Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Verification of the Jacobian Conjecture for $d$-linear maps in two
  variables   For any integer $d \geq 1$, we verify the Jacobian Conjecture for a
$d$-linear map in two variables. We prove that almost all the coefficients of
the formal inverse are in the ideal specified by the Jacobian condition. We
find expressions for certain elements in terms of the generators of this ideal.
To obtain these expressions, we generalize a bijective proof of the
Cayley-Hamilton theorem in two ways.

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The categories of this paper are: math-ph
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The categories of this paper are: stat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org