Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomials nonnegative on the cylinder   In 2010, Marshall settled the strip conjecture, according to which every
polynomial in $\mathbb{R}[x,y]$, nonnegative on the strip
$[-1,1]\times\mathbb{R}$, is a sum of squares and of squares times $1-x^2$. We
consider affine nonsingular curves $C$ over $\mathbb{R}$ with $C(\mathbb{R})$
compact, and study the question whether every $f$ in $\mathbb{R}[C][y]$,
nonnegative on $C(\mathbb{R})\times\mathbb{R}$, is a sum of squares in
$\mathbb{R}[C][y]$. We give an affirmative answer under the condition that $f$
has only finitely many zeros in $C(\mathbb{R})\times\mathbb{R}$. For $C$ the
circle $x_1^2+x_2^2=1$, we prove the result unconditionally.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas