Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the effective impedance of finite and infinite networks   In this paper we deal with the notion of the effective impedance of AC
networks consisting of resistances, coils and capacitors. Mathematically such a
network is a locally finite graph whose edges are endowed with complex-valued
weights depending on a complex parameter $\lambda $ (by the physical meaning,
$\lambda =i\omega $, where $\omega $ is the frequency of the AC). For finite
networks, we prove some estimates of the effective impedance. Using these
estimates, we show that, for infinite networks, the sequence of impedances of
finite graph approximations converges in certain domains in $\mathbb{C}$ to a
holomorphic function of $\lambda$, which allows us to define the effective
impedance of the infinite network.

18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga