SC 99-27 Karin Gatermann, Birkett Huber: A family of sparse polynomial systems arising in chemical
reaction systems
Abstract: We investigate a special sparse polynomial system arising
in the model of
mass action kinetics of chemical reaction systems.
The sparsity of the system is defined by a weighted
directed graph and
weighted bipartite graph. Feinberg has given some results
on the number of positive solutions for two special cases
of sparse systems. We explain is approach and give
alternative
proofs. Then we attack the general case with a new result
by Sturmfels from real algebraic geometry where the number
of
positive solutions is related to the alternating cells of
of mixed subdivision of the Newton polytopes.
Keywords: mass action kinetics,
sparse polynomial systems,
positive solutions
MSC: 68Q40, 14M25