The Strategy-Proofness Landscape of Merging

Merging operators aim at defining the beliefs/goals of a group of agents from the beliefs/goals of each member of the group. Whenever an agent of the group has preferences over the possible results of the merging process (i.e., the possible merged bases), she can try to rig the merging process by lying on her true beliefs/goals if this leads to better merged base according to her point of view. Obviously, strategy-proof operators are highly desirable in order to guarantee equity among agents even when some of them are not sincere. In this paper, we draw the strategy-proof landscape for many merging operators from the literature, including model-based ones and formula-based ones. Both the general case and several restrictions on the merging process are considered

Fluid-fluid demixing transitions in colloid--polyelectrolyte star mixtures

We derive effective interaction potentials between hard, spherical colloidal particles and star-branched polyelectrolytes of various functionalities and smaller size than the colloids. The effective interactions are based on a Derjaguin-like approximation, which is based on previously derived potentials acting between polyelectrolyte stars and planar walls. On the basis of these interactions we subsequently calculate the demixing binodals of the binary colloid--polyelectrolyte star mixture, employing standard tools from liquid-state theory. We find that the mixture is indeed unstable at moderately high overall concentrations. The system becomes more unstable with respect to demixing as the star functionality and the size ratio grow.Comment: 24 pages, 9 figures, submitted to Journal of Physics: Condensed Matte

Directional approach to spatial structure of solutions to the Navier-Stokes equations in the plane

We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity $u_\infty$ at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of $u_\infty$. Furthermore a spacial structure of the solution is obtained in comparison with the Oseen flow. A key element of our new approach is based on a setting which treats the directino of the flow as \emph{time} direction. The analysis is done in framework of the Fourier transform taken in one (perpendicular) direction and a special choice of function spaces which take into account the inhomogeneous character of the symbol of the Oseen system. From that point of view our technique can be used as an effective tool in examining spatial asymptotics of solutions to other systems modeled by elliptic equations

Magnetic systems at criticality: different signatures of scaling

Different aspects of critical behaviour of magnetic materials are presented and discussed. The scaling ideas are shown to arise in the context of purely magnetic properties as well as in that of thermal properties as demonstrated by magnetocaloric effect or combined scaling of excess entropy and order parameter. Two non-standard approaches to scaling phenomena are described. The presented concepts are exemplified by experimental data gathered on four representatives of molecular magnets.Comment: 33 pages, 16 figure

Polyelectrolyte stars in planar confinement

We employ monomer-resolved Molecular Dynamics simulations and theoretical considerations to analyze the conformations of multiarm polyelectrolyte stars close to planar, uncharged walls. We identify three mechanisms that contribute to the emergence of a repulsive star-wall force, namely: the confinement of the counterions that are trapped in the star interior, the increase in electrostatic energy due to confinement as well as a novel mechanism arising from the compression of the stiff polyelectrolyte rods approaching the wall. The latter is not present in the case of interaction between two polyelectrolyte stars and is a direct consequence of the impenetrable character of the planar wall.Comment: 34 pages, 8 figures. Revised version of the manuscript. To appear in J. Chem. Phys. May, 200

Decrement Operators in Belief Change

While research on iterated revision is predominant in the field of iterated belief change, the class of iterated contraction operators received more attention in recent years. In this article, we examine a non-prioritized generalisation of iterated contraction. In particular, the class of weak decrement operators is introduced, which are operators that by multiple steps achieve the same as a contraction. Inspired by Darwiche and Pearl's work on iterated revision the subclass of decrement operators is defined. For both, decrement and weak decrement operators, postulates are presented and for each of them a representation theorem in the framework of total preorders is given. Furthermore, we present two sub-types of decrement operators