The Fa,b,c conjecture, I

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and one part of the conjecture was proved. The conjecture completely determines all finite members of the family. Here we prove another part of the conjecture and foreshadow a paper which completes the proof of the other three parts.

The Fa,b,c conjecture is true, II

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and subsequently two parts of the conjecture were proved. The conjecture completely determines all finite members of the family. Here we complete the proof of the conjecture by giving proofs for the remaining three parts. (c) 2006 Elsevier Inc. All rights reserved.

Improved slope adjustment functions for soil erosion prediction

Numerous studies in the last 60 years have investigated the relationship between land slope and soil erosion rates. However, relatively few of these have investigated slope gradient responses: ( a) for steep slopes, (b) for specific erosion processes, and ( c) as a function of soil properties. Simulated rainfall was applied in the laboratory on 16 soils and 16 overburdens at 100 mm/h to 3 replicates of unconsolidated flume plots 3 m long by 0.8 m wide and 0.15 m deep at slopes of 20, 5, 10, 15, and 30% slope in that order. Sediment delivery at each slope was measured to determine the relationship between slope steepness and erosion rate. Data from this study were evaluated alongside data and existing slope adjustment functions from more than 55 other studies from the literature. Data and the literature strongly support a logistic slope adjustment function of the form S = A + B/[1 + exp (C - D sin theta)] where S is the slope adjustment factor and A, B, C, and D are coefficients that depend on the dominant detachment and transport processes. Average coefficient values when interill-only processes are active are A - 1.50, B 6.51, C 0.94, and D 5.30 (r(2) = 0.99). When rill erosion is also potentially active, the average slope response is greater and coefficient values are A - 1.12, B 16.05, C 2.61, and D 8.32 (r(2) = 0.93). The interill-only function predicts increases in sediment delivery rates from 5 to 30% slope that are approximately double the predictions based on existing published interill functions. The rill + interill function is similar to a previously reported value. The above relationships represent a mean slope response for all soils, yet the response of individual soils varied substantially from a 2.5-fold to a 50-fold increase over the range of slopes studied. The magnitude of the slope response was found to be inversely related ( log - log linear) to the dispersed silt and clay content of the soil, and 3 slope adjustment equations are proposed that provide a better estimate of slope response when this soil property is known. Evaluation of the slope adjustment equations proposed in this paper using independent datasets showed that the new equations can improve soil erosion predictions.

Bajo de la Alumbrera copper-gold deposit: Stable isotope evidence for a porphyry-related hydrothermal system dominated by magmatic aqueous fluids

Alteration zones at the gold-rich Bajo de la Alumbrera porphyry copper deposit in northwestern Argentina are centered on several porphyritic intrusions. They are zoned from a central copper-iron sulfide and gold-mineralized potassic (biotite-K-feldspar +/- quartz) core outward to propylitic (chlorite-illite-epidote-calcite) assemblages. A mineralized intermediate argillic alteration assemblage (chlorite-illite +/- pyrite) has overprinted the potassic alteration zone across the top and sides of the deposit and is itself zoned outward into phyllic (quartzinuscovite-illite +/- pyrite) alteration. This study contributes new data to previously reported delta(18)O and delta D compositions of fluids responsible for the alteration at Bajo de la Alumbrera, and the data are used to infer likely ore-forming processes. Measured and calculated delta(18)O and delta D values of fluids (+8.3 to +10.2 and -33 to -81 parts per thousand, respectively) confirm a primary magmatic origin for the earliest potassic alteration phase. Lower temperature potassic alteration formed from magmatic fluids with lower delta D values (down to -123 parts per thousand). These depleted compositions are distinct from meteoric water and consistent with degassing and volatile exsolution of magmatic fluids derived from an underlying magma. Variability in the calculated composition of fluid associated with potassic alteration is explained in terms of phase separation (or boiling). if copper-iron sulfide deposition occurred during cooling (as proposed elsewhere), this cooling was largely a result of phase separation. Magmatic water was directly involved in the formation of overprinting intermediate argillic alteration assemblages at Bajo de la Alumbrera. Calculated delta(18)O and delta D values of fluids associated with this alteration range from +4.8 to +8.1 and -31 to -71 per mil, respectively Compositions determined for fluids associated with phyllic alteration (-0.8 to +10.2 and -31 to -119 parts per thousand) overlap with the values determined for the intermediate argillic alteration. We infer that phyllic alteration assemblages developed during two stages; the first was a high-temperature (400 degrees-300 degrees C) stage with D-depleted water (delta D = -66 to -119 parts per thousand). This compositional range may have resulted from magma degassing and/or the injection of new magmatic water into a compositionally evolved hydrothermal system. The isotopic variations also can be explained by increased fluid-rock interaction. The second stage of phyllic alteration occurred at a lower temperature (similar to 200 degrees C), and variations in the modeled isotopic compositions imply mixing of magmatic and meteoric waters. Ore deposition that occurred late in the evolution of the hydrothermal system was probably associated with further cooling of the magmatic fluid, in part caused by fluid-rock interaction and phase separation. Changing pH and/or oxygen fuoracity may have caused additional ore deposition. The ingress of meteoric water appears to postdate the bulk of mineralization and occurred as the system at Bajo de la Alumbrera waned.