On extensions of the core and the anticore of transferable utility games

We consider several related set extensions of the core and the anticore of games with transferable utility. An efficient allocation is undominated if it cannot be improved, in a specific way, by sidepayments changing the allocation or the game. The set of all such allocations is called the undominated set, and we show that it consists of finitely many polytopes with a core-like structure. One of these polytopes is the $L_1$ -center, consisting of all efficient allocations that minimize the sum of the absolute values of the excesses. The excess Pareto optimal set contains the allocations that are Pareto optimal in the set obtained by ordering the sums of the absolute values of the excesses of coalitions and the absolute values of the excesses of their complements. The $L_1$ -center is contained in the excess Pareto optimal set, which in turn is contained in the undominated set. For three-person games all these sets coincide. These three sets also coincide with the core for balanced games and with the anticore for antibalanced games. We study properties of these sets and provide characterizations in terms of balanced collections of coalitions. We also propose a single-valued selection from the excess Pareto optimal set, the min-prenucleolus, which is defined as the prenucleolus of the minimum of a game and its dual.     

7‐Methoxy‐2,3‐dioxo‐1,4‐dihydroquinoxalin‐6‐aminium chloride monohydrate

Single crystals of the title compound, C₉H₁₀N₃O₃⁺·Cl⁻·H₂O, were obtained by recrystallization from hydrochloric acid. The cations stack along the crystallographic a direction. The 2,3‐dioxo‐1,4‐dihydroquinoxaline group shows a significant deviation from planarity [r.m.s. deviation from the best plane = 0.063 (2) Å]. Hydrogen bonding links the cations, chloride anions and water molecules to form an extended three‐dimensional architecture.     

Synthesis of tetrahydroisoquinoline-diamine ligands and their application in asymmetric transfer hydrogenation

The use of the tetrahydroisoquinoline scaffold is well documented in biologically active compounds. However, reports of the utilisation of tetrahydroisoquinoline compounds in asymmetric catalysis are limited. The synthesis of novel diamine ligands possessing the tetrahydroisoquinoline (tetrahydroisoquinoline) backbone and evaluation of their activity in the asymmetric transfer hydrogenation of acetophenone are presented. The diamine ligands in conjunction with i-PrOH as the hydrogen source and [RhCl₂(Cp1)]₂ as the metal precursor proved to be the most effective of the tetrahydroisoquinoline derivatives for this catalytic system. Water was found to have a profound influence on the enantioselectivity of the reaction. Optimisation of the amount water, i-PrOH and catalytic loading content rendered the best result of 70% enantioselectivity for the (S)-1-phenylethanol isomer product.     

A rapid method for the sampling of atmospheric water vapour for isotopic analysis

Analysis of the stable isotopic composition of atmospheric moisture is widely applied in the environmental sciences. Traditional methods for obtaining isotopic compositional data from ambient moisture have required complicated sampling procedures, expensive and sophisticated distillation lines, hazardous consumables, and lengthy treatments prior to analysis. Newer laser‐based techniques are expensive and usually not suitable for large‐scale field campaigns, especially in cases where access to mains power is not feasible or high spatial coverage is required. Here we outline the construction and usage of a novel vapour‐sampling system based on a battery‐operated Stirling cycle cooler, which is simple to operate, does not require any consumables, or post‐collection distillation, and is light‐weight and highly portable. We demonstrate the ability of this system to reproduce δ¹⁸O isotopic compositions of ambient water vapour, with samples taken simultaneously by a traditional cryogenic collection technique. Samples were collected over 1 h directly into autosampler vials and were analysed by mass spectrometry after pyrolysis of 1 µL aliquots to CO. This yielded an average error of < ±0.5‰, approximately equal to the signal‐to‐noise ratio of traditional approaches. This new system provides a rapid and reliable alternative to conventional cryogenic techniques, particularly in cases requiring high sample throughput or where access to distillation lines, slurry maintenance or mains power is not feasible. Copyright © 2009 John Wiley & Sons, Ltd.     

Phosphido‐diphosphine pincer group 3 complexes as efficient initiators for lactide polymerization

New Group 3 metal complexes of the type [LM(CH₂SiMe₃)₂(THF)_n] supported by tridentate phosphido‐diphosphine ligands [(o‐C₆H₄PR₂) ₂ PH; L1‐H : R = iPr; L2‐H : R = Ph] have been synthesized by reaction of L1‐H and L2‐H with [M(CH₂SiMe₃)₃(THF)₂)] (M = Y and Sc). All the new complexes [(o‐C₆H₄PR₂) ₂ PM(CH₂SiMe₃)₂(THF)_n] [M = Y, R = iPr (1), R = Ph (2); M = Sc, R = iPr (3), R = Ph (4)] were studied as initiators for the ring opening polymerization of lactide. The yttrium complexes ( 1 and 2 ) exhibited high activity and good polymerization control, shown by the linear fits in the plot of number‐averaged molecular weight (M_n) versus the percentage conversion and versus the monomer/initiator ratio and by the low polydispersity index values. Interestingly, very good molar‐mass control was observed even when L ‐Lactide was polymerized in the absence of solvent at 130 °C. A good molar‐mass control but lower activities were observed in the polymerization reaction of lactide promoted by the analogous scandium complexes 3 and 4 . © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1374–1382, 2010     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Numerical simulation and laser-based imaging of mixture formation, ignition, and soot formation in a diesel spray

Laser-based imaging of fuel vapor distribution, ignition, and soot formation in diesel sprays was carried out in a high-pressure, high-temperature spray chamber under conditions that correspond to temperature and pressure in a diesel engine. Rayleigh scattering and laser-induced incandescence are used to image fuel density and soot volume fraction. The experimental results provide data for comparison with numerical simulations. An interactive cross-sectionally averaged spray model based on Eulerian transport equations was used for the simulation of the spray, and the turbulence-chemistry interaction was modeled with the representative interactive flamelet (RIF) concept. The flamelet calculation is coupled to the Kiva3V computational fluid dynamics (CFD) code using the scalar dissipation rate and pressure as an input to the RIF-code. The flamelet code computes the instationary flamelet profiles for every time step. These profiles were integrated over mixture fraction space using a prescribed β-PDF to obtain mean values, which are passed back to the CFD-code. Thereby, the temperature and the relevant species in each CFD-cell were obtained. The fuel distribution, the average ignition delay as well as the location of ignition are well predicted by the simulation. Furthermore, simulations show that the experimentally observed injection-to-injection variations in ignition delay are due to temperature inhomogeneities. Experimental and simulated spatial soot and fuel vapor density distributions are compared during and after second stage ignition.