Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadratic Hyperbolicity Preservers & Multiplier Sequences   It is known (see \cite[Br\"and\'en, Lemma 2.7]{B10}) that a necessary
condition for $T:=\sum Q_k(x) D^k$ to be hyperbolicity preserving is that
$Q_k(x)$ and $Q_{k-1}(x)$ have interlacing zeros. We characterize all quadratic
linear operators, as a consequence we find several classes of $P_n$-multiplier
sequence.

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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys