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.     

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.     

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.     

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.     

The consistency principle for games in strategic form

We start with giving an axiomatic characterization of the Nash equilibrium (NE) correspondence in terms of consistency, converse consistency, and one-person rationality. Then axiomatizations are given of the strong NE correspondence, the coalition-proof NE correspondence and the semi-strong NE. In all these characterizations consistency and suitable variants of converse consistency play a role. Finally, the dominant NE correspondence is characterized. We also indicate how to generalize our results to Bayesian and extensive games.     

Entiers Lexicographiques

An integer n is called lexicographic if the increasing sequence of its divisors, regarded as words on the (finite) alphabet of the prime factors (arranged in increasing size), is ordered lexicographically. This concept easily yields to a new type of multiplicative structure for the exceptional set in the Maier-Tenenbaum theorem on the propinquity of divisors, which settled a well-known conjecture of Erdös. We provide asymptotic formulae for the number of lexicographic integers not exceeding a given limit, as well as for certain arithmetically weighted sums over the same set. These results are subsequently applied to establishing an Erdös-Kac theorem with remainder for the distribution of the number of prime factors over lexicographic integers. This provides quantitative estimates for lexicographical exceptions to Erdos' conjecture that also satisfy the Hardy-Ramanujan theorem.