Two Approaches to the Problem of Sharing Delay Costs in Joint Projects

This paper concentrates on cost sharing situations which arise when delayed joint projects involve joint delay costs. The problem here is to determine fair shares for each of the agents who contribute to the delay of the project such that the total delay cost is cleared. We focus on the evaluation of the responsibility of each agent in delaying the project based on the activity graph representation of the project and then on solving the important problem of the delay cost sharing among the agents involved. Two approaches, both rooted in cooperative game theory methods are presented as possible solutions. In the first approach delay cost sharing rules are introduced which are based on the delay of the project and on the individual delays of the agents who perform activities. This approach is inspired by the bankruptcy and taxation literature and leads to five rules: the (truncated) proportional rule, the (truncated) constrained equal reduction rule and the constrained equal contribution rule. By introducing two coalitional games related to delay cost sharing problems, which we call the pessimistic delay game and the optimistic delay game, also game theoretical solutions as the Shapley value, the nucleolus and the -value generate delay cost sharing rules. In the second approach the delays of the relevant paths in the activity graph together with the delay of the project play a role. A two-stage solution is proposed. The first stage can be seen as a game between paths, where the delay cost of the project has to be allocated to the paths. Here serial cost sharing methods play a role. In the second stage the allocated costs of each path are divided proportionally to the individual delays among the activities in the path.     

A Simple Algorithm for the Nucleolus of Airport Profit Games

In this paper we present a procedure for calculating the nucleolus for airport profit games which are a generalization of the airport cost games.     

Finite Coverings by Cones and an Application in Multi-Objective Programming

This paper considers analogues of statements concerning compactness and finite coverings, in which the roles of spheres are replaced by cones. Furthermore, one of the finite covering results provides an application in Multi-Objective Programming; infinite sets of alternatives are reduced to finite sets.     

On games corresponding to sequencing situations with ready times

This paper considers the special class of cooperative sequencing games that arise from one-machine sequencing situations in which all jobs have equal processing times and the ready time of each job is a multiple of the processing time.By establishing relations between optimal orders of subcoalitions, it is shown that each sequencing game within this class is convex.This author is financially supported by the Dutch Organization for Scientific Research (NWO).     

New methods for the direct determination of dissolved inorganic, organic and total carbon in natural waters by Reagent-Free Ion Chromatography and inductively coupled plasma atomic emission spectrometry

New methods have been developed and applied successfully for the determination of dissolved inorganic, organic and total carbon in water samples. The new methods utilize two instrumental setups, Reagent-Free™ Ion Chromatography (RF™-IC) and inductively coupled plasma atomic emission spectrometry (ICP-AES). Dissolved inorganic carbon (DIC) was measured in untreated samples along with Cl⁻, F⁻ and SO₄²⁻ using RF™-IC and by in-line mixing with 0.1 M HNO₃ to enhance CO₂ removal in the nebulizer, followed by ICP-AES analysis. Total dissolved carbon (TDC) was measured by in-line mixing with 0.1 M NaOH following ICP-AES analysis. Dissolved organic carbon (DOC) was obtained as the difference between DIC and TDC. Only non-volatile organic carbon could be detected by the present method. The workable limits of detection obtained in the present study were 0.5 mM (RF™-IC) and 0.1 mM (ICP-AES) for dissolved inorganic and organic carbon, respectively. The power of the new methods lies in routine analysis of DIC and DOC in samples of natural waters of variable composition and salinity using analytical techniques and facilities available in most laboratories doing water sample analysis. The techniques are sensitive and precise, can be automated using gas-tight sample vials and auto-samplers, and are independent of most elemental interferences with the exception of chloride overload by saline samples when using RF™-IC. The new methods were successfully applied for analysis of DIC and DOC in selected samples of natural and synthetic waters.     

An average lexicographic value for cooperative games

For games with a non-empty core the Alexia value is introduced, a value which averages the lexicographic maxima of the core. It is seen that the Alexia value coincides with the Shapley value for convex games, and with the nucleolus for strongly compromise admissible games and big boss games. For simple flow games, clan games and compromise stable games an explicit expression and interpretation of the Alexia value is derived. Furthermore it is shown that the reverse Alexia value, defined by averaging the lexicographic minima of the core, coincides with the Alexia value for convex games and compromise stable games.     

Condensation in Nongeneric Trees

We study nongeneric planar trees and prove the existence of a Gibbs measure on infinite trees obtained as a weak limit of the finite volume measures. It is shown that in the infinite volume limit there arises exactly one vertex of infinite degree and the rest of the tree is distributed like a subcritical Galton-Watson tree with mean offspring probability m<1. We calculate the rate of divergence of the degree of the highest order vertex of finite trees in the thermodynamic limit and show it goes like (1−m)N where N is the size of the tree. These trees have infinite spectral dimension with probability one but the spectral dimension calculated from the ensemble average of the generating function for return probabilities is given by 2β−2 if the weight w _n of a vertex of degree n is asymptotic to n ^−β .     

High‐Silica Zeolite SSZ‐61 with Dumbbell‐Shaped Extra‐Large‐Pore Channels

The synthesis of the high‐silica zeolite SSZ‐61 using a particularly bulky polycyclic structure‐directing agent and the subsequent elucidation of its unusual framework structure with extra‐large dumbbell‐shaped pore openings are described. By using information derived from a variety of X‐ray powder diffraction and electron microscopy techniques, the complex framework structure, with 20 Si atoms in the asymmetric unit, could be determined and the full structure refined. The Si atoms at the waist of the dumbbell are only three‐connected and are bonded to terminal O atoms pointing into the channel. Unlike the six previously reported extra‐large‐pore zeolites, SSZ‐61 contains no heteroatoms in the framework and can be calcined easily. This, coupled with the possibility of inserting a catalytically active center in the channel between the terminal O atoms in place of H⁺, afford SSZ‐61 intriguing potential for catalytic applications.