Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

El Corán y la paz.

Después de los ataques del 11-s, este artículo pretende aclarar la raíz del problema entre el mundo musulmán y el occidental, la clave se encuentra en el Corán. Tras una introducción histórica sobre los orígenes del Islam, pasa a analizar el contenido, la estructura y varios versículos (o 'aliyas') del Corán (o 'Alcorán') que tratan sobre el determinismo, la incitación a la guerra, la discriminación de las mujeres, la salvación de los judíos y cristianos y la autorización de la hiperpoligamia.

Esplendores del Corán.

Título anterior de la publicación: Boletín de la Comisión Española de la UNESCO

Does reactive surface area depend on grain size? Results from pH 3, 25 circle C far-from-equilibrium flow-through dissolution experiments on anorthite and biotite

Laboratory determined mineral weathering rates need to be normalised to allow their extrapolation to natural systems. The principle normalisation terms used in the literature are mass, and geometric- and BET specific surface area (SSA). The purpose of this study was to determine how dissolution rates normalised to these terms vary with grain size. Different size fractions of anorthite and biotite ranging from 180-150 to 20-10 mu m were dissolved in pH 3, HCl at 25 degrees C in flow through reactors under far from equilibrium conditions. Steady state dissolution rates after 5376 h (anorthite) and 4992 h (biotite) were calculated from Si concentrations and were normalised to initial- and final- mass and geometric-, geometric edge- (biotite), and BET SSA. For anorthite, rates normalised to initial- and final-BET SSA ranged from 0.33 to 2.77 X 10(-10) mol(feldspar) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 5.74 to 8.88 X 10(-10) mol(feldspar) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.11 to 1.65 mol(feldspar) g(-1) s(-1). For biotite, rates normalised to initial- and final-BET SSA ranged from 1.02 to 2.03 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 3.26 to 16.21 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric edge SSA ranged from 59.46 to 111.32 x 10(-12) mol(biotite) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.81 to 6.93 X 10(-12) mol(biotite) g(-1) s(-1). For all normalising terms rates varied significantly (p <= 0.05) with grain size. The normalising terms which gave least variation in dissolution rate between grain sizes for anorthite were initial BET SSA and initial- and final-geometric SSA. This is consistent with: (1) dissolution being dominated by the slower dissolving but area dominant non-etched surfaces of the grains and, (2) the walls of etch pits and other dissolution features being relatively unreactive. These steady state normalised dissolution rates are likely to be constant with time. Normalisation to final BET SSA did not give constant ratios across grain size due to a non-uniform distribution of dissolution features. After dissolution coarser grains had a greater density of dissolution features with BET-measurable but unreactive wall surface area than the finer grains. The normalising term which gave the least variation in dissolution rates between grain sizes for biotite was initial BET SSA. Initial- and final-geometric edge SSA and final BET SSA gave the next least varied rates. The basal surfaces dissolved sufficiently rapidly to influence bulk dissolution rate and prevent geometric edge SSA normalised dissolution rates showing the least variation. Simple modelling indicated that biotite grain edges dissolved 71-132 times faster than basal surfaces. In this experiment, initial BET SSA best integrated the different areas and reactivities of the edge and basal surfaces of biotite. Steady state dissolution rates are likely to vary with time as dissolution alters the ratio of edge to basal surface area. Therefore they would be more properly termed pseudo-steady state rates, only appearing constant because the time period over which they were measured (1512 h) was less than the time period over wich they would change significantly. (c) 2006 Elsevier Inc. All rights reserved.

Effects of manure and fertilizer on grain yield, soil carbon and phosphorus in a 13-year field trial in semi-arid Kenya

Long-term indicators of soil fertility were assessed by measuring grain yield, soil organic carbon (SOC) and soil Olsen phosphorous for a P-deficient soil. In one set of treatments, goat manure was applied annually for 13 years at 0, 5 and 10 t ha(-1), and intercrops of sorghum/cowpea, millet/green gram and maize/pigeonpea were grown. Yield depended on rainfall and trends with time were not identifiable. Manure caused an upward trend in SOC, but 10 t ha(-1) manure did not give significantly more SOC than 5 t ha(-1). Only 10 t ha(-1) manure increased Olsen P. Measurements of both SOC and Olsen P are recommended. In another set of treatments, manure was applied for four years; the residual effect lasted another seven to eight years when assessed by yield, SOC and Olsen P Treatment with mineral fertilizers provided the same rates of N and P as 5 t hat manure and yields from manure and fertilizer were similar. Fertilizer increased Olsen P but not SOC. Management systems with occasional manure application and intermediate fertilizer applications should be assessed. Inputs and offtakes of C, N and P were measured for three years. Approximately 16, 25 and 11% of C, N and P respectively were stabilized into soil organic matter from 5 t ha(-1) a(-1) manure. The majority of organic P was fixed as soil inorganic P.

Effects of corn silage derived from a genetically modified variety containing two Transgenes on feed intake, milk production, and composition, and the absence of detectable Transgenic deoxyribonucleic acid in milk in holstein dairy cows

The objectives were to compare the chemical composition, nutritive value, feed intake, milk production and composition, and presence in milk of transgenic DNA and the encoded protein Cry1Ab when corn silages containing 2 transgenes (2GM: herbicide tolerance: mepsps and insect resistance: cry1Ab) were fed as part of a standard total mixed ration (TMR) compared with a near isogenic corn silage ( C) to 8 multiparous lactating Holstein dairy cows in a single reversal design study. Cows were fed a TMR ration ad libitum and milked twice daily. Diets contained [ dry matter (DM) basis] 45% corn silage, 10% alfalfa hay, and 45% concentrate (1.66 Mcal of net energy for lactation/kg of DM, 15.8% crude protein, 35% neutral detergent fiber, and 4.1% fat). Each period was 28-d long. During the last 4 d of each period, feed intake and milk production data were recorded and milk samples taken for compositional analysis, including the presence of transgenic DNA and Cry1Ab protein. There was no significant difference in the chemical composition between C and 2GM silages, and both were within the expected range (37.6% DM, 1.51 Mcal of net energy for lactation/kg, 8.6% crude protein, 40% neutral detergent fiber, 19.6% acid detergent fiber, pH 3.76, and 62% in vitro DM digestibility). Cows fed the 2GM silage produced milk with slightly higher protein (3.09 vs. 3.00%), lactose ( 4.83 vs. 4.72%) and solids-not-fat (8.60 vs. 8.40%) compared with C. However, the yield (kg/d) of milk (36.5), 3.5% fat-corrected milk (34.4), fat (1.151), protein (1.106), lactose (1.738), and solids-not-fat ( 3.094), somatic cell count (log(10): 2.11), change in body weight (+ 7.8 kg), and condition score (+ 0.09) were not affected by type of silage, indicating no overall production difference. All milk samples were negative for the presence of transgenic DNA from either trait or the Cry1Ab protein. Results indicate that the 2GM silage modified with 2 transgenes did not affect nutrient composition of the silages and had no effect on animal performance and milk composition. No transgenic DNA and Cry1Ab protein were detected in milk.

The effects of irrigation, nitrogen fertilizer and grain size on Hagberg falling number, specific weight and blackpoint of winter wheat

The effects of irrigation and nitrogen (N) fertilizer on Hagberg falling number (HFN), specific weight (SW) and blackpoint (BP) of winter wheat (Triticum aestivum L) were investigated. Mains water (+50 and +100 mm month(-1), containing 44 mg NO3- litre(-1) and 28 mg SO42- litre(-1)) was applied with trickle irrigation during winter (17 January-17 March), spring (21 March-20 May) or summer (24 May-23 July). In 1999/2000 these treatments were factorially combined with three N levels (0, 200, 400 kg N ha(-1)), applied to cv Hereward. In 2000/01 the 400 kg N ha(-1) treatment was replaced with cv Malacca given 200 kg N ha(-1). Irrigation increased grain yield, mostly by increasing grain numbers when applied in winter and spring, and by increasing mean grain weight when applied in summer. Nitrogen increased grain numbers and SW, and reduced BP in both years. Nitrogen increased HFN in 1999/2000 and reduced HFN in 2000/01. Effects of irrigation on HFN, SW and BP were smaller and inconsistent over year and nitrogen level. Irrigation interacted with N on mean grain weight: negatively for winter and spring irrigation, and positively for summer irrigation. Ten variables derived from digital image analysis of harvested grain were included with mean grain weight in a principal components analysis. The first principal component ('size') was negatively related to HFN (in two years) and BP (one year), and positively related to SW (two years). Treatment effects on dimensions of harvested grain could not explain all of the effects on HFN, BP and SW but the results were consistent with the hypothesis that water and nutrient availability, even when they were affected early in the season, could influence final grain quality if they influenced grain numbers and size. (C) 2004 Society of Chemical Industry

Chemical composition and fermentation characteristics of grain and different parts of the stover from maize land races harvested at different growing periods in two zones of central Mexico

The objective of this work was to determine the rumen fermentation characteristics of maize land races used as forage in central Mexico. In vitro gas production (ml per 200 mg dry matter (DM)) incubations were carried out, and cumulative gas volumes were fitted to the Krishnamoorthy et al. (1991) model. The trial used a split-plot design with cultivation practices associated with maize colour (COL) as the main plot with three levels: white, yellow and black maize; growing periods (PER) were the split plots where PER1, PER2 and PER3 represented the first, second and third periods, respectively and two contrasting zones (Z1 = valley and Z2 = mountain) were used as blocking factors. The principal effects observed were associated with the maturity of the plants and potential gas production increased (P < 0.05) in stems (PER 1 = 51.8, PER2 = 56.3, PER3 = 58.4 ml per 200 mg DM) and in whole plant (PER 1 = 60.9, PER2 = 60.8, PER3= 70.9 ml per 200 mg DM). An inverse effect was observed with fermentation rates in leaves (P < 0.01) with 0.061, 0.053 and 0.0509 (per h) and in whole plant (P < 0.05) with 0.068, 0.057, 0.050 (per h) in PER1, PER2 and PER3 respectively. The digestibility of the neutral-detergent fibre (NDF) decreased with maturity especially in leaves (P < 0.05) with values of 0.71, 0.67 and 0.66 g/kg; in rachis (P < 0.01) 0.75, 0.72, and 0.65 in PER1, PER2 and PER3 respectively. The NDF content in leaves in leaves (668, 705 and 713 g/kg DM for PER1, PER2 and PER3, respectively), stems (580, 594 and 644 g/kg DM) and, husk (663, 774 and, 808 g/kg DM) increased (P < 0.05) with increasing plant maturity, rachis were significantly different between periods (P < 0.01). The structure with-the best nutritive characteristics was the husk, because it had the lowest fibre contents, especially in acid-detergent lignin, with values of 22.6, 28.6 and 37.6 g/kg DM in PER1, PER2 and PER3, respectively.