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Ando, Phl/s. Rev. Lett. 1i7(1986) 3093. (24) H. Aoki and T. Ando in High Magnetic Fielda in Semiconductor PhI/sics ed. by G. Landwehr (Springer, Berlin, 1987), pA5. (25) H. Aoki, J. Phl/s. C 18(1985) L67; H. Aoki, to be published. (26) R. Rammal, J. Phl/. '6(1985) 1345 (energy spectrum); H. Aoki, unpublished (numerical quantum Hall study). M. Chang, G. Y. E. Cunningham, PM. E. E. Howard, Solid State Commun. 67(1988) 769. [28] H. Aoki, Jpn. J. App/. PhI/B. 26-3, 699. (29) H. Aoki, to be published.

Ex~! ' /"'\, \. \\ '. \. °0~LL~2~3~4~5~6~~7~8~9~10 B(T) Fig. 05 K for sample 113. resistivity Pxx (b) at terers were used. realized by silicon and beryllium dopants. respectively, In this contribution. we will focus on results obtained on samples which have been I)-doped with Be. but also shortly discuss results of other structures. g. 3). After the growth process they were etched into a standard Hall bar geometry. The mobility [le and the electron and doping concentrations ne and nS of the samples are summarized in table 1.

19] H. Aoki, J. Phl/s. C 16(1983) 1893. J. G. Smith, M. J. Kelly, R. Newbury, H. G. F. C. A. A. Jones, J. Phl/s. Condens. Matter 1(1989) 6291. J. Thouless, M. P. Nightingale and M. den Nijs, Phl/s. Rev. Lett. '9(1982) 405. J. Thouless, PhI/B. Rep. J. 4, M. Kohmoto, Ann. Phl/s. 160(1985) 343. AUhough the approach has been criticized by J. Riess, Europhl/s. Lett. 12 (1990) 253, numerical results for finite systems confirm that the fluxaveraged q Z7 is an integer[23]. [22] Q. J. S. Wu, Phl/s. Rev.

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A TREATISE ON THE MATHEMATICAL THEORY OF ELASTICITY VOLUME-1 by A. E. H. LOVE


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