The irrationality of a number theoretical series

Denote by $\sigma_k(n)$ the sum of the $k$-th powers of the divisors of $n$, and let $S_k=\sum_{n\geq 1}\frac{\sigma_k(n)}{n!}$. We prove that Schinzel's conjecture H implies that $S_k$ is irrational, and give an unconditional proof for the case $k=3$

Asteroseismology of KIC 8263801:Is it a member of NGC 6866 and a red clump star?

We present an asteroseismic analysis of the Kepler light curve of KIC 8263801, a red-giant star in the open cluster NGC 6866 that has previously been reported to be a helium-burning red-clump star. We extracted the frequencies of the radial and quadrupole modes from its frequency power spectrum and determined its properties using a grid of evolutionary models constructed with MESA. The oscillation frequencies were calculated using the GYRE code and the surface term was corrected using the Ball & Gizon(2014) prescription. We find that the star has a mass of $M/M_{\odot} = 1.793\pm 0.072$, age $t=1.48\pm 0.21$ Gyr and radius $R/R_{\odot} = 10.53\pm 0.28$. By analyzing the internal structure of the best-fitting model, we infer the evolutionary status of the star KIC 8263801 as being on the ascending part of the red giant branch, and not on the red clump. This result is verified using a purely asteroseismic diagnostic, the $\epsilon_{c}-\Delta\nu_{c}$ diagram which can distinguish red giant branch stars from red clump stars. Finally, by comparing its age with NGC 6866 ($t=0.65 \pm 0.1$ Gyr) we conclude that KIC 8263801 is not a member of this open cluster

Stereociliary Myosin-1c Receptors Are Sensitive to Calcium Chelation and Absent from Cadherin 23 Mutant Mice

The identities of some of the constituents of the hair-cell transduction apparatus have been elucidated only recently. The molecular motor myosin-1c (Myo1c) functions in adaptation of the hair-cell response to sustained mechanical stimuli and is therefore an integral part of the transduction complex. Recent data indicate that Myo1c interacts in vitro with two other molecules proposed to be important for transduction: cadherin 23 (Cdh23), a candidate for the stereociliary tip link, and phosphatidylinositol 4,5-bisphosphate (PIP2), which is abundant in the membranes of hair-cell stereocilia. It is not known, however, whether these interactions occur in hair cells. Using an in situ binding assay on saccular hair cells, we demonstrated previously that Myo1c interacts with molecules at stereociliary tips, the site of transduction, through sequences contained within its calmodulin (CaM)-binding neck domain, which can bind up to four CaM molecules. In the current study, we identify the second CaM-binding IQ domain as a region of Myo1c that mediates CaM-sensitive binding to stereociliary tips and to PIP2 immobilized on a solid support. Binding of Myo1c to stereociliary tips of cochlear and vestibular hair cells is disrupted by treatments that break tip links. In addition, Myo1c does not bind to stereocilia from mice whose hair cells lack Cdh23 protein despite the presence of PIP2 in the stereociliary membranes. Collectively, our data suggest that Myo1c and Cdh23 interact at the tips of hair-cell stereocilia and that this interaction is modulated by CaM

Operating characteristics of the Langley Mach 7 Scramjet Test Facility

Operating characteristics of the Langley Mach 7 Scramjet Test Facility are described. The facility is designed for testing airframe integrated scramjet (supersonic combustion ramjet) engine models. Features include duplication of the flight Mach number total enthalpy, flight altitude simulation, and simulation of engine airframe integration effects such a bow shock wave precompression and boundary layer ingestion by the engine. Data obtained from facility calibration and from tests of a hydrogen burning, airframe integrated scramjet are discussed. An adverse interaction between the facility flow and the scramjet engine flow during combustion of the fuel is described

Photometry of supernovae in an image series : methods and application to the Supernova Legacy Survey (SNLS)

We present a technique to measure lightcurves of time-variable point sources on a spatially structured background from imaging data. The technique was developed to measure light curves of SNLS supernovae in order to infer their distances. This photometry technique performs simultaneous PSF photometry at the same sky position on an image series. We describe two implementations of the method: one that resamples images before measuring fluxes, and one which does not. In both instances, we sketch the key algorithms involved and present the validation using semi-artificial sources introduced in real images in order to assess the accuracy of the supernova flux measurements relative to that of surrounding stars. We describe the methods required to anchor these PSF fluxes to calibrated aperture catalogs, in order to derive SN magnitudes. We find a marginally significant bias of 2 mmag of the after-resampling method, and no bias at the mmag accuracy for the non-resampling method. Given surrounding star magnitudes, we determine the systematic uncertainty of SN magnitudes to be less than 1.5 mmag, which represents about one third of the current photometric calibration uncertainty affecting SN measurements. The SN photometry delivers several by-products: bright star PSF flux mea- surements which have a repeatability of about 0.6%, as for aperture measurements; we measure relative astrometric positions with a noise floor of 2.4 mas for a single-image bright star measurement; we show that in all bands of the MegaCam instrument, stars exhibit a profile linearly broadening with flux by about 0.5% over the whole brightness range.Comment: Accepted for publication in A&A. 20 page

Thermal design and analysis of a hydrogen-burning wind tunnel model of an airframe-integrated scramjet

An aerodynamic model of a hydrogen burning, airframe integrated scramjet engine has been designed, fabricated, and instrumented. This model is to be tested in an electric arc heated wind tunnel at an altitude of 35.39 km (116,094 ft.) but with an inlet Mach number of 6 simulating precompression on an aircraft undersurface. The scramjet model is constructed from oxygen free, high conductivity copper and is a heat sink design except for water cooling in some critical locations. The model is instrumented for pressure, surface temperature, heat transfer rate, and thrust measurements. Calculated flow properties, heat transfer rates, and surface temperature distributions along the various engine components are included for the conditions stated above. For some components, estimates of thermal strain are presented which indicate significant reductions in plastic strain by selective cooling of the model. These results show that the 100 thermal cycle life of the engine was met with minimum distortion while staying within the 2669 N (600 lbf) engine weight limitation and while cooling the engine only in critical locations

Determination of the critical current density in the d-wave superconductor YBCO under applied magnetic fields by nodal tunneling

We have studied nodal tunneling into YBa2Cu3O7-x (YBCO) films under magnetic fields. The films' orientation was such that the CuO2 planes were perpendicular to the surface with the a and b axis at 450 form the normal. The magnetic field was applied parallel to the surface and perpendicular to the CuO2 planes. The Zero Bias Conductance Peak (ZBCP) characteristic of nodal tunneling splits under the effect of surface currents produced by the applied fields. Measuring this splitting under different field conditions, zero field cooled and field cooled, reveals that these currents have different origins. By comparing the field cooled ZBCP splitting to that taken in decreasing fields we deduce a value of the Bean critical current superfluid velocity, and calculate a Bean critical current density of up to 3*10^7 A/cm2 at low temperatures. This tunneling method for the determination of critical currents under magnetic fields has serious advantages over the conventional one, as it avoids having to make high current contacts to the sample.Comment: 8 pages, 2 figure

Spatial incoherence of solar granulation: a global analysis using BiSON 2B data

A poor understanding of the impact of convective turbulence in the outer layers of the Sun and Sun-like stars challenges the advance towards an improved understanding of their internal structure and dynamics. Assessing and calibrating these effects is therefore of great importance. Here we study the spatial coherence of granulation noise and oscillation modes in the Sun, with the aim of exploiting any incoherence to beat-down observed granulation noise, hence improving the detection of low-frequency p-modes. Using data from the BiSON 2B instrument, we assess the coherence between different atmospheric heights and between different surface regions. We find that granulation noise from the different atmospheric heights probed is largely incoherent; frequency regions dominated by oscillations are almost fully coherent. We find a randomised phase difference for the granulation noise, and a near zero difference for the evanescent oscillations. A reduction of the incoherent granulation noise is shown by application of the cross-spectrum.Comment: 8 pages, 7 figures, MNRAS in pres

The Stellar Population Histories of Early-Type Galaxies. II. Controlling Parameters of the Stellar Populations

We analyze single-stellar-population (SSP) equivalent parameters for 50 local elliptical galaxies as a function of their structural parameters. These galaxies fill a two-dimensional plane in the four-dimensional space of [Z/H], log t, log $\sigma$, and [E/Fe]. SSP age and velocity dispersion can be taken as the two independent parameters that specify a galaxy's location in this ``hyperplane.'' The hyperplane can be decomposed into two sub-relations: (1) a ``Z-plane,'' in which [Z/H] is a linear function of log $\sigma$ and log t; and (2) a relation between [E/Fe] and $\sigma$ in which [E/Fe] is larger in high-$\sigma$ galaxies. Cluster and field ellipticals follow the same hyperplane, but their ($\sigma$,t) distributions within it differ. Nearly all cluster galaxies are old; the field ellipticals span a large range in SSP age. The tight Mg--$\sigma$ relations of these ellipticals can be understood as two-dimensional projections of the metallicity hyperplane showing it edge-on; the tightness of these relations does not necessarily imply a narrow range of ages at fixed $\sigma$. The relation between [E/Fe] and $\sigma$ is consistent with a higher effective yield of Type II SNe elements at higher $\sigma$. The Z-plane is harder to explain and may be a powerful clue to star formation in elliptical galaxies if it proves to be general. Present data favor a ``frosting'' model in which low apparent SSP ages are produced by adding a small frosting of younger stars to an older base population. If the frosting abundances are close to or slightly greater than the base population, simple two-component models run along lines of constant $\sigma$ in the Z-plane, as required. This favors star formation from well-mixed pre-enriched gas rather than unmixed low-metallicity gas from an accreted object. (Abridged)Comment: To be published in the June 2000 issue of the Astronomical Journal. 28 pages, 13 figures, uses emulateap