Publications - By Topic

Publications - By Topic

Hopf Algebras of Trees and Their Applications

Robert L Grossman and Richard G. Larson, Hopf Algebras of Heap Ordered Trees and Permutations, Communications in Algebra, 2008, to appear. Also arxiv.org/abs/0706.1327. Draft

Robert L. Grossman and Richard G. Larson, Differential Algebra Structures on Families of Trees, Advances in Applied Mathematics, Volume 35, pages 97-119, 2005. Draft

Robert L. Grossman and Richard G. Larson, Bialgebras and Realizations, in Hopf Algebras, Jeffrey Bergen, Stefan Catoiu, and William Chin, editors, Marcel Dekker, Inc., New York, 2004, pages 157-166. Draft

R. L. Grossman and R. G. Larson, An Algebraic Approach to Data Mining: Some Examples, Proceedings of the 2002 IEEE International Conference on Data Mining, IEEE Computer Society, Los Alamitos, California, 2002, pages 613-616. Draft

R. L. Grossman and M. Sweedler Hybrid Systems and Quantum Automata: Preliminary Announcement, Hybrid Systems II, P. Antsaklis, W. Kohn, A. Nerode, S. Sastry, editors, Springer Lecture Notes in Computer Science, Volume 999, pages 191-201, 1995. Draft

M. J. Doffou and R. L. Grossman, The Symbolic Computation of Differential Invariants of Polynomial Vector Field Systems Using Trees, Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation, A. H. M. Levelt, editor, ACM, 1995, pages 26-31. Draft

P. E. Crouch, R. Grossman, Y. Yan, On the numerical integration of the rolling ball equations using geometrically exact algorithms, Mechanics of Structures of Machines, 1994.

P. Crouch and R. Grossman, Numerical integration of ordinary differential equations on manifolds, Journal of Nonlinear Science, Volume 3, pages 1-33, 1993. Draft

R. L. Grossman and R. L. Larson, Some Remarks About Flows in Hybrid Systems, in R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, editors, Hybrid Systems, Lecture Notes in Computer Science, Volume 736, Springer-Verlag, New York, 1993, pp. 357-365.

Robert L. Grossman, Symbolic Computation and Flows of Differential Equations, Second Workshop on Computer Algebra, July 21, 1993, Rio de Janeiro.

R. Grossman and R. G. Larson, The realization of input-output maps using bialgebras, Forum Mathematicum, Volume 4, 1992, pages 109-121. Draft

R. Grossman and R. Larson, The symbolic computation of derivations using labeled trees, Journal of Symbolic Computation, Volume 13, pages 511-523, 1992. Draft

R. Grossman and D. Radford, A simple construction of bialgebra deformations, Contemporary Mathematics: Quantum Groups and Deformations, AMS, pp. 115-117, 1992. Draft

P.E. Crouch and R. L. Grossman, The Explicit Computation of Integration Algorithms and First Integrals for Ordinary Differential Equations With Polynomial Coefficients Using Trees, Proceedings of the 1992 International Symposium on Symbolic and Algebraic Computation, ACM Press, pp. 89-94. Draft

R. L. Grossman and R. G. Larson, Viewing hybrid systems as products of control systems and automata, Proceedings of the 31st IEEE Conference on Decision and Control, IEEE Press, 1992, pages 2953-2955. Draft

P.E. Crouch, R. Grossman, and Y. Yan, On the numeric integration of dynamic attitude equations, Proceedings of the 31st IEEE Conference on Decision and Control, IEEE Press, 1992, pages 1497-1501. Draft

R. Grossman, The evaluation of expressions involving higher order derivations, Journal of Mathematical Systems, Estimation, and Control, Volume 1, 1991, pages 91-106. Draft

R. Grossman, Using trees to compute approximate solutions of ordinary differential equations exactly, Differential Equations and Computer Algebra M. Singer, editor, Academic Press, New York, 1991, pp. 29-59. Draft

P. Crouch, R. Grossman, and R. G. Larson, Computations involving differential operators and their actions on functions, Proceedings of 1991 International Symposium on Symbolic and Algebraic Computation, ACM, 1991, pp. 301-307. Draft

R. Grossman and R. G. Larson, The symbolic computation of vector field expressions, Algebraic Computing in Control 1991, edited by G. Jacob and F. Lamnabhi-Lagarrigue, Springer-Verlag, Berlin, 1991, pp. 1-10. Draft

Robert L. Grossman and David Radford, Bialgebra Deformations of Certain Universal Enveloping Algebras, Laboratory for Advanced Computing Technical Report, University of Illinois at Chicago, 1991. Draft

R. Grossman and R. Larson, Hopf-algebraic structure of combinatorial objects and differential operators, Israel Journal Mathematics, Volume 72, 1990, pages 109-117. Draft

M. Grayson and R. Grossman, Models for free, nilpotent Lie algebras, Journal Algebra, Vol. 35, 1990, pages 177-191. Draft

R. Grossman and R. Larson, Solving nonlinear equations from higher order derivations in linear stages, Advances in Mathematics, Vol. 82, 1990, pages 180-202. Draft

R. Grossman and R. Larson, Hopf algebraic structures of families of trees, Journal Algebra, Vol. 26, 1989, pages 184-210. Draft

R. Grossman and R. Larson, Labeled trees and the algebra of differential operators, Graphs and Algorithms, Contemporary Mathematics, Volume 89, B. Richter, editor, American Mathematical Society, Providence, 1989, pages 81-87. Draft

M. Grayson and R. Grossman, Nilpotent Lie algebras and vector fields, Symbolic Computation: Applications to Scientific Computing, R. Grossman, editor, SIAM, Philadelphia, 1989, pages 77-96. Draft

R. Grossman and R. G. Larson, Labeled trees and the efficient computation of derivations, Proceedings of 1989 International Symposium on Symbolic and Algebraic Computation, ACM, 1989, pages 74-80. Draft

R. Grossman and R. Larson, The symbolic computation of higher order derivations: symmetries of expressions and actions of group algebras, Differential Geometry: The Interface Between Pure and Applied Mathematics, Contemporary Mathematics, 68, M. Luksic, C. Martin and W. Shadwick, editors, American Mathematical Society, Providence, 1987, pages 121-131.

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