Convex and toric geometry to analyze complex dynamics in chemical reaction systems [Elektronische Ressource] / vorgelegt von Anke Sensse

Convex and toric geometry to analyze complexdynamics in chemical reaction systemsDISSERTATIONzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)genehmigt durchdie Fakult at fur? Naturwissenschaftender Otto-von-Guericke-Universit at, Magdeburgvorgelegt von Dipl.-Biophys. Anke Senssegeb. am 14. April 1976 in Kronberg im TaunusGutachter: Prof. Dr. G. ErtlProf. Dr. R. FriedrichPD Dr. M. HauserEingereicht am: 25. Januar 2005Verteidigt am: 11. Juli 2005Dedicatedtothememoryof KARINGATERMANNTable 1: List of mathematical symbolsC field of complex numbersR field of real numbersZ ring of integer numbersC[x] ring of polynomials with coefficients in the field of complex numbersI idealdef;torI deformed toric idealV(I) variety of an idealdef;torV(I ) variety of a deformed toric varietyF family of polynomials depending on the parameters h; jh;jF family of polynomials with a certain sign pattern in the coefficientsP ND family of all matrices emerging from the matrix AAif it is multiplied by a positive definite diagonal matrixS family of all matrices having the same sign pattern as the matrix AAN stoichiometric matrixt th” stoichiometric coefficient of the i h-species in the j -reactionij0 th? ; ?