Axioms for consensus functions on the n-cube

An elementary general result is proved that allows for simple characterizations of well-known location/consensus functions (median, mean and center) on the n-cube. In addition, alternate new characterizations are given for the median and anti-median functions on the n-cube.Comment: 12 page

Superconducting weak links in YBa2Cu3O7-δ an AC magnetic susceptibility study

AC magnetic susceptibility, X' and X'', and ac resistivity, ρ, of two different samples of superconducting YBa2Cu3O7-δ have been measured. The results show a strong non-linear behaviour and are very sensitive to the exciting amplitudes. From the analysis of the data and comparison with appropriate models and other superconducting compounds, evidence for the existence of weak superconducting links is inferred. Finally, the utility of acX measurements for detection of different superconducting phases is made evident. \u

Non-linear response of single-molecule magnets: field-tuned quantum-to-classical crossovers

Quantum nanomagnets can show a field dependence of the relaxation time very different from their classical counterparts, due to resonant tunneling via excited states (near the anisotropy barrier top). The relaxation time then shows minima at the resonant fields H_{n}=n D at which the levels at both sides of the barrier become degenerate (D is the anisotropy constant). We showed that in Mn12, near zero field, this yields a contribution to the nonlinear susceptibility that makes it qualitatively different from the classical curves [Phys. Rev. B 72, 224433 (2005)]. Here we extend the experimental study to finite dc fields showing how the bias can trigger the system to display those quantum nonlinear responses, near the resonant fields, while recovering an classical-like behaviour for fields between them. The analysis of the experiments is done with heuristic expressions derived from simple balance equations and calculations with a Pauli-type quantum master equation.Comment: 4 pages, 3 figures. Submitted to Phys. Rev. B, brief report

Advection-Dominated Accretion and Black Hole Event Horizons

The defining characteristic of a black hole is that it possesses an event horizon through which matter and energy can fall in but from which nothing escapes. Soft X-ray transients (SXTs), a class of X-ray binaries, appear to confirm this fundamental property of black holes. SXTs that are thought to contain accreting black holes display a large variation of luminosity between their bright and faint states, while SXTs with accreting neutron stars have a smaller variation. This difference is predicted if the former stars have horizons and the latter have normal surfaces.Comment: 11 pages, including 2 tables and 2 figures. To appear in The Astrophysical Journal Letter