Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective Construction of a Positive Operator which does not admit
  Triangular Factorization   We have constructed a concrete example of a non-factorable positive operator.
As a result, for the well-known problems (Ringrose, Kadison and Singer
problems) we replace existence theorems by concrete examples.

9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics