Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Some Algebra and the Corresponding Analysis in the Pseudo-Riemannian
  Space with Signature 1,-1,-1,-1   In this paper the certain 4-dimensional algebra in 4-dimensional
pseudo-Riemannian space with signature (1, -1, -1, -1) is constructed. On the
basis of this algebra the elements of the analysis, i.e. the theory of
4-dimensional functions of the 4-dimensional variable are built up. In the
process of designing the analysistwo additional assumptions aboutthe properties
of functions are made. Obtained under different assumptionsabout the properties
of functions, the Cauchy-Riemann equations are solved in flat, spherically and
cylindrically symmetric cases. In the cylindrically symmetric case the wave
solutions were obtained both for the metric tensor and for the 4-dimensional
function. Both waves spreadwith the speed equal to unity along null geodesics.
The properties of the metric tensor as physically real object are postulated,
but the idea what the 4-dimensional function (vector field) is remains unclear.

37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph