The Inhomogeneous Hall's Ray

We show that the inhomogenous approximation spectrum, associated to an irrational number \alpha\ always has a Hall's Ray; that is, there is an \epsilon>0 such that [0,\epsilon) is a subset of the spectrum. In the case when \alpha\ has unbounded partial quotients we show that the spectrum is just a ray.Comment: Fixed typos in bibliograph

V405 Peg (RBS 1955): A Nearby, Low-Luminosity Cataclysmic Binary

(Abridged). The cataclysmic binary V405 Peg, originally discovered as ROSAT Bright Source (RBS) 1955 (= 1RXS J230949.6+213523), shows a strong contribution from a late-type secondary star in its optical spectrum, which led Schwope et al. to suggest it to be among the nearest cataclysmic binaries. We present extensive optical observations of V405 Peg. Time-series spectroscopy shows the orbital period, Porb, to be 0.1776469(7) d (= 4.2635 hr), or 5.629 cycle/d. We classify the secondary as M3 - M4.5. Astrometry with the MDM 2.4m telescope gives a parallax 7.2 +- 1.1 milli-arcsec, and a relative proper motion of 58 mas/yr. Our best estimate of the distance yields d = 149 (+26, -20) pc. The secondary stars's radial velocity has K2 = 92 +- 3 km/s, indicating a fairly low orbital inclination if the masses are typical. Extensive I-band time-series observations in the show the system varying between a minimum brightness level of I = 14.14 and states of enhanced activity about 0.2 mag brighter. While the low-state shows an ellipsoidal modulation, an additional photometric modulation appears in the high state, with 0.1 mag amplitude and period 220-280 min. The frequency of this modulation appears to be stable for a month or so, but no single period was consistently detected from one observing season to the next. We estimate the system luminosity by combining optical measurements with the archival X-ray spectrum. The implied mass accretion rate is orders of magnitudes below the predictions for the standard angular momentum loss above the period gap. The system may possibly belong to a largely undiscovered population of hibernating CVs.Comment: 11 figures; 7 of these are .png or .jpg to save space. In press for Publications of the Astronomical Society of the Pacifi

Reconciling taxonomy and phylogenetic inference: formalism and algorithms for describing discord and inferring taxonomic roots

Although taxonomy is often used informally to evaluate the results of phylogenetic inference and find the root of phylogenetic trees, algorithmic methods to do so are lacking. In this paper we formalize these procedures and develop algorithms to solve the relevant problems. In particular, we introduce a new algorithm that solves a "subcoloring" problem for expressing the difference between the taxonomy and phylogeny at a given rank. This algorithm improves upon the current best algorithm in terms of asymptotic complexity for the parameter regime of interest; we also describe a branch-and-bound algorithm that saves orders of magnitude in computation on real data sets. We also develop a formalism and an algorithm for rooting phylogenetic trees according to a taxonomy. All of these algorithms are implemented in freely-available software.Comment: Version submitted to Algorithms for Molecular Biology. A number of fixes from previous versio

Precision electromagnetic structure of decuplet baryons in the chiral regime

The electromagnetic properties of the baryon decuplet are calculated in quenched QCD on a 20^3 x 40 lattice with a lattice spacing of 0.128 fm using the fat-link irrelevant clover (FLIC) fermion action with quark masses providing a pion mass as low as 300 MeV. Magnetic moments and charge radii are extracted from the electric and magnetic form factors for each individual quark sector. From these, the corresponding baryon properties are constructed. We present results for the higher order moments of the spin-3/2 baryons, including the electric quadrupole moment E2 and the magnetic octupole moment M3. The world's first determination of a non-zero M3 form factor for the Delta baryon is presented. With these results we provide a conclusive analysis which shows that decuplet baryons are deformed. We compare the decuplet baryon results from a similar lattice calculation of the octet baryons. We establish that the environment sensitivity is far less pronounced in the case of the decuplet baryons compared to that in the octet baryons. A surprising result is that the charge radii of the decuplet baryons are generally smaller than that of the octet baryons. The magnetic moment of the Delta^+ reveals a turn over in the low quark mass region, making it smaller than the proton magnetic moment. These results are consistent with the expectations of quenched chiral perturbation theory. A similar turn over is also noticed in the magnetic moment of the Sigma^*0, but not for Xi^* where only kaon loops can appear in quenched QCD. The electric quadrupole moment of the Omega^- baryon is positive when the negative charge factor is included, and is equal to 0.86 +- 0.12 x 10^-2 fm^2, indicating an oblate shape.Comment: 30 pages, 32 figure

High resolution structural characterisation of laser-induced defect clusters inside diamond

Laser writing with ultrashort pulses provides a potential route for the manufacture of three-dimensional wires, waveguides and defects within diamond. We present a transmission electron microscopy (TEM) study of the intrinsic structure of the laser modifications and reveal a complex distribution of defects. Electron energy loss spectroscopy (EELS) indicates that the majority of the irradiated region remains as $sp^3$ bonded diamond. Electrically-conductive paths are attributed to the formation of multiple nano-scale, $sp^2$-bonded graphitic wires and a network of strain-relieving micro-cracks

String effects and the distribution of the glue in mesons at finite temperature

The distribution of the gluon action density in mesonic systems is investigated at finite temperature. The simulations are performed in quenched QCD for two temperatures below the deconfinment phase. Unlike the gluonic profiles displayed at T=0, the action density iso-surfaces display a prolate-spheroid like shape. The curved width profile of the flux-tube is found to be consistent with the prediction of the free Bosonic string model at large distances.Comment: 14 pages,10 figure

Sun-Sized Water Vapor Masers in Cepheus A

We present the first VLBI observations of a Galactic water maser (in Chepeus A) made with a very long baseline interferometric array involving the RadioAstron Earth-orbiting satellite station as one of its elements. We detected two distinct components at -16.9 and 0.6 km/s with a fringe spacing of 66 microarcseconds. In total power, the 0.6 km/s component appears to be a single Gaussian component of strength 580 Jy and width of 0.7 km/s. Single-telescope monitoring showed that its lifetime was only 8~months. The absence of a Zeeman pattern implies the longitudinal magnetic field component is weaker than 120 mG. The space-Earth cross power spectrum shows two unresolved components smaller than 15 microarcseconds, corresponding to a linear scale of 1.6 x 10^11 cm, about the diameter of the Sun, for a distance of 700 pc, separated by 0.54 km/s in velocity and by 160 +/-35 microarcseconds in angle. This is the smallest angular structure ever observed in a Galactic maser. The brightness temperatures are greater than 2 x 10^14K, and the line widths are 0.5 km/s. Most of the flux (about 87%) is contained in a halo of angular size of 400 +/- 150 microarcseconds. This structure is associated with the compact HII region HW3diii. We have probably picked up the most prominent peaks in the angular size range of our interferometer. We discuss three dynamical models: (1) Keplerian motion around a central object, (2) two chance overlapping clouds, and (3) vortices caused by flow around an obstacle (i.e., von Karman vortex street) with Strouhal number of about~0.3.Comment: 15 pages, 9 figures. Accepted for publication in ApJ, February 16, 201

Polarized Broad H-alpha Emission from the LINER Nucleus of NGC 1052

Optical spectropolarimetry of the nucleus of the LINER NGC 1052, obtained at the Keck Observatory, reveals a rise in polarization in the wings of the H-alpha line profile. The polarization vector of H-alpha is offset by 67 degrees from the parsec-scale radio axis and by 83 degrees from the kiloparsec-scale radio axis, roughly in accord with expectations for scattering within the opening cone of an obscuring torus. The broad component of H-alpha has FWHM ~ 2100 km/s in total flux and FWHM ~ 5000 km/s in polarized light. Scattering by electrons is the mechanism most likely responsible for this broadening, and we find T_e ~ 10^5 K for the scattering medium, similar to values observed in Seyfert 2 nuclei. This is the first detection of a polarized broad emission line in a LINER, demonstrating that unified models of active galactic nuclei are applicable to at least some LINERs.Comment: 6 pages, 2 figures, prepared using the emulateapj style file, accepted for publication in The Astrophysical Journal Letter

Random division of an interval

The well-known relation between random division of an interval and the Poisson process is interpreted as a Laplace transformation. With the use of this interpretation a number of (in part known) results is derived very easily