Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

Consistent predictable patterns in the hydrogen and oxygen stable isotope ratios of animal proteins consumed by modern humans in the USA

Published datasets of proteinaceous animal tissues suggest that co‐variation between amino acid hydrogen (δ²H) and oxygen (δ¹⁸O) isotope ratios is a common feature in systems where isotopic variation is driven by geographic or temporal variation in the δ²H and δ¹⁸O values of environmental water. This has led to the development of models relating tissue δ²H and δ¹⁸O values to those of water, with potential application in a number of fields. However, the strength and ubiquity of the influence of environmental water on protein isotope ratios across taxonomic groups, and thus the relevance of predictive models, is an open question. Here we report strong co‐variation of δ²H and δ¹⁸O values across a suite of terrestrial and aquatic animal meats purchased in American food markets, including beef, poultry (chicken and turkey), chicken eggs, pork, lamb, freshwater fish, and marine fish. Significant isotope co‐variation was not found for small collections of marine bivalves and crustaceans. These results imply that isotopic signals from environmental water were propagated similarly through most of the diverse natural and human‐managed foodwebs represented by our samples. Freshwater fish had the largest variation in δ²H and δ¹⁸O values, with ranges of 121 ‰ and 19.2 ‰, respectively, reflecting the large isotopic variation in environmental freshwaters. In contrast marine animals had the smallest variation for both δ²H (7 ‰ range, crustaceans) and δ¹⁸O (3.0 ‰ range, bivalves) values. Known‐origin beef samples demonstrated direct relationships between the variance of environmental water isotope ratios and that of collected meats. Copyright © 2011 John Wiley & Sons, Ltd.     

Accuracy and precision of a laser-spectroscopy approach to the analysis of δ2H and δ18O in human urine

The isotope ratio analysis of body water often involves large sample numbers and lengthy sample processing. Here we demonstrate the ability of isotope ratio infrared spectroscopy (IRIS) to rapidly and accurately analyse the isotope ratios of water in urine. We analysed water extracted from human urine using traditional isotope ratio mass spectrometry (IRMS) and compared those values with IRIS-analysed extracted water and un-extracted urine. Regression analyses for δ²H and δ¹⁸O values between (1) extracted water analysed via IRMS and IRIS and (2) urine and extracted water analysed via IRIS were significant (R ²=0.99). These results indicate that cryogenic distillation of urine was not required for an accurate estimate of the isotopic composition of urine when using IRIS.     

无机酸洗脱对胜利褐煤微晶结构及其自燃倾向性的影响

利用XRD、Raman、XPS和FT-IR表征技术,研究无机酸洗脱(HCl、H2SO4、HCl-HF)处理的胜利褐煤微晶结构的变化,采用自行设计的表面吸附仪-GC联用装置,对样品进行不同温度的低温脉冲氧化实验,考察了煤样在不同温度下氧吸附量的变化规律,通过低温脉冲氧吸附规律与TG/DTG和固定床燃烧实验关联,考察了煤样的自燃倾向。结果表明,无机酸洗脱对矿物质的脱除使得煤结构的有序度增加,石墨化程度提高,无机酸洗脱煤样与原煤相比吸氧量明显下降。随着吸附温度的升高,各煤样吸氧量明显增加,且随着脱除矿物质程度的增加,吸氧量呈减小的趋势,导致自燃倾向降低。     

Temperature dependence of oxygen isotope acid fractionation for modern and fossil tooth enamels

The oxygen isotope ratio of CO(2) liberated from structural carbonate in tooth enamel apatite was measured at phosphoric acid reaction temperatures of 25 degrees C, 60 degrees C and 90 degrees C, and it was found that apparent acid fractionation factors for pristine enamel, fossilized enamel, and calcite follow different temperature relationships. Using sealed vessel reactions normalized to alpha(25) = 1.01025 (the fractionation factor for calcite at 25 degrees C), the apparent fractionation factor at 90 degrees C (alpha*(90)) for pristine enamel ranged between 1.00771 and 1.00820, and between 1.00695 and 1.00772 for fossilized enamel. Apparent fractionation factors for common acid bath reactions are similar to those for sealed vessel reactions. A significant correlation exists between alpha*(90) and F(-) content, suggesting that change in the acid fractionation factor may be related to the replacement of OH(-) with F(-) during fossilization of bioapatite. These results have important implications for making accurate comparisons between modern and fossil tooth enamel delta(18)O values, and for the uniformity of isotope data produced in different laboratories using different acid reaction temperatures.     

Stable hydrogen and oxygen isotope ratios of bottled waters of the world

Bottled and packaged waters are an increasingly significant component of the human diet. These products are regulated at the regional, national, and international levels, and determining the authenticity of marketing and labeling claims represents a challenge to regulatory agencies. Here, we present a dataset of stable isotope ratios for bottled waters sampled worldwide, and consider potential applications of such data for regulatory, forensic and geochemical standardization applications. The hydrogen and oxygen isotope ratios of 234 samples of bottled water range from -147 per thousand to +15 per thousand and from -19.1 per thousand to +3.0 per thousand, respectively. These values fall within and span most of the normal range for meteoric waters, indicating that these commercially available products represent a source of waters for use as laboratory working standards in applications requiring standardization over a large range of isotope ratios. The measured values of bottled water samples cluster along the global meteoric water line, suggesting that bottled water isotope ratios preserve information about the water sources from which they were derived. Using the dataset, we demonstrate how bottled water isotope ratios provide evidence for substantial evaporative enrichment of water sources prior to bottling and for the marketing of waters derived from mountain and lowland sources under the same name. Comparison of bottled water isotope ratios with natural environmental water isotope ratios demonstrates that on average the isotopic composition of bottled water tends to be similar to the composition of naturally available local water sources, suggesting that in many cases bottled water need not be considered as an isotopically distinct component of the human diet. Our findings suggest that stable isotope ratios of bottled water have the power to distinguish ultimate (e.g., recharge) and proximal (e.g., reservoir) sources of bottled water and constitute a potential tool for use in the regulatory monitoring of water products.     

An approximate treatment of scattering based on the delta boundary operator

The development of a scheme to treat two-dimensional electromagneticscattering by electrically large, perfectly conducting bodiesis described. It incorporates the effects of surface curvatureand non-local phenomena and has the potential to provide thebasis for a general technique yielding more accurate predictionsthan the widely used physical optics method.