The congruence of Wolstenholme and generalized binomial coefficients related to Lucas sequences

Using generalized binomial coefficients with respect to fundamental Lucas sequences we establish congruences that generalize the classical congruence of Wolstenholme and other related stronger congruences.Comment: 23 page

On deriving p-mode parameters for inclined solar-like stars

Thanks to their high quality, new and upcoming asteroseismic observations - with CoRoT, Kepler, and from the ground... - can benefit from the experience gained with helioseismology. We focus in this paper on solar-like oscillations, for which the inclination of the rotation axis is unknown. We present a theoretical study of the errors of p-mode parameters determined by means of a maximum-likelihood estimator, and we also analyze correlations and biases. We have used different, complementary approaches: we have performed either semi-analytical computation of the Hessian matrix, fitting of single mean profiles, or Monte Carlo simulations. We give first analytical approximations for the errors of frequency, inclination and rotational splitting. The determination of the inclination is very challenging for the common case of slow rotators (like the Sun), making difficult the determination of a reliable rotational splitting. Moreover, due to the numerous correlations, biases - more or less significant - can appear in the determination of various parameters in the case of bad inclination fittings, especially when a locking at 90 degrees occurs. This issue concerning inclination locking is also discussed. Nevertheless, the central frequency and some derived parameters such as the total power of the mode are free of such biases.Comment: 9 pages, 6 figures, to appear in A&

Mode visibilities in radial velocity and intensity Sun-as-a-star helioseismic measurements

We analyze more than 5000 days of Sun-as-a-star radial velocity GOLF and intensity VIRGO observations to measure the visibilities of the l=0, 1, 2, and 3 modes and the m-amplitude ratios of the l=2 and 3 modes in the solar acoustic spectrum. We provide observational values that we compare to theoretical predictions.Comment: SOHO 24 / GONG 2010 conference, to be published in JPC

Magnetic activity cycles in solar-like stars: The cross-correlation technique of p-mode frequency shifts

Aims. We aim studying the use of cross-correlation techniques to infer the frequency shifts induced by changing magnetic fields in the p-mode frequencies and provide precise estimation of the error bars. Methods. This technique and the calculation of the associated errors is first tested and validated on the Sun where the p-mode magnetic behaviour is very well known. These validation tests are performed on 6000-day time series of Sun-as-a-star observations delivered by the SoHO spacecraft. Errors of the frequency shifts are quantified through Monte Carlo simulations. The same methodology is then applied to three solar-like oscillating stars: HD 49933, observed by CoRoT, as well as KIC 3733735 and KIC 7940546 observed by Kepler. Results. We first demonstrate the reliability of the error bars computed with the Monte Carlo simulations using the Sun. From the three analyzed stars we confirm the presence of a magnetic activity cycle with this methodology in HD 49933 and we unveil seismic signature of on going magnetic variations in KIC 3733735. Finally, the third star, KIC 7940546, seems to be in a quiet regime.Comment: Paper accepted in A&A. 7 pages and 11 figure

Who benefits from training and R&D: The firm or the workers? A study on panels of French and Swedish firms

The present paper offers a novel study of the effects of intangible assets on wages and productivity. Training, R&D, and physical capital are all taken into account, and their joint effects examined. We use panels of firms in order to control for unobserved fixed effects and the potential endogeneity of training and R&D, and have been able to obtain data for two different countries, France and Sweden, in order to explore the effects of institutional or national specificity. The estimation of productivity and wage equations allows us to show how the benefits of investment in physical capital, R&D and training are shared between the firm and the workers. Although the workers obtain significant benefits, the study shows that the firm obtains the largest return on the investments it makes. This is true not only for physical capital and R&D, but also for training. It suggests that firms can rationally invest in training and that the issue of under-investment in training should be re-examined.Training, R&D, productivity, wages

Gravito-inertial waves in a differentially rotating spherical shell

The gravito-inertial waves propagating over a shellular baroclinic flow inside a rotating spherical shell are analysed using the Boussinesq approximation. The wave properties are examined by computing paths of characteristics in the non-dissipative limit, and by solving the full dissipative eigenvalue problem using a high-resolution spectral method. Gravito-inertial waves are found to obey a mixed-type second-order operator and to be often focused around short-period attractors of characteristics or trapped in a wedge formed by turning surfaces and boundaries. We also find eigenmodes that show a weak dependence with respect to viscosity and heat diffusion just like truly regular modes. Some axisymmetric modes are found unstable and likely destabilized by baroclinic instabilities. Similarly, some non-axisymmetric modes that meet a critical layer (or corotation resonance) can turn unstable at sufficiently low diffusivities. In all cases, the instability is driven by the differential rotation. For many modes of the spectrum, neat power laws are found for the dependence of the damping rates with diffusion coefficients, but the theoretical explanation for the exponent values remains elusive in general. The eigenvalue spectrum turns out to be very rich and complex, which lets us suppose an even richer and more complex spectrum for rotating stars or planets that own a differential rotation driven by baroclinicity.Comment: 33 pages, 14 figures, accepted for publication in Journal of Fluid Mechanic