New exact solutions for the three-dimensional Electrical Impedance Equation applying quaternionic analysis and pseudoanalytic function theory

Author

Tachiquin, M. P Ramirez ; Torres, O. Rodriguez ; Cortes, J. J Gutierrez

Author_Institution

Escuela de Ing., Univ. La Salle, Mexico City, Mexico

fYear

2009

fDate

10-13 Jan. 2009

Firstpage

1

Lastpage

6

Abstract

We introduce a set of linearly independent solutions for the three-dimensional quaternionic electrical impedance equation, when the conductivity is a two-dimensional separable-variables function, and using a generalization of the Beltrami equation, we study two particular cases when the electrical impedance equation turns into a p-analytic system. Then we express analytically its general solution in terms of Taylor series in formal powers. This allows us to introduce a new class of exact solutions for the three-dimensional electrical impedance equation.

Keywords

electric impedance; electric impedance imaging; electrical conductivity; functional equations; series (mathematics); 3D electrical impedance equation; Beltrami equation; Taylor series; exact solution; p-analytic system; pseudoanalytic function; quaternionic analysis; Algebra; Boundary value problems; Conductivity; Electric potential; Equations; Impedance; Inverse problems; Quaternions; Taylor series; Tomography; Electrical impedance; pseudoanalytic; quaternions; tomography;

fLanguage

English

Publisher

ieee

Conference_Titel

Electrical Engineering, Computing Science and Automatic Control,CCE,2009 6th International Conference on

Conference_Location

Toluca

Print_ISBN

978-1-4244-4688-9

Electronic_ISBN

978-1-4244-4689-6

Type

conf

DOI

10.1109/ICEEE.2009.5393346

Filename

5393346