Vector Optimization Problems via Improvement Sets

Motivated by applications to the real world, various optimality criteria (also approximate ones) are developed for situations in vector optimization. We propose a new type of solution based on upper comprehensive sets and we discuss the existence of optimal points in multicriteria situations.     

Modulation of the reactivity, stability and substrate- and enantioselectivity of an epoxidation catalyst by noncovalent dynamic attachment of a receptor functionality--aspects on the mechanism of the Jacobsen-Katsuki epoxidation applied to a supramolecular system

The synthesis of the components of the dynamic supramolecular hydrogen-bonded catalytic system 2 + 3 is described. The catalytic performance and substrate- and enantioselectivity of Mn(salen) catalyst 2 were investigated in the presence and absence of the Zn(porphyrin) receptor unit 3. The effects of pyridine and pyridine N-oxide donor ligands were also studied. Some aspects on the mechanism of the Jacobsen-Katsuki epoxidation, based on literature observations, are introduced as a means to analyse the behaviour of 2 and its modulation by the formation of macrocycle 1 with 3. A complete association model of the metal-free system 4 + 5 refutes the earlier assumption that macrocycle 1 is the predominant form of catalyst 2 under the standard epoxidation reaction conditions with 2 + 3. Evidence are provided that receptor-binding substrates and nonbinding substrates, respectively, are epoxidised by two different catalytic species, or two distinct distributions of species in competitive epoxidations using catalytic system 2 + 3. The two species are assigned to the endo and exo faces of the Mn(salen) catalyst in macrocycle 1, and to equivalently folded oligomeric structures with monomers 2 and 3 in adjacent positions.     

Neighbor games and the leximax solution

Neighbor games arise from certain matching or sequencing situations in which only some specific pairs of players can obtain a positive gain. As a consequence, the class of neighbor games is the intersection of the class of assignment games (Shapley and Shubik (1972)) and the class of component additive games (Curiel et al. (1994)). We first present some elementary features of neighbor games. After that we provide a polynomially bounded algorithm of order p ³ for calculating the leximax solution (cf. Arin and Iñarra (1997)) of neighbor games, where p is the number of players. This authors work has been supported by CentER and the Department of Econometrics, Tilburg University and by the Foundation for the Hungarian Higher Education and Research (AMFK).     

Mössbauer and X-ray study of rapidly quenched and mechanically alloyed Al-Fe alloys

Mössbauer spectroscopy and X-ray diffractometry were used to study the effect of the cooling rate as well as of the milling time on the structure of rapidly quenched Al-6.8% Fe, Al-0.5% Fe and mechanically alloyed Al-8% Fe alloys. The main phase of the rapidly quenched alloys was identified as Al _m Fe besides Al₆Fe andAlFe solid solutions. In the mechanically alloyed samples (with milling time between 1.5–43 hours), we have found -Fe, AlFe solid solution and a third phase characterized by a doublet with Mössbauer parameters which are not so far from those of clusters inAlFe alloys. We have observed a continuous increase of the quantity ofAlFe solid solution, together with a significantly less increase of the third phase as a function of the milling time. Simultaneously, the quantity of alpha-iron has gradually decreased.     

Infinite Hierarchical Potential Games

Hierarchical potential games with infinite strategy sets are considered. For these games, pessimistic Stackelberg equilibria are characterized as minimum points of the potential function; properties are studied and illustrated with examples.     

Cost allocation protocols for supply contract design in network situations

The class of Construct and Charge (CC-) rules for minimum cost spanning tree (mcst) situations is considered. CC-rules are defined starting from the notion of charge systems, which specify particular allocation protocols rooted on the Kruskal algorithm for computing an mcst. These protocols can be easily implemented in practical network situations (for instance, in supply transportation networks), are flexible to changes in the network situation and meet the requirement of continuous monitoring by the agents involved. Special charge systems, that we call conservative, lead to a subclass of CC-rules that coincides with the class of obligation rules for mcst situations. The authors thank two anonymous referees both for detailed remarks and for interesting general comments on a previous version of the paper. Stef Tijs and Rodica Branzei are indebted to Daniel Granot for useful discussions on the topics treated in this paper and his hospitality during our research visit at British Columbia University at Vancouver in July–August 2003.     

Non-isothermal film casting: Determination of draw resonance

The important industrial process of casting polymeric films suffers from the “draw resonance” instability that appears as sudden oscillations in the product dimensions. This instability influences the quality of the end-product and negatively limits productivity and efficiency of the process. The draw resonance originates when a material is being processed beyond the limits of its intrinsic properties. Research is conducted with the intention to find those process and material properties that allow to optimize the production process while keeping it stable.This paper concentrates on a non-isothermal analysis of the stability of the film casting. The mathematical model of the process is given by a quasi-linear system of first order PDEs with two point boundary conditions. The constitutive polymer behavior is approximated by the modified Giesekus model. Linear stability analysis combined with the Laplace transformation of the resulting linear system is applied to find parameters that determine mathematical and thus process instability. It all comes down to determining the spectrum of a compact operator; corresponding eigenfunctions can be regarded as the characteristic modes of the system. For implementation, the modification of Galerkin approach is used. The major advantage of the mathematical and numerical method is that the full spectrum is calculated in a matter of seconds. Our results agree perfectly with the ones from literature for isothermal case, and with the experimental data for the non-isothermal case. The results also indicate that non-isothermality is highly important and cannot be excluded from modeling.     

Approximate equilibria for Bayesian games

In this paper the problem of the existence of approximate equilibria in mixed strategies is central. Sufficient conditions are given under which approximate equilibria exist for non-finite Bayesian games. Further one possible approach is suggested to the problem of the existence of approximate equilibria for the class of multicriteria Bayesian games.