Strongly essential coalitions and the nucleolus of peer group games

Most of the known efficient algorithms designed to compute the nucleolus for special classes of balanced games are based on two facts: (i) in any balanced game, the coalitions which actually determine the nucleolus are essential; and (ii) all essential coalitions in any of the games in the class belong to a prespecified collection of size polynomial in the number of players. We consider a subclass of essential coalitions, called strongly essential coalitions, and show that in any game, the collection of strongly essential coalitions contains all the coalitions which actually determine the core, and in case the core is not empty, the nucleolus and the kernelcore. As an application, we consider peer group games, and show that they admit at most 2n−1 strongly essential coalitions, whereas the number of essential coalitions could be as much as 2ⁿ⁻¹. We propose an algorithm that computes the nucleolus of an n-player peer group game in time directly from the data of the underlying peer group situation.Research supported in part by OTKA grant T030945. The authors thank a referee and the editor for their suggestions on how to improve the presentation     

Weighted allocation rules for standard fixed tree games

In this paper we consider standard fixed tree games, for which each vertex unequal to the root is inhabited by exactly one player. We present two weighted allocation rules, the weighted down-home allocation and the weighted neighbour-home allocation, both inspired by the painting story in Maschler et al. (1995) . We show, in a constructive way, that the core equals both the set of weighted down-home allocations and the set of weighted neighbour allocations. Since every weighted down-home allocation specifies a weighted Shapley value (Kalai and Samet (1988)) in a natural way, and vice versa, our results provide an alternative proof of the fact that the core of a standard fixed tree game equals the set of weighted Shapley values. The class of weighted neighbour allocations is a generalization of the nucleolus, in the sense that the latter is in this class as the special member where players have all equal weights.     

Characterizing properties of approximate solutions for optimization problems

Approximate solutions for optimization problems become of interest if the ‘true’ optimum cannot be found: this may happen for the simple reason that an optimum does not exist or because of the ‘bounded rationality’ (or bounded accuracy) of the optimizer. This paper characterizes several approximate solutions by means of consistency and additional requirements. In particular we consider invariance properties. We prove that, where the domain contains optimization problems without maximum, there is no non-trivial consistent solution satisfying non-emptiness, translation and multiplication invariance. Moreover, we show that the class of ‘satisficing’ solutions is obtained, if the invariance axioms are replaced with Chernoff’s Choice Axiom.     

Levels and transitions in126Te

The decay of¹²⁶Sb to¹²⁶Te is studied by use of Ge(Li) detectors in singles and coincidence arrangements. The gamma-gamma directional correlations of six cascades are measured. A level scheme is constructed where all transitions observed are located. The characteristics of several of the levels are assigned, on basis of the logft values deduced and the directional correlation results. Mixing ratios are deduced for three transitions. From the comparison of the relative intensities ofE1 andE2 transitions depopulating the same levels, threeE1 transitions are concluded to be strongly retarded.     

Additive stable solutions on perfect cones of cooperative games

Closed kernel systems of the coalition matrix turn out to correspond to cones of games on which the core correspondence is additive and on which the related barycentric solution is additive, stable and continuous. Different perfect cones corresponding to closed kernel systems are described. Received: December 2001/Revised: July 2002 RID="*" ID="*"  This note contains the new results, which were presented by the first author in an invited lecture at the XIV Italian Meeting on Game Theory and Applications in Ischia, July 2001. The lecture was dedicated to Irinel Dragan on the occasion of his seventieth birthday.     

Characterisation of a hydraulic high-pressure sample introduction assisted flow injection-inductively coupled plasma time-of-flight mass spectrometry system and its application to the analysis of biological samples

A flow injection (FI) method was developed using hydraulic high-pressure nebulization as a sample introduction system, coupled to inductively coupled plasma time-of-flight mass spectrometer (ICP-TOFMS) for rapid and simultaneous determination of 19 elements. The operating conditions of the system (analyte flow rate, heating and cooling temperatures of the desolvation module, carrier gas flow rate) for the simultaneous determination of 19 analytes were optimised. The optimum parameters of the sample introduction system were found to be 1.4 ml min⁻¹ and 1.35 l min⁻¹ for the analyte solution and nebulizer flow rates, respectively. A compromised condition for heating and cooling stage temperatures of 170 and −5 °C was chosen. The detection limits were compared to those obtained by using ICP-TOFMS with alternative sample introduction techniques e.g. conventional nebulization, flow injection chemical hydride generation (FI-CHG) and the obtained results were comparable or better than those resulting from alternative sample introduction. Applying the optimised conditions the simultaneous determination of Ag, As, Ba, Cd, Co, Cu, Ga, In, Li, Mn, Mo, Pb, Sb, Se, Sn, Sr, Tl, V and Zn was carried out. Absolute detection limits (3σ) in the range of 2-750 pg and precision between 0.5 and 9.6% from five replicate measurements of 10 ng ml⁻¹ multielemental sample solutions were achieved by using a 200 μl sample loop. The developed method was applied for the analysis of certified reference materials of biological origin (TORT-2 “Lobster Hepatopancrease”, BCR-422 “Cod Muscle” and IAEA MA-B-3/TM “Fish Homogenate”), and the results showed good agreement with the certified values.     

Improved sample preparation method for environmental plutonium analysis by ICP-SFMS and alpha-spectrometry

A rapid and simple sample preparation method for plutonium determination in environmental samples by inductively coupled plasma sector field mass spectrometry (ICP-SFMS) and alpha-spectrometry is described. The developed procedure involves a selective CaF₂ co-precipitation for preconcentration followed by extraction chromatographic separation. The proposed method effectively eliminates the possible interferences in mass spectrometric analysis and also removes interfering radionuclides that may disturb alpha-spectrometric measurement. For ²³⁹Pu, ²⁴⁰Pu and ²⁴¹Pu limits of detection of 9.0 fg·g⁻¹ (0.021 mBq), 1.7 fg·g⁻¹ (0.014 mBq) and 3.1 fg·g⁻¹ (11.9 mBq) were achieved by ICP-SFMS, respectively, and 0.02 mBq by alpha-spectrometry. Results of certified reference materials agreed well with the recommended values.     

Dexamethasone delivery to posterior segment of the eye

Due to anatomic barriers and lacrimal drainage it is difficult to obtain therapeutic drug concentrations in the posterior part of the eye after topical drug administrations. Lipophilic cyclodextrins, such as randomly methylated β-cyclodextrin (RMβCD), are known to act both as solubilizers of water-insoluble drugs in aqueous solutions and as penetration enhancers that reduce the barrier function of lipophilic membranes. The purpose of this study was to investigate the effects of RMβCD on dexamethasone delivery from aqueous eye drop solution into rabbit eyes. Dexamethasone (0.5 and 1.5% w/v) drops (50 μl) were administered to the left eye of rabbits (n = 6) and the drug levels measured in different eye tissues 2 h after administration. In aqueous humor dexamethasone levels were 1,190 ± 110 and 1,670 ± 630 ng/g (mean ± SD) after administration of the 0.5 and 1.5% dexamethasone eye drops, respectively. In the retina the levels were 33 ± 7 and 66 ± 49 ng/g, and in optic nerve 41 ± 12 and 130 ± 50 ng/g, respectively. In a previous study the dexamethasone concentration in aqueous humor after topical administration of 1.3% (w/v) dexamethasone eye drops in aqueous 2-hydroxypropyl-β-cyclodextrin (HPβCD) solution was determined to be 320 ± 230 ng/g and 66 ± 20 ng/g after administration of Maxidex^® eye drops. Both the hydrophilic HPβCD and the lipophilic RMβCD enhance topical dexamethasone delivery into the eye, but of the two, the lipophilic RMβCD results in higher dexamethasone concentrations.     

Novel separation method for highly sensitive speciation of cancerostatic platinum compounds by HPLC–ICP–MS

A high-performance liquid chromatography–inductively coupled plasma mass spectrometry (HPLC–ICP–MS) method is presented for analysis of cisplatin, monoaquacisplatin, diaquacisplatin, carboplatin, and oxaliplatin in biological and environmental samples. Chromatographic separation was achieved on pentafluorophenylpropyl-functionalized silica gel. For cisplatin, carboplatin, and oxaliplatin limits of detection of 0.09, 0.10, and 0.15 g L^–1, respectively, were calculated at m/z 194, using aqueous standard solutions. (3 L injection volume). The method was utilized for model experiments studying the stability of carboplatin and oxaliplatin at different chloride concentrations simulating wastewater and surface water conditions. It was found that a high fraction of carboplatin is stable in ultrapure water and in solutions containing 1.5 mol L^–1 Cl^–, whereas oxaliplatin degradation was increased by increasing the chloride concentration. In order to support the assessment of oxaliplatin eco-toxicology, the method was tested for speciation of patient urine. The urine sample contained more than 17 different reaction products, which demonstrates the extensive biotransformation of the compound. In a second step of the study the method was successfully evaluated for monitoring cancerostatic platinum compounds in hospital waste water.     

A dynamic supramolecular system exhibiting substrate selectivity in the catalytic epoxidation of olefins

A dynamic supramolecular system involving hydrogen bonding between a Mn(III) salen catalyst and a Zn(II) porphyrin receptor exhibits selectivity for pyridine appended cis-beta-substituted styrene derivatives over phenyl appended derivatives in a catalytic epoxidation reaction.