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 p -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 C_{0}, C_{c}, A^{\\circ} , and A^{c} of each p -network form the building-blocks of an asymmetric "affine connection" \\Gamma _{\\beta \\gamma }^{\\alpha } . 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
Link To Document :
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