Research

Pow-Wow, the Indian Boy

My current research interests are Mathematical Modeling of Biological Systems, Dynamical Systems, Symbolic Integration, Algebraic Methods in Differential Equations, Computer Algebra, Algorithmic Methods in Mathematics

Research Papers (PDF files available in the Papers link on the left or by request):

  1. Space/time evolutionary sthoichiometric model for the algae-daphnia ecosystem, K. Long, C. Dissanayake, A. Peace and L. Juan (in preparation)
  2. Differential Projective Modules and Azumaya Algebras over Differential Rings, with Andy Magid, under review.
  3. Fast Computation of Inverse Transcendental Functions of Polynomial Chaos Expansion Through Iterated Means, with Kevin Long and Kaleb Mackale, under review.
  4. Surjectivities, Octonions and Differential Galois Theory, with Arne Ledet, Comm. Algebra, DOI: 10.1080/00927872.2017.1281932
  5. Generic Picard-Vessiot extensions for nonconnected groups, with Arne Ledet, Comm. Algebra 44 (2016), no. 7, 2989--3004.
  6. Differential `Galois' extensions with new constants, with Andy Magid, Comptes Rendus Mathematique, French Academy of Sciences, to appear.
  7. Picard-Vessiot extensions with specified Galois Group, with Ted Chinburg and Andy Magid, Pacific Journal of Mathematics, 243 (2009), no. 2, 233-242.
  8. Differential central simple algebras and Picard-Vessiot representations, with Andy Magid, Proc. Amer. Math. Soc. 136 (2008), 1911-1918.
  9. On generic differential SOn-extensions, with Arne Ledet, Proc. Amer. Math. Soc. 136 (2008), 1145--1153.
  10. On Picard-Vessiot extensions with group PGL3, with Arne Ledet, Journal of Algebra, 318 (2007), no. 2, 786--793.
  11. Equivariant vector fields on non-trivial SOn-torsors and Differential Galois Theory, with Arne Ledet, Journal of Algebra, 316 (2007), no. 2, 735--745.
  12. Generic Picard-Vessiot extensions for connected-by-finite groups, Journal of Algebra, 312 (2007), no. 1, 194--206.
  13. Generic rings for Picard-Vessiot extensions and generic differential equations , with Andy Magid, Journal of Pure and Applied Algebra, 209 (2007), no. 3, 793--800.
  14. Pure Picard-Vessiot extensions with generic properties, Proceedings of the AMS, 132 (2004), no. 9, 2549--2556.
  15. Principal differential ideals and a generic inverse differential Galois problem for GLn, Communications in Algebra 30 (2002), no. 12, 6071--6103.
  16. Some results about symmetric semigroups, Comm. Algebra 21 (1993), no. 10, 3637--3645.