On the systematic energy difference between states of positive and negative parity

Comparison of the nuclear spectra in the mass region A = 10–40 shows a systematic difference between states of positive and negative parity. This systematic difference can be explained quantitatively with methods derived from statistical spectroscopy. The influence of spurious states is corrected for.     

Molecular reorientation of liquid water studied with femtosecond midinfrared spectroscopy

The molecular reorientation of liquid water is key to the hydration and stabilization of molecules and ions in aqueous solution. A powerful technique to study this reorientation is to measure the time-dependent anisotropy of the excitation of the O-H/O-D stretch vibration of HDO dissolved in D2O/H2O using femtosecond midinfrared laser pulses. In this paper, we present and discuss experiments in which this technique is used to study the correlation between the molecular reorientation of the water molecules and the strength of the hydrogen-bond interactions. On short time scales (<200 fs), it was found that the anisotropy shows a partial decay due to librational motions of the water molecules that keep the hydrogen bond intact. On longer time scale (>200 fs), the anisotropy shows a complete decay with an average time constant of 2.5 ps. From the frequency dependence of the anisotropy dynamics, it follows that a subensemble of the water molecules shows a fast reorientation that is accompanied by a large change of the vibrational frequency. This finding agrees with the molecular jumping mechanism for the reorientation of liquid water that has recently been proposed by Laage and Hynes.     

Bi-analyte SERS with isotopically edited dyes

Isotopically substituted rhodamine dyes provide ideal probes for the study of single-molecule surface enhanced Raman scattering (SM-SERS) events through multiple-analyte techniques. Isotopic editing should, in principle, provide probes that have identical chemical properties (and surface chemistries); while exhibiting at the same time distinct Raman features which enable us to identify single-molecule SERS events. We present here a specific example of two-analyte SM-SERS based on the isotopic substitution of a methyl ester rhodamine dye. The dyes are carefully characterized (in both standard and SERS conditions) to confirm experimentally their similar chemical properties. We then demonstrate their utility for bi-analyte SERS (BiASERS) experiments and, as an example, highlight the transition from a single, to a few, to many molecules in the statistics of SM-SERS signals.     

Identification of a nonlinear circuit

The identification of a differential equation underlying a measured time series is a prerequisite for numerous types of applications. In the validation of a proposed parameterized model one often faces the dilemma that it is hard to decide whether possible discrepancies between the measured time series and the simulated model output are caused by an inappropriate model or by wrongly specified parameters in a correct type of model. We propose a combination of parametric modelling based on Bock's multiple shooting algorithm and nonparametric modelling based on optimal transformations as a strategy to test proposed models and if rejected suggest and test new ones. We exemplify this strategy on an experimental time series from a nonlinear chaotically oscillating circuit where we finally obtain an extremely accurate reconstruction of the observed attractor.     

From 3D to 2D: Structural,Spectroscopic and Theoretical Investigations of the Dimensionality Reduction in the [PtAl2]δ− Polyanions of the Isotypic MPtAl2 Series (M=Ca–Ba,Eu)

Four new MPtAl₂ (M=Ca, Sr, Ba, Eu) compounds, adopting the orthorhombic MgCuAl₂-type structure, have been synthesized from the elements using tantalum ampoules. All compounds are obtained as platelet-shaped crystallites and exhibit an increasing moisture sensitivity with increasing size of the formal M cation. Structural investigations indicate a pronounced elongation of the crystallographic b-axis, which results in a significant distortion of the [PtAl₂]^δ− polyanion. Within the polyanion, layer-like arrangements can be found with bonding Pt−Al interactions within the slab; the increase of the b-axis can be attributed to increasing Al−Al distances and therefore decreasing interactions between the slabs, caused by the differently-sized formal M cations. While the alkaline earth (M=Ca, Sr) representatives exhibit Pauli paramagnetism, BaPtAl₂ shows diamagnetic behavior, finally EuPtAl₂ is ferromagnetic with T_C=54.0(5) K. The effective magnetic moment indicates that the Eu atoms are in a divalent oxidation state, which is confirmed by ¹⁵¹Eu Mössbauer spectroscopic investigations. Measurements below the Curie-temperature show a full magnetic hyperfine field splitting with B_hf=21.7(1) T. ²⁷Al and ¹⁹⁵Pt magic-angle spinning NMR spectroscopy corroborates the presence of single crystallographic sites for the Pt and Al atoms. The large ²⁷Al nuclear electric quadrupolar coupling constants confirm unusually strong electric field gradients, in agreement with the structural distortions and the respective theoretical calculations. X-ray photoelectron spectroscopy has been utilized to investigate the charge transfer within the polyanion. The Pt 4f binding energy decreases with decreasing electronegativity / ionization energy of the alkaline earth elements, suggesting an increasing electron density at the Pt atoms. Theoretical investigations underline the platinide character of the investigated compounds by Bader charge calculations. The analysis of the integrated crystal orbital Hamilton population (ICOHP) values, electron localization function (ELF) and isosurface analyses lead to a consistent structural picture, indicating stable layer-like arrangements of the [PtAl₂]^δ− polyanion.     

The core and related solution concepts for infinite assignment games

Assignment problems where both sets of agents that have to be matched are countably infinite, the so-called infinite assignment problems, are studied as well as the related cooperative assignment games. Further, several solution concepts for these assignment games are studied. The first one is the utopia payoff for games with an infinite value. In this solution each player receives the maximal amount he can think of with respect to the underlying assignment problem. This solution is contained in the core of the game. Second, we study two solutions for assignment games with a finite value. Our main result is the existence of core-elements of these games, although they are hard to calculate. Therefore another solution, the f-strong ε-core is studied. This particular solution takes into account that due to organisational limitations it seems reasonable that only finite groups of agents will eventually protest against unfair proposals of profit distributions. The f-strong ε-core is shown to be nonempty. These authors’ research is partially supported by the Generalitat Valenciana (Grant number GV-CTIDIA-2002-32) and by the Government of Spain (through a joint research grant Universidad Miguel Hernández — Università degli Studi di Genova HI2002-0032).     

The Compromise Value for Cooperative Games with Random Payoffs

This paper introduces and studies the compromise value for cooperative games with random payoffs, that is, for cooperative games where the payoff to a coalition of players is a random variable. This value is a compromise between utopia payoffs and minimal rights and its definition is based on the compromise value for NTU games and the τ-value for TU games. It is shown that the nonempty core of a cooperative game with random payoffs is bounded by the utopia payoffs and the minimal rights. Consequently, for such games the compromise value exists. Further, we show that the compromise value of a cooperative game with random payoffs coincides with the τ-value of a related TU game if the players have a certain type of preferences. Finally, the compromise value and the marginal value, which is defined as the average of the marginal vectors, coincide on the class of two-person games. This results in a characterization of the compromise value for two-person games.I thank Peter Borm, Ruud Hendrickx and two anonymous referees for their valuable comments.