Kit Ian KOU, Anna高潔欣
Associate Professor

Academic Qualification

  • Ph.D. in Mathematics, UM (2005)
  • M.Sc. in Mathematics, UM (1999)
  • B.Ed. in Mathematics, UM (1996)

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)
  16. Fourier and Signal Analysis (MATH3016)

Research

Research Interests

  • Fourier analysis
  • Quaternion and Clifford analysis
  • Windowed linear canonical analysis
  • Shannon sampling theorems
  • Harmonic analysis in Euclidean spaces
  • Signal and image analysis

Research Projects and Grants

External Grants:

  • 22/07/2016-21/07/2019: Macau Government FDCT/031/2016/A1. Quaternion Linear Canonical Transforms and Applications, funded by the FDCT. Principal Investigator.
  • 01/01/2016-31/12/2018: National Natural Foundation for Youth Scholars No. 11501015, 半空间中次调和函数的Matseav 定理, funded by the NSFC, Co-Principal Investigator.
  • 01/01/2015-31/12/2017: National Natural Foundation for Youth Scholars No. 11401606, The related topics about spheroidal wave functions in quaternion analysis (四元数分析中椭球体波函数相关问题的研究), funded by the NSFC，UMacau Research Institute, Zhuhai, Guandong, China. Principal Investigator.
  • 03/10/2013-02/10/2016: Macau Government FDCT/099/2012/A3. Generalized spheroidal wave functions and applications in Quaternion Analysis, funded by the FDCT. Principal Investigator.
  • 05/10/2012-04/10/2014: Macau Government FDCT/094/2011/A. Clifford analysis and applications, funded by the FDCT. Principal Investigator.
  • 01/01/2010-31/12/2012: National Natural Foundation for Youth Scholars No.10901166, Clifford analysis methods in higher dimensional space, by Y. Yang (PI) and  K.I. Kou (Co-PI), funded by the NSFC.

Internal Grants (Principal Investigator)

  • 16/7/2015-15/7/2018:MYRG2015-00058-FST. The Application of Quaternions to Some Signal Problems, funded by the Research Committee of UM.Principle Investigator.
  • 13/03/2014-12/03/2017：MRG012/KKI/2014/FST.Genearlized pheroidal wave functions and applications in Quaternion Analysis, funded by the Research Committee of UM. Principle Investigator.
  • May 2013-June 2016: MYRG099 (Y1-L2)-FST13-KKI. Fourier Analysis and Applications, funded by the Research Committee of UM. Principle Investigator.
  • January 2013-December 2014: MRG002/KKI/2013/FST. Clifford Analysis and Applications, funded by the Research Committee of UM. Principal Investigator.
  • June 2011-April 2015: MYRG142(Y3-L2)-FST11-KKI. Time-Frequency Analysis and Applications, funded by the Research Committee of UM. Principal Investigator.
  • January 2010-December 2011: RG076/09-10S/11R/KKI/FST. Applied Complex and Harmonic Analysis in Euclidean Space, funded by the Research Committee of UM. Principal Investigator.
  • January 2007 – June 2009: RG070/06-07S/09T/KKI/FST. Hardy Spaces of Monogenic Functions & Applications, funded by the Research Committee of University of Macau. Principal Investigator.
  • January 2005 – December 2006: RG059/05-06S/QT/FST. Paley-Wiener and Shannon Sampling Theorems in Hyper-complex Analysis, funded by the Research Committee of University of Macau. Co-Principal Investigator.
  • January 2003 – December 2005: RG091/04-05S/C117. Clifford Analysis Methods in Harmonic Analysis, funded by the Research Committee of University of Macau. Co-Principal Investigator.
  • January 2002 – December 2002: RG055/01-02S/QT/FST. (a) Monogenic Sinc Function and Applications; (b) Harmonic Analysis on the Unit Spheres in Higher Dimensional Euclidean Space, funded by the Research Committee of University of Macau, Co-Principal Investigator.
  • January 2000 – December 2001: RG024/00-01S/QT/FST. Higher Dimensional Sinc Methods and Applications in Partial Differential Equations, funded by the Research Committee of University of Macau, , two years. Co-Principal Investigator.

Academic Activities

Academic Visiting and Delivering Lectures in Mathematical Institutions

Belgium:

  • Ghent University (18-23 June 2006, Frank Sommen, Fred Brackex)

China P.R:

  • Beijing Normal University, Beijing, China (8-15 August, 2012, Guan Tie Deng)
  • Xiamen University, Xiamen (8 – 14 August, 2005, Chun Hui Qiu; 20 – 25 December, 2012, Chun Hui Qiu)

Hong Kong:

  • The Chinese University of Hong Kong, Hong Kong (July 1998, Raymond Chan)

Japan:

  • International Christian University, Tokyo (2-9 Feb, 2014, Eckhard Hitzer)

Malaysia:

  • The institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia (20-26 Dec 2013)

Portugal:

  • Aveiro University, Aveiro (23-29 June 2006, Paula Cerejeiras, Uwe  Kaehler)

Taiwan:

  • Department of Electrical Engineering, National Taiwan University, Taiwan (27 Dec 2013-1 Jan 2014, Jian-Jiun Ding)
  • Notional Center for Theoretical Sciences Mathematics Division, Hsinchu, Taiwan. (1-7 July 2014, Der-Chen Chang)

Thailand:

  • King Mongkut’s University of Technology Thonburi, Bangkok Thailand (23-31 July, 2014, Thiradet Jiarasuksakun)

United Kingdom:

  • University of Cambridge, Cambridge (Clare Hall, 15 Jan -15 July, 2006, A. F. Beardon)

Academic Visitors Invited Supported By My Research Grants:

Australia:

  • 2009: Alan McIntosh (Harmonic Analysis, PDEs, Operator Theory), Macquarie University, the Australian National University (to University of Macau)

Belgium:

  • 2007: Fred Brackx (Clifford Analysis), Ghent University (to University of Macau)
  • 2007: Hennie De Schepper (Clifford Analysis), Ghent University (to University of Macau)

China P.R.:

  • 2011, 2012, 2013, 2014: Yan YANG (Clifford Analysis), Sun Yat-Sen University, Guangzhou
  • 2012: Yan Hui ZHANG (Complex Analysis), Beijing Technology and Business University, Beijing (to University of Macau)
  • 2013, 2014: Ming Sheng LIU (Complex Analysis), South China Normal University, Guangzhou, P. R. China.
  • 2014: Luo Qing LI (Signal Analysis), Hubei University, Wuhan, China
  • 2014: Yang LIU (Clifford Analysis and Control Theory), Zhejiang Normal University, Jinhua, China
  • 2014: Jun Feng XU (Complex Analysis), Wuyi University, Jiangmen, China
  • 2015: Yong Hui  XIA (Partial Differential Equations), Zhejiang Normal University, Jinhua, China

Japan:

  • 2014: Eckhard Hitzer (Clifford Analysis), International Christian University, Tokyo, Japan
  • 2015: (Wavelet Analysis)

Portugal:

  • 2007, 2008: Palua Cerejeiras and Uwe Kaehler (Clifford Analysis), University of Aveiro, Aveiro
  • 2011, 2012, 2013: Joao Morais (Quaternion Analysis), University of Aveiro, Aveiro

Conferences Attended:

  • The 22nd international conference on finite or infinite dimensional complex analysis and applications, 08/08/2014 to 11/08/2014, on the campus of Dongguk University, Gyeongju, Korea.
  • 2014 NCTS Workshop on Geometric and Singular Analysis, July 3-4, 2014, Notional Center for Theoretical Sciences Mathematics Division, Hsinchu, Taiwan.
  • The Sixth International Congress of Chinese Mathematicians (ICCM 2013). Opening ceremony: July 14, 2013, in the Grand Ballroom of the Grand Hotel, Taipei; Lectures and invited talks: July 15 to July 19, 2013, on the campus of National Taiwan University.
  • Harmonic Analysis and its Applications, Jinhua, China, 12-16 October, 2012.
  • International Conference on Several Complex Variables Analysis, Henan, China, 16-21 August, 2012.
  • The 20th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Hanoi, Vietnam, 29 July-3 August, 2012
  • The 9th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2011), G-Hotels, Halkidiki, Greece, 19-25 September 2011
  • The 18th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, the local organization committee, University of Macau, Macau, 13-17 August 2010  
  • Symposium on Hyper-Complex Analysis, University of Macau, Macau, 4-8 December 2006
  • Function Theories in Higher Dimensions, Institute of Mathematics, Tampere University of Technology, Tampere, Finland, 12-16 June 2006
  • Workshop on the recent developments of the Hilbert-Huang Transform methodology and its applications, National Central University, Chungli, Taiwan, 15-17 March 2006
  • International Conference on Several Complex Variables, USTC, Hefei Anhui, P. R. of China, June 2005
  • Fourth ISAAC (International Society for Analysis, its Applications and Computation) Congress 2003, Toronto, Canada, August 2003
  • ICM 2002 International Congress of Mathematicians, Beijing, China, August 2002
  • International Conference on Clifford Analysis and Its Applications, Macau, August 2002
  • ICCA 6th International Conference on Clifford Algebras and Their Applications, Cookeville, Tennessee, USA, May 2002
  • The Center for Mathematics and its Applications National Research Symposium — Banach Spaces, Operators and Algebras, Canberra, Australia, January 2001
  • International Congress of Chinese Mathematicians (ICCM), Beijing, China, December 1998
  • The Eighth International Congress on Computational and Applied Mathematics (ICCAM 98), Leuven, Belgium, August 1998

Ph.D. students and their thesis topics:

  • Graduated
    1. Cui-Ming Zou (Sept 2013-January 2017). Theory and Applications of Spheroidal Wave Quaternionic Signal. (Principle supervisor)
    2. Xiao-Xiao Hu (August 2014-July 2017). Spheroidal Functions in Higher-Dimensional Spaces. (Principle supervisor)
    3. Zhen-Feng Cai (January 2015- January 2018). Quaternion Differential Equations and Applications. (Principle supervisor)
  • On going
    1. Dong Cheng (since 9/2015). (Principle supervisor)
    2. Wen-Shen Bi (since 9/2015). (Principle supervisor)
    3. Wan Kai Liu (since 9/2016). (Principle supervisor)

Master students and their thesis topics:

  • Graduated
    1. Yue-Lin Liu (2009). The linear canonical transform and generalized Hilbert transform with applications in signal processing.
    2. Rui-Hui Xu (2011). Windowed linear canonical transform and its applications.Jian-Yu Ou (2013). Uncertainty principles for quaternionic linear canonical transform and applications.
    3. Le-Ping Liang (2013). Paley Wiener theorem under linear canonical transform of slice monogenic functions
    4. Ze-Zhen Cao (2013). Linear canonical transform and applications.
    5. Ka Man Lei (2014). A tighter uncertainty principle for hypercomplex signals in the linear canonical transform domains.
    6. Dong Cheng (2015). The generalized sampling expansions associated with quaternion Fourier transform
    7. Xiao Jun Li (2016). Linear canonical transform in time-frequency analysis.

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

Robust Sparse Representation in Quaternion Space

Y Wang, KI Kou, C Zou, YY Tang

IEEE Transactions on Image Processing 30, 3637-3649, 2021.

Weighted Truncated Nuclear Norm Regularization for Low-Rank Quaternion Matrix Completion

L Yang, KI Kou, J Miao

arXiv preprint arXiv:2101.02443, 2021.

Quaternion higher-order singular value decomposition and its applications in color image processing

J Miao, KI Kou

arXiv preprint arXiv:2101.00364, 2021.

Controllability and Observability of Linear Quaternion-valued Systems

BX Jiang, Y Liu, KI Kou, Z Wang

Acta Mathematica Sinica, English Series 36 (11), 1299-1314, 2020.

Quaternion block sparse representation for signal recovery and classification

YYT Cuiming Zou, Kit Ian Kou∗ , Yulong Wang

Signal Processing 179, 107849, 2020.

Quaternion-based bilinear factor matrix norm minimization for color image inpainting

J Miao, KI Kou

IEEE Transactions on Signal Processing 68, 5617-5631, 2020.

Constrained low-rank quaternion approximation for color image denoising by bilateral random projections

J Miao, KI Kou

arXiv preprint arXiv:2006.00749, 2020.

Floquet theory for quaternion-valued differential equations

D Cheng, KI Kou, YH Xia

Qualitative Theory of Dynamical Systems 19 (1), 1-23, 2020.

Multichannel interpolation of nonuniform samples with application to image recovery

D Cheng, KI Kou

Journal of Computational and Applied Mathematics 367, 112502, 2020.

Quaternion Hardy Functions for Local Images Feature Representation

X Hu, KI Kou, Y Ting

arXiv preprint arXiv:2002.02262, 2020.

Plancherel Theorems of Quaternion Hilbert Transforms Associated with Linear Canonical Transforms

KI Kou, MS Liu, C Zou

Advances in Applied Clifford Algebras 30 (1), 1-23, 2020.

Low-rank quaternion tensor completion for recovering color videos and images

J Miao, KI Kou, W Liu

Pattern Recognition 107, 107505, 2020.

Quaternion matrix regression for color face recognition

J Miao, KI Kou

arXiv preprint arXiv:2001.10677, 2020.

A Robust Color Edge Detection Algorithm Based on Quaternion Hardy Filter

W Bi, D Cheng, KI Kou

arXiv preprint arXiv:2001.01800, 2020.

From grayscale to color: Quaternion linear regression for color face recognition

C Zou, KI Kou, L Dong, X Zheng, YY Tang

IEEE Access 7, 154131-154140, 2019.

On the ensemble controllability of Boolean control networks using STP method

J Zhong, Y Liu, KI Kou, L Sun, J Cao

Applied Mathematics and Computation 358, 51-62, 2019.

Color image recovery using low-rank quaternion matrix completion algorithm

J Miao, KI Kou

arXiv preprint arXiv:1909.06567, 2019.

FFT multichannel interpolation and application to image super-resolution

D Cheng, KI Kou

Signal Processing 162, 21-34, 2019.

The inverse Fueter mapping theorem for axially monogenic functions of degree k

B Dong, KI Kou, T Qian, I Sabadini

Journal of Mathematical Analysis and Applications 476 (2), 819-835
  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 theorems. Mathematical 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 theorem. Journal of Geometry and Physics, 108, 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 laplacians 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

  • Founding member of the ISAAC interest group on Clifford and Quaternionic analysis since January, 2011;
  • Fellow – Stanley Ho East Asia College (SHEAC), University of Macau.
  • Life Member (ID: 4939) of Clare Hall, A College for Advanced Study in the University of Cambridge, United Kingdom.

Contact Details

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

Room: E11-3067
Telephone: (853) 8822-4472
Fax: (853) 8822-2426
Email: kikou