Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry

We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomial 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...

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Autor principal:	Dickenstein, Alicia Marcela
Publicado:	2016
Materias:	Descartes’ rule of signs Oriented matroid Power-law kinetics Restricted injectivity Sign vector Algebra Chemical reactions Geometry Jacobian matrices Reaction kinetics Descartes Injectivity Sign vectors Polynomials
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16153375_v16_n1_p69_Muller http://hdl.handle.net/20.500.12110/paper_16153375_v16_n1_p69_Muller
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_16153375_v16_n1_p69_Muller
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spelling	paper:paper_16153375_v16_n1_p69_Muller2023-06-08T16:25:22Z Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry Dickenstein, Alicia Marcela Descartes’ rule of signs Oriented matroid Power-law kinetics Restricted injectivity Sign vector Algebra Chemical reactions Geometry Jacobian matrices Reaction kinetics Descartes Injectivity Oriented matroid Power-law kinetics Sign vectors Polynomials We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomial 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 work recognizes a prior result of Craciun, Garcia-Puente, and Sottile, together with work of two of the authors, as 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. © 2015, SFoCM. Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16153375_v16_n1_p69_Muller http://hdl.handle.net/20.500.12110/paper_16153375_v16_n1_p69_Muller
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Descartes’ rule of signs Oriented matroid Power-law kinetics Restricted injectivity Sign vector Algebra Chemical reactions Geometry Jacobian matrices Reaction kinetics Descartes Injectivity Oriented matroid Power-law kinetics Sign vectors Polynomials
spellingShingle	Descartes’ rule of signs Oriented matroid Power-law kinetics Restricted injectivity Sign vector Algebra Chemical reactions Geometry Jacobian matrices Reaction kinetics Descartes Injectivity Oriented matroid Power-law kinetics Sign vectors Polynomials Dickenstein, Alicia Marcela Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
topic_facet	Descartes’ rule of signs Oriented matroid Power-law kinetics Restricted injectivity Sign vector Algebra Chemical reactions Geometry Jacobian matrices Reaction kinetics Descartes Injectivity Oriented matroid Power-law kinetics Sign vectors Polynomials
description	We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomial 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 work recognizes a prior result of Craciun, Garcia-Puente, and Sottile, together with work of two of the authors, as 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. © 2015, SFoCM.
author	Dickenstein, Alicia Marcela
author_facet	Dickenstein, Alicia Marcela
author_sort	Dickenstein, Alicia Marcela
title	Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
title_short	Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
title_full	Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
title_fullStr	Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
title_full_unstemmed	Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
title_sort	sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry
publishDate	2016
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16153375_v16_n1_p69_Muller http://hdl.handle.net/20.500.12110/paper_16153375_v16_n1_p69_Muller
work_keys_str_mv	AT dickensteinaliciamarcela signconditionsforinjectivityofgeneralizedpolynomialmapswithapplicationstochemicalreactionnetworksandrealalgebraicgeometry
_version_	1768544293642829824

Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry

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