Qian Tao  錢濤 Professor

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

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

B.Sc. Courses

1. Complex Analysis
2. Mathematical Analysis III
3. Mathematical Analysis IV
4. Mathematical Physics Methods
5. Functional Analysis
6. Real Analysis

1. Mathematics Seminar
2. Real Analysis
3. Clifford Analysis
4. Functional Analysis
5. Partial Differential Equations
6. Topics in Partial Differential Equations
7. Fourier Analysis
8. Advanced Mathematics

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

• As 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

• Chair of Scientific and Organization Committees, the 18^th 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 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

• 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
• 2013: Multi-Year Research Grant (MYRG) MYRG116(Y1-L3)-FST13-QT  Adaptive Decomposition of Signals and Applications, Level iii project, MOP 120,0000
• 2012: Macao Government FDCT 098/2012/A3, Approximation With Rational Functions In One and Higher Dimensions With Applications, approved MOP 168, 2850.
• 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 - 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)
• Hebei 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, 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, 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, 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)

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, 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:

• 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. 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 19^th 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 20^th 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, graduated in July 2012), Adaptive Fourier Decomposition in Control Theory.


• On going
  
  
  8. S. Li (9/2009), Adaptive Signal Decompositions.
  9. J.X. Wang (9/2010), Adaptive Monogenic Expansions of Signals in Higher-Dimensional Spaces.
  10. J. L. LIU (9/2011), Speech Analysis
  11. Y. MO (9/2011), Greedy Algorithm
  12. H.-C. Li (9/2012), Hardy spaces in hyper-complex spaces
  13. W.-X. Mai (9/2012), Computation theory in relation to AFD

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 (due 2012), Algorithm of Adaptive Fourier Decomposition
  9. W.X. Mai (due 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


• On going
  
  
  12. H L Zhao (9/ 2011), Sampling with Clifford algebra setting
  13. W Y Jia (9/2011), Fourier Pricing Method
  14. P Q Xia (9/2012), Martingale method in proving Lp boundedness
  15. X.-G. Huang (9/2012), to be decided

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

AFD (Adaptive Fourier Decomposition) Algorithm Code Release

Click here for the agreement to obtain the code of our adaptive Fourier 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)

Journal papers ("*" means that the paper is in the latest SCI list).

Submitted or Working Journal Papers:

• Rational Approximation Backward Shift Minimization (DRAFT), Laurent Baratchart and Tao Qian, in preparation.
• On backward shift algorithm for estimating poles of rational functions, Wen Mi and Tao Qian, submitted.
• TM systems are Schauder bases, T. Qian and Q-H. Chen.
• Sampling theorem for non-bandlimited signals with ladder-shaped spectra and reproducing property, You Fa Lee and Tao Qian, submitted.
• Estimations of convergence rate of rational Fourier series and conjugate rational Fourier series and their applications, by Lihui Tan, Tao Qian, submitted.
• Backward Shift Invariant Subspace, Band Preservation and Bedrosian identity, Lihui. Tan and Tao Qian, submitted.
• Best Rational Approximation via Blaschke Forms, T. Qian, submitted.

Accepted and Published Refereed Journal papers (Totally 113)

("*" means that the paper is in the latest SCIE, EI, CPCI-S and CJCR (China Journal of Scientific Research) lists. Percentage of the applicant’s 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)).

• 2013

  *113	[QWY] Matching Pursuits among Shifted Cauchy Kernels in Higher-Dimensional Spaces, Tao Qian, Jinxun Wang and Yan Yang, accepted to appear in Acta Mathematica Sinica.
  *112	[DuQWIII] Lp polyharmonic Dirichlet problems in regular domains III: The Unit Ball, Zhihua Du; Tao Qian; Jinxun Wang, accepted by Complex Variables and Elliptic Equations.
  *111	[DuQW] Lp polyharmonic Dirichlet problems in regular domains IV: The upper-half space, Zhihua Du; Tao Qian; Jinxun Wang, accepted by Journal of Differential Equations.
  *110	[LdfQ]Sufficient conditions that the shift-invariant system is a frame for L2(Rn), D-F. Li    and T. Qian, accepted to appear in Acta Math. Sinica.
  *109	[TQ2013] Estimations of convergence rate of rational Fourier series and conjugate rational Fourier series and their applications, L-H. Tan and T. Qian,accepted by SCIENCE CHINA Mathematics.
  *108	[DDQ1] A Sharper Uncertainty principle, P. Dang, G-T. Deng, T. Qian, accepted to appear in Journal of Functional Analysis.
  *107	[Q22] T. Qian, Cyclic AFD Algorithm for Best Approximation by Rational Functions of Given Order, accepted by Mathematical Methods in the Applied Sciences.
  *106	[ChenQTan] Constructive Proof of Beurling-Lax Theorem, Q-H. Chen, T. Qian and L-H. Tan, accepted to appear in Chin. Ann. of Math.
  *105	[QChen] Rational Orthogonal Systems are Schauder Bases, T. Qian and Q-H. Chen, accepted by Complex Variables and Elliptic Equations.
  *104	[LQM1], Sparse Reconstruction of Hardy Signal And Applications to Time-Frequency   Distribution, S. Li, T. Qian, W-X. Mai, accepted to appear in International Journal of Wavelets, Multiresolution and Information Processing
  *103	[QYQX] Micro-local structure and two kinds of wavelet characterizations about the generalized Hardy spaces, Tao Qian and Qixiang Yang, accepted by Taiwanese Journal of Mathematics.
  *102	[LCQW] Sampling error analysis and some properties of non-bandlimited signals that are reconstructed by generalized sinc functions, You-Fa Li, Qiuhui Chen, Tao Qian, Yi Wang,  accepted by Applicable Analysis, http://dx.doi.org/10.1080/00036811.2013.769135
  *101	[ChenQQLee] Shannon-Type Sampling for Non-Bandlimited Signals in Higher Dimensions, Qiuhui Chen, Tao Qian, Youfa Li, accepted by Sciences in China.
  *100	[QWang] Remarks on Adaptive Fourier Decomposition, Tao Qian and Yan-Bo Wang, accepted to appear in International Journal of Wavelets, Multiresolution and Information Processing, Jan 2013, Vol. 11, Issue 1, p 1-14.

• 2012

  *99	[LyfQ] Analytic sampling approximation by projection operator with application in decomposition of instantaneous frequency, You-fa Lee and Tao Qian, accepted to appear in International Journal of Wavelets, Multiresolution and Information Processing.
  *98	[CCQ] Quasihyperbolic Distance in Punctured Planes, accepted to appear in Complex Analysis and Operator Theory, by M. Chen, X-T. Chen and T. Qian.
  *97	[DQ2] Time-Frequency Distribution based on Mono-component Decomposition, by P. Dang and T. Qian, accepted by International Journal of Wavelets, Multiresolution and Information Processing.
  *96	[CZQ] Higher order boundary integral formula and Integral-differential equation on Stein Mainfolds, by Lv-ping Chen Tongde Zhong and Tao Qian, accepted by Complex Variables and Operator Theory.
  *95	[QLS] Comparison of Adaptive Mono-component Decompositions, by T. Qian, H. Li, M. Stessin, accepted by Nonlinear Analysis: Real World Applications.
  *94	[QWj] Some Remarks on the Boundary Behaviors of Functions in the Monogenic Hardy Spaces, Tao Qian and Jinxun Wang,  Adv. Appl. Clifford Algebras, Volume 22, Number 3, 2012,  819–826.
  *93	[MQ] Frequency Domain Identification: An Algorithm Based On Adaptive Rational Orthogonal System, W. Mi and T. Qian, Automatica, 48(6). pp. 1154-1162.
  *92	[CQRW] B-Splines of Blaschke Product Type,  by  Q H Chen, T Qian, G B Ren, Y Wang,   accepted by Computers and Mathematics with Applications, Volume 62 Issue 10, November, 2011, doi>10.1016/j.camwa.2011.09.002.
  *91	[DQ1] Hardy-Sobolev Derivatives of phase and amplitude and their applications, accepted for publication by Mathematical Methods in the Applied Sciences.
  *90	[QSW] Adaptive Fourier decomposition of functions in quaternionic Hardy spaces, by Tao Qian, Wolfgang Sproessig and Jinxun Wang, accepted to appear in Mathematical Methods in the Applied Sciences. DOI: 10.1002/mma.1532.
  *89	[YQS2] Phase Derivative of Monogenic Signals in Higher Dimensional Spaces, Y. Yang, T.  Qian, F. Sommen, accepted by Complex Analysis and Operator Theory, DOI: 10.1007/s11785-011-0210.
  *88	[DQW1] Lp Polyharmonic Dirichlet problems in regular domains, II: The upper half plane, by Z H Du, T Qian, J X Wang, accepted for publication by Journal of Differential Equations, 2012, Vol 252, Issue 2, Pages 1789-1812.
  *87	[DeQ] An Application of Entire Function Theory to Analytic Signals, by G.T. Deng and T. Qian,   accepted by Journal of Mathematical Analysis and Applications, Volume 389, Issue 1, 1 May 2012, Page 54–57.
  *86	[MQW] A Fast Adaptive Model Reduction Method Based on Takenaka-Malmquist Systems, by W. Mi, T. Qian and F. Wan, Systems & Control Letters. Volume 61, Issue 1, January 2012, Pages 223–230.

• 2011

  *85.	[YQ5] 实系数解析函数的零点集合，by Y. Yang and T. Qian, Acta Mathematica Sinica, 2011,31A(5):1160–1166.
  *84.	[QZL] Algorithm of Adaptive Fourier Decomposition, by Tao Qian, Liming Zhang, Zhixiong Li, IEEE Transactions on Signal Processing, Issue Date: Dec. 2011 Volume: 59 Issue:12 On page(s): 5899 – 5906.
  *83.	[DQ2] Analytic Phase Derivatives, All-Pass Filters and Signals of Minimum Phase, by P. Dang and T. Qian, IEEE Transactions on Signal Processing, Issue Date: Oct. 2011, Volume: 59 Issue:10,  on page(s): 4708 – 4718.
  *82.	[LptLeongQ] A class of Fourier multipliers on starlike Lipschitz surfaces, P.T. Li and T. Qian,  Journal of Functional Analysis, Vol. 261, No. 6. (September 2011), pp. 1415-1445.
  *81.	[CZQ] Higher order boundary integral formula and integro-di®erential equation on Stein   Manifolds, by L.P. Chen, T.D. Zhong and Tao Qian, Complex Analysis and Operator Theory (6 July 2011), pp. 1-18. doi:10.1007/s11785-011-0164-z.
  *80.	[YQ6] Zeroes of Slice Monogenic Functions, by Y. Yang and T. Qian, Mathematical Methods in the Applied Sciences, Volume 34, Issue 11, pages 1398–1405, 30 July 2011.
  *79.	[QWe] Optimal Approximation by Blaschke Forms, by T. Qian and E. Wegert, Complex Variables and Elliptic Equations, preprint Available online: 20 Jun 2011, DOI: 10.1080/17476933.2011.557152.
  *78.	[QTW]Adaptive Decomposition by Weighted Inner Functions: A Generalization of Fourier Serie, by T. Qian, L.H. Tan and Y.B. Wang,accepted to be published in J. Fourier Anal. Appl. 17 (2011), no. 2, 175–190.

• 2010

  *77.	[YQ4] On sets of zeros of Clifford-algebra-valued polynomials, by Y.Yang and T. Qian, Acta Math. Sci. Ser. B Engl. Ed. 30(2010), no.3, 1004-1012.
  *76.	[QWa1] Adaptive Decomposition Into Basic Signals of Non-negative Instantaneous Frequencies - A Variation and Realization of Greedy Algorithm, by T. Qian and Y. B. Wang, Adv. Comput. Math. 34 (2011), no. 3, 279–293.
  *75.	[ZLQ] Fixed trace \beta-Hermite ensembles: Asymptotic Eigenvalue Density and the Edge of the Density, by D.S. Zhou, D.Z. Liu and T. Qian, J. Math. Phys. 51(2010), no. 3, 033301, 19pp. DOI: 10.1063/1.3321578.
  *74.	[Q21] Intrinsic mono-component decomposition of functions: An advance of Fourier theory, by T. Qian, Mathematical Methods in Applied Sciences, 2010, 33, 880-891, DOI: 10.1002/mma.1214.
  *73.	[QWXZ] Orthonormal Bases with Nonlinear Phases, by T. Qian, R. Wang, Y. S. Xu and H. Z. Zhang, Advances in Computational Mathematics (AiCM ), Volume 33, Number 1 / July, 2010,  page 75-95, DOI: 10.1007/s10444-009-9120-0.

• 2009

  *72.	[LLQ] Discrete-Time Analytic Signals and Bedrosian Product Theorems, H. Li, L.Q. Li and T. Qian, Digital Signal Processing 20 (2010) 982–990, DOI:10.1016/j.dsp.2009.11.002.
  *71.	[QWD] Adaptive Decomposition Into Mono-Components, by T. Qian, Y. B. Wang and P. Dang, Advances in Adaptive Data Analysis, DOI No: 10.1142/S1793536909000278.
  *70.	[QHLW] Adaptive decomposition of functions into pieces of non-negative instantaneous frequencies, by T. Qian, I. T. Ho, I. T. Leong, Y. B. Wang, International Journal of Wavelets, Multiresolution and Information Processing, 8 (2010), no. 5, 813–833.(printed in sep 2010) .
  *69.	[DQY] Hardy-Sobolev spaces decomposition and applications in signal analysis, byP. Dang, T. Qian and Z. You, J. Fourier Anal. Appl. 17 (2011), no. 1, 36–64.
  *68.	[CQ] Sampling theorem and multi-scale spectrum based on Fourier atom, by Q. H. Chen and T. Qian, Applicable Analysis,  DOI: 10.1080/00036810903042240.
  *67.	[AKQ] Hilbert transforms and the Cauchy integral in Euclidean space, by A. Axelsson, K. I. Kou and T. Qian,  Studia Mathematica, 193（2），161-187，（2009.
  *66.	[GLQ] Two Integral Operators In Clifford Analysis, by Y. F Gong, I. T Leong and T. Qian,  J. Math. Anal. Appl. 354  (2009)  435–444.  DOI:10.1016/j.jmaa.2008.12.021.
  *65.	[QY] Hilbert Transforms on the Sphere With the Clifford Algebra Setting, by T. Qian and Y. Yang, Journal of Fourier Analysis and Applications,  (2009) 15: 753-774. DOI: 10.1007/s00041-009-9062-4.
  *64.	[QXYYY] Fourier Spectrum Characterization of Hardy Spaces and Applications, by T. Qian, Y. S. Xu, D. Y. Yan, L. X. Yan and B. Yu, Proceedings of the American Mathematical Society, Volume 137, Number 3, March 2009, page 971-980. DOI:10.1090/S0002-9939-08-09544-0.
  *63.	[Q20] Boundary Derivatives of the Phases of Inner and Outer Functions and Applications , by T. Qian, Mathematical Methods in the Applied Sciences (Math. Meth.Appl.Sci.,or Zeitschrift für Analysis and ihre Anwendungen) 2009; 32:253-263. DOI:10.1002/mma.1032.
  *62.	[FQ4] Pointwise convergence for expansions in spherical monigenics, by M. G. Fei and T. Qian, Acta Mathematica Scientia. 2009, 29B(5):1241-1250. DOI:10.1016/S0252-9602(09)60101-6.
  *61.	[FQ3] A note on pointwise convergence for expansions in surface harmonics of higher dimensional Euclidean spaces, by M. G. Fei and T. Qian, Taiwanese Journal of Mathematics June Issue of 2009.

• 2008

  *60.	[LPQ2] Cauchy integrals on Lipschitz surfaces in the octonionic space, by X. M. Li, L. Z. Peng and T. Qian, Math. Anal. Appl. 343(2008), 763-777. DOI:10.1016/j.jmaa.2008.01.079.
  *59.	[LPQ1] The Paley-Wiener Theorem in the non-commutative and non-associative octonions, by X. M. Li, L. Z. Peng and T. Qian, 中國科學 A輯 第38卷第6期, (2008) (English version has also appeared).
  *58.	[QZL] Mono-components vs. IMFs in signal decomposition, by T. Qian, L. M. Zhang and H. Li, International Journal of Wavelets, Multiresolution and Information Processing. Vol. 6, No. 3 (May 2008), 353-374. DOI:10.1142/S0219691308002392.

• 2007

  57.	[DQ] Half Dirichlet problems and decomposition of Posson kernels, by R. Delanghe and T. Qian, 17 (2007), 383-393, Advances in Applied Clifford Algebra. DOI:10.1007/s00006-007-0045-8.
  56.	[YQ3] Co-dimension-p Shannon sampling theorems, by Y. Yang and T. Qian, Complex Variables and Elliptic Equations, 52(1), 2007, 9-20. DOI:10.1080/17476930600784935.
  55.	[KQS2] Sampling in Bessel functions, by K. I. Kou, T. Qian and F. Sommen, Advances in applied Clifford Algebra, 17(3), 2007, 519-536. DOI:10.1007/s00006-007-0046-7.
  *54.	[ZQZ] Radon measure formulation for edge detection using rotational wavelets, by L. M. Zhang, T. Qian and Q. Y. Zeng, Communication on Pure and Applied Analysis , Vol 6, No. 3 (Sept, 2007). 899-915.
  *53.	[YQS] Co-dimension-p Paley-Wiener Theorem, by Y. Yang, T. Qian and F. Sommen, Ark. Mat., 45 (2007) 179-196. DOI:10.1007/s11512-006-0040-7.

• 2006

  *52.	[FQ2] Clifford algebra approach to pointwise convergence of Fourier series on spheres, by M. G.  Fei and T. Qian, Sciences of China, 49(11), 2006, 1553-1575. DOI:10.1007/s11425-006-2053-x.
  51.	[YQ2] Schwarz Lemma in Euclidean spaces, by Y. Yang and T. Qian, Complex Variables and Elliptic Equations, Vol. 51, No.7, July, 2006, 653-659. DOI:10.1080/17476930600688623.
  50.	[PQS] Generalizations of Fueter's theorem, by D. P. Peña, T. Qian and F. Sommen, Complex Var. Elliptic Equ. 51 (2006), no. 8-11, 913--922. DOI:10.1007/s00025-006-0226-0.
  *49.	[CLQ2] Two families of analytic signals with non-linear phase, by Q. H. Chen, L. Q. Li and T. Qian, Physica-D: Non-linear Phenomena, Vol. 221, 1-12, 2006. DOI:10.1016/j.physd.2006.06.013
  *48.	[FQ1] Direct Sum Decomposition of L^2(R^n_1) into Subspaces Invariant Under Fourier Transformation, by M. G. Fei and T. Qian, The Journal of Fourier Analysis and Applications, Volume 12, Issue 2, 2006, 145-155.
  *47.	[QC] Characterization of Analytic Phase Signals, by T. Qian and Q. H. Chen, Computers & Mathematics with Applications, Volume 51, 1471-1482, 2006. DOI:10.1016/j.camwa.2006.01.007
  46.	[YQ1] An elementary proof of Paley-Wiener Theorem in C^n using Clifford algebra, by Y. Yang and T. Qian, Complex Variables and Elliptic Equations, volume 51, number 5-6, 599-609. DOI: 10.1080/17476930500483224.
  *45.	[Q19] Mono-components for decomposition of signals, T. Qian, Mathematical Methods in the Applied Sciences (Zeitschrift für Analysis and ihre Anwendungen), 2006;29:1187-1198.
  *44.	[Q17] Analytic Signals and Harmonic Measures, T. Qian, J. Math. Anal. Appl. 314 (2006) 526-536. DOI:10.1016/j.jmaa.2005.04.003.

• 2005

  *43.	[CLQ1] Stability of frames generalized by nonlinearatoms, by Q. H. Chen, L. Q. Li and T. Qian, International Journal of Wavelets, Multiresolutionand Information Processing, Vol. 3, No. 4 (December 2005) 465-476.
  42.	[Q18] Characterization of boundary values of functions in Hardy spaces with applications in signal analysis, by T. Qian, Journal of Integral Equations and Applications, Volume 17, Number 2, Summer 2005, pp 159-198.
  *41.	[QCL] Analytic unit quadrature signals with non-linear phase, by T. Qian, Q. H. Chen and L.Q.  Li, Physica D: Nonlinear Phenomena, 303 (2005), 80-87. DOI:10.1016/j.physd.2005.03.005.
  *40.	[KQ3] Shannon Sampling in the Clifford Analysis Setting, by K.I.Kou and T. Qian, J. Math Anal. Appl., 24 No. 4, 825-842, (2005).
  *39.	[KQ2] Shannon sampling and estimation of band-limited functions in the several complex variables setting, by K.I.Kou and T. Qian, Acta Mathematica Scientia, 25(4), 2005, 741-754.

• 2004

  38.	[GQD] The structure of solutions of polynomial Dirac equations in Clifford analysis, by Y. F. Gong, T. Qian and J. Y. Du, Complex Variables, vol. 49, No. 1, pp. 15-24, 15 January2004. DOI: 10.1080/02781070310001634593

• 2003

  *37.	[QS] Deriving harmonic functions in higher dimensional spaces, by T. Qian and F. Sommen, Zeitschrift für Analysis and ihre Anwendungen (Mathematical Methods in the Applied Sciences), Vol 22 (2003)2, 275-288.

• 2002

  *36.	[KQS1] Generalizations of Fueter's Theorem, by K. I. Kou, T. Qian and F. Sommen, Method and   Applications of Analysis, Vol. 9, No.2, pp. 273-290, June 2002. DOI: 10.1007/s00025-006-0226-0.
  *35.	[KQ1] The Paley-Wiener theorem in Rn with the Clifford analysis setting, by K. I. Kou and T. Qian, Journal of Functional Analysis, 189 227-241 (2002). DOI:10.1006/jfan.2001.3848.
  *34.	[Q16] Calderon-type reproducing formulae on Lipschitz curves and surfaces, by T. Qian, J. Austral. Math. Soc.  72 (2002),33-45. DOI:10.1017/S1446788700003566.
  33.	[QZ3] Hadamard principal value of higher order singularintegrals, by T. Qian and T. D. Zhong, The Chinese Annals of Mathematics, 23A: 2 (2002), 205-212.

• 2001

  *32.	[Q15] Fourier analysis on starlike Lipschitz surfaces, by T. Qian, Journal of Functional Analysis, 183, 370-412 (2001). DOI:10.1006/jfan.2001.3750.
  31.	[QY] The Schwarzian derivative in $\Bbb R^n$, by T. Qian, and Q. H. Yu, Adv. Appl. Clifford Algebras 11 (2001), no. S2, 257--268.
  *30.	[QZ2] The differential integral equations on smooth closedorientable manifolds, by T. Qian and T. D. Zhong, Acta Mathematica Sinica, 2001, vol 21, Series B, No.1, 1-8.

• 2000

  *29.	[QZ] Transformation formula of higher order singularintegrals on the complex hypersphere, by T. Qian and T. D. Zhong, Austral Math. Soc.,vol. 68, Part 2 (April 2000), 152-164. DOI:10.1017/S1446788700001919.
  *28.	[JQ] Poisson kernel of a degenerate elliptic equation,by X. H. Ji and T. Qian, Zeitschrift für Analysis and ihre Anwendungen (Mathematical Methods in the Applied Sciences),Vol. 23 (2000), pp 71-80. DOI:10.1023/A:1008670032431.

• 1999

  27.	[CQ] A class of singular integralson the n-complex unit sphere, by M. Cowling and T. Qian, Scientia Sinica (Series A), vol 42, No.12 (December 1999), 1233-1245.

• 1998

  26.	[LQ] Clifford martingale Phi-equivalence between S(f) and f* , by R. L. Long and T. Qian, Advances inApplied Clifford Algebras 8 No.1, 95-107 (1998). A Chinese summary appears in Chinese Ann. Math. Ser. A 15 (1994), no. 6, 744. Chinese Ann. Math. Ser. B 15 (1994), no. 4, 507--516.
  *25.	[Q14] Singular integrals on star-shaped Lipschitz surfaces in the quaternionicspace, by T. Qian, Mathematische Annalen, 310 (4) (April, 1998),601-630.

• 1997

  24.	[Q13] Generalization of Fueter's result to R^{n+1}, by T. Qian, Rend. Mat. Acc. Lincei, s.9, v.8 (1997) 111-117.
  23.	[Q12] A holomorphic extension result, by T. Qian, Complex Variables, vol 32(1)(1997), 59-77.
  *22.	[Q11] Singular integrals with holomorphic kernels and Fourier multipliers on star-shape Lipschitz curves, by T. Qian, Studia Mathematica, 123(3) (1997),195-216.

• 1996

  21.	[GQW] Boundedness of singular integrals with holomorphic kernels on star-shaped closed Lipschitz curves, by G. Gaudry, T. Qian and S. L. Wang, Colloq. Math, Vol.LXX (1996),133-150.
  *20.	[QR] Conformal transformations and Hardy spaces arising in Clifford analysis, by T. Qian and J. Ryan, Journal of Operator Theory, 35 1996, 349-372.

• 1994

  *19.	[GQ] Homogeneous even kernels on surfaces, by G. I. Gaudry and T. Qian, Mathematische Zeitschrift  216 (1994), 169-177. DOI:10.1007/BF02572315.
  *18.	[LMQ] Clifford algebras, Fourier transforms, and singularConvolution operators on Lipschitz surfaces, by  C. Li , A. McIntosh and T. Qian , Revista Matematica Iberoamericana, 10 No.3 (1994), 665-695.
  *17.	[QP] Möbius covariance of iterated Dirac operators, by J. Peetre and T. Qian, J. Austral Math. Soc. (Series A) 56 (1994), 1-12.

• 1993 *16.

  *16.	[GLQ] A Martingale proof of L2-boundedness of Clifford-Valued Singular Integrals, by G. I. Gaudry, R. Long and T. Qian,Annali di Mathematica Pura Ed Applicata, vol. 165 (1993), 369-394. DOI:10.1007/BF01765857.

• 1992

  *15.	[GQS] Singular Integrals related to the Laplacian on the affine group ax+b, 1, by G. Gaudry T. Qian and P. Sjögren, Arkiv for matematik, Vol. 30 (1992) No 2, 259--281. DOI: 10.1007/BF02384874.
  *14.	[McQ2] Lp Fourier multipliers along Lipschitz curves, by A. McIntosh and T. Qian, Transactions of The American Mathematical Society, Volume 333, Number 1, September (1992), 157--176.

• 1990

  13.	[McQ1] A note on singular integralsalong Lipschitz curves with holomorphic kernels, by A. McIntosh and T. Qian, Approximation Theory and its Applications, No. 4,vol. 6 (1990) 40--57. DOI:10.1007/BF02836307.

• 1989

  *12.	[PQ] A kind of multilinear operators and the Schatten-von Neumannclasses, by L. Z. Peng and T.  Qian, Arkiv for Mat. 27, (1989), 145--154. DOI:10.1007/BF02386367.

• 1987

  11.	[Q10] BMO boundedness of a certain class of operators, by T. Qian, Research and Reviews in Math., vol.7 no.2, May (1987), 331--332.

• 1986

  *10.	[Q9] BMO boundedness of maximal operators, by T. Qian,  Acta Math. Sinica, vol. 29 no.3, (1986), 317—322.
  *9.	[QL] Pointwise estimates for a class of singular integrals and higher commutators, by T. Qian and C. Li, Acta Math. Sinica, new series (1986), Vol. 2 no.3, 248—259. DOI: 10.1007/BF02582027.
  8.	[Q8] Weighted inequalities concerning the Radon measures of the arc-length of curves on the complex plane, by T. Qian, Journal of SystemsScience and Mathematical Science, vol. 6, no.2, (1986), 146—153.

• 1985

  *7.	[Q7] Commutators of multiplier operators, by T. Qian, Chin. Ann. of Math, 6B (4) (1985), 401—408.
  6.	[Q6] Kakeya needle problem, by T. Qian, Maths in Practice and Theory, no. 3 (1985), 64—67.
  *5.	[Q5] Higher Commutators of pseudo-differential operators, by T. Qian, Chin. Ann. of Math, 6B(2) (1985), 229—240.
  4.	[Q4] Commutators of homogeneous multiplier operators, by T. Qian, ScientiaSinica, vol. XXVIII no.3, March (1985), 225—234.

• 1984

  3.	[Q3] On estimate for a multilinear singular  integral, by T. Qian Scientia Sinica, vol. XXVII, no.11, Nov. (1984), 1143--1154 .
  2.	[Q2] The preservation of the Lipschitz spaces under several maximal operators, by T. Qian, Kexue Tongbao, vol. 29, no.4, April (1984), 443—447.

• 1983

  1.	[Q1] Lip boundedness of some maximal operators defined on ${\scr H}$-families of sets. by T. Qian, (Chinese) Kexue Tongbao (Chinese) 28 (1983), no. 21, 1285--1288.

• 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, accepted to appear in 2012

• 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.

• 2013

  10.

  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 Perturbations,  Advances 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.

• 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.

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

Faculty of Science and Technology
University of Macau
Av. Padre Tomás Pereira, Taipa,
Macau, China (中國澳門氹仔徐日昇寅公馬路)

Room: B2-A402
Telephone: (853) 8397-8547
Fax: (853) 28838314
Email: fsttq, tqian1958@gmail.com