# Mathematical Research

## Research Interest

Analysis, generalized integral transforms in Banach spaces, and differential equations

## Further Information

- An adjunct professor at the Department of Mathematical and Statistical Sciences, the University of Alberta (2001-2006)
- Dr. B. Fisher (Leicester University, England) visited me for two weeks in 1996 (partially supported by the University of Regina). This visit resulted in one joint paper
- An Honorary Research Associate in the School of Graduate Studies at the University of New Brunswick and a member of comprehensive examination committee of Ph.D. students in 1998 and was responsible for the analysis exam
- I have refereed for the following journals.
- Publicationes Mathematicae Debrecen (Hungary)
- Applied Mathematics Letters
- Indian Journal of Pure and Applied Mathematics
- Acta Mathematica Sinica (China)
- Thai Journal of Mathematics
- Center European Mathematics Journal
- The Journal of Analysis (India)
- Journal of Mathematical Analysis and Applications
- Opsearch
- Boletin de la Sociedad Matematica Mexicana
- Pertanika Journal of Science and Technology, and
- International Journal of Mathematics and Mathematical Science
- Abstract and Applied Mathematics

- In July of 2000, I was invited by the organizing committee of the “International Conference on Mathematics and Its Applications in New Millennium” (organized by University of Putra Malaysia) and presented a talk on “A new product of distributions in m variables” and I also served as the chairperson of a session
- I was invited to attend an international conference in Kiev (Ukraine) in May of 2002, where I gave a plenary speech at the conference and presented a research talk on Hankel Transforms in Banach spaces at the functional analysis section
- I was invited to attend the South-North meeting at the University of Alberta in April, 2002
- I supervised two full-time research students at Cape Breton University for their undergraduate projects in the summer of 2000
- I supervised two full-time research students at the University of Alberta (Augustana) for their undergraduate projects in the summers of 2001 and 2002
- I supervised two NSERC undergraduate summer students in 2003 and 2004 on the topics of average-case messy broadcasting
- I supervised two NSERC undergraduate summer students in 2005 and one research student in the summer of 2006 on the topics of analysis
- I accepted a visiting scholar (Vincent Zou) who was supported by the Chinese Government and worked with me from August to December 2003. We had one joint paper published
- I was invited to attend the CMS meeting at the University of Alberta in June 2003 and presented a talk in real analysis section. I also attended the international congress MASSEE 2003 at Borovets, Bulgaria and presented a talk in the section of special functions and integral transforms
- I delivered guest lectures at Nanjing Xiaozhuang University and Nanjing University of Finance and Economics on my research in both mathematics and computer science in June 2004. I also presented three research seminars at the department in 2003 and 2004 and introduced theory of distributions to the departmental members from January to March 2005.
- I was invited to the Universidad Nacional del Centro (Argentina) by Professor Manuel Aguirre and gave a series of talks on the theory of distributions and Hankel transforms in December 2004 and 2008 (partially supported by Aguirre’s University), and worked on the products of distributions with Dr. Aguirre. These collaborations generated several joint papers.
- I was invited to the International Symposium on Analytic Function Theory, Fractional Calculus and Their applications in Honour of Professor H.M. Srivastava on his 65th Birth Anniversary (August 22-27, 2005) at the University of Victoria and presented a talk on the product of particular distributions, and chaired a session.
- I was invited to the International Symposium on Mathematical Methods in Engineering in Ankara (April 27-29, 2006) and presented a talk on the product of distributions by the Laurent series, and chaired an opening plenary speech.
- Dr. M. Aguirre visited me in the summer of 2006. This visit resulted in one joint paper.
- I was invited to have a research visit at Hacettepe University in Ankara, Turkey from September 14 to 30, 2007, which is mainly supported by the Turkish Government Research Fund.
- During my visit, I presented a talk on the Review of Products of Distributions and worked with a couple of co-researchers and one Ph.D. student in distribution theory.
- Conference Presentation: “A review of products of distributions”, Inaugural Annual Meeting of the Prairie Network for Research in Mathematical Sciences, May 3-4 (2007), Regina, Canada.
- I have been a member of the Organizing Committee of the Prairie Network for Research in Mathematical Sciences since 2007, As the chair of the local committee, I organized the Second Annual Conference of the Prairie Network for Research in Mathematical Sciences and the Student Workshop held in Brandon University (May 7-9, 2008), which were supported by the Fields Institute, the Pacific Institute for Mathematical Sciences and the Canadian Mathematical Society.
- I was invited to the Mitacs/IIMS Interactive Media workshop held in Winnipeg October 27-28, 2008.
- Our group solved a problem called “Illusion of 3D” that arose from the Complex Games Inc using algorithm analysis and designs.
- Conference Presentation: “A kernel theorem from the Hankel transform in Banach spaces”, Second Annual Conference of the Prairie Network for Research in Mathematical Sciences, May 7-9 (2008), Brandon, Canada.
- Conference Presentation: “The products of distributions on manifolds and invariant theorem” International Conference on Generalized Functions, August 31-September 4 (2009), Vienna, Austria.
- Conference Presentation: “The distributional products on spheres and Pizzetti’s formula”, Third Annual Meeting of the Prairie Network for Research in Mathematical Sciences, April 29-May 1 (2009), Saskatoon, Canada.

## Publications or Accepted

1. Chenkuan Li and Manuel Aguirre, The distributional products on spheres and Pizzetti’s formula, Journal of Computational and Applied Mathematics, 235 (2011), 1482-1489.

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2. Chenkuan Li, Several products of distributions on manifolds, Novi Sad Journal of Mathematics, 39 (2009), 31-46.

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3. Chenkuan Li, The Hankel convolution of arbitrary order, International Journal of Pure and Applied Mathematics, 55 (2009), 247-256.

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4. Chenkuan Li, The products of distributions on manifolds and invariant theorem, Journal of Analysis and Applications, 6 (2008), 77-95.

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5. Chenkuan Li, Thomas E. Hart, Kevin J. Henry and Ian A. Neufeld, Average-case messy broadcasting, Journal of Interconnection Networks, 19 (2008), 487-505.

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6. Chenkuan Li, Yang Zhang, Manuel Aguirre and Ricky Tang, The product of analytic functionals in Z’, Journal of Korean Mathematical Society, 45 (2008), 455-466.

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7. Chenkuan Li, Several results on the commutative neutrix product of distributions, Integral transforms and Special Functions, 18 (2007), 559-568.

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8. Chenkuan Li, A review on the products of distributions, Mathematical Methods in Engineering, Springer (2007), 71 – 96.

9. Manuel Aguirre and Chenkuan Li, The distributional products of particular distributions, Applied Mathematics and Computation, 187 (2007), 20-26.

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10. Chenkuan Li and Manuel Aguirre, The distributional products by the Laurent series, Thai Journal of Mathematics, 4 (2006), 305-319.

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11. Chenkuan Li, The products on the unit sphere and even-dimension spaces, Journal of Mathematical Analysis and Applications, Number 305 (2005), 97 – 106.

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12. Chenkuan Li, An approach for distributional products on Rm, Integral Transforms and Special Functions, Volume 16, Number 2 (2005), 139 – 151.

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13. Chenkuan Li, A kernel theorem from the Hankel transform in Banach spaces, Integral Transforms and Special Functions, Volume 16, Number 7 (2005), 565-581.

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14. Chenkuan Li and Vincent Zou, On defining the product r -k . l , International Journal of Mathematics and Mathematical Sciences, Number 16 (2004), 833 – 845.

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15.Chenkuan Li, On the Hankel transform, International Journal of Applied Mathematics, Volume 12, Number 4 (2003), 397 – 405.

16. Chenkuan Li, The neutrix square of , International Journal of Applied Mathematics, Volume 12, Number 2 (2003), 115 – 124.

17. Chenkuan Li, The sequential approach to the product of distributions, International Journal of Mathematics and Mathematical Sciences, Volume 28, Number 12 (2001), 743 – 751.

18. Brian Fisher and Chenkuan Li, On the Cosine and Sine Integrals, International Journal of Applied Mathematics, Volume 7, Number 4 (2001), 419 – 437.

19. Chenkuan Li, A new product of distribution in m variables, Proceedings of the “International Conference On Mathematics and Its Applications In The New Millennium”, 18 – 21 July 2000, organized by Department of Mathematics, University of Putra Malaysia, 38 – 51.

20. Chenkuan Li, A note on the product r -k . ( r2-m), Integral Transforms and Special Functions, Volume 12, Number 4 (2001), 341 – 348.

21. Chenkuan Li, The product of r -k and on Rm, International Journal of Mathematics and Mathematical Science, Volume 24, Number 6 (2000), 361 – 369.

22. Brian Fisher, Adem Kilicman and Chenkuan Li, An extension of a result on the non-commutative neutrix convolution product of distributions, International Journal of Applied Mathematics, Volume 3, Number 1 (2000), 71 – 80.

23. Chenkuan Li and E. L. Koh, The neutrix convolution product in Z'(m) and the exchange formula, IJMMS, Volume 21, July 1998, 695 – 700.

24. E. L. Koh and Chenkuan Li, The kernel theorem on the space [H x A; B], The Proceedings of the American Mathematical Society, Volume 123, January 1995, 177 – 182.

25. E. L. Koh and Chenkuan Li, The Hankel transformation on M’ and its Representation, The Proceedings of the American Mathematical Society, Volume 122, December 1994, 1085 – 1094.

26. E. L. Koh and Chenkuan Li, On the inverse of the Hankel Transform, Integral Transforms and Special Functions, Volume 2, Number 4 (1994), 279 – 282.

27. E. L. Koh and Chenkuan Li, The Hankel transformation of Banach-space-valued generalized functions, The Proceedings of the American Mathematical Society, Volume 119, September 1993, 153 – 163.

28. Brian Fisher and Chenkuan Li, A commutative neutrix convolution product of distributions, Review of Research, Volume 23, Number1 (1993), 13 – 27.

29. E. L. Koh and Chenkuan Li, On defending the generalized function (z), and n(x), IJMMS, Volume 16, Number 4 (1993), 749 – 754.

30. Linzhi Cheng and Chenkuan Li, The convolution of distributions, Mathematica Applicata, Volume 5, Number 4 (1992), 103 – 105.

31. E. L. Koh and Chenkuan Li, The complex Hankel Transformation on M’, Congrssus Numerantium, 87 (1992), Winnipeg, Canada, 145 – 151.

32. E. L. Koh and Chenkuan Li, On the distributions k and (‘)k, Math. Nachr. 157 (1992), 243 – 248.

33. Brian Fisher, Emin Ozcag and Chenkuan Li, A commutative neutrix convolution of distributions and exchange formula, Archivum Mathematicum (BRNO) Tomus 28 (1992), 187 – 197.

34. Linzhi Cheng and Chenkuan Li, A commutative product of distributions on Rm, Math. Nachr. 151 (1991), 345 – 355.

35. Brian Fisher and Chenkuan Li, On defending a non-commutative product of distributions in m variables, J. of Natural Sciences and Math., Volume 31, Number 2 (1991), 95 – 102.

36. Brian Fisher and Chenkuan Li, A non-commutative neutrix product of distributions on Rm, Review of Research, 21, 1(1991), 135 – 146.

37. Chenkuan Li and Brian Fisher, Examples of neutrix product of distributions on Rm, Rad. Math. Volume 6, Number 1 (1990), 129 – 137.

38. Brian Fisher, Chenkuan Li and Arpad Takaci, The neutrix convolution product in Z’ and exchange formula, Generalized functions and convergence (Katowice, 1988), 117 – 126. World Sci. Publishing, Teaneck, NJ, 1990.

39. Chenkuan Li and Brian Fisher, A product of distributions on a sphere, J. of Jiangsu Agricultural Institute (China), Volume 11, Number 2 (1990), 77 – 79.

40. Brian Fisher and Chenkuan Li, On the product of distributions in m variables, J. of Jiangsu Agricultural Institute, Volume 11, Number 4 (1990), 1 – 10.

41. Chenkuan Li, Power of Dirac distributions, J. Math. Res. Exposition, Volume 8, Number 4 (1988), 635 – 636.

42. Linzhi Cheng and Chenkuan Li, The product of generalized functions, J. Math. Res. Exposition, Volume 8, Number 4 (1988), 543 – 546.

43. Brian Fisher, Chenkuan Li and Arpad Takaci, The Fourier transform of distributions and exchange formulas, Mat. Vesink, Volume 40, Number 3 – 4 (1988), 209 – 216.