Dimension of the Lisbon voting rules in the EU Council: a challenge and new world record

The Lisbon voting system of the Council of the European Union, which became effective in November 2014, cannot be represented as the intersection of six or fewer weighted games, i.e., its dimension is at least 7. This sets a new record for real-world voting bodies. A heuristic combination of different discrete optimization methods yields a representation as the intersection of 13,368 weighted games. Determination of the exact dimension is posed as a challenge to the community. The system’s Boolean dimension is proven to be 3.     

Quenched Lewis Acidity: Studies on the Medium Dependent Fluorescence of Zinc(II) Complexes

Three new zinc(II) coordination units [Zn(1–3)] based on planar-directing tetradentate Schiff base-like ligands H₂(1 – 3) were synthesized. Their solid-state structures were investigated by single crystal X-ray diffraction, showing the tendency to overcome the square-planar coordination sphere by axial ligation. Affinity in solution towards axial ligation has been tested by extended spectroscopic studies, both in the absorption and emission mode. The electronic spectrum of the pyridine complex [Zn(1)(py)] has been characterized by MC-PDFT to validate the results of extended TD-DFT studies. Green emission of non-emissive solutions of [Zn(1–3)] in chloroform could be switched on in the presence of potent Lewis-bases. While interpretation in terms of an equilibrium of stacked/non-fluorescent and destacked/fluorescent species is in line with precedents from literature, the sensitivity of [Zn(1–3)] was greatly reduced. Results of a computation-based structure search allow to trace the hidden Lewis acidity of [Zn(1–3)] to a new stacking motif, resulting in a strongly enhanced stability of the dimers.     

Measuring Tollmien–Schlichting waves using phase-averaged particle image velocimetry

This article addresses the direct experimental measurement of Tollmien?CSchlichting waves on a flat plate, when the laminar boundary layer is excited by velocity perturbations; the free stream velocity was 16?m/s, the excitation frequency 250?Hz. The two-dimensional velocity field in proximity of the flat plate was captured using a conventional PIV system; however, the image recording was phase locked with the disturbance source and ensemble averaging was used to obtain characteristics of the Tollmien?CSchichting waves. In particular, after subtraction of the mean velocity, the characteristics of the excited waves in terms of streamlines were extracted, revealing that the investigated waves represented velocity deviations with an order of magnitude of 1?% of the undisturbed free stream flow. This study is a prelude to the use of the same technique to visualize the effect of dielectric barrier discharge plasma actuators on the suppression of such Tollmien?CSchlichting waves, which is difficult using other measurement techniques.     

On minimum sum representations for weighted voting games

A proposal in a weighted voting game is accepted if the sum of the (non-negative) weights of the ??yea?? voters is at least as large as a given quota. Several authors have considered representations of weighted voting games with minimum sum, where the weights and the quota are restricted to be integers. In Freixas and Molinero (Ann. Oper. Res. 166:243?C260, 2009) the authors have classified all weighted voting games without a unique minimum sum representation for up to 8 voters. Here we exhaustively classify all weighted voting games consisting of 9?voters which do not admit a unique minimum sum integer weight representation.