|
Online ISSN 1552-4485; Print ISSN 0033-569X
Non-linear network problems
Authors:
Garrett Birkhoff and J. B. Diaz
Journal:
Quart. Appl. Math. 13 (1956), 431-443
MSC:
Primary 78.0X
DOI:
https://doi.org/10.1090/qam/77398
MathSciNet review:
77398
Full-text PDF Free Access
References | Similar Articles | Additional Information
-
G. Kirchhoff, Poggendorf Annalen, 72, 497-508, (1847); Collected Works, p. 22
W. Thomson (Lord Kelvin), Cambridge and Dublin Math. J. 1848, 84-87
J. C. Maxwell, Treatise of electricity and magnetism, 3rd. ed., Oxford, 1892
H. Poincaré, Analysis situs, J. de l’École Polytechnique (2), 1-121 (1895)
- H. Poincaré, Second Complement a l’Analysis Situs, Proc. Lond. Math. Soc. 32 (1900), 277–308. MR 1576227, DOI https://doi.org/10.1112/plms/s1-32.1.277 H. Weyl, Repartición de corriente en una red conductora, Revista Matemática Hispano-Americana 5, 153-164 (1923) O. Veblen, Analysis situs, 2nd. ed., Amer. Math. Soc., New York, 1931 Hardy Cross, The University of Illinois Bulletin #286, 1936 D. König, Theorie der Graphen, Leipzig, 1936 G. M. Fair, Engineering News Record 120, 342-343 (1938) R. V. Southwell, Relaxation methods in engineering science, Oxford, 1940
- W. H. Ingram and C. M. Cramlet, On the foundations of electrical network theory, J. Math. Phys. Mass. Inst. Tech. 23 (1944), 134–155. MR 15330, DOI https://doi.org/10.1002/sapm1944231134 M. Parodi, Sur l’existence des réseaux eléctriques, Compt. Rend. Acad. Sci., Paris 223, 23-25 (1946) A. d’Auriac, A propos de l’unicité de solution dans les problèmes des réseaux maillés, La Houille Blanche 2, 209-11, (1947) E. Setruk and F. Biesel, Etude d’un modèle réduit de réseau maillé de distribution d’eau, La Houille Blanche 2, 213-27 (1947) Ch. Dubin, Le calcul des réseaux maillés, La Houille Blanche 2, 228-32 (1947) R. J. Duffin, Non-linear networks IIA, Bull. Amer. Math. Soc. 53, 963-971 (1947)
- Olga Taussky, A recurring theorem on determinants, Amer. Math. Monthly 56 (1949), 672–676. MR 32557, DOI https://doi.org/10.2307/2305561 P. LeCorbeiller, Matrix analysis of electrical networks, Harvard University Press, Cambridge, 1950
- J. L. Synge, The fundamental theorem of electrical networks, Quart. Appl. Math. 9 (1951), 113–127. MR 42958, DOI https://doi.org/10.1090/S0033-569X-1951-42958-X
- J. Collatz, Einschliessungssätze bei Iteration und Relaxation, Z. Angew. Math. Mech. 32 (1952), 76–84 (German). MR 50381, DOI https://doi.org/10.1002/zamm.19520320206
- J. B. Diaz and R. C. Roberts, On the numerical solution of the Dirichlet problem for Laplace’s difference equation, Quart. Appl. Math. 9 (1952), 355–360. MR 44225, DOI https://doi.org/10.1090/S0033-569X-1952-44225-4
- J. B. Diaz and R. C. Roberts, Upper and lower bounds for the numerical solution of the Dirichlet difference boundary value problem, J. Math. Physics 31 (1952), 184–191. MR 0051589
- Maynard G. Arsove, The algebraic theory of linear transmission networks. I, II, J. Franklin Inst. 255 (1953), 301–318, 427–444. MR 58450, DOI https://doi.org/10.1016/0016-0032%2853%2990393-7
- Garrett Birkhoff and Saunders Mac Lane, A survey of modern algebra, Macmillan Co., New York, N. Y., 1953. Rev. ed. MR 0054551
- R. Bott and R. J. Duffin, On the algebra of networks, Trans. Amer. Math. Soc. 74 (1953), 99–109. MR 56573, DOI https://doi.org/10.1090/S0002-9947-1953-0056573-X
- Charles Saltzer, The second fundamental theorem of electrical networks, Quart. Appl. Math. 11 (1953), 119–123. MR 52984, DOI https://doi.org/10.1090/S0033-569X-1953-52984-2 William Prager, Problems of traffic and transportation, Proc. Symp. Operations Research Business and Industry, Midwest Res. Inst., Kansas City, Missouri, 105-113 (1954)
Retrieve articles in Quarterly of Applied Mathematics with MSC: 78.0X
Retrieve articles in all journals with MSC: 78.0X
Additional Information
Article copyright:
© Copyright 1956
American Mathematical Society