The consensus problem involves an asynchronous system of processes, some of which may be unreliable The problem ~9 for the reliable processes to agree on a binary value We show that every protocol for thus problem has the posslblhty of nontermmatlon, even with only one faulty process By way of contrast, solutions are known for the synchronous case, the "Byzantine Generals" problem

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Experimental investigation into the strength and ductility of serpentinite at temperatures to 700øC and confining pressures to 5 kb has yielded results important to the understanding of the role of serpentinite in orogenesis. Sealed specimens of antigorite-chrysotile serpentinite, with ultimate strength comparable to that of granite at room temperature, showed a marked weakening above 500-600øC; a mesh-textured serpentinite containing lizarditc, chrysotile, and a minor amount of brucite showed a similar loss of strength at 300-350øC. Brittleness always accompanied the high-temperature weakening, although the samples showing high strength at lower temperatures were often ductile. Petrographic and X-ray examinations reveal that serpentine in the weakened and embrittled specimens has undergone partial dehydration to forsteritc and talc. The embrittlement and weakening is attributed to a reduction in the effective confining pressure due to the pore pressure of the water released during dehydration and to a loss in cohesive strength due to changes in the structure upon dehydration. The hypothesis of tectonic emplacement of serpentinites of the alpine type thus becomes highly plausible at temperatures great enough for dehydration weakening, while being difficult to accept at lower temperatures where the strength of the serpentinite is high. Weakening upon heating to the appropriate dehydration temperature in the range 300-600øC of a partially serpentinized oceanic lower crust or upper mantle should also serve to concentrate deformation in the heated belt, thus facilitating mountain building. The embrittlement associated with dehydration extends the maximum theoretical depth for brittle fracture in the mantle to that of the deepest hydrated phases.

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Original citation: Agarwala, R., Bafna, V., Farach, M., Paterson, Michael S. and Thorup, M. (1997) On the approximability of numerical taxonomy (fitting distances by tree metrics Copies of full items can be used for personal research or study, educational, or not-forprofit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A note on versions:The version presented in WRAP is the published version or, version of record, and may be cited as it appears here.For more information, please contact the WRAP