbit of a real form of the complex group. This project will bring new tools to the study of real group orbits such as the theory of cluster algebras recently formulated by Fomin and Zelevnsky. The proposed examples will also shed new lights on the work of Gekhtman, Shapiro, and Vainshtein on the relation between cluster algebras and Poisson geometry.


List of Research Outputs

Evens S. and Lu J., On the variety of Lagrangian subalgebras, II, In: F. Paulin (Editor-in-Chief), Annales Scientifique de L'Ecole Normale Superieure . Elsevier, 2006, 39, No. 2: 347-379.
Foth P. and Lu J., Poisson structures on complex flag manifolds associated with real forms., In: Robert Guralnick (managing editor) , Transactions of the American Mathematical Society. Providence, USA, American mathematical society, 2006, 358: 1705-1714.
Lu J., Double cosets in algebraic groups and Poisson geometry, In: Organizers: A. Alekseev etc, Symposium Lie groups: from toplogy to arithmetics, in memory of Armand Borel, ETH-Zurich and University of Geneva. 2005.
Lu J., Editor of Pacific Journal of Mathematics. 2006.
Lu J., Editorial board, In: Editors-in-Chief: C. Molitor-Braun, N. Poncin, Travaux Mathematiques. 2006.
Lu J., Examples of Poisson varieties associated to semi-simple groups, In: Organizers: Zung, etc, Summer school and conference on Poisson geometry, ICTP, Trieste, Italy. 2005.
Lu J., Introduction to Poisson geometry and Lie theory, In: Y. maeda, Pathway lecture series, Center for Integrative Mathematical Science, Keio University, Yokohama, Japan. 2005.
Lu J., Some aspects of a Poisson structure on a complex semi-simple Lie group, In: Organizers: Y. Maeda et, Poisson 2006: Poisson geometry in Mathematics and Physics, June 5-9, 2006, Tokyo, Japan. 2006.


Researcher : Ma Q
List of Research Outputs

Cheung W.S., Ma Q. and Pecaric J., Discrete Nonlinear Inequalities and Applications to Difference Equations, Proceedings of the 5th Annual Hawaii International Conference on Statistics, Mathematics & Related Fields, Jan 16-18, 2006. 367-376.


Researcher : Mok N
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:Topological aspects of degeneration of moduli spaces of vector bundles
Investigator(s):Mok N, Sun X
Department:Mathematics
Source(s) of Funding:Merit Award for RGC CERG Funded Projects
Start Date:09/2003
Abstract:
N/A


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: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:
N/A


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:
N/A


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.


List of Research Outputs

Mok N., Editor of Chinese Annals of Mathematics. Springer, 2006.
Mok N., Editor of Inventiones Mathematicae. Berlin-Heidelberg-New York, Springer-Verlag, 2005.
Mok N., Editor of Mathematische Annalen. Berlin-Heidelberg-New York, Springer-Verlag, 2005.


Researcher : Ng KP
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: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: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:
N/A


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:
N/A


Project Title:Efficient minimization methods of mixed l1-l1 and l2-l1 norms for image restoration
Investigator(s):Ng KP
Department:Mathematics
Source(s) of Funding:Competitive Earmarked Research Grants (CERG)
Start Date:09/2005
Completion Date:08/2005
Abstract:
(a) Project Objectives: Image restoration problems are often solved by finding the minimizer of a suitable objective function. Usually this function consists of a data-fitting term and a regularization term. For the least squares solution, both the data-fitting and the regularization terms are in the l2 norm. In this proposal, we consider the least absolute deviation (LAD) solution and the least mixed norm (LMN) solution. For the LAD solution, both the data-fitting and the regularization terms are in the l1 norm. For the LMN solution, the regularization term is in the l1 norm but the data-fitting term is in the l2 norm. The quality of the restored images using the minimization of mixed l1-l1 and l2-l1 norms is better than that using only l2 norm approach. The LAD and LMN solutions are reformulated as the solutions to a linear programming problem and a quadratic programming problem respectively which are solved by interior point methods. At each iteration of the interior point method, a large structured linear system must be solved. Such linear systems become ill-conditioned as the iterates get close to the solution. Thus preconditioners are required to accelerate the convergence of the conjugate gradient iterations. The main aim of this proposal is to develop effective preconditioners for these structured linear systems. Our idea is to use the Hermitian and skew-Hermitian preconditioner and the shift-variant preconditioner for these systems. Their convergence rates will be analyzed in detail, and their performance will also be compared. On the application side, we will study our efficient minimization methods of mixed l1-l1 and l2-l1 norms for super-resolution image reconstruction. (b) Long-term Significance: Applications of our methods for solving image restoration and reconstruction problems are important. We therefore expect our methods to be profitable across a broad spectrum of mathematics, engineering and medicine. The convergence analysis of our methods will have to make use results from optimization, numerical analysis and image processing. A better understanding of the relationship between mathematical analysis and these computational problems will be beneficial to both fields.


List of Research Outputs

Akutsu T., Hayashida M., Ching W.K. and Ng K.P., On the Complexity of Finding Control Strategies for Boolean Networks, Advances in Bioinformatics and Computational Biology, (Editors: T. Jiang, U. Yang, Y. Chen L. Wong) Proceedings of the 4th Asia Pacific Bioinformatics Conference, 13-16 Feb, 2006, Taiwan. Imperial College Press, 2006, 3: 99-108.
Bai Z., Ching W.K. and Ng K.P., Special Issue on Scientific Computing, Invited Editor of Vol. 172, of Journal of Applied Mathematics and Computations. Elsevier Publisher, 2006, 172(2): 153-160.
Ching W.K. and Ng K.P., Markov Chains : Models, Algorithms and Applications, International Series on Operations Research and Management Science. Springer, 2006, 224pp.
Ching W.K., Yuen W.O., Ng K.P. and Zhang S., Optimal Pulsation Advertising Policy with Wearout Effect: A Linear Programming Approach , IMA Journal of Management Mathematics. 2006, 17: 83-96.
Fung S.L., Ching W.K., Lee Y.F. and Ng K.P., A Recursive Method for Solving Haplotype Frequencies in Multiple Loci Linkage Analysis, Advances in Bioinformatics and Computational Biology, (Editors: T. Jiang, U. Yang, Y. Chen, L. Wong), Proceedings of the 4th Asia Pacific Bioinformatics Conference, 13-16 Feb, 2006, Taiwan. Imperial College Press, 2006, 3: 129-138.
Siu T., Ching W.K. and Ng K.P., Extracting Information from Spot Interest Rates and Credit Ratings using Double Higher-Order Hidden Markov Models, Computational Economics. 2005, 26: 251-284.
Siu T., Ching W.K., Ng K.P. and Fung S.L., On Multivariate Credibility Approach for Portfolio Credit Risk Measurement, Quantitative Finance. 2005, 5: 543-556.
Wen Y., Ching W.K., Ng K.P. and Liu H., A Hybrid Algorithm for Spatial and Wavelet Domain Image Restoration, Visual Communications and Image Processing 2005, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE) (Editor(s): Li SP, Pereira F, Shum HY, Tescher AG) . 2005, PTS 1-4 5960: 2004-2011: Part 1-4.
Yuen W.O., Ching W.K. and Ng K.P., A Direct Method for Solving Block-Toeplitz with Near-Circulant-Block Systems with Applications to Hybrid Manufacturing Systems, Numerical Linear Algebra with Applications. 2005, 12: 957-966.
Zhang S., Ng K.P., Ching W.K. and Akutsu T., A Linear Control Model for Gene Intervention in a Genetic Regulatory Network, Proceedings of IEEE International Conference on Granular Computing, Beijing, 25-27 July 2005. 1: 354-358.


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
Department:Mathematics
Source(s) of Funding:Merit Award for RGC CERG Funded Projects
Start Date:10/2003
Abstract:
N/A


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: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.


Project Title:D-Companion Matrices and Geometry of Polynomials
Investigator(s):Ng TW
Department:Mathematics
Source(s) of Funding:Merit Award for RGC CERG Funded Projects
Start Date:09/2005
Abstract:
N/A


Project Title:D-Companion Matrices and Geometry of Polynomials
Investigator(s):Ng TW, Li CK
Department:Mathematics
Source(s) of Funding:Competitive Earmarked Research Grants (CERG)
Start Date:09/2005
Abstract:
The main objective of this project is to use techniques in matrix inequalities to study the geometry of polynomials. For example, we obtained a one parameter family version of Schoenberg-type inequality on the relative locations of zeros and critical points of a polynomial, and proved a result related to Sendov conjecture for polynomials.


Project Title:Exact solutions of algebraic differential equations
Investigator(s):Ng TW, Conte R, Lu J, Choi YY, Raynaud F
Department:Mathematics
Source(s) of Funding:France/Hong Kong Joint Research Scheme - Travel Grants
Start Date:01/2006
Abstract:
To study the zero distribution and growth rate of the solutions of certain algebraic differential equations by using Nevanlinna Theory and Wiman-Valiron theory; to study the meromorphic traveling wave solutions of some partial differential equations; to develop some algebraic method to find exact traveling wave solutions of some partial differential equations.


List of Research Outputs

Cheung W.S. and Ng T.W., A companion matrix approach to the study of zeros and criticalpoints of a polynomial, Journal of Mathematical Analysis and Its application. 2006, 319: 690-707.
Ng T.W., On Briot-Bouquet differential equations, Centre for Mathematical Studies, University of Cambridge. 2006.
Ng T.W., On Briot-Bouquet differential equations, Workshop on Complex Analysis, Tsinghua University. 2006.
Ng T.W., On Briot-Bouquet differential equations, Workshop on Complex and Algebraic Geometry, HKU. 2005.
Ng T.W., Residual Julia sets of meromorphic functions, The 13th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Shantou University, China. 2005.


Researcher : Pecaric J
List of Research Outputs

Cheung W.S., Ma Q. and Pecaric J., Discrete Nonlinear Inequalities and Applications to Difference Equations, Proceedings of the 5th Annual Hawaii International Conference on Statistics, Mathematics & Related Fields, Jan 16-18, 2006. 367-376.
Cheung W.S., Zhao D. and Pecaric J., Opial-Type Inequalities for Differential Operators, Proceedings of the 5th Annual Hawaii International Conference on Statistics, Mathematics & Related Fields, Jan 16-18, 2006. 377-383.


Researcher : Ren X
List of Research Outputs

Ren X. and Tsang K.M., On representation of integers by sums of a cube and three cubes of primes, Michigan Math. J.. 2005, 53: 571-577.


Researcher : Shpilrain V
List of Research Outputs

Yu J., Gutierrez J. and Shpilrain V., Affine Algebraic Geometry, Contemparary Mathematics, Special Session On Affine Algebraic Geometry At The First Joint AMS-RSME Meeting, Seville, Spain, June 18-21, 2003. America Mathematical Society, 2005, 369: 276 pages.
Yu J. and Shpilrain V., Test polynomials, retracts, and the Jacobian conjecture, Affine algebraic geometry. Providence, RI, Amer. Math. Soc., 2005, Contemp. Math. 369: 253-259.


Researcher : Siu MK
List of Research Outputs

Siu M.K., Mathematics in teaching and teaching of mathematics, Proceedings of 4th Asian Mathematical Conference, July 2005, Singapore. 2005, (in CD-Rom).


Researcher : So BK
List of Research Outputs

So B.K., On some examples of Poisson homology and cohomology--analytic and Lie theoretic approaches, HKU Mphil Thesis. 2005.


Researcher : Tai AHL
List of Research Outputs

Tai A.H.L., Ching W.K. and Chan P.L.Y., Hidden Markov Model for the Detection of Machine Failure (in CD-ROM), Proceeding of the 36th International Conference on Computers and Industrial Engineering, Taiwan, June (2006) . 2006.
Tai A.H.L., Ching W.K. and Cheung W.S., On Computing Prestige in a Network with Negative Relations, International Journal of Applied Mathematical Sciences. 2005, 2: 97-104.
Tai A.H.L. and Ching W.K., On the Use of Renewal Theory in Machine Replacement Models, International Journal of Applied Mathematical Sciences. 2005, 2: 230--239.


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:Competitive Earmarked Research Grants (CERG)
Start Date:10/2003
Completion Date:09/2005
Abstract:
To extend our knowledge on the inter-relationship between the integers and the powers of prime numbers; to refine the existing tools and develop new techniques; to sharpen some of the estimates for exponential sums over primes and over power of two. Such improvements will be very useful in a whole range of related problems.


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:
N/A


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:
N/A


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.


List of Research Outputs

Lau Y.K. and Tsang K.M., A mean square formula for central values of twisted automorphic L-functions, Acta Arithematica. 2005, 118: 231-262.
Ren X. and Tsang K.M., On representation of integers by sums of a cube and three cubes of primes, Michigan Math. J.. 2005, 53: 571-577.
Tsang K.M., Almost prime k-tuples, Annual General Meeting of the Hong Kong Mathematical Society 2006, City University of Hong Kong. 2006.
Tsang K.M., Error terms of some arithmetical functions in number theory, School of Mathematics and System Sciences, Shandong University. 2005.


Researcher : Tseng S
List of Research Outputs

Tseng S., Wang P.C., Cheung W.S. and Chen C.J., Integral Inequalities in Higher Dimensional Spaces, Zeitschrift für Analysis und ihre Anwendungen. 2005, 24, No.2: 389-400.


Researcher : Wang J
List of Research Outputs

Guo B.Z., Wang J. and Yung S.P., Boundary stabilization of a flexible manipulator with rotational inertia, Journal Differential and Integral Equations. 2005, 18, number 9: 1013-1038.
Guo B.Z., Wang J. and Yung S.P., On the C_0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam, Systems & Control Letters. 2005, 54: 557-574.
Wang J., Xu G.Q. and Yung S.P., Exponential Stabilization of Laminated Beams with Structural Damping and Boundary Feedback Controls, SIAM J. on Control and Optimization. 2005, 44: 1575-1597.


Researcher : Wen Y
List of Research Outputs

Wen Y., Ching W.K., Ng K.P. and Liu H., A Hybrid Algorithm for Spatial and Wavelet Domain Image Restoration, Visual Communications and Image Processing 2005, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE) (Editor(s): Li SP, Pereira F, Shum HY, Tescher AG) . 2005, PTS 1-4 5960: 2004-2011: Part 1-4.


Researcher : Wong CW
List of Research Outputs

Lee R.C.H., Wong C.W., Xu C.Z., Yim L.H. and Yung S.P., A Lyapunov-type condition for robust feedback stability of delay control systems, IMA Journal of Mathematical Control and Information. 2006, 23: 97-111.


Researcher : Wong P
List of Research Outputs

Wong P. and Wong P.P.W., Bisectional Curvature of Complements of Curves in P2, Journal of Mathematics of Kyoto University. 2005, 45, No.3: 599-625.


Researcher : Wong PPW
List of Research Outputs

Wong P. and Wong P.P.W., Bisectional Curvature of Complements of Curves in P2, Journal of Mathematics of Kyoto University. 2005, 45, No.3: 599-625.


Researcher : Wu S
List of Research Outputs

Wu S., Fiber Integration of Deligne Cohomology Classes, Noncommutative Geometry 2006 Kyoto, Kyoto, Japan. 2006.
Wu S., Mathai-Quillen Formalism, Encyclopedia of Mathematical Physcis. Netherlands, Academic Press, 2006, 3: 390-398.
Wu S., Projective Flatness in the Quantisation of Bosons and Fermions, Geometry and Analysis Workshop, Chern Institute of Mathematics, Tianjin, China. 2005.
Wu S., Projective Flatness in the Quantisation of Bosons and Fermions, International Workshop on Noncommutative Geometry and Physics, Sendai, Japan. 2005.
Wu S., Seiberg-Witten Theory, Encyclopedia of Mathematical Physics. Netherlands, Elvester, 2006, 4: 503-511.
Wu S., Some Remarks on Homological Algebra and Gerbes, International Workshop on Noncommutative Geometry and Physics, Beijing, China. 2005.


Researcher : Yu J
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
Completion Date:12/2006
Abstract:
The purpose of this project is to attack the below three problems and other related problems for polynomial algebras by ombinatorial methods, in particular the small cancellation method. 1/ Let Pn (n>2) be a polynomial algebra over a field K. Does there exist a wild automorphisms of Pn 2/ Let Pn be a polynomial algebra over a field K. Does there exist a wild coordinate p=Pn? If so, how to effectively characterize whether a coordinate in Pn is wide? 3/ For two polynomials p and q in Pn, how to effectively decide whether there exists a tame automorphism ψ of Pn such that ψ(p)=q?


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:
N/A


Project Title:Degree estimate for subalgebras of a free associative algebra
Investigator(s):Yu J
Department:Mathematics
Source(s) of Funding:Merit Award for RGC CERG Funded Projects
Start Date:12/2005
Abstract:
N/A


Project Title:Degree estimate for subalgebras of a free associative algebra
Investigator(s):Yu J
Department:Mathematics
Source(s) of Funding:Competitive Earmarked Research Grants (CERG)
Start Date:12/2005
Abstract:
This proposal is devoted to the following problem. What is the lowest possible degree for the nontrivial elements of β? Here degree is the ordinary (total) homo-geneous degree. In the proposal it will be shown the idea to get an estimate of this degree, and how this estimate can be used to attack long-standing open problem of structure of automorphism group of the free associative algebra of rank three over the field κ.


List of Research Outputs

Yu J., Gutierrez J. and Shpilrain V., Affine Algebraic Geometry, Contemparary Mathematics, Special Session On Affine Algebraic Geometry At The First Joint AMS-RSME Meeting, Seville, Spain, June 18-21, 2003. America Mathematical Society, 2005, 369: 276 pages.
Yu J. and Drensky V.S., Automorphisms fixing a variable of K<x,y,z>, Journal of Algebra. 2005, 291, no.1: 250-258.
Yu J. and Belov A., Cancellation Problems And Dimension Theory, Comm. Algebra . 2006, 34: 1521--1540.
Yu J., Editor of International Journal of Mathematics: Game Theory and Algebra . 2006.
Yu J., Editor of Serdica. Mathematical Journal. 2005.
Yu J., Invited Speaker: 70-year Anniversary Meeting of the Chinese Mathematical Society, Weihai, China, July 24-29. Weihai, China, 2005.
Yu J., Invited Speaker: Asian Mathematical Conference, Singapore, July 19-23. Singapore, 2005.
Yu J., Organizer: International Algebra Research Programme, May 22-June 10, Peking University, Beijing. 2006.
Yu J., Organizer: Joint AMS/TMS Special Session on 'Affine Algebraic Geometry', December 14-18, Taichung, Taiwan. 2005.
Yu J., Organizer: Workshop on Algebra and Mathematical Physics, May 16, USTC-SIAS, Shanghai. 2006.
Yu J. and Shpilrain V., Test polynomials, retracts, and the Jacobian conjecture, Affine algebraic geometry. Providence, RI, Amer. Math. Soc., 2005, Contemp. Math. 369: 253-259.
Yu J. and Drensky V., The strong Anick conjecture, Proc. Natl. Acad. Sci. USA . 2006, 103: 4836--4840.


Researcher : Yuen WO
List of Research Outputs

Ching W.K., Yuen W.O., Ng K.P. and Zhang S., Optimal Pulsation Advertising Policy with Wearout Effect: A Linear Programming Approach , IMA Journal of Management Mathematics. 2006, 17: 83-96.
Yuen W.O., Ching W.K. and Ng K.P., A Direct Method for Solving Block-Toeplitz with Near-Circulant-Block Systems with Applications to Hybrid Manufacturing Systems, Numerical Linear Algebra with Applications. 2005, 12: 957-966.


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
Completion Date:08/2005
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:Generating wavelet filters via lifting schemes
Investigator(s):Yung SP
Department:Mathematics
Source(s) of Funding:Small Project Funding
Start Date:11/2003
Completion Date:10/2005
Abstract:
To develop the theoretical background of generating wavelet filters that are pertinent for specific applications via lifting schemes.


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
Completion Date:01/2006
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).


Project Title:On the snake method for 3D reconstruction of neuron axons from their cross-sections
Investigator(s):Yung SP
Department:Mathematics
Source(s) of Funding:Seed Funding Programme for Basic Research
Start Date:01/2006
Abstract:
We propose to use the snake method to track and reconstruct 3D image of neuron axons from their consecutive cross-section slices.


List of Research Outputs

Cai H., Xu X., Lu J., Lichtman J., Yung S.P. and Wong S., Segment and Track Neurons in 3D by Repulsive Snake Method, Proceedings of 2005 International Symposium on Intelligent Signal Processing and Communication Systems. USA, IEEE, 2005, 529-531.
Guo B.Z., Wang J. and Yung S.P., Boundary stabilization of a flexible manipulator with rotational inertia, Journal Differential and Integral Equations. 2005, 18, number 9: 1013-1038.
Guo B.Z., Wang J. and Yung S.P., On the C_0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam, Systems & Control Letters. 2005, 54: 557-574.
Lee R.C.H., Wong C.W., Xu C.Z., Yim L.H. and Yung S.P., A Lyapunov-type condition for robust feedback stability of delay control systems, IMA Journal of Mathematical Control and Information. 2006, 23: 97-111.
Wang J., Xu G.Q. and Yung S.P., Exponential Stabilization of Laminated Beams with Structural Damping and Boundary Feedback Controls, SIAM J. on Control and Optimization. 2005, 44: 1575-1597.
Yung S.P., Repulsive Snake Model for Segmentations and 3D Trackings of Axons, The 2nd International Conference on Scientific Computing and Partial Differential Equations & The First East Asia SIAM Symposium. 2005.
Yung S.P., Repulsive Snake Model for Segmentations and 3D Trackings of Axons, The 2nd International Conference on Scientific Computing and Partial Differential Equations & The First East Asia SIAM Symposium . 2005.


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:Competitive Earmarked Research Grants (CERG)
Start Date:08/2003
Completion Date:07/2005
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:Merit Award for RGC CERG Funded Projects
Start Date:08/2003
Completion Date:07/2005
Abstract:
N/A


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:
N/A


Project Title:Combinatorial Optimization Problems Involving Cycles
Investigator(s):Zang W
Department:Mathematics
Source(s) of Funding:Merit Award for RGC CERG Funded Projects
Start Date:01/2005
Abstract:
N/A


Project Title:Combinatorial Optimization Problems Involving Cycles
Investigator(s):Zang W
Department:Mathematics
Source(s) of Funding:Competitive Earmarked Research Grants (CERG)
Start Date:09/2005
Abstract:
The main objectives of this project are: (1) To investigate the Jackson-Wormald conjecture which asserts that every 3-connected graph on n vertices with maximum degree d>3 contains a cycle of length at least n^{log_{d-1} 2}, and the following conjecture made by Chen, Yu and myself: there exists a function f(t)>0 such that every 4-connected graph on n vertices with no K(3,t)-minors, where t>2, contains a cycle of length at least f(t)n; (2) To characterize all graphs G such that for any nonnegative integral weight function defined on the vertex set, the maximum size of a feedback vertex set (FVS) packing of G is equal to the minimum weight of a cycle in G; (3) To describe all digraphs G in terms of forbidden structures such that the clutter of all mininal dicycles of G (with respect to vertices) is ideal; (4) To design an efficient algorithm for finding a maximum cycle packing in any weighted reducible flow graph.


List of Research Outputs

Chen G., Gao Z., Yu X. and Zang W., "Approximating the Longest Cycle Problem on Graphs with bounded degree" was awarded the Hao Wang Prize (the best paper award), The 11th Annual International Computing and Combinatorics Conference (COCOON2005). 2005.
Chen X. and Zang W., An Efficient Algorithm for Finding Maximum Cycle Packings in Reducible Flow Graphs, Algorithmica. New York, USA, Springer, 2006, 44: 195-211.
Li Y. and Zang W., Differential Methods for Finding Independent Sets in Hypergraphs, SIAM Journal on Discrete Mathematics. Philadelphia, USA, SIAM, 2006, 20: 96-104.
Li Y., Tang X. and Zang W., Ramsey Functions Involving K(m,n) with n Large, Discrete Mathematics. The Netherlands, North-Holland, 2005, 300: 120-128.
Thomas R., Yu X. and Zang W., Hamilton Paths in Toroidal Graphs, Journal of Combinatorial Theory Series B . San Diego, USA, Elsevier, Inc., 2005, 94: 214-236.
Zang W., A Min-Max Relation on Packing Feedback Vertex Sets, INFORMS International, Hong Kong, China. 2006.
Zang W., In: Series Editor, Algorithm Theory and Applications. China, Higher Education Publisher, 2006.
Zang W., Bonds with Parity Constraints, International Conference on Graph Structure Theory, Wuhan, China. 2005.
Zang W., Bonds with Parity Constraints, Third Pacific Rim Conference on Mathematics, Shanghai, China. 2005.
Zang W., Guest Editor, Discrete Mathematics. The Netherlands, North-Holland, 2005, on-going.
Zang W., The Graphical Traveling Salesman Problem and a Related Integral Polyhedron, INFORMS International, Hong Kong, China . 2006.


Researcher : Zhang S
List of Research Outputs

Ching W.K., Yuen W.O., Ng K.P. and Zhang S., Optimal Pulsation Advertising Policy with Wearout Effect: A Linear Programming Approach , IMA Journal of Management Mathematics. 2006, 17: 83-96.
Zhang S., Ng K.P., Ching W.K. and Akutsu T., A Linear Control Model for Gene Intervention in a Genetic Regulatory Network, Proceedings of IEEE International Conference on Granular Computing, Beijing, 25-27 July 2005. 1: 354-358.


Researcher : Zhao D
List of Research Outputs

Cheung W.S., Zhao D. and Pecaric J., Opial-Type Inequalities for Differential Operators, Proceedings of the 5th Annual Hawaii International Conference on Statistics, Mathematics & Related Fields, Jan 16-18, 2006. 377-383.


-- End of Listing --