• 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