Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
Abstract 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 det...
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Gespeichert in:
| Autor*in: |
Müller, Stefan [verfasserIn] Feliu, Elisenda [verfasserIn] Regensburger, Georg [verfasserIn] Conradi, Carsten [verfasserIn] Shiu, Anne [verfasserIn] Dickenstein, Alicia [verfasserIn] |
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E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Foundations of Computational Mathematics - Springer-Verlag, 2001, 16(2015), 1 vom: 06. Jan., Seite 69-97 |
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| Übergeordnetes Werk: |
volume:16 ; year:2015 ; number:1 ; day:06 ; month:01 ; pages:69-97 |
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| DOI / URN: |
10.1007/s10208-014-9239-3 |
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SPR009136835 |
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| 520 | |a Abstract 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. | ||
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10.1007/s10208-014-9239-3 doi (DE-627)SPR009136835 (SPR)s10208-014-9239-3-e DE-627 ger DE-627 rakwb eng Müller, Stefan verfasserin aut Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract 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. Sign vector (dpeaa)DE-He213 Restricted injectivity (dpeaa)DE-He213 Power-law kinetics (dpeaa)DE-He213 Descartes’ rule of signs (dpeaa)DE-He213 Oriented matroid (dpeaa)DE-He213 Feliu, Elisenda verfasserin aut Regensburger, Georg verfasserin aut Conradi, Carsten verfasserin aut Shiu, Anne verfasserin aut Dickenstein, Alicia verfasserin aut Enthalten in Foundations of Computational Mathematics Springer-Verlag, 2001 16(2015), 1 vom: 06. Jan., Seite 69-97 (DE-627)SPR009133062 nnns volume:16 year:2015 number:1 day:06 month:01 pages:69-97 https://dx.doi.org/10.1007/s10208-014-9239-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 16 2015 1 06 01 69-97 |
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10.1007/s10208-014-9239-3 doi (DE-627)SPR009136835 (SPR)s10208-014-9239-3-e DE-627 ger DE-627 rakwb eng Müller, Stefan verfasserin aut Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract 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. Sign vector (dpeaa)DE-He213 Restricted injectivity (dpeaa)DE-He213 Power-law kinetics (dpeaa)DE-He213 Descartes’ rule of signs (dpeaa)DE-He213 Oriented matroid (dpeaa)DE-He213 Feliu, Elisenda verfasserin aut Regensburger, Georg verfasserin aut Conradi, Carsten verfasserin aut Shiu, Anne verfasserin aut Dickenstein, Alicia verfasserin aut Enthalten in Foundations of Computational Mathematics Springer-Verlag, 2001 16(2015), 1 vom: 06. Jan., Seite 69-97 (DE-627)SPR009133062 nnns volume:16 year:2015 number:1 day:06 month:01 pages:69-97 https://dx.doi.org/10.1007/s10208-014-9239-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 16 2015 1 06 01 69-97 |
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Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry Sign vector (dpeaa)DE-He213 Restricted injectivity (dpeaa)DE-He213 Power-law kinetics (dpeaa)DE-He213 Descartes’ rule of signs (dpeaa)DE-He213 Oriented matroid (dpeaa)DE-He213 |
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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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Abstract 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. |
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Abstract 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. |
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Abstract 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. |
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| up_date |
2024-07-04T00:48:36.342Z |
| _version_ |
1803607465099526144 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR009136835</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20201124063530.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2015 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10208-014-9239-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR009136835</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10208-014-9239-3-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Müller, Stefan</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract 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.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sign vector</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Restricted injectivity</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Power-law kinetics</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Descartes’ rule of signs</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Oriented matroid</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Feliu, Elisenda</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Regensburger, Georg</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Conradi, Carsten</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Shiu, Anne</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Dickenstein, Alicia</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Foundations of Computational Mathematics</subfield><subfield code="d">Springer-Verlag, 2001</subfield><subfield code="g">16(2015), 1 vom: 06. 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7.3997917 |