Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Electromagnetic-Power-based Modal Classification, Modal Expansion, and
  Modal Decomposition for Perfect Electric Conductors   Traditionally, all working modes of a perfect electric conductor are
classified into capacitive modes, resonant modes, and inductive modes, and the
resonant modes are further classified into internal resonant modes and external
resonant modes. In this paper, the capacitive modes are further classified into
intrinsically capacitive modes and non-intrinsically capacitive modes; the
resonant modes are alternatively classified into intrinsically resonant modes
and non-intrinsically resonant modes, and the intrinsically resonant modes are
further classified into non-radiative intrinsically resonant modes and
radiative intrinsically resonant modes; the inductive modes are further
classified into intrinsically inductive modes and non-intrinsically inductive
modes. Based on the modal expansion corresponding to these new modal
classifications, an alternative modal decomposition method is proposed. In
addition, it is also proved that: all intrinsically resonant modes and all
non-radiative intrinsically resonant modes constitute linear spaces
respectively, but other kinds of resonant modes cannot constitute linear
spaces; by including the mode 0 into the intrinsically capacitive mode set and
the intrinsically inductive mode set, these two modal sets become linear spaces
respectively, but other kinds of capacitive modes and inductive modes cannot
constitute linear spaces.

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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat