Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Criteria for singularities of smooth maps from the plane into the plane
  and its applications   We shall give useful criteria of lips, beaks and swallowtail singularities of
smooth map from the plane into the plane. As an application of criteria, we
will discuss the singularities of Cauchy problem of single conservation law.

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The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom