Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Affine transformations of circle and sphere   A non-degenerate two-dimensional linear operator $\varphi$ transforms the
unit circle into ellipse. Let $p$ be the length of its bigger axis and $q$ --
the length of smaller. We can define the deformation coefficient $k(\varphi)$
as $q/p$. Analogously, if $\varphi$ is a non-degenerate three-dimensional
operator, then it transforms the unit sphere into ellipsoid. If $p>q>r$ are
lengths of its axes, then deformation coefficient $k(\varphi)$ will be defined
as $r/p$. In this work we compute the mean value of deformation coefficient in
two-dimensional case and give an estimation of mean value in three-dimensional
case.

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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom