Banach ultrapowers and multivalued nonexpansive mappings

The Banach ultrapower construction is applied in fixed point theory for multivalued mappings. We introduce the notion of ultra-asymptotic centers and use it to remove the separability assumption from the results of Domínguez Benavides, Lorenzo Ramírez (2004) and Dhompongsa, Kaewcharoen, Kaewkhao (2006).     

Spectroscopy using stimulated electron–ion recombination

Spectroscopic results obtained on multiply charged few electron ions by using laser stimulated two-step recombination in ion storage rings are presented in an overview. Line splittings in transitions between Rydberg levels were observed for helium like and beryllium like ions. Emphasis is given to results on the beryllium like system N³⁺ where information about the splitting between high angular momentum levels (l⩾4) was obtained for the Rydberg levels n=13 and 8 with experimental errors of about ±0.02 meV. This revised version was published online in August 2006 with corrections to the Cover Date.     

Direct mass measurements of exotic nuclei at the FRS-ESR facility at GSI

An overview of direct mass measurements of exotic nuclei at the FRS-ESR facility at GSI is given. The nuclides are produced at relativistic energies by projectile fragmentation and fission, separated in-flight at the fragment separator FRS and injected into the storage ring ESR. Mass measurements are performed using Schottky and Isochronous Mass Spectrometry, which both allow for high precision measurements with single-ion sensitivity. Recent experimental developments are summarized, and examples for measurement results are given, including applications in nuclear structure physics and astrophysics, comparisons with mass predictions, and the search for new isotopes and isomers. Further research potential will be available at next-generation fragment-separator-storage-ring facilities such as the Super-FRS-CR-NESR complex at the future FAIR facility.     

Some recent results in baryon chiral perturbation theory

I present and discuss recent results on elastic pion-nucleon scattering and near-threshold neutral-pion electroproduction off deuterium obtained in the framework of chiral perturbation theory.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.75.Gx Pion-baryon interactions - 25.30.Rw Electroproduction reactions - 12.39.Fe Chiral Lagrangians     

On the existence of almost-pure-strategy Nash equilibrium in <Emphasis Type="Italic">n</Emphasis>-person finite games

This paper gives wide characterization of n-person non-coalitional games with finite players’ strategy spaces and payoff functions having some concavity or convexity properties. The characterization is done in terms of the existence of two-point-strategy Nash equilibria, that is equilibria consisting only of mixed strategies with supports being one or two-point sets of players’ pure strategy spaces. The structure of such simple equilibria is discussed in different cases. The results obtained in the paper can be seen as a discrete counterpart of Glicksberg’s theorem and other known results about the existence of pure (or “almost pure”) Nash equilibria in continuous concave (convex) games with compact convex spaces of players’ pure strategies.     

Mass measurements in the endpoint region of the rp-process at SHIPTRAP

The Penning-trap mass spectrometer SHIPTRAP was designed for precision mass measurements of radionuclides produced in fusion–evaporation reactions. The latest measurement campaign covered heavy nuclei (A>90) related to the astrophysical rapid proton capture process. The masses of 34 neutron-deficient radionuclides have been measured since February 2006 with relative uncertainties between 5×10⁻⁸ and 1×10⁻⁷. Furthermore, the use of an octupolar RF excitation for the time-of-flight ion-cyclotron-resonance technique was investigated and an increase of the resolving power by a factor of ten was observed in agreement with simulations. This will allow to resolve isomeric states with excitation energies of a few 10 keV only.      

Sol–gel processing and electrochemical characterization of monoclinic Li3FeF6

To find new cathode materials for future applications in lithium-ion batteries, lithium transition metal fluorides represent an interesting class of materials. In principle the Li intercalation voltage can be increased by replacing oxygen in the cathode host structure with the more electronegative fluorine. A facile pyrolytic sol–gel process with trifluoroacetic acid as fluorine source was established to synthesize monoclinic Li₃FeF₆ using nontoxic chemicals. The acicular Li₃FeF₆ powder was characterized with X-ray diffraction and a detailed structure model was calculated by Rietveld analysis. For the preparation of cathode films to cycle versus lithium monoclinic Li₃FeF₆ was ball milled with carbon and binder down to nanoscale. After 100 cycles galvanostatic cycling (C/20) 47 % fully reversible capacity of the initial capacity (129 mAh/g) could be retained. To the best of our knowledge the results presented in this work include the first rate performance test for monoclinic Li₃FeF₆ up to 1 C maintaining a capacity of 71 mAh/g. The redox reaction involving Fe³⁺/Fe²⁺ during Li insertion/extraction was confirmed by post-mortem XPS and cyclic voltammetry.     

On the Oxidation of the Three‐Dimensional Aromatics [B12X12]2− (X=F,Cl, Br,I)

The perhalogenated closo‐dodecaborate dianions [B₁₂X₁₂]^2? (X=H, F, Cl, Br, I) are three‐dimensional counterparts to the two‐dimensional aromatics C₆X₆ (X=H, F, Cl, Br, I). Whereas oxidation of the parent compounds [B₁₂H₁₂]^2? and benzene does not lead to isolable radicals, the perhalogenated analogues can be oxidized by chemical or electrochemical methods to give stable radicals. The chemical oxidation of the closo‐dodecaborate dianions [B₁₂X₁₂]^2? with the strong oxidizer AsF₅ in liquid sulfur dioxide (lSO₂) yielded the corresponding radical anions [B₁₂X₁₂] ^{? ?} (X=F, Cl, Br). The presence of radical ions was proven by EPR and UV/Vis spectroscopy and supported by quantum chemical calculations. Use of an excess amount of the oxidizing agent allowed the synthesis of the neutral perhalogenated hypercloso‐boranes B₁₂X₁₂ (X=Cl, Br). These compounds were characterized by single‐crystal X‐ray diffraction of dark blue B₁₂Cl₁₂ and [Na(SO₂)₆][B₁₂Br₁₂] ? B₁₂Br₁₂. Sublimation of the crude reaction products that contained B₁₂X₁₂ (X=Cl, Br) resulted in pure dark blue B₁₂Cl₁₂ or decomposition to red B₉Br₉, respectively. The energetics of the oxidation processes in the gas phase were calculated by DFT methods at the PBE0/def2‐TZVPP level of theory. They revealed the trend of increasing ionization potentials of the [B₁₂X₁₂]^2? dianions by going from fluorine to bromine as halogen substituent. The oxidation of all [B₁₂X₁₂]^2? dianions was also studied in the gas phase by mass spectrometry in an ion trap. The electrochemical oxidation of the closo‐dodecaborate dianions [B₁₂X₁₂]^2? (X=F, Cl, Br, I) by cyclic and Osteryoung square‐wave voltammetry in liquid sulfur dioxide or acetonitrile showed very good agreement with quantum chemical calculations in the gas phase. For [B₁₂X₁₂]^2? (X=F, Cl, Br) the first and second oxidation processes are detected. Whereas the first process is quasi‐reversible (with oxidation potentials in the range between +1.68 and +2.29 V (lSO₂, versus ferrocene/ferrocenium (Fc^0/+))), the second process is irreversible (with oxidation potentials ranging from +2.63 to +2.71 V (lSO₂, versus Fc^0/+)). [B₁₂I₁₂]^2? showed a complex oxidation behavior in cyclic voltammetry experiments, presumably owing to decomposition of the cluster anion under release of iodide, which also explains the failure to isolate the respective radical by chemical oxidation.