On the topology of initial data sets with higher genus ends

In this note we study the topology of 3-dimensional initial data sets with horizons of a sort associated with asymptotically locally anti-de Sitter spacetimes. We show that, within this class, those initial data sets which contain no (immersed) marginally outer trapped surfaces in their interior must have simple topology: they are a product of a surface and an interval, or a mild variation thereof, depending on the connectedness of the horizon and on its genus relative to that of the end. The results obtained here extend results in [11] to the case of higher genus ends.Comment: v2: 13 pages, 1 figure; minor corrections and changes, Lemma 2.2 added. To appear in Commun Math Phy

Grid Diagrams and Legendrian Lens Space Links

Grid diagrams encode useful geometric information about knots in S^3. In particular, they can be used to combinatorially define the knot Floer homology of a knot K in S^3, and they have a straightforward connection to Legendrian representatives of K in (S^3, \xi_\st), where \xi_\st is the standard, tight contact structure. The definition of a grid diagram was extended to include a description for links in all lens spaces, resulting in a combinatorial description of the knot Floer homology of a knot K in L(p, q) for all p > 0. In the present article, we explore the connection between lens space grid diagrams and the contact topology of a lens space. Our hope is that an understanding of grid diagrams from this point of view will lead to new approaches to the Berge conjecture, which claims to classify all knots in S^3 upon which surgery yields a lens space.Comment: 27 pages, 20 figure

Bidirectional step torque filter with zero backlash characteristic Patent

Gearing system for eliminating backlash and filtering input torque fluctuations from high inertia loa

An Early Bronze Age 'dagger grave' from Rameldry Farm, near Kingskettle, Fife

In February 2000, ploughing disturbed the capstone of a cist, located on the side of a prominent knowe at Rameldry Farm, near Kingskettle in central Fife. Excavation by Headland Archaeology Ltd on behalf of Historic Scotland revealed a short cist which contained the crouched inhumation of a man aged 40-50, who had suffered from arthritis, some tooth loss and possibly Paget's Disease. He had been buried wearing a garment adorned with six V-pelforated buttons. Five of these are of Whitby jet (including one with unique decoration including inlaid tin); the sixth is of the mineral lizardite, and has an enigmatic coating, possibly a glaze. Behind his shoulder was a dagger, of 'Milston type (East Kennet variant) it had had a fancy horn hilt and a scabbard lined with animal skin. The scabbard yielded two A MS radiocarbon dates, with a mean value of 2280-1970 cal Bc at 2

Ignition of binary alloys of uranium

Experiments determine the effect of alloying additives on the ignition of uranium. Data on oxidation rates, ignition temperatures, and burning curves are provided in the report

Graphics and composite material computer program enhancements for SPAR

User documentation is provided for additional computer programs developed for use in conjunction with SPAR. These programs plot digital data, simplify input for composite material section properties, and compute lamina stresses and strains. Sample problems are presented including execution procedures, program input, and graphical output

Exciton-polaron complexes in pulsed electrically-detected magnetic resonance

Several microscopic pathways have been proposed to explain the large magnetic effects observed in organic semiconductors, but identifying and characterising which microscopic process actually influences the overall magnetic field response is challenging. Pulsed electrically-detected magnetic resonance provides an ideal platform for this task as it intrinsically monitors the charge carriers of interest and provides dynamical information which is inaccessible through conventional magnetoconductance measurements. Here we develop a general time domain theory to describe the spin-dependent reaction of exciton-charge complexes following the coherent manipulation of paramagnetic centers through electron spin resonance. A general Hamiltonian is treated, and it is shown that the transition frequencies and resonance positions of the exciton-polaron complex can be used to estimate inter-species coupling. This work also provides a general formalism for analysing multi-pulse experiments which can be used to extract relaxation and transport rates

Simultaneous chromatic dispersion, polarization-mode-dispersion and OSNR monitoring at 40Gbit/s

A novel method for independent and simultaneous monitoring of chromatic dispersion ( CD), first-order PMD and OSNR in 40Gbit/s systems is proposed and demonstrated. This is performed using in-band tone monitoring of 5GHz, optically down-converted to a low intermediate-frequency (IF) of 10kHz. The measurement provides a large monitoring range with good accuracies for CD (4742 +/- 100ps/nm), differential group delay (DGD) (200 +/- 4ps) and OSNR (23 +/- 1dB), independently of the bit-rate. In addition, the use of electro-absorption modulators (EAM) for the simultaneous down-conversion of all channels and the use of low-speed detectors makes it cost effective for multi-channel operation. (C) 2008 Optical Society of Americ

Stable divisorial gonality is in NP

Divisorial gonality and stable divisorial gonality are graph parameters, which have an origin in algebraic geometry. Divisorial gonality of a connected graph $G$ can be defined with help of a chip firing game on $G$. The stable divisorial gonality of $G$ is the minimum divisorial gonality over all subdivisions of edges of $G$. In this paper we prove that deciding whether a given connected graph has stable divisorial gonality at most a given integer $k$ belongs to the class NP. Combined with the result that (stable) divisorial gonality is NP-hard by Gijswijt, we obtain that stable divisorial gonality is NP-complete. The proof consist of a partial certificate that can be verified by solving an Integer Linear Programming instance. As a corollary, we have that the number of subdivisions needed for minimum stable divisorial gonality of a graph with $n$ vertices is bounded by $2^{p(n)}$ for a polynomial $p$