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Application of the Abel integral equation to an inverse problem in thermoelectricity

Published online by Cambridge University Press:  05 November 2009

GIOVANNI CIMATTI
GIOVANNI CIMATTI*
Affiliation:
Dipartimento di Matematica, Largo Bruno Pontecorvo 5, Pisa, Italy email: cimatti@dm.unipi.it
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Abstract

This paper deals with a new method to determine the dependence of the electrical conductivity of metals or semiconductors on temperature. It is based on the fact that the current–voltage relationship is easily measurable. This inverse problem is solved by the classical Abel integral equation.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 20 , Issue 6 , December 2009 , pp. 519 - 529
Copyright
Copyright © Cambridge University Press 2009

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References

[1]Abel, N. H. (1826) Résolution d'un problèm de mécanique. Journal für die reine und angewandte Mathematik 1, 97–101.Google Scholar
[2]Cimatti, G. (in press) The mathematics of the Thomson effect, Quart. Appl. Math.Google Scholar
[3]Corless, R. M., Gonnet, G. H., Hare, D. E. G, Jeffrey, D. J. & Knuth, D. E. (1996) On Lambert W function, Adv. Comput. Math. 5, 329–359.CrossRefGoogle Scholar
[4]Geronflo, R. & Vessella, S. (1991) Abel Integral Equation: Analysis and Applications, Springer-Verlag, Berlin.CrossRefGoogle Scholar
[5]Howison, S. (2005) Practical Applied Mathematics, Cambridge Texts in Applied Mathematics, Cambridge University Press, New York.CrossRefGoogle Scholar
[6]Landau, L. & Lifchitz, E. (1969) Électrodynamique des Milieux Continus, Éditions MIR, Moscow.Google Scholar
[7]Marciá, E. & Rodríguez-Oliveros, R. (2007) Theoretical assessment on the validity of the Wiedemann–Franz law for icosahedral quasicrystals, Phys. Rev. B 75, 1042210.Google Scholar
[8]Ockendon, J., Howison, S., Lacey, A. & Movchan, A. (1999) Applied Partial Differential Equations, Oxford University Press, Oxford.Google Scholar
[9]Tonelli, L. (1928) Su un problema di Abel, Math. Ann. 99, 125–134.CrossRefGoogle Scholar
[10]Tricomi, F. G. (1957) Integral Equations, Dover Company, London.Google Scholar
[11]Volterra, V. (1913) Lecons sur les Équations Integrales et les E´uations Intégro-différentielles, Gauthier-Villars, Paris.CrossRefGoogle Scholar
[12]Wiedemann, G. & Franz, R. (1853) Über die Wärme-leitungsfähigkeit der Metalle, Annalen der Physik 89, 497–531.Google Scholar