Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperplane mass equipartition problem and the shielding functions of
  Ramos   We give a proof of the result of Edgar Ramos which claims that two finite,
continuous Borel measures $\mu_1$ and $\mu_2$ defined on $\mathbb{R}^5$ admit
an equipartition by a collection of three hyperplanes. Our proof illuminates
one of the central methods developed and used in our earlier papers and may
serve as a good `test case' for addressing (and resolving) the `issues' raised
in the paper "Topology of the Gr\"unbaum-Hadwiger-Ramos hyperplane mass
partition problem", arXiv:1502.02975 [math.AT]. We also offer a
degree-theoretic interpretation of the `parity calculation method' developed by
Ramos and demonstrate that, up to minor corrections or modifications, it
remains a rigorous and powerful tool for proving results about mass
equipartitions.

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The categories of this paper are: physics
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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: ao-sci
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The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: astro-ph