DocumentCode
1402532
Title
Electrical network theory of countable graphs
Author
Larsen, Jens Chr
Author_Institution
Math. Inst., Tech. Univ., Lyngby, Denmark
Volume
44
Issue
11
fYear
1997
fDate
11/1/1997 12:00:00 AM
Firstpage
1045
Lastpage
1055
Abstract
The purpose of this dissertation is to derive the equations governing electrical networks of countable graphs and to give conditions assuring that these are gradient dynamical systems on semi-Riemannian Hilbert manifolds. Furthermore, we show how symmetries in the graph give rise to a G-action on the manifold of states. Finally, we present some mathematical results about gradient dynamical systems on semi-Riemannian Banach manifolds
Keywords
Banach spaces; Hilbert spaces; graph theory; nonlinear network analysis; G-action; countable graphs; electrical network theory; gradient dynamical systems; graph symmetries; semi-Riemannian Banach manifolds; semi-Riemannian Hilbert manifolds; Circuits; Equations; Hilbert space; Network theory (graphs);
fLanguage
English
Journal_Title
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
Publisher
ieee
ISSN
1057-7122
Type
jour
DOI
10.1109/81.641767
Filename
641767
Link To Document