Kit Ian KOU, Anna  高潔欣
Associate Professor

Academic Qualifications | Google Scholar Address | Working Experience | Teaching | Research | Academic Activities | Publications | Professional Affiliations | Contact Details

Academic Qualifications
Google Scholar Address

http://scholar.google.co.uk/citations?hl=en&user=iamGZR0AAAAJ&view_op=list_works&gmla=AJsN-F7NlbSteJ5pmQ7PNB1i8X5bf2H0JLi_rW5ij-_IYdyM0jQfjFoO6ZxG3DfDyumzX1KjgeDD2IvphgMoIet1egy6wMsdgQ0GSCGOjhzwNzaUauPckhQilgJv8j1P6wyTmHCKApb8


Working Experience

  • 08/2013 -present

Associate Professor, Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao.

  • 08/2006-07/2013

Assistant Professor, Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao.

  • 01/2006-07/2006

Research Fellow, Clare Hall, University of Cambridge, Cambridge United Kingdom

  • 06/2005-12/2005

Assistant Professor, Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao.

  • 09/1999-05/2005

Lecturer, Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao.

  • 09/1996-08/1999

Teaching Assistant, Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao.


Teaching

M.Sc. and Ph.D Courses

  1. Topics in Analysis (IMAT016)
  2. Reading course (IMAT012)
  3. Clifford Analysis (IMAT005)
  4. Advance in Mathematics (IMSE002)
  5. Advanced Engineering Mathematics (MATH801)

B.Sc. Courses

  1. Mathematical Analysis I (MATH101)
  2. Mathematical Analysis II (MATB221)
  3. Finite Mathematics (EDUC106)
  4. Mathematical Analysis III (MATH200/ EDUC352)
  5. Mathematical Analysis IV (MATH201)
  6. Numerical Methods and Computation (MATH207)
  7. Probability and Statistics (EDUC212/254)
  8. Probability (MATB213)
  9. Multivariate Calculus (EDUC252)
  10. Ordinary Differential Equations (EDUC320)
  11. Mathematical Analysis III (EDUC352)
  12. Complex Analysis (EDUC354/MATB311)
  13. Mathematical Physics Methods (EDUC414)
  14. Partial Differential Equations (EDUC446)
  15. Seminar (EDUC491)

Research

Research Interests

Research Projects and Grants

External Grants: Internal Grants (Principal Investigator)
Academic Activities

Academic Visiting and Delivering Lectures in Mathematical Institutions

Belgium: China P.R: Hong Kong: Japan: Malaysia: Portugal: Taiwan: Thailand: United Kingdom:

Academic Visitors Invited Supported By My Research Grants:

Australia: Belgium: China P.R.: Japan: Portugal:

Conferences Attended:

Ph.D. students and their thesis topics:

Master students and their thesis topics:

Post-doctoral and Research Associate Fellows and their Major Research Areas

  1. 2010, 2012, 2013: Joao MORAIS (Hyper-complex and Clifford Analysis), University of Aveiro, Portugal.
  2. 2012, 2013, 2014: Ming Sheng LIU (Complex Analysis), South China Normal University, Guangzhou, P. R. China.
  3. 2012, 2013, 2014:Yan YANG (Clifford Analysis and Signal Analysis), Sun Yat-Sen University, Guangzhou, P. R. China.
  4. 2013, 2014: Yang LIU (Signal and Control Theory), Zhejiang Normal University, Jinhua, P. R. China.
  5. 2014: Hong LI (Signal and Data Analysis), Huazhong University of Science and Technology. P. R. China.
  6. 2014, 2015:  Jun Ming LIU (Complex and Signal Analysis), Shantou University, P. R. China.
  7. 2014: Jun Feng XU (Complex and Signal Analysis), Wuyi University, Jiangmen, P. R. China.
  8. 2015: Ming Sheng LIU (Quaternion Analysis), South China Normal University, Gauangzhou, P.R. China; Yonghui XIA (Partial Differential Equations), Zhejiang Normal University, Jinhua, P. R. China.
  9. 2016: Ming Sheng LIU (Quaternion Analysis), South China Normal University, Gauangzhou, P.R. China; Yonghui XIA (Partial Differential Equations), Zhejiang Normal University, Jinhua, P. R. China.

Publications
  1. Z. Cai, K.I. Kou,Solving Quaternion Ordinary Differential Equations with Two-Sided Coefficients, Qualitative Theory of Dynamical Systems, 2017. Page 1-12. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
  2. B. Li, Y. Liu, K.I. Kou and L. Yu, Event-Triggered Control for the Disturbance Decoupling Problem of Boolean Control Networks, IEEE Transactions on Cybernetics, 2017. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
  3. D. Cheng, K.I. Kou, Novel Sampling Formulas Associated with Quaternionic Prolate Spheroidal Wave functions, Adv. Appl. Clifford Algebras, 2017. (NSFC11401606, MYRG2015, FDCT094, FDCT099)
  4. K.I. Kou, J. Liu, Which Linear Operators Preserve Outer Functions? Indagationes Mathematicae, 23 August, 2017. (NSFC11401606, MYRG2015, FDCT094, FDCT099)
  5. J. Chu, S. Heidarkhani, K.I. Kou, and A. Salari, Weak Solutions and Energy Estimates for a Degenerate Nonlocal Problem Involving Sub-linear Nonlinearities, J. Korean Math. Soc. 54 (2017), No. 5, pp. 1573-1594. (NSFC11401606, MYRG2015, FDCT099)
  6. C. Zou, K.I. Kou and J. Morais, Prolate spheroidal wave functions associated with the quaternionic Fourier transform, Mathematical Methods in Applied Sciences, 2017. (NSFC11401606, MYRG2015, FDCT094, FDCT099)
  7. D Zhang, K.I. Kou, Y Liu, J Cao, Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field, Neural Networks, 2017. (NSFC11401606, MYRG2015, FDCT099)
  8. J. Li and K.I. Kou, Dynamics of Traveling Wave Solutions to a New Highly Nonlinear Shallow Water Wave Equation, International Journal of Bifurcation and Chaos, 27 (03), 1750044, 2017. (NSFC11401606, MYRG2015, FDCT099, FDCT031)
  9. Y. Zhang, K.I. Kou, Integral representation and estimation of harmonic functions in the quaternionic half space, Mathematical Methods in the Applied Sciences, 27 April, 2017. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
  10. Y. Zhang, K.I. Kou, G. Deng, T. Qian, The generalized Matsave theorem on grwth of subharmonic functions admitting a lower bound in Rn, Complex Variables and Elliptic Equations, 62(5), 642-653, 2017. (FDCT099)
  11. Z. Cai and K.I. Kou, Laplace transform: a new approach in solving linear quaternion differential equations, Mathematical Methods in the Applied Sciences, 2017. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
  12. D. Cheng and K.I. Kou, Generalized Sampling Expansions Associated with Quaternion Fourier Transform, Mathematical Methods in the Applied Sciences, 2017. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
  13. C. Zou, K.I. Kou, J. Morais, Prolate Spheroidal Wave Functions Associated with the Quaternionic Fourier Transform, Mathematical Methods in the Applied Sciences, 2017. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
  14. Y. Yang, K.I. Kou, C. Zou. Edge detection methods based on modified differential phase congruency of monogenic signal, Multidimensional Systems and Signal Processing, 2017: 1-21. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
  15. K.I. Kou, Yang~Y, Zou~C. Uncertainty Principle for Measurable Sets and Signal Recovery in Quaternion Domains, to appear in Mathematical Methods in the Applied Sciences, 2017. (NSFC11401606, MYRG2015, FDCT094, FDCT099)
  16. X. Hu and K.I. Kou. Quaternion Fourier and linear canonical inversion theoremsMathematical Methods in the Applied Sciences (2016). (NSFC11401606, MYRG2015, FDCT099)
  17. X. Fan, K.I. Kou and M. Liu, Quaternion Wigner–Ville distribution associated with the linear canonical transforms, Signal Processing, 130 (2017), 129-141. (NSFC11401606, MYRG2015, FDCT099)
  18. K.I. Kou and J. Li, Bifurcations and Exact Traveling Wave Solutions of a Modified Nonlinear Schr¨odinger Equation, Int. J. Bifurcation and Chaos 26 (6) 1650106 (2016)[22 pages] (NSFC11401606, MYRG2015,MYRG099, FDCT094, FDCT099)
  19. Dong, B., K. I. Kou., Qian, T., & Sabadini, I. (2016). On the inversion of Fueter’s theoremJournal of Geometry and Physics108, 102-116. (MYRG2015)
  20. K. I. Kou, Yijun Lou, and Yong-Hui Xia, Zeros of a Class of transcendental Equation with Application to Bifurcation of DDE, Int. J. Bifurcation and Chaos 26, 1650062 (2016) [14 pages] DOI:http://dx.doi.org/10.1142/S0218127416500620(NSFC10901166, MYRG099, MYRG2015, FDCT094, FDCT099)
  21. Y. Xia, L. Chen, K. I. Kou, D. O’Regan, Hölder Regularity of Grobman–Hartman Theorem for Dynamic Equations on Measure Chains, Bulletin of the Malaysian Mathematical Sciences Society, pp 1-28, First online: 12 May 2016 (NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
  22. C. Zou, K. I. Kou, and Y. Wang, Quaternion Collaborative and Sparse Representation with Application to Color Face Recognition, IEEE Transactions on Image Processing, 2016. (NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
  23. K. I. Kou, Ming-Sheng Liu and Shu-Zhen Tao,Herglotz’s theorem and quaternion series of positive term, Mathematical Methods in the Applied Sciences, 2016, 39(18): 5607-5618. (NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
  24. K. I. Kou, M. Liu, J. Morais, C. Zou, Envelope Detection Using Generalized Analytic Signal in 2D QLCT Domains, Multidimensional Systems and Signal Process, 2016. (NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099) DOI :10.1007/s11045-016-0410-7.
  25. K.I. Kou and H. Li, Greedy adaptive decomposition of signals based on nonlinear Fourier atoms, International Journal of Wavelets, Multiresolution and Information Processing, 2016.(NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
  26. Y. Songy, H. Li, J. Wang, K. I. Kou, Multiple One-Dimensional Embedding Clustering Scheme for Hyperspectral Image Classification, International Journal of Wavelets, Multiresolution and Information Processing, 14 (2), 2016. (NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
  27. J. Morais and K. I. Kou, Constructing Prolate Spheroidal Quaternion Wave Functions on the Sphere, Mathematical Methods in the Applied Sciences, 2016. (NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
  28. Y. Yang and K.I. Kou, Novel uncertainty principles associated with 2D quaternion Fourier transforms, Integral Transforms and Special Functions, 27 (3), 213-226, 2016.(NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
  29. K. I. Kou, Y. Liu, D. Zhang and Y. Tu, Ensemble control of linear systems with parameter uncertainties, International Journal of Control, 27 (3), 213-226, 2016. (NSFC11401606, FDCT094, FDCT099, MYRG099, MYRG2015))
  30. W Zhang, KI Kou, J Lou, Y Liu, Observer based consensus for nonlinear multi-agent systems with communication failures, Neurocomputing, Vol. 173, 1034-1043. (NSFC11401606, MYRG099, MYRG142, FDCT094, FDCT099)
  31. K. I. Kou, J. Ou and J. Morais, Uncertainty principles associated with quaternionic linear canonical transforms, Mathematical Methods in the Applied Sciences, Vol. 39, 10, 2722–2736 July (2016). (MYRG099, MYRG2015, FDCT094, FDCT099)
  32. J. Morais, M.A. Pérez-de la Rosa, K.I. Kou, Computational Geometric and Boundary Value Properties of Oblate Spheroidal Quaternionic Wave Functions, Wave Motion, 57 (2015) 112-128. (MYRG142, FDCT094)
  33. J. Morais, H.M. Nguyen, K.I. Kou,  On 3D Orthogonal Prolate Spheroidal Monogenics, Mathematical Methods in the Applied Sciences. (MRG002, MYRG142, MYRG099, FDCT094, FDCT099, MRG012)
  34. M. Liu, K.I. Kou, J. Morais and P. Dang, Sharper Uncertainty Principles for the Windowed Fourier Transform, Journal of Modern Optics, 62 (1), 46-55, 2015. (MRG002, MYRG142, MYRG099, FDCT094, FDCT099, MRG012)
  35. Y. Zhang, G. Deng, K.I. Kou, Asymptotic behavior of fractional aplacians in the half space, Applied Mathematics and Computation 254, 125-132, 2015. (MYRG099, MYRG142, FDCT094, FDCT099)
  36. L. Chen, K.I. Kou, M. Liu, Pitt's inequality and the uncertainty principle associated with the quaternion Fourier transform, Journal of Mathematical Analysis and Applications 423 (1), 681-700, 2015. (NSFC10901166, MYRG099, MYRG142, FDCT094, FDCT099)
  37. L Lee, K.I. Kou, W Zhang, J Liang, Y Liu, Robust finite-time boundedness of multi-agent systems subject to parametric uncertainties and disturbances, International Journal of Systems Science, 1-9, 2015 (NSFC10901166, MYRG099, MYRG142, FDCT094, FDCT099)
  38. YH Xia, R Wang, K.I. Kou, D O'Regan,  On the linearization theorem for nonautonomous differential equations, Bulletin des Sciences Mathématiques, 2014. (NSFC10901166, MYRG099, MYRG142, FDCT094, FDCT099)
  39. Y. Yang and K. I. Kou, Uncertainty Principles for Hypercomplex Signals in the Linear Canonical Transform Domains, Signal Processing. Vol. 95, Feb 2014, 67-75. ISSN 0165-1684 [YK13.pdf] (SCIE) (NSFC10901166, MRG002, MYRG099, MYRG142, FDCT094)
  40. K.I. Kou and J. Morais, Asymptotic Behaviour of the Quaternion Linear Canonical Transform and the Bochner-Minlos Theorem, Applied Mathematics and Computation, 247, 675-688, 2014. (MRG002, MYRG142, MYRG099, FDCT094, FDCT099, MRG012)
  41. M. Liu, K.I. Kou, J. Morais and P. Dang, Signal Moments for the Short-Time Fourier Transform Associated with Hardy-Sobolev Derivatives, Mathematical Methods in the Applied Sciences, 2014. (MRG002, MYRG142, MYRG099, FDCT094, FDCT099, MRG012)
  42. J. Morais, K.I. Kou and H.T. Le, Generalized Holomorphic Orthogonal Function Systems over Infinite Cylinders, Mathematical Methods in the Applied Sciences. Article first published online: 12 AUG 2014, DOI: 10.1002/mma.3243 (MRG002, MYRG142, MYRG099, FDCT094, FDCT099, MRG012)
  43. Y. H. Zhang, K.I. Kou and G. T. Deng, Integral Representation and Asymptotic Behavior of Harmonic Functions in Half Space, Journal of Differential Equations, 257(8), 2753-2764 (2014) , DOI: 10.1016/j.jde.2014.05.047 (MRG002, MYRG142, MYRG099, FDCT094, FDCT099, MRG012)
  44. K. I. Kou, J. Ou^ and J. Morais, On uncertainty principle for quaternionic linear canonical transform, Abstract and Applied Analysis, Vol. 2013, Article ID 725952, 14 pages, (2013). doi:10.1155/2013/725952. [KOM13.pdf] (MYRG142, FDCT094)
  45. J. Morais, K.I. Kou and W. Sproessig, Generalized holomorphic Szego kernel in 3D spheroids, Computers and Mathematics with Applications, Vol. 65 (4), Feb 2013, 576 – 588, (2013). ISSN: 0898-1221 [MKS13.pdf] (SCIE) (MYRG142, FDCT094)
  46. J. Morais, K.I. Kou and S. Georgiev, On convergence properties of 3D spheroidal monogenics, International Journal of wavelets multiresolution and information processing, Vol. 11, 1350024, (2013) [19 pages] doi: 10.1142/S0219691313500240, ISSN 0219-6913 [MKG12.pdf] (MYRG142, FDCT094)
  47. K. Kou, J. Morais and Y. Zhang, Generalized prolate spheroidal wave functions for offset linear canonical transform in Clifford analysis, Mathematical Methods in the Applied Sciences, 36: 1028–1041, (2013). doi: 10.1002/mma.2657, ISSN 1073-2772 [KMZ12.pdf] (MYRG142)
  48. Z. Du, K. Kou and J. Wang^, Lp polyharmonic Dirichlet problems in regular domains I: The unit disc, Complex Variables and Elliptic Equations, Vol. 1, 1-19, (2012). ISSN 1747-6933 (Print), 1747-6941 (Online) [DKW12.pdf(SCIE) DOI: 10.1080/17476933.2012.678993
  49. K. Kou, R. Xu^ and Y. Zhang, Paley-Wiener theorems and uncertainty principles for the windowed linear canonical transform, Mathematical Methods in the Applied Sciences, 35: 2122–2132. doi: 10.1002/mma.2642 (2012), ISSN 1073-2772 [KXZ11.pdf] (SCIE )
  50. K. Kou and R. Xu^, Windowed linear canonical transform and its applications, Signal Processing, 92(1), 179-188, (2012). ISSN 0165-1684 [KX12.pdf] (SCI)
  51. Y. Zhang, G. Deng and K. Kou, On the lower bound for a class of harmonic functions in the half space, Acta Mathematica Scientia, 2012, 32 B (4), 1487-1494. ISSN  0252-9602 [ZDK12.pdf] (SCI)
  52. Y. Liu^, K. Kou and I. Ho, New sampling formulae for non-bandlimited signals associated with linear canonical transform and nonlinear Fourier atoms, Signal Processing, 90(3), 933-945, (2010). ISSN 0165-1684 [LKH10.pdf] (SCI)
  53. A. Axelsson, K. Kou and T. Qian, Hilbert transforms and the Cauchy integral in Euclidean space, Studia Mathematica, 193(2), 161-187, (2009). [AKQ09.pdf](SCI)
  54. F. Brackx, N. De Schepper, K. Kou and F. Sommen, The Mehler Formula for the Generalized Clifford-Hermite Polynomials, Acta Mathematica Sinica, English Series, 23(4), 697-704, (2007). ISSN 1439-8516 CN: 11-2039/O1 [FSKS07.pdf](SCI)
  55. K. Kou , T. Qian and F. Sommen, Sampling with Bessel Functions, Advances in Applied Clifford Albebras, 17(3), 519-536, (2007).  ISSN 0188-7009 [KQS07.pdf]
  56. K. Kou and T. Qian, Shannon Sampling in the Clifford Analysis Setting, Journal for Analysis and its Applications (ZEITSCHRIFT FÜR ANALYSIS UND IHRE ANWENDUNGEN), 24(4), 853-870, (2005). ISSN 0972-5954 [KQ05b.pdf]
  57. K. Kou and T. Qian, Shannon Sampling and Estimation of Band-limited Functions in the Several Complex Variables Setting, Acta Mathematica Scientia, Series B, English Edition, 25(4), 741-754, Oct (2005). ISSN  0252-9602 CN: 42-1227/0 [KQ05a.pdf]
  58. K. Kou, T. Qian and F. Sommen, Generalizations of Fueter's Theorem, Methods and Applications of Analysis, 9(2), 273-290, June (2002). ISSN 1073-2772 [KQS02.pdf]
  59. K. Kou and T. Qian, The Paley-Wiener Theorem in R^n  with the Clifford Analysis Setting, Journal of  Funcnctional Analysis, 189(1), 227-241(15), Feb (2002). ISSN 0022-1236 [KQ02.pdf] (SCI)
  60. K. Kou, V. Sin and X. Jin, A Note on the Fast Algorithm for Block Toeplitz Systems with Tensor Structure, Applied Mathematics and Computation, 126, 187-197 (2002). ISSN 0096-3003 [KSJ02.pdf]
  61. S. Lei, K. Kou and X. Jin, Circulant-like Block Preconditioners for Ill-Conditioned Block Toeplitz Systems, East-West Journal of Numerical Mathematics, 7(3), 175-185 (1999). ISSN 1513-489X[LKJ99.pdf]
  62. K. Kou, X. Jin and V. Sin, The Sine Transform Operator in the Banach Space of Symmetric Matrices and Its Application in Image Restoration, Numerical Mathematics, A Journal of Chinese Universities, English series, 8(2), 231-242 (1999). ISSN 1004-8979 [KJS99.pdf]

^ This author is a student under my supervision when he/she completed this article.

Book Chapters

  1. S. Georgiev, J. Morais, K.I. Kou and W. Sprößig. Bochner-Minlos Theorem and Quaternion Fourier Transform. In Eckhard Hitzer and Steve Sangwine, Quaternion and Clifford Fourier Transforms and Wavelets, Springer, Birkhauser Trends in Mathematics Series, 105-120 (2013). [GMKS13.pdf]
  2. X. Jin and K. Kou, A Brief Survey of Block Toeplitz Iterative Solvers, Transactions of K. C.Wong Education Foundation Supported Lectures, Vol. 22, pp. 1-27. Ed: W. Qian, Shanghai University Press, 2002.

Refereed Proceeding Papers

  1. K. Kou, New generalizations of Fueter's theorem, American Institute of Physics Conference Proceedings, DOI:10.1063/1.3636722 Vol. 1389, pp. 284-287; NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. Date: 19 -- 25 September 2011 Location: Halkidiki, (Greece) ISBN: 978-0-7354-0956-9.
  2. X. Jin and K. Kou, A Brief Survey of Block Toeplitz Iterative Solvers, Transactions of K. C.Wong Education Foundation Supported Lectures, Vol. 22, pp. 1-27. Ed: W. Qian,  Shanghai University Press, 2002.

Professional Affiliations
Contact Details

Faculty of Science and Technology
University of Macau, E11
Avenida da Universidade, Taipa,
Macau, China

Room: E11-3078
Telephone: (853) 8822-4472
Fax: (853) 8822-2426
Email: kikou