Tao QIAN錢濤
Emeritus Professor

Academic Qualifications | AFDs Algorithm Code Release | Google Scholar Address | Working Experience | Teaching | Honorary Positions | International Journal Editorial Board Positions | Mathematical Conference Organization | Research | Publications (Summary) | Professional Affiliations | Contact Details


Academic Qualification

  • Ph.D. 1984 Peking University, Beijing, China. (Harmonic Analysis).
  • Master 1981 Peking University, Beijing, China. (Harmonic Analysis).

Google Scholar Address

http://scholar.google.co.uk/citations?user=FQ6tQe4AAAAJ&hl=en


Working Experience

  • 08/2013 –
Distinguished Professor, University of Macau
  • 2003 – 2012
Full Professor, University of Macau
  • 2005 – 2011
Head of Dept of Math, Full Professor ,University of Macau
  • 2000 – 2002
Associate Professor, University of Macau
  • 1992–2000
Senior Lecturer, Lecturer (English system) , University of New England, Australia
  • 1988–1992
Research Fellow, Flinders University of South Australia, Australia
  • 1986–1988
Research Fellow, Macquarie University, Australia
  • 1984–1986  
Research Fellow, Institute of Systems Sciences, the Chinese Academy of Sciences

 


Teaching

B.Sc. Courses

  • Complex Analysis
  • Mathematical Analysis III
  • Mathematical Analysis IV
  • Mathematical Physics Methods
  • Functional Analysis
  • Real Analysis

M.Sc. Courses

  • Mathematics Seminar
  • Real Analysis
  • Clifford Analysis
  • Functional Analysis
  • Partial Differential Equations
  • Topics in Partial Differential Equations
  • Fourier Analysis
  • Advanced Mathematics

University and Faculty/Unit Service (Position Held, Dates, etc.)

  • Head of Department of Mathematics for 6 years from 2005 to 2011.
  • Service as members of University Senate, University GSC and Faculty GSC.
  • Establishment of a New BSc Program in Mathematics with two branches in University of Macau
    Before 2011 Dept of Math taught only service courses for BSc in Math Education of Faculty of Education, and service courses for engineering departments of Faculty of Science and Technology, and Master and Ph.D. programs in mathematics. Supported by the university authority, as Head of Dept of Math, I led colleagues in Dept of Math to establish a new BSc program in mathematics in University of Macau with two streams (Mathematical Education and Mathematics and Applications). The program proposal has passed all the required procedures and become effective since November 2010. In Sep 2011 Dept of Math started to have freshmen for the new BSc in math.

Honorary Positions

  • Honorary Professor of Huaqiao University since 2011 by invitation
  • Honorary Professor of Wuhan University since 2005 by invitation
  • Honorary Professor of Xiamen University since 2003 by invitation

International Journal Editorial Board Positions

  • Associate Editor: Mathematical Methods in the Applied Sciences (SCI), published by Wiley-Blackwell
  • Associate Editor: Complex Analysis and Operator Theory (SCI), published by Birkhauser-Springer
  • Associate Editor: Complex Variables and Elliptic Equations (SCI), Published by Taylor & Francis Group

Mathematical Conference Organization

  • To host ISAAC 2015 in University of Macau
  • Chair of Scientific and Organization Committees, the 18th International Conference on Finite and Infinite Complex Analysis and Applications, University of Macau, 2010 (120 speakers and two special issues with the SCI journals MMAS and CV&EE as related publications)
  • Chair of Scientific and Organization Committees, Symposium on Hyper-Complex Analysis, activity of Silver Jubilee of UM, December, 2006 (a conference proceedings published by Univ. of Macau)
  • Chair of Scientific Committee, the 4th International Conference on Wavelet Analysis and Applications, 29th Nov to 2nd December, 2005, University of Macau (with 150 speakers and a conference book published by Springer)
  • Chair of Scientific Committee, Satellite Conference to ICM2002
    (International Congress for Mathematicians, 2002, Beijing) on Clifford Analysis and its Applications, August, 2002, University of Macau (a conference book published by Birkhäuser)

Research

Research Interests

  • Harmonic Analysis in Euclidean Spaces
  • Partial Differential Equations
  • Complex Analysis of One and Several variables
  • Clifford Analysis
  • Time-Frequency Analysis
  • Signal and Image Processing (Edge Detection)
  • Control Theory (System Identification)

Major Research Grants Obtained From My Working Institutions (1 MOP is approximately equal to 1 HKD)

Active Research Grants are with blue color

  • 2018: Macao Government FDCT 0123/2018/A3, Theory and applications of adaptive fourier decomposition in reproducing Kernel Hilbert spaces.
  • 2018: University of Macau Multi-Year Research Grant (MYRG) MYRG2018-00168-FST, Adaptive rational approximation in weighted Hardy spaces and applications, 1120700 MOP. Funding starts from January 2019.
  • 2017: Macao Government FDCT 079/2016/A2, Studies and Applications of Unwinding Fourier Expansions of Signals. Finding started in January 2018.
  • 2016: University of Macau Multi-Year Research Grant (MYRG) MYRG2016-00053-FST AFD applications in Control Theory, 1458500 MOP.
  • Annual Research Grant for the position of Distinguished ProfessorMOP 350000.
  • 2015: Joined with 乔玉英  NSFC, 11571089, Clifford分析中Dirac型算子及相关问题研究.
  • 2015: Joined with 张艳慧 NSFC, 11501015, 半空间中次调和函数的Matseav定理.
  • 2014: Macao Government FDCT 099/2014/A2, Two Related Topics in Clifford Analysis, Duration: 3 years, MOP 2130000.
  • 2013: Multi-Year Research Grant (MYRG) MYRG116(Y1-L3)-FST13-QT  Adaptive Decomposition of Signals and Applications, Level iii project, MOP 120,0000
  • 2013: Multi-Year Research Grant (MYRG) MYRG115(Y1-L4)-FST13-QT Variational Problem on sub-Riemannian geometry with Application in Harmonic analysis and PDE, Level iv research proposal, MOP 221,0000
  • 2012: Macao Government FDCT 098/2012/A3, Approximation With Rational Functions In One and Higher Dimensions With Applications, approved MOP 168, 2850.
  • 2011: Joined with 娄增建,NSFC, 11171203,临街Q型空间及其在流体方程中的应用.
  • 2011: Macao Government FDCT/056/2010/A3, Adaptive Decomposition of Signals and Applications (信号的自适应分解及其应用), Proposed Duration: 3 years. APPROVED MOP 1760000
  • 2009 – 2010: UL017/08-Y3/MAT/QT01/FST, Applications of Hyper-Complex Analysis -1st Sub-project: Signal Analysis. Proposed Duration: 5 years (3rd). Approved 401250 MOP
  • – 2010:  Macao Government FDCT/014/2008/A1, Clifford and Harmonic Analysis 克利福德及調和分析Proposed Duration: 3 years.  APPROVED MOP$ 1196000
  • – 2009: UL017/08-Y2/MAT/QT01/FST, Applications of Hyper-Complex Analysis -1st Sub-project: Signal Analysis. Proposed Duration: 5 years (2nd). Approved 195450 MOP
  • 2007: Joined with 娄增建,NSFC, 10771130,Hardy-Sobolev空间及相关问题.
  • 2007 – 2008: RG-UL/07-08S/Y1/QT/FST, Applications of Hyper-Complex Analysis – 1st Sub-project: Signal Analysis. Proposed Duration: Spring of 2008 to End of 2012. Approved 78000 MOP
  • -2007: RG071/06-07S/QT/FST, Singular Integrals in Hyper-complex Analysis. Proposed Duration: 2 years. Approved 195850 MOP
  • -2007: RG071/06-07S/08R/QT/FST, Singular Integrals in Hyper-Complex Analysis. Proposed Duration: 2 years. Approved 31000 MOP
  • 2005-2008: Macao Government FDCT/051/2005/A, Time-Frequency Representation and Realization of Algorithm of Transient Signals (瞬變信號的時頻表示及算法實現), Proposed Duration: 3 years. APPROVED MOP$ 500000. Joined by Qiuhui Chen.
  • 2005 -2006: RG059/05-06S/07R/QT/FST, Paley-Wiener and Shannon Sampling Theorems in Hyper-complex Analysis. Proposed Duration: 2 years.  Approved 45176.6 MOP
  • 2005 – 2006: RG059/05-06S/08T/QT/FST, Paley-Wiener and Shannon Sampling Theorems in Hyper-Complex Analysis. Proposed Duration: 12 months. Approved 21440 MOP
  • 2004 – 2005: RG059/05-06S/QT/FST (RG079/04-05S), Paley-Wiener and Shannon Sampling Theorems in Hyper-complex Analysis. Proposed Duration: Two year (The present one is the second half). Approved 85580 MOP
  • 2004 – 2005: RG079/04-05S/QT/FST, Paley-Wiener and Shannon Sampling Theorems in Hyper-complex Analysis. Proposed Duration: 24 months. Approved 52170 MOP
  • 2004 – 2005: RG091/04-05S/C117/QT/FST, Clifford Analysis Methods in Harmonic Analysis. Proposed Duration: 2 years. Approved 9487 MOP
  • 2004 – 2005: RG092/04-05S/C118/QT/FST, Analysis Methods in Signal Processing. Proposed Duration: 2 years. Approved 35355.8 MOP
  • 2003 – 2004: RG065/03-04S/QT/FST, Analysis Methods in Signal Processing. Proposed Duration: 2 years. Approved 41700 MOP
  • 2003 – 2004: RG021/03-04S/QT/FST (RG024/02-03S/…), Clifford Analysis Methods in Harmonic Analysis. Proposed Duration: 2 years. Approved 49800 MOP
  • 2002 – 2003: RG024/02-03S/QT/FST, Clifford Analysis Methods in Harmonic Analysis. Proposed Duration: 2 years. Approved 47440 MOP
  • 2002 – 2003: RG080/02-03S/C41/QT/FST (RG055/01-02S…), Mathematical Formulation of Image Edge Detection With Wavelet Method. Proposed Duration: 2 years. Approved 34040 MOP
  • 2001 – 2002: RG055/01-02S/QT/FST (RG002/00-01W.), Monogenic Sinc Function and Applications (Jan to June 2002) & Harmonic Analysis on the Unit Spheres in Higher Dimensional Euclidean Spaces (Jul to Dec2002)  Note:  Project renewal under the title “Higher Dimensional Sine Methods and Applications in Partial Differential Equations”  with a progress report Proposed Duration : one year. Approved 43900 MOP
  • 2001 – 2002: RG056/01-02S/QT/FST, Mathematical Formulation of Image Edge Detection with Wavelet Methods. Proposed Duration: 2 years. Approved 30900 MOP
  • 2001 – 2002: RG056/01-02S/C19/QT/FST, Mathematic Sinc Function and Applications & Harmonic Analysis on the unit Spheres in Higher Dimensional Euclidean Spaces Note: Transfer from 2002 Funding to 2003. Approved MOP$ 26914 MOP
  • 2000 – 2001: RG024/00-01S/QT/FST, Higher Dimensional Sine Methods and Applications in Partial Differential Equations – part 2 (previous ref.  RG002/00-01W/QT/FST). Proposed Duration: 1year 3 months (parts 1&2). Approved 39915 MOP
  • 2000 – 2001: RG002/00-01W/QT/FST, Higher Dimensional Sine Methods and Applications in Partial Differential Equations. Proposed Duration: 1 year. Approved 11315 MOP
  • 1993 – 1999 Research Grants obtained yearly from New England University, Australia.

Research Grants Obtained Outside My Affiliation Universities

  1. D.A.A.D. the German Research Foundation, Research Stay for Professor (3 months), 2009.
  2. Joint with Z-J. Lou, NNSF of China (grant no. 10771130), 2008 – 2010:  Harmonic Analysis in Hardy-Sobolev Spaces.
  3. Joint with X-M. Li, Guangdong Province Natural Science Foundation 030497, 2003 – 2005: Octonions Analysis.
  4. Conference Grant for the ICM Satellite Conference on Clifford Analysis, August, 2002, by the Guangdong New Oasis Life Science and Technology Co., Ltd.
  5. Conference Grant for the ICM Satellite Conference on Clifford Analysis, August, 2002, by the Chinese Mathematical Society. Representing UM I was the sole organizer.
  6. Research funding provided by the Foundation of Special Fund for Scientific Research, Belgium for my visit to Ghent Univ. for four months in 1999 to 2000 (invited by R. Delanghe, F. Brackx and F. Sommen, Clifford analysis).
  7. Programme of the Swedish Foundation for International Cooperation in Research and High Education (STINT). The period is for maximum nine months. The host institutions are Chalmers Univ of Technology and the Univ of G¨oteborg (invited by Peter Sj¨ogren, potential theory and harmonic analysis)
  8. “Transfer of Knowledge Through Expatriate National” supported by the United Nations Development Program. The assignment is for one month (July 1998) in Beijing. The host institute is the Mathematical Institute of the Chinese Academy of Sciences. (Through X-H. Ji, partial differential equations)
  9. A grant from the Chinese Science Foundation based on a joint research project between Prof Tongde Zhong and myself to cover Zhong’s travelling expenses (from China) to visit UNE in August 1998 (T-D. Zhong: several complex variables)
  10. A grant from the DFG the German Research Society based on a joint research project with Prof Wolfgang Spr¨ossig to cover Wolfgang’s travelling expenses (from Germany) to visit UNE in December 1997 and January 1998
  11. A grant from the German Foundation D.A.A.D. to support my visit to Kiel Univ. in Nov and Dec 1996 (invited by D. M¨uller, harmonic analysis)
  12. Support from the German Volkswagen-Foundation to cover full travel (Armidale-Seiffen-Armidale) and living expenses to attend Symposium on Analytical and Numerical Methods in Quaternionic and Clifford Analysis as a plenary speaker in Seiffen, Germany, June 1996 (invited by W. Spr¨ossig)
  13. NSF (USA) to support my visit to the Univ. of Illinois at Urbana-Champaign for two months in 1996 (invited by D. Burkholder, probability and stochastic processes)
  14. A research grant of the Netherlands Science Foundation to support my visit to Delft Univ. of Technology for one month in 1993 (invited by Ben de Pagter, functional analysis)
  15. Swedish researches grant to support my visit to Chalmers Univ. of Technology and Univ. of G¨oteborg for one month in 1990 (invited by P. Sj¨ogren, potential theory and harmonic analysis).
  16. Research grant of Swedish Science Foundation to support my visit to Mittag-Leffler Institute and the Univ. of Stockholm for two months in 1990 (invited by Jaak Peetre, at the occasion Special Year of Harmonic Analysis)
  17. NSF (U.S.A.) to support my visit to Univ. of Chicago for three months in 1987 (invited by C. Kenig, harmonic analysis and partial differential equations)

Summary on Academic Visiting and Delivering Lectures in Mathematical Institutions

Australia:

    • The Univ. of New South Wales (1998, M. Cowling)
    • Queensland Univ. (1992)
    • Univ. of Sydney (1988, 1994)
    • The Center for Mathematical Analysis, the Australian National University (1987, 1989, 2002, N. Trudinger, A. McIntosh)

Austria:

    • Johannes Kepler University at Linz (1993 P. M¨uller)

Belgium:

    • Ghent University (2001, 2002, 2006, 2008, 2011, F. Sommen, R. Delanghe, F. Brackex)

China P.R.: An incomplete list includes

    • Peking University (L-Z. Peng)
    • Beijing Normal University (S-Z. Lu, K-Y. Wang)
    • Nankai University, Tianjin (X-W. Zhou)
    • Wuhan University (P-D. Liu, J-Y. Du)
    • Hubei University, Wuhan (L-Q. Li)
    • Henan University, Kaifeng (D-F. Li)
    • Xiamen University, Xiamen (T-D. Zhong)
    • Zhejiang University, Hangzhou (S-L. Wang, J-C. Chen)
    • Zhongshan University, Guangzhou (L-X. Yan, D-G. Deng, L-H. Yang)
    • Shantou University, Shantou (Z-J. Lou)
    • Math. Inst. Chinese Academy of Sci., Beijing  (X.H. Ji)
    • Math and Physics Inst., Wuhan, Chinese Academy of Sci. (C-H. Ouyang)
    • The Chinese University of Sci. and Tech., Hefei (S. Gong)
    • Fudan University, Shanghai (Li Da-Qian)
    • Tongji University, Shanghai (Chen Zhi-Hua)
    • Jiaotong University, Shanghai (Han Jin-Sheng)

Czech Republic:

    • Charles University (1996, 2007, V. Soucek)

Finland:

    • University of Helsinki (2007)
    • Tempare University of Technology (2006, 2007, 2012, Sirkka-Liisa Erikson)

France:

    • INRIA Institut national de recherche en informatique et en automatique (The National Institute for Research in Computer Science and Control) (2011, 2013, L. Baratchart)

Germany:

    • Wuerzburg Universität (2009, S. Ruscheweyh)
    • TU Freiberg University (1996, 2007, 2008, 2009, 2011, W. Sproessig, E. Wegert)
    • Kiel University (1996, 2007,  G. Sommer)

Hong Kong:

    • HK City U. (2010, C. Micchelli)
    • Hong Kong Univ. (2008, Ngaiming Mok)
    • Baptist Univ. (2005,2007, T. Tang)
    • The Chinese University of Hong Kong, Hong (2001, K-S. Lau)
    • UKUST (2001, 2006, C-C. Yang, Y-M. Cheang)

Italy:

    • Seminario Matematico e Fisico di Milano (2008, 2013, I. Sabadini)
    • Università degli Studi di Firenze (2008, F. Vlaci)

The Netherland:

    • Delft University of Technology (1993, Ben De Pagter)

New Zealand:

    • The University of Auckland (1998, B. Pavlov)

Norway:

    • The Norway Academy of Science (2012)

Poland:

    • Banach Center (invitation, 1996, Banach Center, B. Bojarski)

Portugal:

    • Aveiro University (2003, 2006, 2009, P. Cerejeiras, U. Kaehler)

Sweden:

    • Mittag- Leffler Institute (1992, J. Peetre)
    • Chalmers University of Technology (1992,1994,1999, P. Sj¨ogren)
    • University of Stockholm(1992, J. Peetre)
    • Univ. of Göteborg (1992, 1994, 1999, 2012, P. Sj¨ogren)

USA:

    • Auburn University at Montgomery (2009, 2011, Y. Wang)
    • University at Albany, State University of New York (2009, C. Micchelli, M. Stessin, K-H. Zhu)
    • The University of Alabama (2006, Z-J. Wu)
    • Princeton University (2006, A. S-R. Chang)
    • Syracuse University New York (1996, 2009, T. Iwaniec, G. Verchota, Y-S. Xu)
    • University of Illinois at Urbana-Champaign (1996, D. Burkholder)
    • Washington University at St Louis (1994, G. Weiss, M. Taibleson)
    • University of Arkansas (1994, 1996, J. Ryan)
    • University of Chicago (1987, C. Kenig)
    • Indiana University (1987, A. Torchinski)

Academic Visitors Invited Supported By My Research Grants (Incomplete list):

Australia:

    • 2008: B. Jefferies (Harmonic and Clifford Analysis), University of New South Wales, Australia (to University of Macau)
    • 2007: X. Doung (Harmonic Analysis and PDEs), Macquarie University (to University of macau)
    • 2007: X.J. He (Image Processing), Sydney University of Sci and Tech (to University of Macau)
    • 2005: M. Cowling (Harmonic Analysis), University of New South Wales (to University of Macau)
    • 2005: You-Song Luo, (Partial Differential Equations), RTMI (to University of Macau)
    • 1996, 2002, 2009: McIntosh (Harmonic Analysis, PDEs, Operator Theory), Macquarie Univ., the Australian National Univ.,(to Flinders Univ. of South Australia and Univ. of Macau)

Belgium:

    • 2007: F. Brackx (Clifford Analysis), Ghent University (to University of Macau)
    • 2007: H. De Schepper (Clifford Analysis), Ghent University (to University of Macau)
    • 2006: EM Professor Richard J. Delanghe (Clifford Analysis), Ghent University (to University of Macau)
    • 2004, 2008, 2009, 2010: Frank Sommen (Clifford Analysis), State Univ Ghent (to University of Macau)
    • 2004: David Eelbode (Clifford Analysis), State Univ Ghent (to University of Macau)
    • 2004: Bram De Knock (Clifford Analysis ), State Univ Ghent (to University of Macau)
    • 2004: Nele De Schepper (Clifford Analysis), State Univ Ghent (to University of Macau)

Canada:

    • 2004: Gen-kai Zhang (Pattern Recognition), the University of Western Ontario (to University of Macau)

China P.R.:

    • 2011, 2012: Q-X. Yang (Harmonic Analysis), Mid China University of Science and Technology (to University of Macau)
    • 2011: J-Z. Liu (Math Computation), Beijing Research Institute of Rail Sciences (to University of Macau)
    • 2011: G-T. Deng (Complex Analysis), Beijing Normal University (to University of Macau)
    • 2011: Y-H. Zhang (Complex Analysis), Beijing Normal University (to University of Macau)
    • 2010: D-F. Li (Wavelet and Functional Analysis), Henan University (to University of Macau)
    • 2010: Xue-An Zheng (Harmonic Analysis), Beijing Normal University (to University of Macau)
    • 2009: Z.J. Lou (Harmonic Analysis), Shantou University (to University of Macau)
    • 2009: L-H. Tan (Complex and Signal Analysis), Guangdong University of Sci and Tech (to University of Macau)
    • 2009: W-J Yuan (Complex Analysis), Guangzhou University (to University of Macau)
    • 2008: L-Z. Peng (Harmonic and Wavelet Analysis), Peking University (to University of Macau)
    • 2008, 2010, 2011: L-H. Yang (Signal and Image Analysis), Zhongshan University (to University of Macau)
    • 2008: Jian-Xun He (Complex and Harmonic Analysis), Guangzhou University (to University of Macau)
    • 2005: J-Y Du (Analytic Boundary Value Problems), Wuhan University (to University of Macau)
    • 2005: Y-Y. Qiao (Clifford Analysis), He Bei Normal University (to University of Macau)
    • 2006, 2008, 2011: X.M. Li (Quaternionic and Octonionic Analysis, and Image Analysis) Guangzhou University (to University of Macau)
    • 2006: Q-S. Cheng (Signal Analysis), Peking University (to University of Macau)
    • 2006, 2007, 2008, 2009, 2010: Q.H. Chen (Wavelet and Signal Analysis), Zhongshan University, Hubei University, Aveiro University (to University of Macau)
    • 2004, 2006, 2008: H. Li (Algorithm and Approximation), Huazhong University of Sci and Tech (to University of Macau)
    • 2004: Chu-Hui Qiu (Complex Analysis), Xiaman University (to University of Macau)
    • 2003: P-D. Liu (Geomery in Banach Spaces), Wuhan University (to University of Macau)
    • 2002: B.H. Li (Differential Geometry and PDE), Inst. of Math,Fellow of the Chinese Academy of Sciences (to University of Macau)
    • 2002: Sun Daochun (Complex Analysis), South China Normal Univ (to University of Macau)
    • 2002: Yu Jiarong (Complex Analysis), Wuhan Univ (to University of Macau)
    • 2002: Li Xingmin (Harmonic Analysis and Hypercomplex Analysis),Guangzhou Univ (to University of Macau)
    • 1999: Q-H Yu (Several Complex Variables), Inst. of Math., Academia Sinica (The Chinese Academy of Sciences), P.R. China (to Univ of New England)
    • 1998: T-D Zhong (Several Complex Variables), Xiamen Univ, P.R. China (to Univ of New England and University of Macau)
    • 1997, 2005: L-X Yan (Harmonic Analysis), Zhongshan Univ, P.R. China (to Univ of New England and University of Macau)
    • 1997: X-H. Ji (Partial Differential Equations), Inst of Maths the Chinese Academy of Sciences (to Univ of New England)
    • 1994, 1998, 2000: K-Y Wang (Approximation Theory), Beijing Normal Univ, P.R. China (to Univ of New England and University of Macau)
    • 1994: Y-B Zhang (Algebra), Beijing Normal Univ, P.R. China (to Univ of New England)
    • 1992, 2004: S-L Wang (Harmonic Analysis), Hangzhou Univ, P.R. China, (to Flinders Univ of South Australia and University of Macau)
    • 1991: R-L Long (Harmonic Analysis), Inst of Math, Academia Sinica, P.R. China (to Flinders Univ of South Australia)

Finland:

    • S-L. Eriksson (Clifford Analysis), Tampere University of Technology (to University of Macau)

France:

    • 2010: L. Baratchart (Harmonic Analysis and Approximation Theory), Recherche at INRIA (Sophia-Antipolis) (to University of Macau)
    • 2006: J.P. Kahane (Fourier and Complex Analysis), Universite Paris-Sud Orsay (to University of Macau)
    • 2003: Robert Conte (Ordinary Differential Equations), CEA Research Institute, Saclay (to University of Macau)

Germany:

    • 2013: Bert. Wolfgang Schulze, University of Potsdam
    • 2010: Elias Wegert (Complex Analysis, Riemann-Hilbert Boundary Value problems, Control Theory), TU Bergakademie Freiberg (to Univ of New England and University of Macau)
    • 2008: G.erold Sommer (Pattern Recognition and Image Processing), Kiel University (to University of Macau)
    • 2008: H. Begehr (Complex Analysis and Boundary Value Problems), Mathematisches Institut Freie Univesitat Berlin (to University of Macau)
    • 2002: T. Hempfling (Clifford Analysis), Freiberg Univ (to University of Macau)
    • 1998, 2002, 2006, 2011: Dr Wolfgang Sproessig (Clifford Analysis and Applied P.D.E’s),TU Bergakademie Freiberg (to Univ of New England and University of Macau)

Hong Kong:

    • 2009: Y.M. Chiang (Special Functions and ODEs), Hong Kong University of Science and Technology (to University of Macau)
    • 2007: T. Tao (Scientific Computing), Hong Kong Baptist University (to University of Macau)
    • 2004: Jin-Song Huang (Representation theory), University of Hong Kong (to University of Macau)
    • 2003, 2008, 2010: Chong-Cun Yang (Complex Analysis), Hong Kong University of  Science and Technology (to University of Macau)
    • 2002: You Xingge (Signal Processing), Hong Kong Baptist Univ.

Portugal:

    • 2007, 2008: P. Cerejeiras (Clifford Analysis), University of Aveiro, Portugal (to University of Macau)
    • 2007, 2008: U. Kaehler (Clifford Analysis), University of Aveiro, Portugal (to University of Macau)
    • 2002: H. Malonek (Clifford Analysis), Aveiro Univ. Portugal (to University of Macau)

Sweden:

    • 1995, 1997, 2000: Peter Sj¨ogren (Potential Theory and Harmonic Analysis), Chalmers Univ of Technology and G¨oteborg Univ,Sweden (to Univ of New England and University of Macau)

The Netherland:

    • 1993: Ben de Pagter (Functional Analysis), Delft Univ of Technology, the Netherlands (to Univ of New England)

Taiwan:

    • 2008: S.S. Cheng (Complex Analysis), Tsing Hua University, Taiwan (to University of Macau)

USA:

    • 2010: M. Stessin (Complex Analysis and Operator Theory), Albany University, New York, USA (to University of Macau).
    • 2008: Der-Chen Chang (Harmonic and Complex Analysis), Department of Mathematics, Georgetown University, USA (to University of Macau)
    • 2006: Z-J. Wu (Harmonic and Complex Analysis, Operator Theory), University of Alabama, USA (to University of Macau)
    • 2005: Yue-sheng Xu (Applied Mathematical Analysis), Syracuse University (to University of Macau)
    • 2004, 2010: Charles Micchelli (Applied Analysis), State University of  New York, the University at Albany, Chair Prof of Hong Kong City University (to University of Macau)
    • 2003: George Csordas (Complex Analysis), Univ. of Hawaii (to University of Macau)
    • 2002: M. Ismail, (Special Functions), The Univ of Florida, USA (to University of Macau)
    • 1998: Prof Dmitry Khavinson (Complex Analysis), Univ of Arkansas, USA (Univ of New England)
    • 1998, 2003: K-S Lau (Functional and Harmonic Analysis), Univ of Pittsburgh and the Chinese Univ of Hong Kong (to Univ of New England and to University of Macau)
    • 1994, 2007: John Ryan (Hyper-Complex and Clifford Analysis), Univ of Arkansas, USA (to Univ of New England and University of Macau)
  •  

Awards

  • 澳门特别行政区科学技术奖:自然科学奖一等奖, 二零一二年十月十九日
    (Macao SAR Science and Technology Research Award: Natural Science First Prize, the 19th October, 2012)
  • Research Prize for Senior Faculty Members, Faculty of Science and Technology, University of Macau, 2007-2009 (The Second Research Competition of University of Macau with only one winner in the category)
  • 2nd Prize of University of Macau Research Award, University of Macau, 2001 (My second year in UM, the first Research Competition of University of Macau)
  • Vice Chancellor’s Award for Excellency in Research, New England University, Australia, 2000 (One award after several years)
  • Prize of Scientific Progress, China, 1984, 1985 (joint with M.T. Cheng and D.G. Deng, based on my Doctorate thesis).

Keynote and Plenary Speaker Financially Supported By Conferences

  • The The 20th International Conference of Finite and Infinite Dimensional Complex Analysis and Applications, Hanoi, Vietnam, July 2012
  • The 2nd International conference on the Advances of Hilbert-Huang Transform and Its Applications,  Zhongshan University, Guangzhou, 2008
  • The 16th International Conference of Finite and Infinite Dimensional Complex Analysis and Applications, Gyeongju, Korea, 2008
  • The 1st International conference on the Advances of Hilbert-Huang Transform and Its Applications, Taoyuan, 2006
  • International conference on Function Theories in Higher Dimensions, Tampere University of Technology, Finland, 2006
  • The 4th International conference in Wavelet Analysis and Applications, Macao, 2005
  • Conference For Mathematical Achievements of Garth Gaudry, University of New South Wales, Australia, 2004
  • The 6th International Conference on Clifford Algebras and their Applications, Cookeville, Tennessee, ISAAC, USA, 2002
  • Satellite Conference on Clifford Analysis and Applications to ICM 2002, Macao.
  • Symposium on Analysis and Numerical Methods in Clifford, Analysis-Theory and Applications, Seiffen, Germany, 1996

Ph.D. students and their thesis topics:

  • Graduated
    1. K.I. Kou (4/2001-5/2005), Paley-Wiener Theorem and Shannon Sampling in the Clifford Algebra Setting. University of Macau.
    2. Y. Yang (9/2003-9/2006), Co-dimension p- Paley-Wiener Theorems and Shannon Theorems in the Clifford Algebra Setting.
    3. M.G. Fei (9/2007-9/2009), Approximation in Clifford Analysis.
    4. D.S. Zhou (12/2006-8/2009), Random Matrix.
    5. Y.B. Wang (9/2007-8/2010), Adaptive Decomposition of Signals into Mono-Components.
    6. P. Dang (9/2008-8/2011), Time-Frequency Analysis Based on Mono-Components.
    7. W. Mi (9/2009-7/2012), Adaptive Fourier Decomposition in Control Theory.
    8. S. Li (9/2009-07/2013), Compressed Sensing and Szego Kernels.
    9. J. X. Wang (9/2011-09/2014), Adaptive Fourier Decomposition in Quaternionic and Clifford Algebra settings.
    10. Y. MO (9/2011-07/2015), Non-maximal selection principle for Adaptive Fourier Decomposition and its applications.
    11. H. C. Li (9/2012-12/2015), The spectrum characterizations and integral representations of functions in Hardy spaces on hyper-complex Tubes.
    12. W. X. Mai (9/2012-07/2016), Reproducing Kernel Hilbert spaces and the Adaptive Fourier Decomposition in Hardy spaces on Tubes.
    13. Y. Gao (9/2013-8/2017) FFT Formulation of Adaptive Fourier Decomposition and Its Application to Image Representation
    14. B. H. Dong (12/2014-8/2017) Aspects of the Fueter Mapping Theorem

 

  • On going
    1. Y. T. Li (9/2015- ) Two Dimensional Unwinding Decomposition
    2. X. Y. Wang (9/2015- ) Two Dimensional System Identification in Frequency Domain
    3. Y. Huang (9/2016- ) Paley-Wiener Theorem in Hardy Space on Tubes

Master students and their thesis topics:

  • Graduated
    1. S. Liu (2004), Pointwise Convergence of Fourier Series on the Unit Sphere of R4
    2. Y.C. Lin (2005), Hilbert Transformation of the Unit Sphere
    3. L.M. Guan (2006), Analytic Signals
    4. W. Mi (2008), Analytic Signal Analytic Robust Control Theory
    5. S.H. Xu (2008), Random Analytic Signals
    6. I.T. Ho (2009), Analytic Signal Decomposition into Starlike Functions
    7. Z.L. Liu (2011), Sound Analysis in Mono-components
    8. Z.X. Li ( 2012), Algorithm of Adaptive Fourier Decomposition
    9. W.X. Mai (2012), Time Frequency Distributions
    10. R. Shi (due 2012), Application of AFD in Finance signals
    11. S F Wu (due 2012), Speech Analysis by AFD
    12. H L Zhao (9/ 2011), Sampling with Clifford algebra setting
    13. W Y Jia (9/2011), Fourier Pricing Method
    14. X.G. Huang (2014) Kind of Frequency Distribution in Higher Dimensional Spaces
    15. P.Q. Xia (2014) Martingales and Martingale Transform Theory
    16. X.F.Li (2015) Time-Frequency Analysis of Heart Sound Signal based on Unwinding AFD
    17. J.H. Lv (2016) Class of Unbounded Fourier Multipliers on the Unit Complex Ball
    18. J. J. Liu (2017) Applications of Hardy-Hodge Decomposition on the Decomposition of Magnetization
    19. S. M. Li (2017) Exponential Decay of the Remainder of the Unwinding Blaschke Expansion

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

  1. Yan Yang (2009, 2010): Hyper-complex and Clifford Analysis
  2. Lihui. Tan (2010, 2011,2012): Complex and Signal Analysis
  3. Pengtao Li (2009, 2010): Harmonic and Clifford Analysis
  4. Zhihua Du (2010, 2011): Analytic Boundary Value Problems
  5. Hong Li (2010, 2011): Algorithm of Adaptive Fourier Decomposition
  6. Youfa Lee (2011): Wavelet, Frame and AFD
  7. Qiuhui Chen (2012): Wavelet and Signal Analysis
  8. Xing-Di Chen (2012): Quasi-conformal Mapping
  9. Guan-Tie Deng (2012, 2013): Analytic Signals, Hardy spaces 0<p<1, Hardy spaces on Tubes, Uncertainty Principles

AFD (Adaptive Fourier Decomposition) Algorithm Code Release

  1. 1D AFD Click here for the agreement to obtain the code of our adaptive Fourier decompositions.
  2. 2D PUD Click here for the agreement to obtain the code of 2D partial unwinding decompositions.

Introduction: AFD is a new decomposition model that decomposes a given signal/function into a sum of mono-components (signals of non-negative analytic phase derivative) with fast convergence in energy. Iteration based on AFD gives rise to a conditional solution of the n-best rational approximation: a long standing open algorithm problem.


Publications (Summary)

Refereed Journal Papers 187
Refereed Edited Books and Journal Special Issues 10
Refereed Book Chapters 12
Refereed Conference Proceedings 16
TOTALLY Published 225

 

Accepted and Published Refereed Journal papers

    (“*” means that the paper is in the latest SCIE, EI, CPCI-S and CJCR (China Journal of Scientific Research) lists. Percentage of the applicants contribution is cited to the end of the item. Before 2000 the authors name order was basically according to the alphabetical way, and after 2000 it was according to variable criteria and requests of the collaborator(s)).

Articles with their titles in blue have links to their respective PDF files.

Books and Journal Special Issues Editor

  • 2019
    10. Qian, Tao; Li, Pengtao. Singular integrals and Fourier theory on Lipschitz boundaries. Science Press Beijing, Beijing; Springer, Singapore, 2019. xv+306 pp. ISBN: 978-981-13-6499-0; 978-981-13-6500-3 42-02 (42B20 42B25 46E35)
  • 2017
    9. New Trends in Analysis and Interdisciplinary Applications, by P. Dang, M. Ku, T. Qian and L. G. Rodino, Trends in Mathematics Research Perspectives.
    8. Lipschitz 边界上的奇异积分与 Fourier 理论, by T. Qian and P. T. Li, 科学出版社.
  • 2016
    7. Mathematical Analysis, Probability and Applications– Plenary Lectures, by Qian, T. and Rodino, L., Springer Proceedings in Mathematics & Statistics.
  • 2015
    6. 自适应 Fourier 变换, by Qian, T., 科学出版社.
  • 2012
    5. Complex Variables and Elliptic Equations, by T. Qian and Z.H. Du, accepted to appear in 2012.
    4. Mathematical Methods in the Applied Sciences, by T. Qian, I.T. Leong, 30 November 2012 Volume 35, Issue 17, Page 1999-2140, Special Issue: Complex Analytic Methods in Signal Processing
  • 2007
    3. Communication on Pure and Applied Analysis , by T. Qian and Y. S. Xu (Editors),invited as guest editor for the special issue 6 (3), 2007.
    2. Wavelet Analysis and Applications,by T. Qian, V. M. I and Y. S. Xu (Editors), the book series in Applied and Numerical Harmonic Analysis, Springer, 2007.
  • 2004
    1. Advances in Analysis and Geometry, by T. Qian, T. Hempfling, A. McIntosh and F. Sommen (Editors) ,book series in Trends in Mathematics, Birkhäuser, 2004.

Book Chapters

  • 2014
    12. [Q24] T. Qian, Fueter mapping theorem in hypercomplex analysis, Springer References: General Aspects of Quaternionic and Clifford Analysis, Operator Theory, edited by Daniel Alpay.
  • 2013
    11. Sparse Representation of Signals in Hardy Space, Quaternionic and Clifford Fourier Transforms and Wavelets, by Eckhard Hitzer and Stephen J. Sangwine, Trends in Mathematics, Birkh\”aser, 2013.
    10. [bookchapter10] HOW TO CATCH SMOOTHING PROPERTIES AND ANALYTICITY OF FUNCTIONS BY COMPUTERS, L.P. Castro,  H. Fujiwara, T. Qian and Saburou Saitoh, MATHEMATICS WITHOUT BOUNDARIES: SURVEYS IN INTERDISCIPLINARY RESEARCH, Edited by Panos Pardalos  and  Themistocles  M.  Rassias, The volume will be published by Springer in 2014.
  • 2008
    9. Hilbert Transforms on the Sphere and Lipschitz Surfaces, by T. Qian, Quaternionic and Clifford Analysis, Trends in Mathematics, Birkhäuser Verlag Basel/Switzerland, 259-275, 2008.
  • 2007
    8. Mono-components for signal decomposition, book series in Applied and Numerical Harmonic Analysis, Springer, 2007.
    7.

    Time-frequency aspects of nonlinear Fourier atoms, by T. Qian, Q. H. Chen and L. Q. Li, the book series in Applied and Numerical Harmonic Analysis, Springer, 2007.

  • 2004
    6. Advances in Analysis and Geometry, by T. Qian, T. Hempfling, A. McIntosh and F. Sommen (Editors), bookseries in Trends in Mathematics, Birkhäuser, 2004.
    5. Dini-type convergence of Fourier series on the unit sphere of Euclidean spaces, by T. Qian and  S. Liu, book series in Trends in Mathematics, Birkhäuser, 2004, pp131-148.
  • 2001
    4. Singular Integrals and Fourier Multipliers On the Unit Spheres and Their Lipschitz PerturbationsAdvances in Applied Clifford Algebras, Vol 11, (S1) 53-76, November (2001)– Special Issue, Clifford Analysis Proceedings of the Clifford Analysis Conference, Cetraro, Italy, October, 1998, John Ryan and Daniele C. Struppa Editors.
  • 2000
    3. Fourier theory under Möbius transformations, by T. Qian, X. H. Ji, and J. Ryan, CliffordAlgebras and Their Applications in Mathematical Physics, Volume2, edited by John Ryan and Wolfgang Sprössig, Birkhäuser,Boston-Basel-Berlin (April 2000), 51-80.
  • 1995
    2. Singular integrals on the m-torus and its Lipschitz perturbations, Clifford Algebras in Analysis and Related Topics, book chapter in the series: Studies in Advanced Mathematics, CRC Press (1995), 94-108.
  • 1991
    1. Convolution singular integrals on Lipschitz curves,byT. Qian and A.McIntosh, Springer-Verlag, Lecture Notes in Maths 1494 (1991) 142–162.

Conference Proceedings

  • 2012
    16. Sparse Reconstruction of Signals in hardy Spaces, S. Li and T. Qian, the proceeding​s of QCFTW (of ICCA9) for TIM/Birkha​user, edited by Eckhard MS Hitzer and Steve Sangwine.
  • 2011
    15. An adaptive method of model reduction in frequency domain, by Mi Wen and T Qian,IEEE Power Engineering and Automation Conference  (PEAM 2011), Sep, Wuhan.
    14. Adaptive Fourier Transform Based Signal Denoising, by Zhang, L. M. & Li, H. and Qian, T. (2011). ICSP 2011: International Conference on Signal Processing.
    13. Instantaneous Frequencies of Simple Waves and Their application to Sleep Spindle Detection, by   Zhang, L.M., Li, H., Wei,Y.T. & Qian, T., Proceedings of 2011 IEEE International Conference on Systems, Man, and Cybernetics (2011).
    12. Non-harmonic system with greedy algorithm, by S. Li and T. Qian, accepted to appear in the   International Workshop on Electromagnetism and Communication Engineering”. (ECE 2011), IEEE Catalog Number: CF1143k-DVD, ISBN: 978-1-4244-9438-5, Conference Code: #18262
  • 2010
    11. Frequency Domain Identification with Adaptive Rational Orthogonal System, with M. Wen, Proceedings of 2010 International Conference on System Science and Engineering, Taiwan.
  • 2008
    10. A new property of Nevanlinna Functions, by T. Qian, Proceedings of the 16th International Conference of Finite and Infinite Dimensional Complex Analysis and Applications, Dongguk University, Gyeongju, KOREA, July 28-August 1, 2008, pp 38-49.
  • 2003
    9. A mathematical model for edge detection using rotational wavelet transformation, by T. Qian andL. M. Zhang, the 6th IASTED International Conference onComputers, Graphics, and Imaging,} August 13-15, 2003, Honolulu,USA.
    8. Parameter Analysis of Morlet Wavelet Transform Based Edge Detection, by T. Qian and L. M. Zhang, Proceedings of the 7th WSEASInt. Conf. on CSCC (Circuits, Systems, Communications andComputers)} in Corfu Island, Greece, July 7-10, 2003.
    7. Derivation of monogenic functions and applications, Proceedings of the Centre for Mathematics and its applications, Australian University, Volume 41, 2003,118-127.
  • 2002
    6. Radon measure formulation of edge detection using rotational wavelets, by T. Qian andL. M. Zhang, Proceedings of the WSEAS conference,Singapore, December, 2002.
    5. Paley-Wiener theorem and Shannon Sampling in the Clifford analysis setting, Proceedings of the 6th International Conference on Clifford Algebras and their Applications, Invited Volume for Plenary Talks,May 20-25, 2002, Cookeville, Tennessee, USA.
  • 1996
    4. Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space and generalisations to Rn, Proceedings of the Symposium on Analytical and Numerical Methods in Quaternionic and Clifford Analysis, Seiffen, 1996,187-196.
  • 1994
    3. Transference between infinite Lipschitz graphs and periodic Lipschitz graphs, Proceedings of the Center for Mathematics and its Applications, ANU, vol.33 (1994), 189-194.
  • 1989
    2. A note on martingales with respect to complex measures, by T. Qian, M. Cowling and G. Gaudry, Miniconference onOperators in Analysis (1989), Proceedings of the Center forMathematical Analysis, 24,  ANU, Canberra, (1989), 10–27.
  • 1987
    1. Fourier transform on Lipschitz curves, by T. Qian and A. McIntosh, Proceedings of the Center for Mathematical Analysis, ANU, vol. 15, (1987), 157–166.

Professional Affiliations

  • Member of the American Mathematical Society
  • Member of the Australian Mathematical Society

Contact Details

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

Room: E11-3084, 3085
Telephone: (853) 8822-8547
Fax: (853) 8822-2426
Email: fsttq, tqian1958@gmail.com