Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lecture Notes: Non-Standard Approach to J.F. Colombeau's Theory of
  Generalized Function: University of Vienna, Austria, May 2006   In these lecture notes we present an introduction to non-standard analysis
especially written for the community of mathematicians, physicists and
engineers who do research on J. F. Colombeau' theory of new generalized
functions and its applications. The main purpose of our non-standard approach
to Colombeau' theory is the improvement of the properties of the scalars of the
varieties of spaces of generalized functions: in our non-standard approach the
sets of scalars of the functional spaces always form algebraically closed
non-archimedean Cantor complete fields. In contrast, the scalars of the
functional spaces in Colombeau's theory are rings with zero divisors. The
improvement of the scalars leads to other improvements and simplifications of
Colombeau's theory such as reducing the number of quantifiers and possibilities
for an axiomatization of the theory. Some of the algebras we construct in these
notes have already counterparts in Colombeau's theory, other seems to be
without counterpart. We present applications of the theory to PDE and
mathematical physics. Although our approach is directed mostly to Colombeau's
community, the readers who are already familiar with non-standard methods might
also find a short and comfortable way to learn about Colombeau's theory: a new
branch of functional analysis which naturally generalizes the Schwartz theory
of distributions with numerous applications to partial differential equations,
differential geometry, relativity theory and other areas of mathematics and
physics.

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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat