Professor
Department of Mathematics and Computer Science
Distribution theory, generalized integral transforms in Banach spaces, and fractional calculus.
Fractional calculus is the theory of integrals and derivatives of arbitrary order, which unifies and generalizes integer-order differentiation and n-fold integration. The beginning of fractional calculus is considered to be Leibniz’s letter to L’Hospital in 1695, where the notation for differentiation of non-integer orders was discussed. I am currently working on fractional calculus of distributions and generalized integral equations.
Algorithm analysis and data networking.
Current studies of messy broadcasting have so far concentrated on finding worst-case times. However, such worst-case scenarios are extremely unlikely to occur in general. Hence, finding average-case times for completing messy broadcasting in various network topologies is both necessary and meaningful in practice. The area of my research is focused on seeking the average messy broadcast times of networks such as hypercubes, d-ary trees and complete graphs using randomized algorithms and probability theory. Furthermore, the approach I introduced for average-case time complexity can also be used to simplify the proofs of existing results of worst-case situations.
I have worked at the University of Regina, University of Lethbridge, University New Brunswick, Cape Breton University, University of Alberta (Augustana)
before joining Brandon University in the summer of 2002, and have taught a wide range of courses from Mathematics to Computer Science. Here are the courses I have done in Brandon:
70. Chenkuan Li and Joshua Beaudin, Uniqueness of Abel’s integral equations of the second kind with variable coefficients. Symmetry 2021, 13, 1064. https://doi.org/10.3390/sym13061064
69. Chenkuan Li, On the generalized fractional Laplacian (36 pages). Submitted.
68. Chenkuan Li, Uniqueness of the partial integro-differential equations. Accepted by Journal of Integral Equations and Applications in April 2021.
67. Chenkuan Li, On the nonlinear Hadamard-type integro-differential equation, Fixed Point Theory and Algorithms for Sciences and Engineering (2021) 2021:7
66. Chenkuan Li, Uniqueness of the Hadamard-type integral equations, Advances in Diﬀerence Equations (2021) 2021:40
65. Chenkuan Li, An example of the generalized fractional Laplacian, Contemporary Mathematics 1 (2020), 215-226. doi.org/10.37256/cm.142020489
64. Chenkuan Li and Joshua Beaudin, On the generalized Riesz derivative, Mathematics 2020, 8, 1089; doi:10.3390/math8071089
63. Chenkuan Li, The generalized Abel’s integral equations on R^n with variable coefficients, Fractional Differential Calculus 10, (2020), 129-140.
62. Chenkuan Li and Jianfei Huang, Remarks on the linear fractional integro-differential equation with variable coefficients in distribution, Fractional Differential Calculus 10, (2020), 57-77.
61. Chenkuan Li and Changpin Li, The Fractional Green’s Function by Babenko’s Approach, Tbilisi Mathematical Journal 13 (2020), 19-42.
60. Chenkuan Li and Hunter Plowman, Solutions of the Generalized Abel’s Integral Equations of the Second Kind with Variable Coefficients, Axioms 2019, 8, 137; doi:10.3390/axioms8040137
59. Chenkuan Li, Changpin Li, Thomas Humphries, and Hunter Plowman, Remarks on the generalized fractional Laplacian operator, Mathematics 2019, 7, 320; doi:10.3390/math7040320.
58. Chenkuan Li, Thomas Humphries, and Hunter Plowman, Solutions to Abel’s integral equations in distributions, Axioms 2018, 7(3), 66; doi:10.3390/axioms7030066.
57. Chenkuan Li, Changpin Li and Kyle Clarkson, Several Results of Fractional Differential and Integral Equations in Distribution, Mathematics 2018, 6, 97; doi:10.3390/math6060097
56. Chenkuan Li, The Convolution of Analytic Functionals, The Journal of Analysis, 78 (2018); doi.org/10.1007/s41478-018-0078-5
55. Chenkuan Li and Kyle Clarkson, Babenko’s Approach to Abel’s Integral Equations, Mathematics 2018, 6, 32; doi:10.3390/math6030032
54. Chenkuan Li and Kyle Clarkson, Remarks On the Convolutions and Fractional
Derivative of Distributions, Journal of Mathematics Research, 10 (2018), 6-19.
53. Chenkuan Li, Kyle Clarkson and Vrajna Patel, The Convolution and Fractional Derivative of Distributions, Advances in Analysis 3 (2018), 82-99.
52. Chenkuan Li, The Product and Fractional Derivative of
Analytic Functionals, International Journal of Mathematical Analysis, 11 (2017), 955-972.
51. Chenkuan Li, Changpin Li, Bailey Kacsmar, Roque Lacroix and Kyle Tilbury, The Abel integral equations in distribution, Advances in Analysis, 2 (2017), 88-104.
50. Chenkuan Li and Changpin Li, Remarks on fractional derivatives of distributions, Tbilisi Mathematical Journal, 10 (2017), 1-18.
49. Chenkuan Li, The powers of the Dirac delta function by Caputo fractional derivatives, Journal of Fractional Calculus and Applications (JFCA), 7 (2016), 12-23.
48. Chenkuan Li, Several results of fractional derivatives in D'(R_+), Fractional Calculus and Applied Analysis (FCAA), 18 (2015), 192-207.
47. Chenkuan Li and Changpin Li, On defining the distributions delta^k and delta’^k by fractional derivatives, Appl. Math. Comput., 246 (2014), 502-513.
46. Chenkuan Li, Asymptotic expressions of several distributions on the sphere, BJMCS, 3 (2013), 73-85.
45. Chenkuan Li, Several asymptotic products of particular distributions, BJMCS, 3 (2013), 291-303.
44. Chenkuan Li and Manuel Aguirre, The distributional products on spheres and Pizzetti’s formula, J. Comput. Appl. Math., 235 (2011), 1482-1489.
43. Chenkuan Li, An asymptotic product for $X^s \delta^{(k)}(r^2 – t^2)$, IJPAM, 72 (2011), 65-80.
42. Chenkuan Li, Several products of distributions on manifolds, NSJOM, 39 (2009), 31-46.
41. Chenkuan Li, The Hankel convolution of arbitrary order, IJPAM, 55 (2009), 247-256.
40. Chenkuan Li, The products of distributions on manifolds and invariant theorem, JAA, 6 (2008), 77-95.
39. Chenkuan Li, Thomas E. Hart, Kevin J. Henry and Ian A. Neufeld, Average-case messy broadcasting, JOIN, 19 (2008), 487-505.
38. Chenkuan Li, Yang Zhang, Manuel Aguirre and Ricky Tang, The product of analytic functionals in Z’, J. Korean Math. Soc., 45 (2008), 455-466.
37. Chenkuan Li, Several results on the commutative neutrix product of distributions, Integral transforms Spec. Funct., 18 (2007), 559-568.
36 Chenkuan Li and Manuel Aguirre, The distributional products by the Laurent series, Thai J. Math., 4 (2006), 305-319.
35. Chenkuan Li, The products on the unit sphere and even-dimension spaces, J. Math. Anal. Appl. 305 (2005), 97 – 106.
34. Chenkuan Li, An approach for distributional products on R^m, Integral Transforms Spec. Funct. 16 (2005), 139 – 151.
33. Chenkuan Li, A kernel theorem from the Hankel transform in Banach spaces, Integral Transforms Spec. Funct. 16 (2005), 565-581.
32. Chenkuan Li and Vincent Zou, On defining the product $r^{-k}.\nabla^l \delta$, IJMMS, 16 (2004), 833 – 845.
31.Chenkuan Li, On the Hankel transform, International Journal of Applied Mathematics, Volume 12, Number 4 (2003), 397 – 405.
30. Chenkuan Li, The neutrix square of $\delta$, International Journal of Applied Mathematics, Volume 12, Number 2 (2003), 115 – 124.
29. Chenkuan Li, The sequential approach to the product of distributions, IJMMS, 28 (2001), 743 – 751.
28. Brian Fisher and Chenkuan Li, On the Cosine and Sine Integrals, International Journal of Applied Mathematics, Volume 7, Number 4 (2001), 419 – 437.
27. Chenkuan Li, A note on the product $r^{-k} . \nabla(\triangle r^{2-m})$, Integral Transforms Spec. Funct. 12(2001), 341 – 348.
26. Chenkuan Li, The product of $r^{-k}$ and $\nabla\delta$ on R^m, IJMMS, 24 (2000), 361 – 369.
25. 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.
24. Chenkuan Li and E. L. Koh, The neutrix convolution product in Z'(m) and the exchange formula, IJMMS, 21 (1998), 695 – 700.
23. E. L. Koh and Chenkuan Li, The kernel theorem on the space [H x A; B], Proc. Amer. Math. Soc. 123 (1995), 177 – 182.
22. E. L. Koh and Chenkuan Li, The Hankel transformation on M’ and its Representation, Proc. Amer. Math. Soc. 122 (1994), 1085 – 1094.
21. 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.
20. E. L. Koh and Chenkuan Li, The Hankel transformation of Banach-space-valued generalized functions, Proc. Amer. Math. Soc. 119 (1993), 153 – 163.
19. Brian Fisher and Chenkuan Li, A commutative neutrix convolution product of distributions, Review of Research, 23 (1993), 13 – 27.
18. E. L. Koh and Chenkuan Li, On defending the generalized functions $\delta^{\alpha}(z)$ and $\delta^n(x)$, IJMMS, 16 (1993), 749 – 754.
17. Linzhi Cheng and Chenkuan Li, The convolution of distributions, Mathematica Applicata, Volume 5, Number 4 (1992), 103 – 105.
16. E. L. Koh and Chenkuan Li, On the distributions $(\delta’^k$ and $(\delta”)^k$, Math. Nachr. 157 (1992), 243 – 248.
15. Brian Fisher, Emin Ozcag and Chenkuan Li, A commutative neutrix convolution of distributions and exchange formula, Archivum Mathematicum (BRNO) Tomus 28 (1992),
187 – 197.
14. Linzhi Cheng and Chenkuan Li, A commutative neutrix product of distributions on R^m, Math. Nachr. 151 (1991), 345 – 355.
13. 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.
12. Brian Fisher and Chenkuan Li, A non-commutative neutrix product of distributions on R^m, Review of Research, 21 (1991), 135 – 146.
11. Chenkuan Li and Brian Fisher, Examples of neutrix product of distributions on Rm,
Rad. Math. Volume 6, Number 1 (1990), 129 – 137.
10. 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.
9. 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.
8. Chenkuan Li, Power of Dirac distributions, J. Math. Res. Exposition, 8 (1988), 635 – 636.
7. Linzhi Cheng and Chenkuan Li, The product of generalized functions, J. Math. Res. Exposition, 8 (1988), 543 – 546.
6. 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.
5. Chenkuan Li, A review on the products of distributions, Mathematical Methods in Engineering, Springer (2007), 71 – 96.
4. Manuel Aguirre and Chenkuan Li, The distributional products of particular distributions, Appl. Math. Comput., 187 (2007), 20-26.
3. 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.
2. E. L. Koh and Chenkuan Li, The complex Hankel Transformation on M’, Congrssus Numerantium, 87 (1992), Winnipeg, Canada, 145 – 151.
1. 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.
Dr. Chenkuan Li
Professor, Department of Mathematics and Computer Science
Room 1-78, Brodie Building
270-18th Street
Brandon, Manitoba
R7A 6A9
Phone: (204) 571-8549
E-mail: lic@brandonu.ca