Abstract
We explore mathematical knowledge in the field of electrical engineering and claim that electrical engineering is a suitable area of application for mathematical knowledge management: We show that mathematical knowledge arising in electrical engineering can be successfully handled by existing MKM systems, namely by the Mizar system. To this end we consider in this paper network theory and in particular stability of networks. As an example for mathematical knowledge in electrical engineering we present a Mizar formalization of Schur’s theorem. Schur’s theorem provides a recursive, easy method to check for BIBO-stability of networks.
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References
Byliński, C.: The Complex Numbers. Formalized Mathematics 1(3), 507–513 (1990)
Bancerek, G.: On the Structure of Mizar Types. In: Geuvers, H., Kamareddine, F. (eds.) Proc. of MLC 2003, ENTCS, vol. 85(7) (2003)
Davies, M.: Obvious Logical Inferences. In: Proceedings of the 7th International Joint Conference on Artificial Intelligence, pp. 530–531 (1981)
de Bruijn, N.G.: The Mathematical Vernacular, a language for mathematics with typed sets. In: Dybjer, P., et al. (ed.) Proc. of the Workshop on Programming Languages, Marstrand, Sweden (1987)
von zur Gathen, J., Gerhard, J.: Modern Computer Algebra. Cambridge University Press, Camebridge (1999)
Hilf, E., Kohlhase, M., Stamerjohanns, H.: Capturing the Content of Physics: Systems, Observables, and Experiments. In: Borwein, J.M., Farmer, W.M. (eds.) MKM 2006. LNCS (LNAI), vol. 4108, pp. 165–178. Springer, Heidelberg (2006)
Jaśkowski, S.: On the Rules of Suppositon in Formal Logic. Studia Logica 1 (1934)
Milewska, A.J.: The Field of Complex Numbers. Formalized Mathematics 9(2), 265–269 (2001)
Milewski, R.: The Ring of Polynomials. Formalized Mathematics 9(2), 339–346 (2001)
The Mizar Home Page, http://mizar.org
Naumowicz, A., Byliński, C.: Improving Mizar texts with properties and requirements. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 190–301. Springer, Heidelberg (2004)
Oppenheim, A.V., Schafer, R.W.: Discrete-Time Signal Processing, 2nd edn. Prenctice-Hall, New Jersey (1998)
Rudnicki, P., Trybulec, A.: Mathematical Knowledge Management in Mizar. In: Buchberger, B., Caprotti, O. (eds.) Proc. of MKM 2001, Linz, Austria (2001)
The SESAME Network, http://www.mkm-ig.org/projects/sesame/
Schur, J.: Über Algebraische Gleichungen, die nur Wurzeln mit negativen Realteilen besitzen. Zeitschrift für angewandte Mathematik und Mechanik 1, 95–110 (1921)
Tarski, A.: On Well-Ordered Subsets of Any Set. Fundamenta Mathematicae 32, 176–183 (1939)
Unbehauen, R.: Netzwerk- und Filtersynthese: Grundlagen und Anwendungen (4. Auflage); Oldenbourg-Verlag (1993)
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Rowinska-Schwarzweller, A., Schwarzweller, C. (2007). Towards Mathematical Knowledge Management for Electrical Engineering. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds) Towards Mechanized Mathematical Assistants. MKM Calculemus 2007 2007. Lecture Notes in Computer Science(), vol 4573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73086-6_29
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DOI: https://doi.org/10.1007/978-3-540-73086-6_29
Publisher Name: Springer, Berlin, Heidelberg
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