Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Descartes' rule of signs and moduli of roots   A hyperbolic polynomial (HP) is a real univariate polynomial with all roots
real. By Descartes' rule of signs a HP with all coefficients nonvanishing has
exactly $c$ positive and exactly $p$ negative roots counted with multiplicity,
where $c$ and $p$ are the numbers of sign changes and sign preservations in the
sequence of its coefficients. For $c=1$ and $2$, we discuss the question: When
the moduli of all the roots of a HP are arranged in the increasing order on the
real half-line, at which positions can be the moduli of its positive roots
depending on the positions of the sign changes in the sequence of coefficients?

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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph