Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof of a conjecture on unimodality   Let $P(x)$ be a polynomial of degree $m$, with nonnegative and non-decreasing
coefficients. We settle the conjecture that for any positive real number $d$,
the coefficients of $P(x+d)$ form a unimodal sequence, of which the special
case $d$ being a positive integer has already been asserted in a previous work.
Further, we explore the location of modes of $P(x+d)$ and present some
sufficient conditions on $m$ and $d$ for which $P(x+d)$ has the unique mode
$\lceil{m-d\over d+1}\rceil$.

27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ