Characterizing the Banzhaf and Shapley values assuming limited linearity

This paper presents characterizations of the Banzhaf-Coleman and Shapley-Shubik indices for monotonic simple games. The characterizations are obtained without explicitly requiring that the indices satisfy the linearity assumptionψ (v∧ w) +ψ (v ∨ w) =ψ (v) + ψ (w). The ideas developed are then used to obtain a characterization of the Banzhaf value for the class of alln-person games in characteristic function form.     

Neutron and proton components of nuclear transitions in pion inelastic scattering on 26Mg

The elastic and inelastic scattering of 180 MeV positive and negative pions from ²⁶Mg has been measured. From these data the ratios of neutron and proton nuclear transition matrix elements have been determined for the first and second excited states. These ratios are compared with those obtained from electromagnetic transitions in mirror nuclei and with shell model predictions.     

Energy dependence of π+ induced two- and four-nucleon removal

De-excitation γ-rays have been detected from nuclear states following positive pion induced two-nucleon removal from ¹²C and four-nucleon removal from ¹⁶O. Excitation functions for population of discrete states were obtained for positive pions of 75, 125, 150, 200, 225, 250 and 290 MeV. The pion-nucleon (3, 3) resonance is not reflected in the cross sections for either reaction. Implications of the observed energy dependence are discussed.     

Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers

We experimentally and numerically investigate femtosecond-pulse propagation in a microstructured optical fiber consisting of a silica core surrounded by airholes that are filled with a high-index fluid. This fiber combines the resonant properties of hollow-core bandgap fibers and the high nonlinearity of index-guiding waveguides. A range of nonlinear optical effects can be observed, including soliton propagation, dispersive wave generation, and a Raman self-frequency shift. Tuning the center wavelength of the laser and varying the refractive index of the fluid lead to different propagation effects, mediated by the strongly wavelength-dependent group-velocity dispersion in these photonic bandgap confining structures.     

Peroxycarbenium-mediated C-C bond formation: applications to the synthesis of hydroperoxides and peroxides

The Lewis acid-mediated reaction of alkene nucleophiles with peroxyacetals provides an effective route for the synthesis of homologated peroxides and hydroperoxides. In the presence of Lewis acids such as TiCl(4), SnCl(4), and trimethylsilyl triflate, peroxyacetals and peroxyketals undergo reaction with allyltrimethylsilane, silyl enol ethers, and silyl ketene acetals to afford homoallyl peroxides, 3-peroxyketones, and 3-peroxyalkanoates, respectively. Reactions of peroxyacetals are Lewis acid dependent; TiCl(4) promotes formation of ethers while SnCl(4) and trimethylsilyl triflate promote formation of peroxides. Lewis acid-promoted reactions of silylated hydroperoxyacetals furnish silylated hydroperoxides, which can be deprotected to homologated hydroperoxides. Hydroperoxyketals undergo Lewis acid-mediated allylation to furnish 1,2-dioxolanes via attack of hydroperoxide on the intermediate carbocation. Lewis acid-mediated cyclization of unsaturated peroxyacetals furnishes 1,2-dioxanes, 1,2-dioxepanes, and 1,2-dioxacanes through 6-endo/exo, 7-endo/endo, and 8-endo/endo pathways. The corresponding reactions involving 6-endo/endo and 5-endo/exo pathways were unsuccessful.