

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):

 Space/time evolutionary sthoichiometric model for the algaedaphnia ecosystem,
K. Long,
C. Dissanayake, A. Peace
and L. Juan (in preparation)
 Differential Projective Modules and Azumaya Algebras over
Differential Rings, with Andy Magid, under review.
 Fast Computation of Inverse Transcendental Functions of Polynomial Chaos Expansion Through Iterated Means, with Kevin Long and Kaleb Mackale, under review.
 Surjectivities, Octonions and Differential Galois Theory, with Arne Ledet, Comm. Algebra, DOI: 10.1080/00927872.2017.1281932
 Generic PicardVessiot extensions for nonconnected groups, with Arne Ledet, Comm. Algebra 44 (2016), no. 7, 29893004.
 Differential `Galois' extensions with new constants, with Andy Magid, Comptes Rendus Mathematique, French Academy of Sciences, to appear.
 PicardVessiot extensions with specified Galois Group, with Ted Chinburg and Andy Magid, Pacific Journal of Mathematics, 243 (2009), no. 2, 233242.
 Differential central simple algebras and PicardVessiot representations, with Andy Magid, Proc. Amer. Math. Soc. 136 (2008), 19111918.
 On generic differential SO_{n}extensions, with Arne
Ledet, Proc. Amer. Math. Soc. 136 (2008), 11451153.
 On PicardVessiot extensions with group PGL_{3}, with Arne Ledet, Journal of Algebra, 318 (2007), no. 2, 786793.
 Equivariant vector fields on nontrivial SO_{n}torsors and Differential Galois Theory, with Arne
Ledet, Journal of Algebra, 316 (2007), no. 2, 735745.
 Generic PicardVessiot
extensions for connectedbyfinite groups, Journal of Algebra, 312 (2007), no. 1, 194206.
 Generic rings for PicardVessiot
extensions and generic differential equations , with Andy Magid, Journal
of Pure and Applied Algebra, 209 (2007), no. 3, 793800.
 Pure PicardVessiot extensions with generic properties, Proceedings of the AMS,
132 (2004), no. 9, 25492556.
 Principal differential ideals and a generic inverse differential Galois
problem for GL_{n}, Communications in
Algebra 30 (2002), no. 12, 60716103.
 Some results about symmetric semigroups, Comm. Algebra 21 (1993), no. 10, 36373645.

