Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposition of a Nonlinear Multivariate Function using the Heaviside
  Step Function   Whereas the Dirac delta function introduced by P. A. M. Dirac in 1930 in his
famous quantum mechanics text has been well studied, a not famous formula
related to the delta function using the Heaviside step function in a
single-variable form, also given in Dirac's text, has been poorly studied. We
demonstrate the decomposition of a nonlinear multivariate function into a sum
of integrals in which each integrand is composed of a derivative of the
function and a direct product of Heaviside step functions. It is an extension
of Dirac's single-variable form to that for multiple variables. Moreover, it
remains mathematically equivalent to the definition of the Dirac delta function
with multiple variables, and offers a mathematically unified expression.

28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin