Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $G$-deviations of polygons and their applications in Electric Power
  Engineering   For any metric space $X$ endowed with the action of a group $G$, and two
$n$-gons $\vec x=(x_1,\dots,x_n)\in X^n$ and $\vec y=(y_1,\dots,y_n)\in X^n$ in
$X$, we introduce the $G$-deviation $d(G\vec x,\vec y\,)$ of $\vec x$ from
$\vec y$ as the distance in $X^n$ from $\vec y$ to the $G$-orbit $G\vec x$ of
$\vec x$ in the $n$-th power $X^n$ of $X$. For some groups $G$ of affine
transformations of the complex plane, we deduce simple-to-apply formulas for
calculating the $G$-derviation between $n$-gons on the complex plane. We apply
these formulas for defining new measures of asymmetry of triangles. These new
measures can be applied in Electric Power Engineering for evaluating the
quality of 3-phase electric power. One of such measures, namely the affine
deviation, is espressible via the unbalance degree, which is a standard
characteristic of quality of three-phase electric power.

20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th