Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Apparent Rate Constant for Diffusion-Controlled Three molecular
  (catalytic) reaction   We present simple explicit estimates for the apparent reaction rate constant
for three molecular reactions, which are important in catalysis. For small
concentrations and $d> 1$, the apparent reaction rate constant depends only on
the diffusion coefficients and sizes of the particles. For small concentrations
and $d\le 1$, it is also time -- dependent. For large concentrations, it gains
the dependence on concentrations.

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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
2
The categories of this paper are: math