Schwinger Representation for the Symmetric Group: Two explicit constructions for the Carrier Space

We give two explicit construction for the carrier space for the Schwinger representation of the group $S_n$. While the first relies on a class of functions consisting of monomials in antisymmetric variables, the second is based on the Fock space associated with the Greenberg algebra.Comment: Latex, 6 page

The Variability of Seyfert 1.8 and 1.9 Galaxies at 1.6 microns

We present a study of Seyfert 1.5-2.0 galaxies observed at two epochs with the Hubble Space Telescope (HST) at 1.6 microns. We find that unresolved nuclear emission from 9 of 14 nuclei varies at the level of 10-40% on timescales of 0.7-14 months, depending upon the galaxy. A control sample of Seyfert galaxies lacking unresolved sources and galaxies lacking Seyfert nuclei show less than 3% instrumental variation in equivalent aperture measurements. This proves that the unresolved sources are non-stellar and associated with the central pc of active galactic nuclei. Unresolved sources in Seyfert 1.8 and 1.9 galaxies are not usually detected in HST optical surveys, however high angular resolution infrared observations will provide a way to measure time delays in these galaxies.Comment: accepted by ApJLetters (emulateapj latex

DMTPC: A dark matter detector with directional sensitivity

By correlating nuclear recoil directions with the Earth's direction of motion through the Galaxy, a directional dark matter detector can unambiguously detect Weakly Interacting Massive Particles (WIMPs), even in the presence of backgrounds. Here, we describe the Dark Matter Time-Projection Chamber (DMTPC) detector, a TPC filled with CF4 gas at low pressure (0.1 atm). Using this detector, we have measured the vector direction (head-tail) of nuclear recoils down to energies of 100 keV with an angular resolution of <15 degrees. To study our detector backgrounds, we have operated in a basement laboratory on the MIT campus for several months. We are currently building a new, high-radiopurity detector for deployment underground at the Waste Isolation Pilot Plant facility in New Mexico.Comment: 4 pages, 2 figures, proceedings for the CIPANP 2009 conference, May 26-31, 200

Why 'scaffolding' is the wrong metaphor : the cognitive usefulness of mathematical representations.

The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least (and plausibly for others), scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts.Peer reviewe

Effects of crack tip geometry on dislocation emission and cleavage: A possible path to enhanced ductility

We present a systematic study of the effect of crack blunting on subsequent crack propagation and dislocation emission. We show that the stress intensity factor required to propagate the crack is increased as the crack is blunted by up to thirteen atomic layers, but only by a relatively modest amount for a crack with a sharp 60$^\circ$ corner. The effect of the blunting is far less than would be expected from a smoothly blunted crack; the sharp corners preserve the stress concentration, reducing the effect of the blunting. However, for some material parameters blunting changes the preferred deformation mode from brittle cleavage to dislocation emission. In such materials, the absorption of preexisting dislocations by the crack tip can cause the crack tip to be locally arrested, causing a significant increase in the microscopic toughness of the crack tip. Continuum plasticity models have shown that even a moderate increase in the microscopic toughness can lead to an increase in the macroscopic fracture toughness of the material by several orders of magnitude. We thus propose an atomic-scale mechanism at the crack tip, that ultimately may lead to a high fracture toughness in some materials where a sharp crack would seem to be able to propagate in a brittle manner. Results for blunt cracks loaded in mode II are also presented.Comment: 12 pages, REVTeX using epsfig.sty. 13 PostScript figures. Final version to appear in Phys. Rev. B. Main changes: Discussion slightly shortened, one figure remove

Differential postural effects of plantar-flexor muscles fatigue under normal, altered and improved vestibular and neck somatosensory conditions

The aim of the present study was to assess the effects of plantar-flexor muscles fatigue on postural control during quiet standing under normal, altered and improved vestibular and neck somatosensory conditions. To address this objective, young male university students were asked to stand upright as still as possible with their eyes closed in two conditions of No Fatigue and Fatigue of the plantar-flexor muscles. In Experiment 1 (n=15), the postural task was executed in two Neutral head and Head tilted backward postures, recognized to degrade vestibular and neck somatosensory information. In Experiment 2 (n=15), the postural task was executed in two conditions of No tactile and Tactile stimulation of the neck provided by the application of strips of adhesive bandage to the skin over and around the neck. Centre of foot pressure displacements were recorded using a force platform. Results showed that (1) the Fatigue condition yielded increased CoP displacements relative to the No Fatigue condition (Experiment 1 and Experiment 2), (2) this destabilizing effect was more accentuated in the Head tilted backward posture than Neutral head posture (Experiment 1) and (3) this destabilizing effect was less accentuated in the condition of Tactile stimulation than that of No tactile stimulation of the neck (Experiment 2). In the context of the multisensory control of balance, these results suggest an increased reliance on vestibular and neck somatosensory information for controlling posture during quiet standing in condition of altered ankle neuromuscular function