DocumentCode
1160879
Title
Invisible Dual (n-l)-Networks Induced by Electric 1-Networks
Author
Kron, Gabriel
Volume
12
Issue
4
fYear
1965
fDate
12/1/1965 12:00:00 AM
Firstpage
464
Lastpage
470
Abstract
Since Kirchhoff\´s current-law prohibits the use of "nodes," and Kirchhoff\´s voltage-law prohibits the use of the "planes over the meshes," the topological theory of electric networks must be based upon the utilization of "branches" only (1-network) and their surroundings. A large number of visible and invisible multidimensional
-networks surrounding the branches can be introduced, that collectively form neither a graph nor a polyhedron, but a nonRiemannian space. All the parameters of Maxwell\´s field equations propagate in this space. Thus the four rectangular connection-matrices
, and
of each
-network form the building-blocks of an asymmetric "affine connection"
. It defines the "covariant" space-derivatives, that replace in networks the familiar gradient, divergence, and curl concepts of fields.
-networks surrounding the branches can be introduced, that collectively form neither a graph nor a polyhedron, but a nonRiemannian space. All the parameters of Maxwell\´s field equations propagate in this space. Thus the four rectangular connection-matrices
, and
of each
-network form the building-blocks of an asymmetric "affine connection"
. It defines the "covariant" space-derivatives, that replace in networks the familiar gradient, divergence, and curl concepts of fields.Keywords
Differential equations; Electromagnetic fields; H infinity control; Hypercubes; Impedance; Maxwell equations; Milling machines; Multidimensional systems; Tensile stress; Transportation;
fLanguage
English
Journal_Title
Circuit Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9324
Type
jour
DOI
10.1109/TCT.1965.1082489
Filename
1082489
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