Range convexity,continuity, and strategy-proofness of voting schemes

A voting scheme assigns to each profile of alternatives reported byn individuals a compromise alternative. A voting scheme is strategy-proof if no individual is better off by lying, i.e., not reporting a best alternative. In this paper the main results concern the case where the set of alternatives is the Euclidean plane and the preferences are Euclidean. It is shown that for strategy-proof voting schemes continuity is equivalent to convexity of the range of the voting scheme. Using a result by Kim and Roush (1984), this leads to characterizations of surjective or unanimous, anonymous, strategy-proof voting schemes.Furthermore, the paper contains an extensive discussion of related results in the area.     

Superfluid3He in high magnetic fields: New results

The superfluid A₁ an A₂ transitions have been studied by means of vibrating wire viscosimeters in magnetic fields up to 9.3 T. Using the technique of quick melting of polarized solid (Castaing-Nozières effect) we have succeeded in increasing the superfluid transition temperature from 2.86 to 3.23 mK, which is the highest up to now. Using this method, with some improvements, it should be possible to test some of the present theoretical models for³He. A minimum of the viscosity in the A₁ phase has been observed for the first time. Very close to the A₂ transition an anomaly in the amplitude of the viscometers seems to indicate the presence of a new phase, or some textural change due to dipole locking.Invited talk at the International Conference on Macroscopic Quantum Phenomena, Smolenice Castle, Czechoslovakia, September 18–22, 1989.The authors wish to thank C. C. Kranenburg and C. M. C. M. van Woerkens for their various contributions to the experiments. Very helpful discussions with K. S. Bedell, B. Castaing, H. Capel, P. Nozières, D. Rainer, A. Schakel, and G. A. Vermeulen are gratefully acknowledged. This work was financially supported by the Stichting voor Fundamenteel Onderzoek der Materie F. O. M.     

Inclusive production of vector mesons in π+ p interactions at 250 GeV/c

We report on a study of ρ⁰, ρ⁺, ω, \(\bar K^{*0} (892)\) andK ^*0 (892) inclusive production in π⁺ p interactions at 250 GeV/c, for ρ⁺, \(\bar K^{*0} (892)\) for the first time in a π⁺ p experiment. The data are compared withK ⁺ p data in the same experiment, with results of other experiments and with quark-parton models. Interesting differences are found between ρ^+,0 and ω production.     

The decay of theZ boson into four massive fermions

We calculate, the partial width for the tree level decay of theZ boson into four massive fermions atO(α²) and \(O(\alpha _s^2 )\) . Analytic expressions for the helicity amplitudes are presented. We also present ‘observable’ widths for the case when the fermions are energetic and well separated, and make a comparison between the massive and massless matrix elements in this region. We make a direct comparison between the four fermion decay and the production and decay of the Higgs boson via the Bjorken mechanism, \(Z \to H\mu ^ + \mu ^ - \to q\bar q\mu ^ + \mu ^ - \) . Provided the detector resolution is good, \(\Delta m_{q\bar q} \) ～ few GeV, the Higgs signal stands clearly above the four fermion background for all Higgs boson masses considered.