On network models and the symbolic solution of network equations
International Journal of Applied Mathematics and Computer Science (2001)
- Volume: 11, Issue: 1, page 237-269
- ISSN: 1641-876X
Access Full Article
topAbstract
topHow to cite
topReferences
top- Bellert S. (1962): Topological analysis and synthesis of linear systems. - J. Franklin Inst., Vol.274, No.6, pp.425-443. Zbl0142.12703
- Branin F.H.jr. (1966): The algebraic-topological basis for network analysis and the vector calculus. - Proc. Symp. Generalized Networks, Brooklyn, pp.453-491. Zbl0163.39604
- Bott R. and Duffin R.J. (1953): On the algebra of networks. - Trans. AMS, Vol.74, pp.99-109. Zbl0050.25104
- Cauchy A.L. (1815): Memoire sur les fonctions qui ne peuvent obtenir que deux valeurs. - J. l'Ecole Polytechnique, Vol.10, pp.29-97, reprinted in Oeuvres Complètes, Serie II, Tome I, pp.91-169.
- Cayley A. (1857): On the theory of the analytical forms called trees. - Philos. Mag., Vol.4, No.13, pp.172-176.
- Chen W.K. (1967): Topological network analysis by algebraic methods. - Proc. IEE, Vol.114, No.1, pp.86-88.
- Chua L.O. and Lin P.-M. (1975): Computer Aided Analysis of Electronic Circuits-Algorithms and Computational Techniques. - New Jersey: Prentice-Hall. Zbl0358.94002
- Coates C.L. (1959): Flow-graph solutions of algebraic equations. - IEEE Trans. Circuit Theory, Vol.6, No.2, pp.170-187.
- Dmitrischin R.W. (1969): Rasčet linejnych cepej s metodom rasširennych strukturnych čisel. - Isv. Vuzov SSSR, Radioelektreonnika, Vol.12, No.8, pp.806-813 (in Russian).
- Duffin R.J. (1959): An analysis of the Wang algebra of networks. - Trans. AMS, Vol.93, pp.114-131. Zbl0114.06503
- Firestone B.F. (1933): A new analogy between mechanical and electrical systems. - J. Acoust. Soc. Am., Vol.4, pp.249-267.
- Gieben G. and Sansen W. (1991): Symbolic Analysis for Automated Design of Analog Integrated Circuits. - Boston: Kluwer.
- Gnther M. and Feldmann U. (1999): CAD-based electric-circuit modeling in industry, Part I and II. - Surv. Math. Ind., Vol.8, pp.97-129 and 131-157.
- Hhnle W. (1932): Die Darstellung elektromechanischer Gebilde durch rein elektrische Schaltbilder. - Wiss. Verff. a. d. SIEMENS-Konzern, Vol.11, No.1, pp.1-23.
- Jacobi C.G.J. (1841): De formatione et proprietatibus determinantium. - Crelle's J. f. reine und angew. Mathem., Vol.22, pp.285-318.
- Kirchhoff G. (1845): Uber den Durchgang eines elektrischen Stromes durch eine Ebene, insbesondere durch eine kreisfrmige. - Poggendorfs Annalen der Physik und Chemie, Vol.64, pp.497-514.
- Kirchhoff G. (1847): Uber die Auflsung der Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung galvanischer Strme gefhrt wird. - Poggendorfs Annalen der Physik und Chemie, Vol.72, pp.497-508.
- Knig D. (1936): Theorie der Endlichen und Unendlichen Graphen. - Leipzig: Akademische Verlagsgesellschaft.
- Krtzig W.B. (1998): Tragwerke 2. 3. Aufl. - Berlin: Springer,
- Kron G. (1939): Tensor Analysis of Networks. - New York: Wiley. Zbl0022.16801
- Le Corbeiller P. (1950): Matrix Analysis of Networks. - New York: Wiley. Zbl0041.55304
- Lin P.-M. (1991): Symbolic Network Analysis. - Amsterdam: Elsevier.
- Mason S.J. (1953): Feedback theory; some properties of signal-flow-graphs. - Proc. IRE, Vol.41, No.9, pp.1144-1156.
- Maxwell J.C. (1870): On reciprocal figures, frames and diagrams of forces. - Trans. Roy. Soc. Edinb., Vol.26, pp.1-40.
- Maxwell J.C. (1882): Electricity and magnetism I, 3rd Ed, (Ch. VI and Appendix). - Oxford: Clarendon Press.
- Mayeda W. and Seshu S. (1965): Generation of trees without duplication. - IEEE Trans. Circuit Theory, Vol.12, No.2, pp.181-185.
- Poincar'e H. (1895): Analysis situs. -J. de l'Ecole Polytech., Vol.2, No.1, pp.1-121.
- Reibiger A. and Elst G. (1983): Network theoretic interpretation of multibody systems. - Acta Polytechnica Prague, Vol.8, pp.109-129.
- Reinschke K.J. (1988): Multivariable Control-A Graph-Theoretic Approach. - Berlin: Springer-Verlag. Zbl0682.93006
- Reinschke K. and Schwarz P. (1976): Verfahren zur Rechnergesttzten Analyse Linearer Netzwerke. - Berlin: Akademie-Verlag. Zbl0325.94015
- Roth J.P. (1959): An application of algebraic topology: Kron's method of tearing. - Quart. Appl. Math., Vol.17, No.1, pp.1-24.
- Seshu S. and Reed M.B. (1961): Linear Graphs and Electrical Networks. - Reading: Addison-Wesley. Zbl0102.34001
- Synge J.L. (1951): The fundamental theorem of electrical networks. - Quart. Appl. Math., Vol.9, No.2, pp.113-127. Zbl0043.20003
- Tellegen B.D.H. (1948): The gyrator, a new electric network element. - Philips Res. Rep., Vol.3, pp.81-101.
- Tellegen B.D.H. (1953): A general network theorem with applications. - Proc. Inst. Radio Engrs. Australia, Vol.14, pp.265-270.
- Ting S.L. (1935): On the general properties of electrical network determinants. - Chinese J. Phys., No.1, pp.18-40.
- Trent H.M. (1955): Isomorphismus between oriented linear graphs and lumped physical systems. - J. Acoust. Soc. Am., Vol.27, No.3, pp.500-527.
- Trochimenko J.K. (1972): Metod obobščennych čisel i analiz linejnych cepej. - Moscow: Izd. Sov. Radio (in Russian).
- Tsai C.T. (1939): Short cut methods for expanding determinants involved in network problems. - Chinese J. Phys., No.3, pp.148-181. Zbl0022.27704
- Veblen O. (1916): Analysis situs. - (The Cambridge Colloquium, Part II, Lectures 1916); New York: AMS, 1922.
- Wang K.T. (1934): On a new method for the analysis of electrical networks. - Nat. Res. Inst. Eng. Acad. Sinica, Memoir No.2, pp.1-11.
- Weyl H. (1923): Repartici'on de corriente en una red conductora (Introducci'on al an'alisis combinatorio). - Revista Matematica Hispano-Americana, Vol.5, pp.153-164. Zbl49.0412.03
- Weyl H. (1924): An'alisis situs combinatorio (continuaci'on). - Revista Matematica Hispano-Americana, Vol.6, pp.1-9 and pp.33-41.