Determining all Nash equilibria in a (bi-linear) inspection game

This paper addresses a “game” between an inspection agency and multiple inspectees that are subject to random inspections by that agency. We provide explicit (easily computable) expressions for all possible Nash equilibria and verify that none is left out. In particular, our results characterize situations when there exists a unique Nash equilibrium. We also explore special features of the Nash equilibria and the solution of the problem the inspection agency faces in a non-strategic environment.     

Stepwise Metal–Ligand Cooperation by a Reversible Aromatization/Deconjugation Sequence in Ruthenium Complexes with a Tetradentate Phenanthroline‐Based Ligand

The synthesis and reactivity of ruthenium complexes containing the tetradentate phenanthroline‐based phosphine ligand 2,9‐bis((di‐tert‐butylphosphino)methyl)‐1,10‐phenanthroline (PPhenP) is described. The hydrido chloro complex [RuHCl(PPhenP)] ( 2 ) undergoes facile dearomatization upon deprotonation of the benzylic position, to give [RuH(PPhenP‐H)] ( 4 ). Addition of dihydrogen to 4 causes rearomatization of the phenanthroline moiety to trans‐[Ru(H)₂(PPhenP)] ( 5 ), followed by hydrogenation of an aromatic heterocycle in the ligand backbone, to give a new dearomatized and deconjugated complex [RuH(PPhenP*‐H)] ( 6 ). These aromatization/deconjugation steps of the coordinated ligand were demonstrated to be reversible and operative in the dehydrogenation of primary alcohols without the need for a hydrogen acceptor. This aromatization/deconjugation sequence constitutes an unprecedented mode of a stepwise cooperation between the metal center and the coordinated ligand.     

Quantization of presymplectic manifolds and circle actions

We prove several versions of ``quantization commutes with reduction' for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin structure. Our theorems work whenever the quantization data and the reduction data are compatible; this condition always holds if we start from a presymplectic (in particular, symplectic) manifold.

     

The impact of weak C-H...Rh interactions on the structure and reactivity of trans-[Rh(CO)2(phosphine)2]+: an experimental and theoretical examination

The crystal structure of the new cationic Rh(I) complex trans-[Rh(CO)(2)(L)(2)]BF(4) (L=alpha(2)-(diisopropylphosphino)isodurene) was found to exhibit a nonlinear OC-Rh-CO fragment and weak intramolecular C-H...Rh interactions. These interactions, which have also been shown to occur in solution, have been examined by density functional theory calculations and found to be inextricably linked to the presence of the distorted OC-Rh-CO fragment. This linkage has also been demonstrated by comparison with a highly similar Rh(I) complex, in which these C-H...Rh interactions are absent. Furthermore, the presence of these weak interactions has been shown to have a significant effect on the reactivity of the metal center.     

Solar Ultraviolet Radiation,Skin Cancer and Photoprotective Strategies in South Africa†

The most recent data relating to the incidence of, and mortality from, the three commonest forms of skin cancer, namely basal cell carcinoma (BCC), squamous cell carcinoma (SCC) and cutaneous melanoma (CM), in the Black African, Colored, Asian/Indian and White population groups in South Africa are reviewed. While exposure to solar ultraviolet radiation is the major environmental risk factor for BCC in all four groups, for SSC in the White and Asian/Indian groups and for CM in the White group, this is unlikely to be the case for most SCCs in the Black African group and for most CMs in the Black African and Asian/Indian groups. Strategies for practical personal photoprotection in South Africa are discussed with particular emphasis on people at heightened risk of skin cancer including the White population group, those with HIV or oculocutaneous albinism and outdoor workers.     

Rapid and simultaneous determination of U,F, Al,Ca and V in phosphate rocks by a combination of delayed neutron and γ-ray spectrometry techniques

Delayed neutron counting for uranium assay was coupled with -ray spectrometry in order to measure radionuclides of F, Al, Ca and V produced by neutron activation. For this measurement, the delay time required for U determination was exploited. Calibration of the method was provided by standards based on a CaCO₃ matrix and validity of results was verified against other analytical methods. A single sample can be analyzed for the five elements in 3 min with a precision of ±10%. The method developed was applied in the exploration of phosphate ores. The measured total concentrations permitted the disclosure of correlations between various elements and constituents in the samples. Chemical and mineralogical properties were obtained as well.