Non-unimodular transversely homogeneous foliations

We give sufficient conditions for the tautness of a transversely homogenous foliation defined on a compact manifold, by computing its base-like cohomology. As an application, we prove that if the foliation is non-unimodular then either the ambient manifold, the closure of the leaves or the total space of an associated principal bundle fiber over $S^1$.Comment: 33 pages. This paper will appear in Annales de l'Institut Fourier, Grenobl

A Precise Determination of tan⁡β\tan\beta from Heavy Charged Higgs Decay

We compute the energy spectrum of charged leptons in the decay $H^+\to \bar b+(t\to bl\nu_l)$. The shape of the lepton spectrum obtained, and also the mean lepton energy, are sensitive to the handedness of the intermediate top quark. This sensitivity can be used to precisely determine $\tan\beta$, a fundamental parameter of two Higgs doublet models.Comment: 5 pages plus 2 figures available upon request, latex, MZ-TH/94-0

Pigou's Dividend versus Ramsey's Dividend in the Double Dividend Literature

The aims of this paper are to highlight misinterpretations of policy assessments in the double dividend literature, to specify which of the efficiency costs and benefits should be ascribed to each dividend, and then, to propose a definition for the first dividend and the second dividend. We found the Pigou's dividend more appropiate for policy guidance than the usual Ramsey's dividend. Finally, the paper analyzes a green tax reform for the US economy to illustrate the advantages of the new definitions proposed in this paper: i) overcome some shortcoming of the mainstream current definitions in the literature regarding overestimation of the efficiency costs; and, ii) provide information by themselves and not as a partial view of the whole picture.Double dividend, Green Tax Reforms, Ramsey's dividend, Pigou's dividend

Restricted rr-Stirling Numbers and their Combinatorial Applications

We study set partitions with $r$ distinguished elements and block sizes found in an arbitrary index set $S$. The enumeration of these $(S,r)$-partitions leads to the introduction of $(S,r)$-Stirling numbers, an extremely wide-ranging generalization of the classical Stirling numbers and the $r$-Stirling numbers. We also introduce the associated $(S,r)$-Bell and $(S,r)$-factorial numbers. We study fundamental aspects of these numbers, including recurrence relations and determinantal expressions. For $S$ with some extra structure, we show that the inverse of the $(S,r)$-Stirling matrix encodes the M\"obius functions of two families of posets. Through several examples, we demonstrate that for some $S$ the matrices and their inverses involve the enumeration sequences of several combinatorial objects. Further, we highlight how the $(S,r)$-Stirling numbers naturally arise in the enumeration of cliques and acyclic orientations of special graphs, underlining their ubiquity and importance. Finally, we introduce related $(S,r)$ generalizations of the poly-Bernoulli and poly-Cauchy numbers, uniting many past works on generalized combinatorial sequences

Properties of bars in the local universe

We studied the fraction and properties of bars in a sample of about 3000 galaxies extracted from SDSS-DR5. This represents a volume limited sample with galaxies located between redshift 0.01-20, and inclination i < 60. Interacting galaxies were excluded from the sample. The fraction of barred galaxies in our sample is 45%. We found that 32% of S0s, 55% of early-type spirals, and 52% of late-type spirals are barred galaxies. The bars in S0s galaxies are weaker than those in later-type galaxies. The bar length and galaxy size are correlated, being larger bars located in larger galaxies. Neither the bar strength nor bar length correlate with the local galaxy density. On the contrary, the bar properties correlate with the properties of their host galaxies. Galaxies with higher central light concentration host less and weaker bars.Comment: 2 pages, 1 figure to appear in the proceedings of "Formation and Evolution of Galaxy Disks", Rome, October 2007, Eds. J. Funes and E. M. Corsin

Deconstructing double-barred galaxies in 2D and 3D. II. Two distinct groups of inner bars

The intrinsic photometric properties of inner and outer stellar bars within 17 double-barred galaxies are thoroughly studied through a photometric analysis consisting of: i) two-dimensional multi-component photometric decompositions, and ii) three-dimensional statistical deprojections for measuring the thickening of bars, thus retrieving their 3D shape. The results are compared with previous measurements obtained with the widely used analysis of integrated light. Large-scale bars in single- and double-barred systems show similar sizes, and inner bars may be longer than outer bars in different galaxies. We find two distinct groups of inner bars attending to their in-plane length and ellipticity, resulting in a bimodal behaviour for the inner/outer bar length ratio. Such bimodality is related neither to the properties of the host galaxy nor the dominant bulge, and it does not show a counterpart in the dimension off the disc plane. The group of long inner bars lays at the lower end of the outer bar length vs. ellipticity correlation, whereas the short inner bars are out of that relation. We suggest that this behaviour could be due to either a different nature of the inner discs from which the inner bars are dynamically formed, or a different assembly stage for the inner bars. This last possibility would imply that the dynamical assembly of inner bars is a slow process taking several Gyr to happen. We have also explored whether all large-scale bars are prone to develop an inner bar at some stage of their lives, possibility we cannot fully confirm or discard.Comment: 14 pages, 8 figures, 1 table. Accepted for publication in MNRA