Sharing costs in highways: A game theoretic approach

This paper introduces a new class of games, highway games, which arise from situations where there is a common resource that agents will jointly use. That resource is an ordered set of several indivisible sections, where each section has an associated fixed cost and each agent requires some consecutive sections. We present an easy formula to calculate the Shapley value, and we present an efficient procedure to calculate the nucleolus for this class of games.     

The influence of hydrogen bonding and pi-pi stacking interactions on the self-assembly properties of C3-symmetrical oligo(p-phenylenevinylene) discs

Three C3-symmetrical discotics containing a 1,3,5-benzenetricarboxamide unit functionalized with pi-conjugated oligo(p-phenylenevinylene)s (OPV)s have been synthesized and fully characterized. For the two amide OPV discs a two-step transition from helical stacks to molecularly dissolved species was observed and surprisingly, the topology of the amide determines the stability and helicity of the fibers in solution and the length of the fibrils at a surface. In case of the bipyridine disc, aggregates were formed that show little chiral ordering while the stacks remain present over a large temperature range. At a surface, completely disordered structures exist probably as a result of competing types of pi-pi stacking interactions that differ in strength and orientation. The results show that the design of functional self-assembled architectures based on hydrogen bonding and pi-pi stacking interactions is an extremely delicate matter and reveal that special demands have to be taken into account to balance the topology, directionality and strength of multiple secondary interactions.     

On the presence of Fe(IV) in Fe-ZSM-5 and FeSrO3-x --unequivocal detection of the 3d4 spin system by resonant inelastic X-ray scattering

The contribution of a 3d(4) spin configuration to the valence electronic structure of Fe compounds can be probed via spin-selective Fe K-pre-edge absorption spectra, using resonant inelastic X-ray scattering (RIXS). The 3d(4) configuration of Fe(IV) can be unequivocally detected even in a mixture with the high-spin 3d(5) configuration of Fe(III). This is demonstrated on the perovskite FeSrO(3-x) with formal oxidation state Fe(IV). When the technique was applied to an Fe-ZSM-5 catalyst during reaction with N(2)O, no 3d(4) configuration was detected. The formation of Fe(IV) upon reaction of Fe-ZSM-5 with N(2)O can, therefore, be ruled out.     

Second order front tracking for the Euler equations

A second order front tracking method is developed for solving the hyperbolic system of Euler equations of inviscid fluid dynamics numerically. Meshless front tracking methods are usually limited to first order accuracy, since they are based on a piecewise constant approximation of the solution. Here second order convergence is achieved by deriving a piecewise linear reconstruction of the piecewise constant front tracking solution. The linearization is performed by decomposing the front tracking solution into its wave components and by linearizing the wave solutions separately. In order to construct a physically correct linearization, the physical phenomena of the front are taken into account in terms of the front types of the previously developed improved front interaction model. This front interaction model is also extended to include front numbers used in the wave decomposition. It is illustrated numerically for Sod’s Riemann problem, the two interacting blast waves problem, and a two-dimensional supersonic airfoil flow validation study that the proposed front tracking method achieves second order convergence also in the presence of strong discontinuities and their interactions.     

Comparing league formats with respect to match importance in Belgian football

Recently, most clubs in the highest Belgian football division have become convinced that the format of their league should be changed. Moreover, the TV station that broadcasts the league is pleading for a more attractive competition. However, the clubs have not been able to agree on a new league format, mainly because they have conflicting interests. In this paper, we compare the current league format, and three other formats that have been considered by the Royal Belgian Football Association. We simulate the course of each of these league formats, based on historical match results. We assume that the attractiveness of a format is determined by the importance of its games; our importance measure for a game is based on the number of teams for which this game can be decisive to reach a given goal. Furthermore, we provide an overview of how each league format aligns with the expectations and interests of each type of club.     

Thermodynamical properties of glass forming systems: A Nuclear Magnetic Resonance analysis

We present a Nuclear Magnetic Resonance (NMR) study of the thermal evolution of the magnetic properties of three different glass formers: glycerol, o-terphenyl and salol. In particular, we analyze how the response of these liquids to the applied magnetic field changes with temperature. We focus on the total magnetization and on the chemical shift of each protonated group. By means of these quantities we account that the dynamics of the glass forming materials, on decreasing the temperature, is dominated by the onset of well defined local inhomogeneities due to precise microscopic cooperative processes. Just these “dynamical heterogeneities” and their energetic topology determine the dynamic crossover from fragile (super Arrhenius) to strong (pure Arrhenius) glass forming behavior. The specific heat changes evaluable from the measured NMR chemical shift associate this phenomenon, and all the related ones, to local configurational changes.     

Minimum cost forest games

In this paper we consider a generalization of the minimum cost spanning tree game. The generalized model allows for more than one supplier, where each supplier offers a different type of service to the customers and each customer specifies a non-empty subset of these suppliers to which he wishes to be connected. We show that the core of such a game may be empty, but that it is always non-empty if there is at least one customer who wants to be connected to all suppliers. Furthermore, the core is always non-empty if there are at most two suppliers.     

Magnetic properties of Fe and Tb in TbxFe1−x amorphous films studied with soft X-ray circular and linear dichroism

We have used linearly and circularly polarized X-rays to determine the magnetic properties of several Tb_xFe_1−x amorphous films. Absorption measurements on the M_4.5 edges of Tb and the L_2.3 edges of Fe allowed us to obtain information about the size and direction of local magnetic moments. Our results confirm that linear dichorism in rare earth M_4.5 edges can give useful information about both crystal field and magnetic effects.