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.     

Continuity of bargaining solutions

Upper semicontinuous solutions of the bargaining problem are studied and also lower semicontinuous weak solutions of that problem are considered. Though mainly compact bargaining pairs are investigated, extensions to non-compact bargaining pairs are indicated. The continuity properties of some well known bargaining solutions are discussed.     

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).     

Fictitious play applied to sequences of games and discounted stochastic games

In this paper, we show that the iterative method of Brown and Robinson, for solving a matrix game, is also applicable to a converging sequence of matrices, where the players choose at staget a row and a column of thet-th matrix in the sequence. As an application of this result, we describe a new solution method for discounted stochastic games with finite state and action spaces.     

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.     

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 .     

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.