Traveling salesman games

In this paper we discuss the problem of how to divide the total cost of a round trip along several institutes among the institutes visited. We introduce two types of cooperative games—fixed-route traveling salesman games and traveling salesman games—as a tool to attack this problem. Under very mild conditions we prove that fixed-route traveling salesman games have non-empty cores if the fixed route is a solution of the classical traveling salesman problem. Core elements provide us with fair cost allocations. A traveling salesman game may have an empty core, even if the cost matrix satisfies the triangle inequality. In this paper we introduce a class of matrices defining TS-games with non-empty cores.     

Measurements of γ-γ and γ-electron directional correlations in119Sb

The directional correlations ofγ-γ andγ-electron cascades in¹¹⁹Sb are measured, in the decay of^119mTe. Bothγ-γ andγ-electron directional correlation coefficients are determined for the cascades (energies in keV): 153.5-1212.7, 942.3-270.5, (976.2+979.3)-270.5, 1095.7-270.5 and 1136.8-270.5. For the cascades 912.6-1366.2, 2013.4-270.5 and 2089.9-270.5γ-γ directional correlations are measured. The mixing ratios evaluated are:δ(M2/E1, 153.5 keV)=0.0003±0.0023,δ(E2/M1, 270.5 keV)=-0.39±0.29,δ(E2/M1, 942.3 keV)= ?0.26±0.12,δ(E3/M2,1095.7 keV)=?0.01±0.07, andδ(M3/E2,1212.7 keV) =0.004±0.007. The result is compared with theoretical predictions.     

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.     

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.     

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.     

Robustness and nondegenerateness for linear complementarity problems

In this paper the main focus is on a stability concept for solutions of a linear complementarity problem. A solution of such a problem is robust if it is stable against slight perturbations of the data of the problem. Relations are investigated between the robustness, the nondegenerateness and the isolatedness of solutions. It turns out that an isolated nondegenerate solution is robust and also that a robust nondegenerate solution is isolated. Since the class of linear complementarity problems with only robust solutions or only nondegenerate solutions is not an open set, attention is paid to Garcia's classG _n of linear complementarity problems. The nondegenerate problems inG _n form an open set.     

A constrained egalitarian solution for convex multi-choice games

This paper deals with a constrained egalitarian solution for convex multi-choice games named the d value. It is proved that the d value of a convex multi-choice game belongs to the precore, Lorenz dominates each other element of the precore and possesses a population monotonicity property regarding players’ participation levels. Furthermore, an axiomatic characterization is given where a specific consistency property plays an important role.     

Accumulation of uranium, transuranium and fission products on stainless steel surfaces II. Sorption studies in a laboratory model system

Within the frame of a joint project, the accumulation of the uranium and transuranium (TRU) species on some structural materials used at Soviet made VVER-type pressurized water reactors (such as heat exchanger tube of steam generators and stainless steel canister material) has been studied. The experiments were carried out in a laboratory model system. During the sorption studies, boric acid coolants provided by the Paks Nuclear Power Plant (Paks NPP) were circulated for a period of 30 h. Solution and tube samples obtained in the course of above experiments were analyzed by independent methods (??- and ??-spectrometry, ICP-MS, SEM-EDX, voltammetry and XPS). The experimental results reveal that: (i) the surface excess of the TRU nuclides studied is extremely low (less than 1% of a monolayer coverage); (ii) the surface excess of uranium species measured on the SG tube surfaces is significantly higher, after 30 h sorption period (??_sample = 1.0 ??g cm^?2 U ? 3.7 × 10^?9 mol cm^?2 UO₂) exceeds a monolayer coverage; (iii) the mechanistic features of the contamination processes (specific or non-specific adsorption, deposition of colloidal and/or disperse particles) depend decisively upon the nature of the studied radionuclides and the chemical structure and composition of the oxide layer formed on stainless steel surfaces.