Tighter αBB relaxations through a refi nement scheme for the scaled Gerschgorin theorem

Of central importance to the αBB algorithm is the calculation of the α values that guarantee the convexity of the underestimator. Improvement (reduction) of these values can result in tighter underestimators and thus increase the performance of the algorithm. For instance, it was shown by Wechsung et al. (J Glob Optim 58(3):429-438, 2014) that the emergence of the cluster effect can depend on the magnitude of the α values. Motivated by this, we present a refinement method that can improve (reduce) the magnitude of α values given by the scaled Gerschgorin method and thus create tighter convex underestimators for the αBB algorithm. We apply the new method and compare it with the scaled Gerschgorin on randomly generated interval symmetric matrices as well as interval Hessians taken from test functions. As a measure of comparison, we use the maximal separation distance between the original function and the underestimator. Based on the results obtained, we conclude that the proposed refinement method can significantly reduce the maximal separation distance when compared to the scaled Gerschgorin method. This approach therefore has the potential to improve the performance of the αBB algorithm

Global patterns of nitrate isotope composition in rivers and adjacent aquifers reveal reactive nitrogen cascading

Remediation of nitrate pollution of Earth’s rivers and aquifers is hampered by cumulative biogeochemical processes and nitrogen sources. Isotopes (δ15N, δ18O) help unravel spatiotemporal nitrogen(N)-cycling of aquatic nitrate (NO3−). We synthesized nitrate isotope data (n = ~5200) for global rivers and shallow aquifers for common patterns and processes. Rivers had lower median NO3− (0.3 ± 0.2 mg L−1, n = 2902) compared to aquifers (5.5 ± 5.1 mg L−1, n = 2291) and slightly lower δ15N values (+7.1 ± 3.8‰, n = 2902 vs +7.7 ± 4.5‰, n = 2291), but were indistinguishable in δ18O (+2.3 ± 6.2‰, n = 2790 vs +2.3 ± 5.4‰, n = 2235). The isotope composition of NO3− was correlated with water temperature revealing enhanced N-cascading in warmer climates. Seasonal analyses revealed higher δ15N and δ18O values in wintertime, suggesting waste-related N-source signals are better preserved in the cold seasons. Isotopic assays of nitrate biogeochemical transformations are key to understanding nitrate pollution and to inform beneficial agricultural and land management strategies

Transport and fate of BTEX vapours in unsaturated soil

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A new corrosion casting technique

A technique is described, employing polyester as the injection material, for preparing a casting of all cardiac vessels or of arteries or veins separately. This technique was used in 10 bovine and 40 fresh human hearts. The technique is simple, rapid, economical and the required equipment is available in the average laboratory. The extent of vascular penetration is controlled by the viscosity of the polyester solutions, some of which at a certain density can penetrate through the net of capillaries with an injection pressure of no more than 220 mm Hg. Our technique does not require any special handling of the heart and it makes no difference to the quality of the casting whether the blood is drained or flushed from the vessels prior to the perfusion. There is no noted shrinkage or crumbling of our specimens stored at room temperature. The heart size, configuration and the anatomical relationship of the cardiac vessels are preserved without the need for casting cardiac chambers. The injection materials are cheap, easily transported and can be stored without special care. Injection, solidification and corrosion are carried out at room temperature. Copyright © 1978 Wiley‐Liss, Inc

Multiple parameterization for hydraulic conductivity identification

Hydraulic conductivity identification remains a challenging inverse problem in ground water modeling because of the inherent nonuniqueness and lack of flexibility in parameterization methods. This study introduces maximum weighted log-likelihood estimation (MWLLE) along with multiple generalized parameterization (GP) methods to identify hydraulic conductivity and to address nonuniqueness and inflexibility problems in parameterization. A scaling factor for information criteria is suggested to obtain reasonable weights of parameterization methods for the MWLLE and model averaging method. The scaling factor is a statistical parameter relating to a desired significance level in Occam\u27s window and the variance of the chi-squares distribution of the fitting error. Through model averaging with multiple GP methods, the conditional estimate of hydraulic conductivity and its total conditional covariances are calculated. A numerical example illustrates the issue arising from Occam\u27s window in estimating model weights and shows the usefulness of the scaling factor to obtain reasonable model weights. Moreover, the numerical example demonstrates the advantage of using multiple GP methods over the zonation and interpolation methods because GP provides better models in the model averaging method. The methodology is applied to the Alamitos Gap area, California, to identify the hydraulic conductivity field. The results show that the use of the scaling factor is necessary in order to incorporate good parameterization methods and to avoid a dominant parameterization method