Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry

Stefan Müller; Elisenda Feliu; Georg Regensburger; Carsten Conradi; Anne Shiu; Alicia Dickenstein

doi:10.1007/s10208-014-9239-3

Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry

Stefan Müller, Elisenda Feliu, Georg Regensburger, Carsten Conradi, Anne Shiu, Alicia Dickenstein

Institut for Matematiske Fag

55 Citationer (Scopus)

Abstract

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 partial multivariate generalization of the classical Descartes' rule, which bounds the number of positive real roots of a univariate real polynomial in terms of the number of sign variations of its coefficients.

Originalsprog	Engelsk
Tidsskrift	Foundations of Computational Mathematics
Vol/bind	16
Udgave nummer	1
Sider (fra-til)	69-97
Antal sider	29
ISSN	1615-3375
DOI	https://doi.org/10.1007/s10208-014-9239-3
Status	Udgivet - 1 feb. 2016

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math.AG
math.DS

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10.1007/s10208-014-9239-3

Citationsformater

Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry. / Müller, Stefan; Feliu, Elisenda; Regensburger, Georg et al.

I: Foundations of Computational Mathematics, Bind 16, Nr. 1, 01.02.2016, s. 69-97.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

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AU - Shiu, Anne

AU - Dickenstein, Alicia

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Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry

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