later did) that transformers can always be avoided. The eponymous Brune cycle continued fractions were invented by Brune to facilitate this proof. The Brune theorem is: The impedance Z(s) of any electric network composed of passive components is positive-real. If Z(s) is positive-real it is realisable by a network having as components passive (positive) R, C, L, and ideal transformers T. Brune is also responsible for the Brune test for determining the permissibility of interconnecting two-port networks. Legacy For his work, Brune is recognized as one of those who laid the foundation of network analysis by means of mathematics. For instance, American computer scientist Ernst Guillemin dedicated his book Synthesis of Passive Network to Brune, describing him with these words: "In my opinion the one primarily responsible for establishing a very broad and mathematically rigorous basis for realization theory generally was Otto Brune." References Bibliography Cauer, E.; Mathis, W.; Pauli, R., "Life and Work of Wilhelm Cauer (1900–1945)", Proceedings of the Fourteenth International Symposium of Mathematical Theory of Networks and Systems (MTNS2000), Perpignan, June, 2000. Chen, Wai-Kai, Active Filters: Theory and Implementation, Wiley, 1986 . Brune, O., "Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency", Doctoral thesis, 5 May 1931a, republished in, MIT Journal of Mathematics and Physics, vol. 10, pp 191–236, 1931b. Brune O., "Equivalent Electrical Networks", Physical Review, vol. 38, pp 1783–1783, 1931c. Galkowski, Krzysztof; Wood, Jeff David, Multidimensional Signals, Circuits and Systems, Taylor & Francis, 2001 . Horrocks, D. H.; Nightingale, C., "The compatibility of n-ports in parallel", International Journal of Circuit Theory and Applications, vol. 4, pp. 81–85, January 1976. Seising, Rudolf, Die Fuzzifizierung der Systeme, Franz Steiner Verlag, 2005 Seising, Rudolf, The Fuzzification of Systems: The Genesis of Fuzzy Set Theory and its Initial Applications - Developments up to the 1970s Springer, 2007 . Wildes, Karl L.; Lindgren, Nilo A., A century of electrical engineering and computer science at MIT, 1882-1982, MIT Press, 1985 . Willems, Jan; Hara, Shinji; Ohta, Yoshito; Fujioka, Hisaya, Perspectives in Mathematical System Theory, Control, and Signal Processing, Springer, 2010 . South African mathematicians 1901 births 1982 deaths 20th-century South African mathematicians Stellenbosch University alumni Massachusetts Institute of Technology alumni South African scientists South African emigrants to the United States