Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A four--dimensional Neumann ovaloid   What is the shape of a uniformly massive object that generates a
gravitational potential equivalent to that of two equal point-masses? If the
weight of each point-mass is sufficiently small compared to the distance
between the points then the answer is a pair of balls of equal radius, one
centered at each of the two points, but otherwise it is a certain domain of
revolution about the axis passing through the two points. The existence and
uniqueness of such a domain is known, but an explicit parameterization is known
only in the plane where the region is referred to as a Neumann oval. We
construct a four-dimensional "Neumann ovaloid", solving explicitly this inverse
potential problem.

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The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
18
The categories of this paper are: econ
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The categories of this paper are: quant-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph