Magnification relations for Kerr lensing and testing Cosmic Censorship

A Kerr black hole with mass parameter m and angular momentum parameter a acting as a gravitational lens gives rise to two images in the weak field limit. We study the corresponding magnification relations, namely the signed and absolute magnification sums and the centroid up to post-Newtonian order. We show that there are post-Newtonian corrections to the total absolute magnification and centroid proportional to a/m, which is in contrast to the spherically symmetric case where such corrections vanish. Hence we also propose a new set of lensing observables for the two images involving these corrections, which should allow measuring a/m with gravitational lensing. In fact, the resolution capabilities needed to observe this for the Galactic black hole should in principle be accessible to current and near-future instrumentation. Since a/m >1 indicates a naked singularity, a most interesting application would be a test of the Cosmic Censorship conjecture. The technique used to derive the image properties is based on the degeneracy of the Kerr lens and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple physical explanation for this degeneracy is also given.Comment: 13 pages, version 2: references added, minor changes. To appear in Phys. Rev.

The Geometry of Warped Product Singularities

In this article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.Comment: 14 page

Causes of Prolonged Waiting Time in Public Health Facilities among Health Care Seekers in Calabar Municipal Council of Cross River State, Nigeria

The purpose of this study was to investigate the causes of prolonged waiting time in public health care facilities among health care seekers in Calabar Municipal Council of Cross River State, Nigeria. To carry out this investigation, two hypotheses were formulated to guide the study. Survey research design was adopted for this study. A sample of one hundred and eighteen (118) respondents was selected. The selection was done through cluster sampling technique. The questionnaire was the main instrument used for data collection. It was constructed by the researchers with assistance of some measurement experts that gave it face and content validity. The Chi-square (X2) inferential statistics set at 0.05 was used to test the hypothesis. The result shows that there is significant contribution of poor record keeping and inadequate health personnel to the prolonged waiting time in public health care facilities among health care seekers. Based on these findings, some recommendations and suggestions for further studies were made. Keywords: Prolong waiting time; Public health facilities, Health care seekers. Poor record keeping; inadequate health personnel

Synchrotron radiation study of the relation between structure and strain in polyurethane elastomers

This paper describes a system for the study of the relation between structure and applied strain in thermoplastic polyurethane elastomers using the Australian National Beamline Facility at the Photon Factory, KEK, Tsukuba, Japan. The system uses the sagittal focusing monochromator at beamline 20B to provide a high-intensity focused beam which then falls on the specimen mounted in a miniature tensometer mounted in the unique vacuum diffractometer (BIGDIFF). Imaging plates were used to record simultaneously SAXS and WAXS patterns from the specimen at a particular strain. The change in SAXS and WAXS patterns with loading and unloading was recorded using a ten-plate imaging-plate changer

Cryptic Diversity and Conservation of Gopher Frogs across the Southeastern United States

Identifying cryptic biodiversity is fundamental to evolutionary biology and to conservation efforts. This study investigated range-wide genetic diversity of Gopher Frogs, Lithobates capito, across the southeastern United States coastal plain to determine implications for taxonomy and conservation. We collected data for two mtDNA regions in 21 populations to identify genetic structure across the geographic distribution of the species. Based on population genetic, phylogenetic, and genealogical analyses, we recovered three reciprocally monophyletic mtDNA lineages corresponding to mainland coastal plain populations and two lineages within peninsular Florida. Breakpoints for these lineages did not occur in previously identified hotspots of amphibian phylogeographic breaks and did not follow currently recognized subspecies designations. We recommend these lineages be recognized as separate distinct population segments and be considered separately by the U.S. Fish and Wildlife Service for listing under the Endangered Species Act. Additionally, we propose an evolutionary hotspot for amphibians that deserves further attentio

On paraquaternionic submersions between paraquaternionic K\"ahler manifolds

In this paper we deal with some properties of a class of semi-Riemannian submersions between manifolds endowed with paraquaternionic structures, proving a result of non-existence of paraquaternionic submersions between paraquaternionic K\"ahler non locally hyper paraK\"ahler manifolds. Then we examine, as an example, the canonical projection of the tangent bundle, endowed with the Sasaki metric, of an almost paraquaternionic Hermitian manifold.Comment: 13 pages, no figure

Using the stated preference method for the calculation of social discount rate

The aim of this paper is to build the stated preference method into the social discount rate methodology. The first part of the paper presents the results of a survey about stated time preferences through pair-choice decision situations for various topics and time horizons. It is assumed that stated time preferences differ from calculated time preferences and that the extent of stated rates depends on the time period, and on how much respondents are financially and emotionally involved in the transactions. A significant question remains: how can the gap between the calculation and the results of surveys be resolved, and how can the real time preferences of individuals be interpreted using a social time preference rate. The second part of the paper estimates the social time preference rate for Hungary using the results of the survey, while paying special attention to the pure time preference component. The results suggest that the current method of calculation of the pure time preference rate does not reflect the real attitudes of individuals towards future generations

The Dirac system on the Anti-de Sitter Universe

We investigate the global solutions of the Dirac equation on the Anti-de-Sitter Universe. Since this space is not globally hyperbolic, the Cauchy problem is not, {\it a priori}, well-posed. Nevertheless we can prove that there exists unitary dynamics, but its uniqueness crucially depends on the ratio beween the mass $M$ of the field and the cosmological constant $\Lambda>0$ : it appears a critical value, $\Lambda/12$, which plays a role similar to the Breitenlohner-Freedman bound for the scalar fields. When $M^2\geq \Lambda/12$ there exists a unique unitary dynamics. In opposite, for the light fermions satisfying $M^2<\Lambda/12$, we construct several asymptotic conditions at infinity, such that the problem becomes well-posed. In all the cases, the spectrum of the hamiltonian is discrete. We also prove a result of equipartition of the energy.Comment: 33 page

The prevalence of radiographic vertebral fractures in Mexican men

The prevalence of radiographically ascertained vertebral fractures in a random sample of 413 in Mexican men is 9.7% (95% CI 6.85–12.55). Increase of vertebral fracture rises with age from 2.0% in the youngest group (50–59 years) to 21.4% in the oldest group (80 years and over). This is the first population-based study of vertebral fractures in Mexican men using a standardized methodology reported in other studies. The presence of radiographic vertebral fractures increases with age. This same pattern was found in Mexican women with steady age increments, but the higher prevalence of fractures in women starts at age 70, whereas in men, the higher prevalence starts a decade later (80 years and over). The standardized prevalence per 1,000 men 50 years and over in the Mexican population for the year 2005 is 65.8 (95% CI 29.9–105.5), and it is 68.6 (95% CI 32.2–108.7) in the US population for the year 2000