Mean values of multiplicative functions over function fields

We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors’ new proof of Halász’s theorem on mean values to this simpler setting. Several of the technical difficulties that arise over the integers disappear in the function field setting, which helps bring out more clearly the main ideas of the proofs over number fields. We also obtain Lipschitz estimates showing the slow variation of mean values of multiplicative functions over function fields, which display some features that are not present in the integer situation

Nd:YAG development for spaceborne laser ranging system

The results of the development of a unique modelocked laser device to be utilized in future NASA space-based, ultraprecision laser ranger systems are summarized. The engineering breadboard constructed proved the feasibility of the pump-pulsed, actively modelocked, PTM Q-switched Nd:YAG laser concept for the generation of subnanosecond pulses suitable for ultra-precision ranging. The laser breadboard also included a double-pass Nd:YAG amplifier and provision for a Type II KD*P frequency doubler. The specific technical accomplishment was the generation of single 150 psec, 20-mJ pulses at 10 pps at a wavelength of 1.064 micrometers with 25 dB suppression of pre-and post-pulses

TEXES Observations of M Supergiants: Dynamics and Thermodynamics of Wind Acceleration

We have detected [Fe II] 17.94 um and 24.52 um emission from a sample of M supergiants using TEXES on the IRTF. These low opacity emission lines are resolved at R = 50, 000 and provide new diagnostics of the dynamics and thermodynamics of the stellar wind acceleration zone. The [Fe II] lines, from the first excited term, are sensitive to the warm plasma where energy is deposited into the extended atmosphere to form the chromosphere and wind outflow. These diagnostics complement previous KAO and ISO observations which were sensitive to the cooler and more extended circumstellar envelopes. The turbulent velocities, Vturb is about 12 to 13 km/s, observed in the [Fe II] forbidden lines are found to be a common property of our sample, and are less than that derived from the hotter chromospheric C II] 2325 Angstrom lines observed in alpha Ori, where Vturb is about 17 to 19 km/s. For the first time, we have dynamically resolved the motions of the dominant cool atmospheric component discovered in alpha Ori from multi-wavelength radio interferometry by Lim et al. (1998). Surprisingly, the emission centroids are quite Gaussian and at rest with respect to the M supergiants. These constraints combined with model calculations of the infrared emission line fluxes for alpha Ori imply that the warm material has a low outflow velocity and is located close to the star. We have also detected narrow [Fe I] 24.04 um emission that confirms that Fe II is the dominant ionization state in alpha Ori's extended atmosphere.Comment: 79 pages including 10 figures and 2 appendices. Accepted by Ap

Fractional processes: from Poisson to branching one

Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Levy stable densities are discussed and used for construction of the Monte Carlo algorithm for simulation of random waiting times in fractional processes. Numerical calculations are performed and limit distributions of the normalized variable Z=N/ are found for both processes.Comment: 11 pages, 6 figure

Imaging the dynamical atmosphere of the red supergiant Betelgeuse in the CO first overtone lines with VLTI/AMBER

We present the first 1-D aperture synthesis imaging of the red supergiant Betelgeuse in the individual CO first overtone lines with VLTI/AMBER. The reconstructed 1-D projection images reveal that the star appears differently in the blue wing, line center, and red wing of the individual CO lines. The 1-D projection images in the blue wing and line center show a pronounced, asymmetrically extended component up to ~1.3 stellar radii, while those in the red wing do not show such a component. The observed 1-D projection images in the lines can be reasonably explained by a model in which the CO gas within a region more than half as large as the stellar size is moving slightly outward with 0--5 km s^-1, while the gas in the remaining region is infalling fast with 20--30 km s^-1. A comparison between the CO line AMBER data taken in 2008 and 2009 shows a significant time variation in the dynamics of the CO line-forming region in the photosphere and the outer atmosphere. In contrast to the line data, the reconstructed 1-D projection images in the continuum show only a slight deviation from a uniform disk or limb-darkened disk. We derive a uniform-disk diameter of 42.05 +/- 0.05 mas and a power-law-type limb-darkened disk diameter of 42.49 +/- 0.06 mas and a limb-darkening parameter of (9.7 +/- 0.5) x 10^{-2}. This latter angular diameter leads to an effective temperature of 3690 +/- 54 K for the continuum-forming layer. These diameters confirm that the near-IR size of Betelgeuse was nearly constant over the last 18 years, in marked contrast to the recently reported noticeable decrease in the mid-IR size. The continuum data taken in 2008 and 2009 reveal no or only marginal time variations, much smaller than the maximum variation predicted by the current 3-D convection simulations.Comment: 21 pages, 12 figures, accepted for publication in Astronomy and Astrophysic

Helium, Oxygen, Proton, and Electron (HOPE) Mass Spectrometer for the Radiation Belt Storm Probes Mission

The HOPE mass spectrometer of the Radiation Belt Storm Probes (RBSP) mission (renamed the Van Allen Probes) is designed to measure the in situ plasma ion and electron fluxes over 4π sr at each RBSP spacecraft within the terrestrial radiation belts. The scientific goal is to understand the underlying physical processes that govern the radiation belt structure and dynamics. Spectral measurements for both ions and electrons are acquired over 1 eV to 50 keV in 36 log-spaced steps at an energy resolution ΔE FWHM/E≈15 %. The dominant ion species (H+, He+, and O+) of the magnetosphere are identified using foil-based time-of-flight (TOF) mass spectrometry with channel electron multiplier (CEM) detectors. Angular measurements are derived using five polar pixels coplanar with the spacecraft spin axis, and up to 16 azimuthal bins are acquired for each polar pixel over time as the spacecraft spins. Ion and electron measurements are acquired on alternate spacecraft spins. HOPE incorporates several new methods to minimize and monitor the background induced by penetrating particles in the harsh environment of the radiation belts. The absolute efficiencies of detection are continuously monitored, enabling precise, quantitative measurements of electron and ion fluxes and ion species abundances throughout the mission. We describe the engineering approaches for plasma measurements in the radiation belts and present summaries of HOPE measurement strategy and performance

Reduced regional brain cortical thickness in patients with heart failure.

AimsAutonomic, cognitive, and neuropsychologic deficits appear in heart failure (HF) subjects, and these compromised functions depend on cerebral cortex integrity in addition to that of subcortical and brainstem sites. Impaired autoregulation, low cardiac output, sleep-disordered-breathing, hypertension, and diabetic conditions in HF offer considerable potential to affect cortical areas by loss of neurons and glia, which would be expressed as reduced cortical thicknesses. However, except for gross descriptions of cortical volume loss/injury, regional cortical thickness integrity in HF is unknown. Our goal was to assess regional cortical thicknesses across the brain in HF, compared to control subjects.Methods and resultsWe examined localized cortical thicknesses in 35 HF and 61 control subjects with high-resolution T1-weighted images (3.0-Tesla MRI) using FreeSurfer software, and assessed group differences with analysis-of-covariance (covariates; age, gender; p<0.05; FDR). Significantly-reduced cortical thicknesses appeared in HF over controls in multiple areas, including the frontal, parietal, temporal, and occipital lobes, more markedly on the left side, within areas that control autonomic, cognitive, affective, language, and visual functions.ConclusionHeart failure subjects show reduced regional cortical thicknesses in sites that control autonomic, cognitive, affective, language, and visual functions that are deficient in the condition. The findings suggest chronic tissue alterations, with regional changes reflecting loss of neurons and glia, and presumably are related to earlier-described axonal changes. The pathological mechanisms contributing to reduced cortical thicknesses likely include hypoxia/ischemia, accompanying impaired cerebral perfusion from reduced cardiac output and sleep-disordered-breathing and other comorbidities in HF

Feeling good about being hungry: food-related thoughts in eating disorder

Objectives: This study explores the relationships to food and hunger in women living with anorexic type eating difficulties and asks how imagery-based elaborations of food and eating thoughts are involved in their eating restraint, and recovery. Design: The qualitative idiographic approach of Interpretative Phenomenological Analysis (IPA) was used. Four in-depth semi-structured interviews were conducted with women self-selected as having experienced anorexia or anorexic like behaviour. Methods: The data was analysed using IPA and an audit of the analysis was conducted to ensure that the process followed had been systematic and rigorous and appropriately considered reflexivity. Results: Hunger was perceived positively by participants as confirmation that they were achieving their goal of losing weight, or avoiding weight gain. Hunger conferred a sense of being in control for the participants. Intrusive thoughts about food were reported as being quickly followed by elaborative mental imagery of the positive aspects of weight loss, and the negative consequences of eating. Imagery appeared to serve to maintain anorexic behaviours rather than to motivate food seeking. However, negative imagery of the consequences of anorexia were also described as supporting recovery. Conclusions: The finding that physiological sensations of hunger were experienced as positive confirmation of maintaining control has potentially important clinical and theoretical implications. It suggests further attention needs to be focused upon how changes in cognitive elaboration, involving mental imagery, are components of the psychological changes in the development of, maintenance of, and recovery from, anorexia

Parsimonious Kernel Fisher Discrimination

By applying recent results in optimization transfer, a new algorithm for kernel Fisher Discriminant Analysis is provided that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The algorithm is simple, easily programmed and is shown to perform as well as or better than a number of leading machine learning algorithms on a substantial benchmark. It is then applied to a set of extreme small-sample-size problems in virtual screening where it is found to be less accurate than a currently leading approach but is still comparable in a number of cases