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.

The 2df SDSS LRG and QSO survey: evolution of the luminosity function of luminous red galaxies to z=0.6

We present new measurements of the luminosity function (LF) of luminous red galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS) and the 2dF SDSS LRG and Quasar (2SLAQ) survey. We have carefully quantified, and corrected for, uncertainties in the K and evolutionary corrections, differences in the colour selection methods, and the effects of photometric errors, thus ensuring we are studying the same galaxy population in both surveys. Using a limited subset of 6326 SDSS LRGs (with 0.17 < z < 0.24) and 1725 2SLAQ LRGs (with 0.5 < z < 0.6), for which the matching colour selection is most reliable, we find no evidence for any additional evolution in the LRG LF, over this redshift range, beyond that expected from a simple passive evolution model. This lack of additional evolution is quantified using the comoving luminosity density of SDSS and 2SLAQ LRGs, brighter than M-0.2r - 5 log h(0.7) = - 22.5, which are 2.51 +/- 0.03 x 10(-7) L circle dot Mpc(-3) and 2.44 +/- 0.15 x 10(-7) L circle dot Mpc(-3), respectively (< 10 per cent uncertainty). We compare our LFs to the COMBO-17 data and find excellent agreement over the same redshift range. Together, these surveys show no evidence for additional evolution (beyond passive) in the LF of LRGs brighter than M-0.2r - 5 log h(0.7) = - 21 ( or brighter than similar to L-*).. We test our SDSS and 2SLAQ LFs against a simple 'dry merger' model for the evolution of massive red galaxies and find that at least half of the LRGs at z similar or equal to 0.2 must already have been well assembled (with more than half their stellar mass) by z similar or equal to 0.6. This limit is barely consistent with recent results from semi-analytical models of galaxy evolution.

Maximal triangle trades with foundation 5 (mod 6) - the final case

The maximum possible volume of a simple, non-Steiner (v, 3, 2) trade was determined for all v by Xhosrovshahi and Torabi (Ars Combinatoria 51 (1999), 211-223), except that in the-case v equivalent to 5 (mod 6), v >= 23, they were only able to provide an upper, bound on the volume. In this paper we construct trades with volume equal to that bound for all v equivalent to 5 (mod 6), thus completing the problem.