Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Modes of Polynomials Derived from Nondecreasing Sequences   Wang and Yeh proved that if $P(x)$ is a polynomial with nonnegative and
nondecreasing coefficients, then $P(x+d)$ is unimodal for any $d>0$. A mode of
a unimodal polynomial $f(x)=a_0+a_1x+\cdots + a_mx^m$ is an index $k$ such that
$a_k$ is the maximum coefficient. Suppose that $M_*(P,d)$ is the smallest mode
of $P(x+d)$, and $M^*(P,d)$ the greatest mode. Wang and Yeh conjectured that if
$d_2>d_1>0$, then $M_*(P,d_1)\geq M_*(P,d_2)$ and $M^*(P,d_1)\geq M^*(P,d_2)$.
We give a proof of this conjecture.

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The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int