Extensions of abelian varieties defined over a number field

We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.Comment: 11 page

Searching for annihilation radiation from SN 1006 with SPI on INTEGRAL

Historical Type Ia supernovae are a leading candidate for the source of positrons observed through their diffuse annihilation emission in the Galaxy. However, search for annihilation emission from individual Type Ia supernovae has not been possible before the improved sensitivity of \integral. The total 511 keV annihilation flux from individual SNe Ia, as well as their contribution to the overall diffuse emission, depends critically on the escape fraction of positrons produced in $^{56}$Co decays. Late optical light curves suggest that this fraction may be as high as 5%. We searched for positron annihilation radiation from the historical Type Ia supernova SN 1006 using the SPI instrument on \integral. We did not detect significant 511 keV line emission, with a 3$\sigma$ flux upper limit of 0.59 x 10$^{-4}$ ergs cm^-2 s^-1 for \wsim 1 Msec exposure time, assuming a FWHM of 2.5 keV. This upper limit corresponds to a 7.5% escape fraction, 50% higher than the expected 5% escape scenario, and rules out the possibility that Type Ia supernovae produce all of the positrons in the Galaxy (~ 12% escape fraction), if the mean positron lifetime is less than 10$^{5}$ years. Future observations with \integral will provide stronger limits on the escape fraction of positrons, the mean positron lifetime, and the contribution of Type Ia supernovae to the overall positron content of the Galaxy.Comment: 3 pages, 2 figures, accepted for publication in ApJ

X_System

The X_System makes the playing, writing, and learning of music – even when using unconventional tunings – more intuitive, more logical, more expressive, and better sounding. The X_System allows for: • different temperaments to be chosen at the flick of a switch; • tunings to be dynamically altered at the push of a lever; • the use of a special hexagonal button-field that allows for any given interval or chord always to have the same shape on that button-field; • consonant chords to have their consonance maximised, whatever the tuning actually chosen; • radical changes to be made to the timbral character of tones using a minimal number of controls; • a choice of keyboard mappings, which enable for the balance between number of intervals and octaves to be altered

Quantum steering ellipsoids, extremal physical states and monogamy

A Corrigendum for this article has been published in 2015 New J. Phys. 17 019501Any two-qubit state can be faithfully represented by a steering ellipsoid inside the Bloch sphere, but not every ellipsoid inside the Bloch sphere corresponds to a two-qubit state. We give necessary and sufficient conditions for when the geometric data describe a physical state and investigate maximal volume ellipsoids lying on the physical-unphysical boundary. We derive monogamy relations for steering that are strictly stronger than the Coffman-Kundu- Wootters (CKW) inequality for monogamy of concurrence. The CKW result is thus found to follow from the simple perspective of steering ellipsoid geometry. Remarkably, we can also use steering ellipsoids to derive non-trivial results in classical Euclidean geometry, extending Eulers inequality for the circumradius and inradius of a triangle.The EPSRC and the ARC Centre of Excellence grant no. CE110001027. DJ is funded by the Royal Society. TR would like to thank the Leverhulme Trust. SJ acknowledges EPSRC grant EP/ K022512/1

The First Ten Years of Swift Supernovae

The Swift Gamma Ray Burst Explorer has proven to be an incredible platform for studying the multiwavelength properties of supernova explosions. In its first ten years, Swift has observed over three hundred supernovae. The ultraviolet observations reveal a complex diversity of behavior across supernova types and classes. Even amongst the standard candle type Ia supernovae, ultraviolet observations reveal distinct groups. When the UVOT data is combined with higher redshift optical data, the relative populations of these groups appear to change with redshift. Among core-collapse supernovae, Swift discovered the shock breakout of two supernovae and the Swift data show a diversity in the cooling phase of the shock breakout of supernovae discovered from the ground and promptly followed up with Swift. Swift observations have resulted in an incredible dataset of UV and X-ray data for comparison with high-redshift supernova observations and theoretical models. Swift's supernova program has the potential to dramatically improve our understanding of stellar life and death as well as the history of our universe.Comment: Invited review paper accepted into the Journal of High Energy Astrophysics for the dedicated issue: "Swift: Ten Years of Discovery" 8 pages, 4 figure