Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The sum of squared logarithms inequality in arbitrary dimensions   We prove the \emph{sum of squared logarithms inequality} (SSLI) which states
that for nonnegative vectors $x, y \in \mathbb{R}^n$ whose elementary symmetric
polynomials satisfy $e_k(x)\le e_k(y)$ (for $1\le k < n$) and $e_n(x)=e_n(y)$,
the inequality $\sum_i (\log x_i)^2 \le \sum_i (\log y_i)^2$ holds. Our proof
of this inequality follows by a suitable extension to the complex plane. In
particular, we show that the function $f\colon M\subseteq \mathbb{C}^n\to
\mathbb{R}$ with $f(z)=\sum_i(\log z_i)^2$ has nonnegative partial derivatives
with respect to the elementary symmetric polynomials of $z$. This property
leads to our proof. We conclude by providing applications and wider connections
of the SSLI.

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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an