Camouflaging electrical $1$-networks as graphs
Author:
Gabriel Kron
Journal:
Quart. Appl. Math. 20 (1962), 161-174
MSC:
Primary 94.30; Secondary 53.45
DOI:
https://doi.org/10.1090/qam/148347
MathSciNet review:
148347
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Abstract: Lately it has become fashionable to develop the theory of electrical networks by starting first with a detailed, scholarly exposition of the theory of graphs (containing both nodes and branches), as given in textbooks on algebraic topology. However, when the graph analysis finally gets down to the study of actual electrically excited networks, it will invariably be found that all traces of the concepts of nodes and their associated “incidence-matrices” have disappeared from the final $e = zi$ and other equations of state that are to be solved. In their place only the branches and the associated “connection-matrices” have been put to use, all still wrapped up however in an ill-fitting graph terminology. Of course such legerdemain had to be resorted to, since graph theorists happened to pick the wrong topological model for an electrical network. A graph possesses enough structure to propagate an electromagnetic wave and not an electrical current.
G. Kron, Tensor analysis of networks, John Wiley and Sons, New York, (1931)
G. Kron, Diakoptics—The piecewise solution of large-scale systems, a serial of 20 chapters in the June 7, 1957 to Feb. 13, 1959 issues of the Electrical Journal (London)
G. Kron, Non-Riemannian dynamics of rotating electrical machinery, J. of Math, and Physics, 13, 103-194 (1934)
G. Kron, Tensor analysis of multi-electrode tube circuits Trans, AIEE, 55, 1220-42 (1936)
- Gabriel Kron, Equivalent circuit of the field equations of Maxwell. I, Proc. I.R.E. 32 (1944), 289–299. MR 10695
O. Veblen, Analysis situs, American Math. Soc. New York, 1931
- W. V. D. Hodge, The theory and applications of harmonic integrals, Cambridge, at the University Press, 1952. 2d ed. MR 0051571
G. Kron, A generalization of the calculus of finite differences to nonuniformly spaced variables, Trans. AIEE 1, Communications and Electronics 77, 539-44 (1958)
G. Kron, Basic concepts of multidimensional space filters, Trans. AIEE 1, Communications and Electronics 78, 554-61 (1959)
G. Kron, Self-organizing dynamo-type automata, Matrix and Tensor Quarterly 11, 2 (1960)
G. Kron, Power-system type self-organizing automata, to appear in R.A.A.G. Memoirs III of the Basic Problems in Engineering and Physical Sciences by Means of Geometry (Japan)
- Gabriel Kron, Tensors for circuits, Dover Publications, Inc., New York, 1959. 2nd ed; With an introduction by Banesh Hoffmann. MR 0111460
- Gabriel Kron, Multidimensional curve-fitting with self-organizing automata, J. Math. Anal. Appl. 5 (1962), 46–69. MR 150978, DOI https://doi.org/10.1016/0022-247X%2862%2990005-7
G. Kron, The misapplication of graph theory to electrical networks, Trans. AIEE 1, Communications and Electronics, 81 (1962)
G. Kron, Tensor analysis of networks, John Wiley and Sons, New York, (1931)
G. Kron, Diakoptics—The piecewise solution of large-scale systems, a serial of 20 chapters in the June 7, 1957 to Feb. 13, 1959 issues of the Electrical Journal (London)
G. Kron, Non-Riemannian dynamics of rotating electrical machinery, J. of Math, and Physics, 13, 103-194 (1934)
G. Kron, Tensor analysis of multi-electrode tube circuits Trans, AIEE, 55, 1220-42 (1936)
G. Kron, Equivalent circuits of the field equations of Maxwell-I, Proc. IRE, 32, 289-299 (1944)
O. Veblen, Analysis situs, American Math. Soc. New York, 1931
W. V. C. Hodge, The theory and application of harmonic integrals, Cambridge University Press (1952)
G. Kron, A generalization of the calculus of finite differences to nonuniformly spaced variables, Trans. AIEE 1, Communications and Electronics 77, 539-44 (1958)
G. Kron, Basic concepts of multidimensional space filters, Trans. AIEE 1, Communications and Electronics 78, 554-61 (1959)
G. Kron, Self-organizing dynamo-type automata, Matrix and Tensor Quarterly 11, 2 (1960)
G. Kron, Power-system type self-organizing automata, to appear in R.A.A.G. Memoirs III of the Basic Problems in Engineering and Physical Sciences by Means of Geometry (Japan)
G. Kron, Tensors for circuits, Dover Publications, Inc. New York (1959)
G. Kron, Multidimensional curve-fitting with self-organizing automata. Scheduled to appear in the Journal of Mathematical Analysis and Applications
G. Kron, The misapplication of graph theory to electrical networks, Trans. AIEE 1, Communications and Electronics, 81 (1962)
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Article copyright:
© Copyright 1962
American Mathematical Society
