Fuse and switch functions combined within a single housing

Fuswitch provides both switch and fuse functions within a single housing. A mercury capillary is used to alternately vaporize and condense the mercury within a reservoir. The housing is impervious to mercury and the fuse portion of the device operates on the principle of the self-healing mercury fuse

Stably free modules over virtually free groups

Let $F_m$ be the free group on $m$ generators and let $G$ be a finite nilpotent group of non square-free order; we show that for each $m\ge 2$ the integral group ring ${\bf Z}[G\times F_m]$ has infinitely many stably free modules of rank 1.Comment: 9 pages. The final publication is available at http://www.springerlink.com doi:10.1007/s00013-012-0432-

A remark on power series rings

A trivializability principle for local rings is described which leads to a form of weak algorithm for local semifirs with a finitely generated maximal ideal whose powers meet in zero

Characterisation and representation of non-dissipative electromagnetic medium with a double light cone

We study Maxwell's equations on a 4-manifold N with a medium that is non-dissipative and has a linear and pointwise response. In this setting, the medium can be represented by a suitable (2,2)-tensor on the 4-manifold N. Moreover, in each cotangent space on N, the medium defines a Fresnel surface. Essentially, the Fresnel surface is a tensorial analogue of the dispersion equation that describes the response of the medium for signals in the geometric optics limit. For example, in isotropic medium the Fresnel surface is at each point a Lorentz light cone. In a recent paper, I. Lindell, A. Favaro and L. Bergamin introduced a condition that constrains the polarisation for plane waves. In this paper we show (under suitable assumptions) that a slight strengthening of this condition gives a pointwise characterisation of all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. This is for example the behaviour of uniaxial medium like calcite. Moreover, using the representation formulas from Lindell et al. we obtain a closed form representation formula that pointwise parameterises all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. Both the characterisation and the representation formula are tensorial and do not depend on local coordinates

Addendum: "The Dynamics of M15: Observations of the Velocity Dispersion Profile and Fokker-Planck Models" (ApJ, 481, 267 [1997])

It has recently come to our attention that there are axis scale errors in three of the figures of Dull et al. (1997, hereafter D97). D97 presented Fokker-Planck models for the collapsed-core globular cluster M15 that include a dense, centrally concentrated population of neutron stars and massive white dwarfs, but do not include a central black hole. In this Addendum, we present corrected versions of Figures 9, 10, and 12, and an expanded version of Figure 6. This latter figure, which shows the full run of the velocity dispersion profile, indicates that the D97 model predictions are in good agreement with the moderately rising HST-STIS velocity dispersion profile for M15 reported by Gerssen et al. (2002, astro-ph/0209315). Thus, a central black hole is not required to fit the new STIS velocity measurements, provided that there is a sufficient population of neutron stars and massive white dwarfs. This conclusion is consistent with the findings of Gerssen et al. (2002, astro-ph/0210158), based on a reapplication of their Jeans equation analysis using the corrected mass-to-light profile (Figure 12) for the D97 models.Comment: 4 pages, 4 figures, submitted to Ap

A transform of complementary aspects with applications to entropic uncertainty relations

Even though mutually unbiased bases and entropic uncertainty relations play an important role in quantum cryptographic protocols they remain ill understood. Here, we construct special sets of up to 2n+1 mutually unbiased bases (MUBs) in dimension d=2^n which have particularly beautiful symmetry properties derived from the Clifford algebra. More precisely, we show that there exists a unitary transformation that cyclically permutes such bases. This unitary can be understood as a generalization of the Fourier transform, which exchanges two MUBs, to multiple complementary aspects. We proceed to prove a lower bound for min-entropic entropic uncertainty relations for any set of MUBs, and show that symmetry plays a central role in obtaining tight bounds. For example, we obtain for the first time a tight bound for four MUBs in dimension d=4, which is attained by an eigenstate of our complementarity transform. Finally, we discuss the relation to other symmetries obtained by transformations in discrete phase space, and note that the extrema of discrete Wigner functions are directly related to min-entropic uncertainty relations for MUBs.Comment: 16 pages, 2 figures, v2: published version, clarified ref [30