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- W4299969686 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." @default.
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- W4299969686 date "2013-11-21" @default.
- W4299969686 modified "2023-10-04" @default.
- W4299969686 title "Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry" @default.
- W4299969686 doi "https://doi.org/10.48550/arxiv.1311.5493" @default.
- W4299969686 hasPublicationYear "2013" @default.
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