A note on theβ-measure for digraph competitions

Digraph games are cooperative TU-games associated to digraph competitions: domination structures that can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles for a group of individuals within the framework of social choice theory. Brink and Gilles (2000) defined theβ-measure of a digraph competition as the Shapley value of the corresponding digraph game. This paper provides a new characterization of theβ-measure.     

Aggregation effects in maximum covering models

The level of aggregation is critical in discrete location analyses as it affects the level of data collection required, computation times and the usefulness of the analyses. We examine the effects of three alternative nodal aggregation schemes on (i) the model's solution times, (ii) the locational decisions indicated by the maximum covering model, (iii) the coverage provided by the aggregate solutions compared with the optimal solutions, and (iv) the coverage predicted by the aggregate model compared with the coverage that results from using the aggregate model's facility sites and the disaggregate demands. The results suggest that considerable aggregation can be tolerated without incurring large errors in total coverage, but that location errors are introduced at moderate levels of aggregation. The magnitude of these errors is significantly affected by the aggregation scheme employed.     

Optimal bounds for ratios of eigenvalues of one-dimensional Schrödinger operators with Dirichlet boundary conditions and positive potentials

Consider the Schrödinger equation –u+V(x)u=u on the intervalI, whereV(x)0 forxI and where Dirichlet boundary conditions are imposed at the endpoints ofI. We prove the optimal bound

Quantification of copper and zinc species fractions in legume seeds extracts by SEC/ICP-MS: validation and uncertainty estimation

Fractions of Cu and Zn species in legume samples (common white bean, pea, chick pea and lentil seeds and defatted soybean flour) were analysed by on-line hyphenation of size exclusion chromatography and inductively coupled plasma-mass spectrometry. Samples were extracted by 0.02 mol l⁻¹ Tris–HCl buffer solution, pH 7.5. The extraction efficiency lay in the region 60–90 and 60–80% for Cu and Zn, respectively. Quantification of elements in the individual chromatographic fractions was carried out by isotope dilution (ID) and external calibration (EC) techniques. For ID analysis the chromatographic effluent was mixed with the flow of ⁶⁵Cu and ⁶⁸Zn isotope enriched solution and the isotope ratio values ⁶³Cu/⁶⁵Cu and (⁶⁴Zn+⁶⁶Zn)/⁶⁸Zn were measured. In the case of EC technique calibration solutions of elements were injected to the flow of mobile phase by the second injector. Prior entering detector the effluent was mixed with the flow of internal standard solution (In, 50 μg l⁻¹). Both methods have similar precision, however the behaviour of both studied elements was not the same. The chromatographic analysis itself was the main source of variability in the case of Cu. For Zn species analysis, the extraction process and the manipulation with the extract, played the significant role too. It was probably caused by lower stability of the present zinc chelates. The total amounts of Zn found in all chromatographic fractions represented 85–95% of Zn in sampled extract whereas those of Cu approached 100%. In case of small peaks the results of ID and EC were not the same. The EC results were lower then ID results. The great deal of results uncertainty accounts for the precision.     

Bis(amino acid) derivatives of 1,4-diamino-2-butyne that adopt a C2-symmetric turn conformation

1,4-Diamino-2-butyne was prepared from 1,4-dichloro-2-butyne via 1,4-diazido-2-butyne. Bis(amino acid) derivatives of 1,4-diamino-2-butyne having the general structure (Boc-Xxx-NHCH2C[triple bond])2 (Xxx = Ala, Phe and Met) were prepared and examined by 1H NMR spectroscopy. Using chemical shift, coupling constant and DMSO titration data it is found that these compounds adopt a C2-symmetric turn conformation featuring two intramolecular hydrogen bonds.     

Group additive values for the gas phase standard enthalpy of formation of hydrocarbons and hydrocarbon radicals

A complete and consistent set of 95 Benson group additive values (GAV) for the standard enthalpy of formation of hydrocarbons and hydrocarbon radicals at 298 K and 1 bar is derived from an extensive and accurate database of 233 ab initio standard enthalpies of formation, calculated at the CBS-QB3 level of theory. The accuracy of the database was further improved by adding newly determined bond additive corrections (BAC) to the CBS-QB3 enthalpies. The mean absolute deviation (MAD) for a training set of 51 hydrocarbons is better than 2 kJ mol(-1). GAVs for 16 hydrocarbon groups, i.e., C(C(d))(3)(C), C-(C(d))(4), C-(C(t))(C(d))(C)(2), C-(C(t))(C(d))(2)(C), C-(C(t))(C(d))(3), C-(C(t))(2)(C)(2), C-(C(t))(2)(C(d))(C), C-(C(t))(2)(C(d))(2), C-(C(t))(3)(C), C-(C(t))(3)(C(d)), C-(C(t))(4), C-(C(b))(C(d))(C)(H), C-(C(b))(C(t))(H)(2), C-(C(b))(C(t))(C)(H), C-(C(b))(C(t))(C)(2), C(d)-(C(b))(C(t)), for 25 hydrocarbon radical groups, and several ring strain corrections (RSC) are determined for the first time. The new parameters significantly extend the applicability of Benson's group additivity method. The extensive database allowed an evaluation of previously proposed methods to account for non-next-nearest neighbor interactions (NNI). Here, a novel consistent scheme is proposed to account for NNIs in radicals. In addition, hydrogen bond increments (HBI) are determined for the calculation of radical standard enthalpies of formation. In particular for resonance stabilized radicals, the HBI method provides an improvement over Benson's group additivity method.     

Accuracy and long-term reproducibility of lead isotopic measurements by multiple-collector inductively coupled plasma mass spectrometry using an external method for correction of mass discrimination

The precision of isotopic measurements of Pb by thermal ionization mass spectrometry (TIMS) is limited by the fact that this element does not possess an invariant isotope ratio that can be used for the correction of mass fractionation by internal normalization. Multiple-collector inductively coupled plasma mass spectrometry (MC-ICPMS) can overcome this limitation, because with plasma ionization, elements with overlapping mass ranges are thought to display identical mass discrimination. With respect to Pb, this can be exploited by the addition of Tl to the sample solutions; the mass discrimination factor obtained for Tl can then be used for the correction of the measured Pb isotope ratios. In this article we present the results of a detailed study that investigates the accuracy and precision of such an external correction technique for mass discrimination based upon the results of multiple analyses of a mixed standard solution of NIST SRM-981 Pb and SRM-997 Tl. Our data indicate that normalization of the Pb isotope ratios to the certified isotopic composition of SRM-997 Tl produces Pb isotopic results that are significantly lower than recently published reference values by TIMS. This systematic offset can be eliminated by renormalization of the Pb data to a different Tl isotopic composition to obtain an empirically determined mass discrimination factor for Pb that generates accurate results. It is furthermore shown that a linear law is least suited for the correction of mass discrimination, whereas a power or exponential law function provide significantly more accurate and precise results. In detail, it appears that a power law may provide the most appropriate correction procedure, because the corrected Pb isotope ratios display less residual correlations with mass discrimination compared to the exponentially corrected data. Using an exponential or power law correction our results, obtained over a period of over seven months, display a precision (2σ) of better than 60 parts per million (ppm) for ²⁰⁸Pb/²⁰⁶Pb and ²⁰⁷Pb/²⁰⁶Pb and of better than 350 ppm for ²⁰⁶Pb/²⁰⁴Pb, ²⁰⁷Pb/²⁰⁴Pb/²⁰⁴Pb, and ²⁰⁸Pb/²⁰⁴Pb. This represents a significant improvement compared to conventional TIMS techniques and demonstrates the potential of MC-ICPMS for routine, high-precision measurements of Pb isotopic compositions.