Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the common points of two families of $N$-spheres in the flat $N+1$
  dimensional space, each of which passes through the vertexes of a given
  $N$-simplex   Let two distinct $N$-simplexes be given in an Euclidean or pseudo-Euclidean
$N+1$ dimensional space as each is defined by the coordinates of its $N+1$
vertexes. We consider the two families of $N$-spheres passing through the
vertexes of the given $N$-simplexes and the set of couples of $N$-spheres (one
belonging to first family and the other to the second one). The elements of
this set have at least one common point; moreover, it is such that for the
angle $\alpha$ between the segments connecting that point and the centers of
the corresponding $N$-spheres, there holds $\cos^{2}\alpha=const$ for each of
the elements of the defined set of $N$-spheres. In the present work we find the
geometric place of all these common points, including the special cases when
$\cos^{2}\alpha$ is equal to $0$ or $1$.

34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas