Tight bounds on the competitive ratio on accomodating sequences for the seat reservation problem

The unit price seat reservation problem is investigated. The seat reservation problem is the problem of assigning seat numbers on-line to requests for reservations in a train traveling through $k$ stations. We are considering the version where all tickets have the same price and where requests are treated fairly, i.e., a request which can be fulfilled must be granted. For fair deterministic algorithms, we provide an asymptotically matching upper bound to the existing lower bound which states that all fair algorithms for this problem are frac{1{2-competitive on accommodating sequences, when there are at least three seats. Additionally, we give an asymptotic upper bound of frac{7{9 for fair randomized algorithms against oblivious adversaries. We also examine concrete on-line algorithms, First-Fit and Random, for the special case of two seats. Tight analyses of their performance are given

The origin of hydrogen line emission for five Herbig Ae/Be stars spatially resolved by VLTI/AMBER spectro-interferometry

To trace the accretion and outflow processes around YSOs, diagnostic spectral lines such as the BrG 2.166 micron line are widely used, although due to a lack of spatial resolution, the origin of the line emission is still unclear. Employing the AU-scale spatial resolution which can be achieved with infrared long-baseline interferometry, we aim to distinguish between theoretical models which associate the BrG line emission with mass infall or mass outflow processes. Using the VLTI/AMBER instrument, we spatially and spectrally (R=1500) resolved the inner environment of five Herbig Ae/Be stars (HD163296, HD104237, HD98922, MWC297, V921Sco) in the BrG emission line as well as in the adjacent continuum. All objects (except MWC297) show an increase of visibility within the BrG emission line, indicating that the BrG-emitting region in these objects is more compact than the dust sublimation radius. For HD98922, our quantitative analysis reveals that the line-emitting region is compact enough to be consistent with the magnetospheric accretion scenario. For HD163296, HD104237, MWC297, and V921Sco we identify a stellar wind or a disk wind as the most likely line-emitting mechanism. We search for general trends and find that the size of the BrG-emitting region does not seem to depend on the basic stellar parameters, but correlates with the H-alpha line profile shape. We find evidence for at least two distinct BrG line-formation mechanisms. Stars with a P-Cygni H-alpha line profile and a high mass-accretion rate seem to show particularly compact BrG-emitting regions (R_BrG/R_cont<0.2), while stars with a double-peaked or single-peaked H-alpha-line profile show a significantly more extended BrG-emitting region (0.6<R_BrG/R_cont<1.4), possibly tracing a stellar wind or a disk wind.Comment: 20 pages; 11 figures; Accepted by A&A; a high quality version of the paper can be obtained at http://www.skraus.eu/papers/kraus.HAeBe-BrGsurvey.pd

Properties of the H-alpha-emitting Circumstellar Regions of Be Stars

Long-baseline interferometric observations obtained with the Navy Prototype Optical Interferometer of the H-alpha-emitting envelopes of the Be stars eta Tauri and beta Canis Minoris are presented. For compatibility with the previously published interferometric results in the literature of other Be stars, circularly symmetric and elliptical Gaussian models were fitted to the calibrated H-alpha observations. The models are sufficient in characterizing the angular distribution of the H-alpha-emitting circumstellar material associated with these Be stars. To study the correlations between the various model parameters and the stellar properties, the model parameters for eta Tau and beta CMi were combined with data for other Be stars from the literature. After accounting for the different distances to the sources and stellar continuum flux levels, it was possible to study the relationship between the net H-alpha emission and the physical extent of the H-alpha-emitting circumstellar region. A clear dependence of the net H-alpha emission on the linear size of the emitting region is demonstrated and these results are consistent with an optically thick line emission that is directly proportional to the effective area of the emitting disk. Within the small sample of stars considered in this analysis, no clear dependence on the spectral type or stellar rotation is found, although the results do suggest that hotter stars might have more extended H-alpha-emitting regions.Comment: 24 pages, 16 figures, accepted for publication in Ap

An investigation of the close environment of beta Cep with the VEGA/CHARA interferometer

High-precision interferometric measurements of pulsating stars help to characterize their close environment. In 1974, a close companion was discovered around the pulsating star beta Cep using the speckle interferometry technique and features at the limit of resolution (20 milli-arcsecond or mas) of the instrument were mentioned that may be due to circumstellar material. Beta Cep has a magnetic field that might be responsible for a spherical shell or ring-like structure around the star as described by the MHD models. Using the visible recombiner VEGA installed on the CHARA long-baseline interferometer at Mt. Wilson, we aim to determine the angular diameter of beta Cep and resolve its close environment with a spatial resolution up to 1 mas level. Medium spectral resolution (R=6000) observations of beta Cep were secured with the VEGA instrument over the years 2008 and 2009. These observations were performed with the S1S2 (30m) and W1W2 (100m) baselines of the array. We investigated several models to reproduce our observations. A large-scale structure of a few mas is clearly detected around the star with a typical flux relative contribution of 0.23 +- 0.02. Our best model is a co-rotational geometrical thin ring around the star as predicted by magnetically-confined wind shock models. The ring inner diameter is 8.2 +- 0.8 mas and the width is 0.6 +- 0.7 mas. The orientation of the rotation axis on the plane of the sky is PA = 60 +- 1 deg, while the best fit of the mean angular diameter of beta Cep gives UD[V] = 0.22 +- 0.05 mas. Our data are compatible with the predicted position of the close companion of beta Cep. These results bring additional constraints on the fundamental parameters and on the future MHD and asteroseismological models of the star.Comment: Paper accepted for publication in A&A (in press

Near-Infrared interferometry of Eta Carinae with high spatial and spectral resolution using the VLTI and the AMBER instrument

We present the first NIR spectro-interferometry of the LBV Eta Carinae. The K band observations were performed with the AMBER instrument of the ESO Very Large Telescope Interferometer using three 8.2m Unit Telescopes with baselines from 42 to 89m. The aim of this work is to study the wavelength dependence of Eta Car's optically thick wind region with a high spatial resolution of 5 mas (11 AU) and high spectral resolution. The medium spectral resolution observations (R=1,500) were performed in the wavelength range around both the HeI 2.059 micron and the Br gamma 2.166 micron emission lines, the high spectral resolution observations (R=12,000) only in the Br gamma line region. In the K-band continuum, a diameter of 4.0 +/-0.2 mas (Gaussian FWHM, fit range 28-89m) was measured for Eta Car's optically thick wind region. If we fit Hillier et al. (2001) model visibilities to the observed AMBER visibilities, we obtain 50 % encircled-energy diameters of 4.2, 6.5 and 9.6mas in the 2.17 micron continuum, the HeI, and the Br gamma emission lines, respectively. In the continuum near the Br gamma line, an elongation along a position angle of 120+/-15 degrees was found, consistent with previous VLTI/VINCI measurements by van Boekel et al. (2003). We compare the measured visibilities with predictions of the radiative transfer model of Hillier et al. (2001), finding good agreement. Furthermore, we discuss the detectability of the hypothetical hot binary companion. For the interpretation of the non-zero differential and closure phases measured within the Br gamma line, we present a simple geometric model of an inclined, latitude-dependent wind zone. Our observations support theoretical models of anisotropic winds from fast-rotating, luminous hot stars with enhanced high-velocity mass loss near the polar regions.Comment: 22 pages, 14 figures, 2 tables; A&A in pres