Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Criteria for cuspidal S_k singularities and their applications   We give useful criteria for S_1 singularities in the Mond classification
table, and cuspidal S_k singularities. As applications, we give a simple proof
of a result given by Mond and a characterization of cuspidal S_k singularities
for the composition of a cuspidal edge and a fold map indicated by Arnol'd for
the case k=1.

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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: physics