Encoding algebraic power series

Algebraic power series are formal power series which satisfy a univariate polynomial equation over the polynomial ring in n variables. This relation determines the series only up to conjugacy. Via the Artin-Mazur theorem and the implicit function theorem it is possible to describe algebraic series completely by a vector of polynomials in n+p variables. This vector will be the code of the series. In the paper, it is then shown how to manipulate algebraic series through their code. In particular, the Weierstrass division and the Grauert-Hironaka-Galligo division will be performed on the level of codes, thus providing a finite algorithm to compute the quotients and the remainder of the division.Comment: 35 page

Near-infrared K-band Spectroscopic Investigation of Seyfert 2 Nuclei in the CfA and 12 Micron Samples

We present near-infrared K-band slit spectra of the nuclei of 25 Seyfert 2 galaxies in the CfA and 12 micron samples. The strength of the CO absorption features at 2.3-2.4 micron produced by stars is measured in terms of a spectroscopic CO index. A clear anti-correlation between the observed CO index and the nuclear K-L color is present, suggesting that a featureless hot dust continuum heated by an AGN contributes significantly to the observed K-band fluxes in the nuclei of Seyfert 2 galaxies. After correction for this AGN contribution, we estimate nuclear stellar K-band luminosities for all sources, and CO indices for sources with modestly large observed CO indices. The corrected CO indices for 10 (=40%) Seyfert 2 nuclei are found to be as high as those observed in star-forming or elliptical (=spheroidal) galaxies. We combine the K-band data with measurements of the L-band 3.3 micron polycyclic aromatic hydrocarbon (PAH) emission feature, another powerful indicator for star-formation, and find that the 3.3 micron PAH to K-band stellar luminosity ratios are substantially smaller than those of starburst galaxies. Our results suggest that the 3.3 micron PAH emission originates in the putative nuclear starbursts in the dusty tori surrounding the AGNs, because of its high surface brightness, whereas the K-band CO absorption features detected at the nuclei are dominated by old bulge (=spheroid) stars, and thus may not be a powerful indicator for the nuclear starbursts. We see no clear difference in the strength of the CO absorption and PAH emission features between the CfA and 12 micron Seyfert 2s.Comment: 28 pages, 6 figures, accepted for publication in ApJ (10 October 2004, v614 issue

Cooler and bigger than thought? Planetary host stellar parameters from the InfraRed Flux Method

Effective temperatures and radii for 92 planet-hosting stars as determined from the InfraRed Flux Method (IRFM) are presented and compared with those given by other authors using different approaches. The IRFM temperatures we have derived are systematically lower than those determined from the spectroscopic condition of excitation equilibrium, the mean difference being as large as 110 K. They are, however, consistent with previous IRFM studies and with the colors derived from Kurucz and MARCS model atmospheres. Comparison with direct measurements of stellar diameters for 7 dwarf stars, which approximately cover the range of temperatures of the planet-hosting stars, suggest that the IRFM radii and temperatures are reliable in an absolute scale. A better understanding of the fundamental properties of the stars with planets will be achieved once this discrepancy between the IRFM and the spectroscopic temperature scales is resolved.Comment: 15 pages, 4 figures. Accepted for publication in Ap

Angular Momenta and Spin-Orbit Interaction of Nonparaxial Light in Free Space

We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are presented. We apply the general theory to symmetric and asymmetric Bessel beams exhibiting spin- and orbital-dependent intensity profiles. The exact wave solutions are clearly interpreted in terms of the Berry phases, quantization of caustics, and Hall effects of light, which can be readily observed experimentally.Comment: 8 pages, 3 figure

On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

A photometric study of the hot exoplanet WASP-19b

Context: When the planet transits its host star, it is possible to measure the planetary radius and (with radial velocity data) the planet mass. For the study of planetary atmospheres, it is essential to obtain transit and occultation measurements at multiple wavelengths. Aims: We aim to characterize the transiting hot Jupiter WASP-19b by deriving accurate and precise planetary parameters from a dedicated observing campaign of transits and occultations. Methods: We have obtained a total of 14 transit lightcurves in the r'-Gunn, IC, z'-Gunn and I+z' filters and 10 occultation lightcurves in z'-Gunn using EulerCam on the Euler-Swiss telescope and TRAPPIST. We have also obtained one lightcurve through the narrow-band NB1190 filter of HAWK-I on the VLT measuring an occultation at 1.19 micron. We have performed a global MCMC analysis of all new data together with some archive data in order to refine the planetary parameters and measure the occultation depths in z'-band and at 1.19 micron. Results: We measure a planetary radius of R_p = 1.376 (+/-0.046) R_j, a planetary mass of M_p = 1.165 (+/-0.068) M_j, and find a very low eccentricity of e = 0.0077 (+/-0.0068), compatible with a circular orbit. We have detected the z'-band occultation at 3 sigma significance and measure it to be dF_z'= 352 (+/-116) ppm, more than a factor of 2 smaller than previously published. The occultation at 1.19 micron is only marginally constrained at dF_1190 = 1711 (+/-745) ppm. Conclusions: We have shown that the detection of occultations in the visible is within reach even for 1m class telescopes if a considerable number of individual events are observed. Our results suggest an oxygen-dominated atmosphere of WASP-19b, making the planet an interesting test case for oxygen-rich planets without temperature inversion.Comment: Published in Astronomy & Astrophysics. 11 pages, 11 figures, 4 table

Intrinsic structure of two-phonon states in the interacting boson model

A general study of excitations up to two-phonon states is carried out using the intrinsic-state formalism of the Interacting Boson Model (IBM). Spectra and transitions for the different dynamical symmetries are analyzed and the correspondence with states in the laboratory frame is established. The influence of multi-phonon states is discussed. The approach is useful in problems where the complexity of the IBM spectrum renders the analysis in the laboratory frame difficult.Comment: 22 pages, TeX (ReVTeX). 7 eps figures. Submitted to Nucl. Phys.

A Comparison of Learning Speed and Ability to Cope Without Exploration between DHP and TD(0)

This paper demonstrates the principal motivations for Dual Heuristic Dynamic Programming (DHP) learning methods for use in Adaptive Dynamic Programming and Reinforcement Learning, in continuous state spaces: that of automatic local exploration, improved learning speed and the ability to work without stochastic exploration in deterministic environments. In a simple experiment, the learning speed of DHP is shown to be around 1700 times faster than TD(0). DHP solves the problem without any exploration, whereas TD(0) cannot solve it without explicit exploration. DHP requires knowledge of, and differentiability of, the environment's model functions. This paper aims to illustrate the advantages of DHP when these two requirements are satisfied

Value-Gradient Learning

We describe an Adaptive Dynamic Programming algorithm VGL(λ) for learning a critic function over a large continuous state space. The algorithm, which requires a learned model of the environment, extends Dual Heuristic Dynamic Programming to include a bootstrapping parameter analogous to that used in the reinforcement learning algorithm TD(λ). We provide on-line and batch mode implementations of the algorithm, and summarise the theoretical relationships and motivations of using this method over its precursor algorithms Dual Heuristic Dynamic Programming and TD(λ). Experiments for control problems using a neural network and greedy policy are provided