Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boolean representation of manifolds and functions   It is shown that a smooth n dimensional manifold with a boundary in R^n
admits a Boolean representation in terms of closed half spaces defined by the
tangent hyperplanes at the points on its boundary. A similar result is
established for smooth functions on closed convex domains in R^n. The latter
result is considered as a form of the Legendre transformation.

26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat