Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Neutral inclusions, weakly neutral inclusions, and an over-determined
  problem for confocal ellipsoids   An inclusion is said to be neutral to uniform fields if upon insertion into a
homogenous medium with a uniform field it does not perturb the uniform field at
all. It is said to be weakly neutral if it perturbs the uniform field mildly.
Such inclusions are of interest in relation to invisibility cloaking and
effective medium theory. There have been some attempts lately to construct or
to show existence of such inclusions in the form of core-shell structure or a
single inclusion with the imperfect bonding parameter attached to its boundary.
The purpose of this paper is to review recent progress in such attempts. We
also discuss about the over-determined problem for confocal ellipsoids which is
closely related with the neutral inclusion, and its equivalent formulation in
terms of Newtonian potentials. The main body of this paper consists of reviews
on known results, but some new results are also included.

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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th