Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
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- 作者：Stefan Müller ; Elisenda Feliu…
- 关键词：Sign vector ; Restricted injectivity ; Power ; law kinetics ; Descartes’ rule of signs ; Oriented matroid ; 13P15 ; 12D10 ; 70K42 ; 37C10 ; 80A30 ; 52C40
- 刊名：Foundations of Computational Mathematics
- 出版年：2016
- 出版时间：February 2016
- 年：2016
- 卷：16
- 期：1
- 页码：69-97
- 全文大小：792 KB
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Elisenda Feliu (2)
Georg Regensburger (1)
Carsten Conradi (3)
Anne Shiu (4)
Alicia Dickenstein (5)
1. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstraße 69, 4040, Linz, Austria
2. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark
3. Max-Planck-Institut Dynamik komplexer technischer Systeme, Sandtorstr. 1, 39106, Magdeburg, Germany
4. Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX, 77843-3368, USA
5. Dto. de Matemática, FCEN, Universidad de Buenos Aires, and IMAS (UBA-CONICET), Ciudad Universitaria, Pab. I, C1428EGA, Buenos Aires, Argentina - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Numerical Analysis
Computer Science, general
Math Applications in Computer Science
Linear and Multilinear Algebras and Matrix Theory
Applications of Mathematics - 出版者：Springer New York
- ISSN：1615-3383
文摘
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. Keywords Sign vector Restricted injectivity Power-law kinetics Descartes’ rule of signs Oriented matroid