Year: 2016
Type: preprint
Abstract: A quaternionic field is a pair $p=\{α,u\}$ of function $α$ and vector field $u$ given on a 3d Riemannian maifold $Ω$ with the boundary. The field is said to be harmonic if $\nabla α={\rm rot\,}u$\, in $Ω$. The linear space of harmonic fields is not an algebra w.r.t. quaternion multiplication. However, it may contain the commutative algebras, what is the subject of the paper. Possible application of these algebras to the impedance tomography problem is touched on.
Source: arXiv (Cornell University)
Author: Belishev, M. I.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394668585