Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Floating Bodies of Equilibrium at Density 1/2 in Arbitrary Dimensions   Bodies of density one half (of the fluid in which they are immersed) that can
float in all orientations are investigated. It is shown that expansions
starting from and deforming the (hyper)sphere are possible in arbitrary
dimensions and allow for a large manifold of solutions: One may either (i)
expand r(n)+r(-n) in powers of a given difference r(u)-r(-u), (r(n) denoting
the distance from the origin in direction n). Or (ii) the envelope of the water
planes (for fixed body and varying direction of gravitation) may be given.
Equivalently r(n) can be expanded in powers of the distance h(u) of the water
planes from the origin perpendicular to u.

18
The categories of this paper are: econ
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat