Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Static Maxwell System in Three Dimensional Inhomogeneous Isotropic
  Media, Generalized Non-Euclidean Modification of the System $(R)$ and
  Fueter's Construction   This paper extends approach of our joint paper with K\"{a}hler and recent
paper of the author, published in 2021, on problems of the static Maxwell
system in three dimensional inhomogeneous media. Applied pseudoanalytic
function theory developed by Kravchenko et al. allows to characterize, in
particular, meridional and transverse fields in cylindrically layered media.
Geometric properties of the electric field gradient ($EFG$) tensor within a
wide range of meridional fields allows us to introduce the concept of
$\alpha$-meridional mappings of the first and second kind depending on the
values of a real parameter $\alpha$. In case $\alpha =1$ tools of the radially
holomorphic potential provide essentially new meridional models in the context
of generalized axially symmetric potential theory (GASPT). Integral
representations of Bessel functions of the first kind of integer order and the
reduced quaternionic argument are first established. In case $\alpha =0$
geometric properties of harmonic meridional mappings of the second kind are
described. Some open problems in three dimensional inhomogeneous anisotropic
media are discussed using a generalized Riemannian modification of the system
$(R)$.

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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph