Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry
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Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry. / Müller, Stefan; Feliu, Elisenda; Regensburger, Georg; Conradi, Carsten; Shiu, Anne; Dickenstein, Alicia.
I: Foundations of Computational Mathematics, Bind 16, Nr. 1, 01.02.2016, s. 69-97.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry
AU - Müller, Stefan
AU - Feliu, Elisenda
AU - Regensburger, Georg
AU - Conradi, Carsten
AU - Shiu, Anne
AU - Dickenstein, Alicia
PY - 2016/2/1
Y1 - 2016/2/1
N2 - We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomials maps with arbitrary real exponents defined on the positive orthant. Our work relates and extends existing injectivity conditions expressed in terms of Jacobian matrices and determinants. In the context of chemical reaction networks with power-law kinetics, our results can be used to preclude as well as to guarantee multiple positive steady states. In the context of real algebraic geometry, our results reveal the first ...
AB - We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomials maps with arbitrary real exponents defined on the positive orthant. Our work relates and extends existing injectivity conditions expressed in terms of Jacobian matrices and determinants. In the context of chemical reaction networks with power-law kinetics, our results can be used to preclude as well as to guarantee multiple positive steady states. In the context of real algebraic geometry, our results reveal the first ...
KW - math.AG
KW - math.DS
U2 - 10.1007/s10208-014-9239-3
DO - 10.1007/s10208-014-9239-3
M3 - Journal article
VL - 16
SP - 69
EP - 97
JO - Foundations of Computational Mathematics
JF - Foundations of Computational Mathematics
SN - 1615-3375
IS - 1
ER -
ID: 94752755