Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On generalizing Descartes' rule of signs to hypersurfaces   We give partial generalizations of the classical Descartes' rule of signs to
multivariate polynomials (with real exponents), in the sense that we provide
upper bounds on the number of connected components of the complement of a
hypersurface in the positive orthant. In particular, we give conditions based
on the geometrical configuration of the exponents and the sign of the
coefficients that guarantee that the number of connected components where the
polynomial attains a negative value is at most one or two. Our results fully
cover the cases where such an upper bound provided by the univariate Descartes'
rule of signs is one. This approach opens a new route to generalize Descartes'
rule of signs to the multivariate case, differing from previous works that aim
at counting the number of positive solutions of a system of multivariate
polynomial equations.

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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci