×

An analysis of the Wang algebra of networks. (English) Zbl 0114.06503


PDFBibTeX XMLCite
Full Text: DOI

References:

[1] K. T. Wang, On a new method of analysis of electrical networks, Memoir 2, National Research Institute of Engineering, Academia Sinica, 1934.
[2] S. L. Ting, On the general properties of electrical network determinants, Chinese Journal of Physics vol. 1 (1935) pp. 18-40.
[3] Chin-Tao Tsai, Short cut methods for expanding the determinants involved in network problems, Chinese Journal of Physics vol. 3 (1939) pp. 148-181. · Zbl 0022.27704
[4] Mong-Kang Ts’en, Indicial impedances and admittances, Chinese Journal of Physics vol. 4 (1940) pp. 89-96.
[5] Wei-Liang Chow, On electric networks, J. Chinese Math. Soc. 2 (1940), 321 – 339. · Zbl 0063.00868
[6] T. Muir, Contributions to the history of determinants (1900-1920), London Blackie, 1930. · JFM 56.0005.01
[7] J. C. Maxwell, A treatise on electricity and magnetism, 3rd. ed., Oxford, Clarendon Press, 1891. · JFM 05.0556.01
[8] R. Bott and R. J. Duffin, On the algebra of networks, Trans. Amer. Math. Soc. 74 (1953), 99 – 109. · Zbl 0050.25104
[9] S. MacLane, Grassman algebras and determinants, mimeographed lectures, University of Chicago.
[10] J. H. M. Wedderburn, Lectures on matrices, Dover Publications, Inc., New York, 1964. · Zbl 0121.26101
[11] W. H. Ingram and C. M. Cramlet, On the foundations of electrical network theory, J. Math. Phys. Mass. Inst. Tech. 23 (1944), 134 – 155. · Zbl 0063.02976 · doi:10.1002/sapm1944231134
[12] J. L. Synge, The fundamental theorem of electrical networks, Quart. Appl. Math. 9 (1951), 113 – 127. · Zbl 0043.20003
[13] R. M. Cohn, The resistance of an electrical network, Proc. Amer. Math. Soc. 1 (1950), 316 – 324. · Zbl 0038.12402
[14] R. J. Duffin, Nonlinear networks. IV, Proc. Amer. Math. Soc. 1 (1950), 233 – 240. · Zbl 0036.41601
[15] H. Weyl, Repartición de corriente en una red eléctrica, Rev. Mat. Hisp.-Amer. vol. 5 (1923) pp. 153-164. · JFM 49.0412.03
[16] Philip Franklin, The electric currents in a network, J. Math. Phys. vol. 4 (1925) pp. 97-102. · JFM 51.0089.01
[17] B. D. H. Tellegen, A general network theorem, with applications, Philips Research Rep. 7 (1952), 259 – 269. · Zbl 0049.42301
[18] S. MacLane, A combinatorial condition for planar graphs, Fund. Math. vol. 28 (1936) p. 22. · JFM 62.0694.06
[19] A. Lichnerowicz, Algèbre et analyse linéaires, Paris, Masson, 1947. · Zbl 0031.00206
[20] N. Bourbaki, Éléments de mathématique, Livre II, Algebre, Chapitre III, Paris, Herman, 1948. · Zbl 0039.25902
[21] Hassler Whitney, Geometric integration theory, Princeton University Press, Princeton, N. J., 1957. · Zbl 0083.28204
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.