Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We show that, for any finite field Fq , there exist infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is a separable polynomial. As pointed out by Anglès, this is a necessary condition for the existence, for any finite field Fq, of infinitely many real function fields over Fq with ideal class number one (the so-called Gauss conjecture for function fields). We also show conditionally the existence of infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is an irreducible polynomial.
ISSN: 0022-314X

hal-00978911
https://hal.archives-ouvertes.fr/hal-00978911
https://hal.archives-ouvertes.fr/hal-00978911/document
https://hal.archives-ouvertes.fr/hal-00978911/file/AubryBlache5_10.pdf
DOI : 10.1016/j.jnt.2007.10.014

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The objectives are to study and model the aggregate wind power fluctuations dynamics in the multifractal framework. We present here the analysis of aggregate power output sampled at 1 Hz during three years. We decompose the data into several Intrinsic Mode Functions (IMF) using Empirical Mode Decomposition (EMD). We use a new approach, arbitrary order Hilbert spectral analysis, a combination of EMD approach with Hilbert spectral analysis (or Hilbert Huang Transform) and the classical structure function analysis to extract the scaling exponents or multifractal spectrum $zeta(q)$: this function provides a full characterization of a process at all intensities and all scales. The application of both methods, i.e. structure function and arbitrary-order Hilbert spectral analyses, give similar results indicating that the aggregate power output from a wind farm, possesses intermittent and multifractal properties. In order to check this result, we generate stochastic simulations of a Multifractal Random Walk (MRW) using a log-normal stochastic equation. We show that the simulation results are fully compatible with the experimental results.
Physica A

hal-01527887
https://hal.archives-ouvertes.fr/hal-01527887
DOI : 10.1016/j.physa.2013.04.038