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By J.C. Phillips, M.F. Thorpe

Carrying on with the point of interest of the sequence on uncomplicated technology instead of purposes, 29 papers from a workshop in Cambridge, England, in July 2000 document on contemporary study into part transitions in either ordered and disordered fabric. They emphasize new thoughts in community glasses, easy mechanical structures within which new phenomena were found due to exploring stiffness transitions either experimentally and in numerical simulations; the metal-insulator transition in semiconductor impurity bands, the place an intermediate section has additionally been pointed out; and in general cuprate perovskites, the place an intermediate section happens which can have superconductive transition temperatures good above a hundred Kelvin.

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28. Phys. Rev. B 54, 9054 (1996); Phys. Rev. Lett. 76, 439 (1996). Yu. , Phys. Rev. B 58, 12 350 (1998). 35 This page intentionally left blank THE SIXTEEN-PERCENT SOLUTION: CRITICAL VOLUME FRACTION FOR PERCOLATION RICHARD ZALLEN Department of Physics, Virginia Tech Blacksburg, VA 24061 INTRODUCTION The English call it “value for money” (vfm). The American equivalent is “bang for the buck”. The idea is simple: to provide a rough measure of the ratio of benefit to cost. For an author of scientific papers, one possibility for a vfm-type measure of “benefit” (impact) to “cost” (time and effort) is this: vfm = (number of citations)/(paper’s length in printed pages).

Hill, J. Math. Phys. 18, 2316(1977). 19. 20. 21. B. Zumino, J. Math. Phys. 6, Coleman, Bull. Can. Math. Soc. 4, 209 (1961). 22. 23. 24. 25. K. Nakamura, Progr. Theor. Phys. (Kyoto) 21, 273 (1959). J. Coleman, Can. Math. Bull. 7. N. Whitehead, Universal Algebra, Cambridge University Press, 1898. C. Phillips, Physics of High-Tc Superconductors, Academic Press, 1989. 26. I. Yukalov, Phase Transitions and Hetrophase Fluctuations, Physics Reports 206, 395–488(1991). 27. 28. Phys. Rev. B 54, 9054 (1996); Phys.

Because only the electron-phonon interaction is needed to explain all other interactions (such as electron-[magnon, plasmon, any-old-whaton] interactions) are excluded by experiment [31,33]. The remarkable aspect of this experiment and theory is that the conclusion transcends all the details of structure and large-scale relaxation around dopants in these complex materials. Note that once again, the success of this approach rests on identifying two different sets, interaction space and real space, and then connecting them, just as in constraint theory and the proof of FLT.

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