Poisson smooth structures on stratified symplectic spaces

In this paper we introduce the notion of a smooth structure on a stratified space, the notion of a Poisson smooth structure and the notion of a weakly symplectic smooth structure on a stratified symplectic space, refining the concept of a stratified symplectic Poisson algebra introduced by Sjamaar and Lerman. We show that these smooth spaces possess several important properties, e.g. the existence of smooth partitions of unity. Furthermore, under mild conditions many properties of a symplectic manifold can be extended to a symplectic stratified space provided with a smooth Poisson structure, e.g. the existence and uniqueness of a Hamiltonian flow, the isomorphism between the Brylinski-Poisson homology and the de Rham homology, the existence of a Leftschetz decomposition on a symplectic stratified space. We give many examples of stratified symplectic spaces possessing a Poisson smooth structure which is also weakly symplectic.Comment: 21 page, final version, to appear in the Proceedings of the 6-th World Conference on 21st Century Mathematic

Radiative non-isothermal Bondi accretion onto a massive black hole

In this paper, we present the classical Bondi accretion theory for the case of non-isothermal accretion processes onto a supermassive black hole (SMBH), including the effects of X-ray heating and the radiation force due to electron scattering and spectral lines. The radiation field is calculated by considering an optically thick, geometrically thin, standard accretion disk as the emitter of UV photons and a spherical central object as a source of X-ray emission. In the present analysis, the UV emission from the accretion disk is assumed to have an angular dependence, while the X-ray/central object radiation is assumed to be isotropic. This allows us to build streamlines in any angular direction we need to. The influence of both types of radiation is evaluated for different flux fractions of the X-ray and UV emissions with and without the effects of spectral line driving. We find that the radiation emitted near the SMBH interacts with the infalling matter and modifies the accretion dynamics. In the presence of line driving, a transition resembles from pure type 1 & 2 to type 5 solutions (see Fig2.1 of Frank etal. 2002), which takes place regardless of whether or not the UV emission dominates over the X-ray emission. We compute the radiative factors at which this transition occurs, and discard type 5 solution from all our models. Estimated values of the accretion radius and accretion rate in terms of the classical Bondi values are also given. The results are useful for the construction of proper initial conditions for time-dependent hydrodynamical simulations of accretion flows onto SMBH at the centre of galaxies.Comment: 10 pages, 10 figures, Accepted to be published in A&

Variable stars in the globular cluster M28 (NGC 6626)

We present a new search for variable stars in the Galactic globular cluster M28 (NGC 6626). The search is based on a series of BVI images obtained with the SMARTS Consortium's 1.3m telescope at Cerro Tololo Inter-American Observatory, Chile. The search was carried out using the ISIS v2.2 image subtraction package. We find a total of 25 variable stars in the field of the cluster, 9 being new discoveries. Of the newly found variables, 1 is an ab-type RR Lyrae star, 6 are c-type RR Lyrae, and 2 are long-period/semi-regular variables. V22, previously classified as a type II Cepheid, appears as a bona-fide RRc in our data. In turn, V20, previously classified as an ab-type RR Lyrae, could not be properly phased with any reasonable period. The properties of the ab-type RR Lyrae stars in M28 appear most consistent with an Oosterhoff-intermediate classification, which is unusual for bona-fide Galactic globulars clusters. However, the cluster's c-type variables do not clearly support such an Oosterhoff type, and a hybrid Oosterhoff I/II system is accordingly another possibility, thus raising the intriguing possibility of multiple populations being present in M28. Coordinates, periods, and light curves in differential fluxes are provided for all the detected variables.Comment: A&A, in pres

Comment on Ricci Collineations of Static Spherically Symmetric Spacetimes

We present a counter example to a theorem given by Amir {\em et al.} J. Math. Phys. {\bf 35}, 3005 (1994). We also comment on a misleading statements of the same reference.Comment: 4 pages,LaTex fil

Religiosity and Sexual Risk Behaviors Among Latina Adolescents: Trends from 1995 to 2008

Purpose: The purpose of this study was to determine trends in the influence of religiosity on sexual activity of Latina adolescents in the United States from 1995 to 2008 and to determine if differences existed between the Mexican American and other Latina groups. Methods: The sample comprised the subset of unmarried, 15–21-year-old (mean 17 years) Latina female respondents in the 1995 (n=267), 2002 (n=306), and 2006–2008 (n=400) National Survey of Family Growth (NSFG) datasets. Associations between religiosity (importance of religion and service attendance) and history of ever having sex, number of sex partners, and age of sexual debut were investigated. Results: Less than one half of Latinas in 1995 (44%) and in 2006–2008 (44%) reported that religion was very important to them, whereas in 2002, 50% reported it was important. Only in 1995 did Latinas who viewed religion as very important have a significantly lower level of sexual initiation. In 1995 and in 2006–2008, Latinas who held religion as very important had significantly fewer partners. In all three cohorts, the higher religious importance group had higher virgin survival rates. Across cohorts, approximately one third of respondents reported frequent religious attendance. In all cohorts, frequent attenders were less likely to have had sex, had fewer partners, and had older age at sexual debut. The survival rate as virgins for Mexican origin Latinas was higher in 1995 and 2002 compared to non-Mexican Latinas but was almost the same in 2006–2008. Conclusions: Religiosity had a protective association with sexual activity among Latina adolescents. The association of importance of religion with sexual activity has diminished from 1995 to 2008, however, whereas the importance of service attendance has remained stable. The influence of religion was more apparent among the Latinas of Mexican origin, but this greater influence also diminished by 2006–2008