Remarks on the extension of the Ricci flow

We present two new conditions to extend the Ricci flow on a compact manifold over a finite time, which are improvements of some known extension theorems.Comment: 9 pages, to appear in Journal of Geometric Analysi

Design of the Annular Suspension and Pointing System (ASPS) (including design addendum)

The Annular Suspension and Pointing System is an experiment pointing mount designed for extremely precise 3 axis orientation of shuttle experiments. It utilizes actively controlled magnetic bearing to provide noncontacting vernier pointing and translational isolation of the experiment. The design of the system is presented and analyzed

Symptom appraisal and help-seeking in men with symptoms of possible prostate cancer: a qualitative study with an ethnically diverse sample in London

This is the final version. Available on open access from the Royal College of General Practitioners via the DOI in this recordBACKGROUND: Prostate cancer mortality in Black males is disproportionately high. This problem may be overcome by reducing delays in the pathway to diagnosis, particularly those occurring before initial medical help seeking. A greater understanding of symptom appraisal and help seeking could support the development of targeted interventions for improving early presentation among Black males. AIM: To provide an in-depth understanding of males' pre-consultation experiences following the onset of symptoms of possible prostate cancer, identifying both general trends as well as potential differences that may exist between Black and White males. DESIGN AND SETTING: Qualitative study of 18 males (nine Black, nine White) in London, UK, who had recently seen their GP with urinary symptoms, erectile dysfunction, or haematuria. METHOD: Semi-structured interviews from a previous multi-methods study of primary care use by males with symptoms of possible prostate cancer were analysed using thematic framework analysis. RESULTS: Symptoms were often interpreted by patients as unimportant. Most delays occurred due to the absence of reasons to seek help, which, in Black males, often stemmed from poor awareness of prostate cancer. This lack of awareness could have been a consequence of their reluctance to seek health information and discuss health issues with others in their social network. Friends and relatives played an important role in symptom appraisal and help seeking. CONCLUSION: Cognitive biases, cultural stigmas, and everyday interpersonal interactions should be important areas at which to target strategies seeking to reduce delays and improve early presentation in males with possible prostate cancer, particularly Black males.Cancer Research UKNational Institute for Health and Care Research (NIHR

Angular Power Spectrum Estimation of Cosmic Ray Anisotropies with Full or Partial Sky Coverage

We study the angular power spectrum estimate in order to search for large scale anisotropies in the arrival directions distribution of the highest-energy cosmic rays. We show that this estimate can be performed even in the case of partial sky coverage and validated over the full sky under the assumption that the observed fluctuations are statistically spatial stationary. If this hypothesis - which can be tested directly on the data - is not satisfied, it would prove, of course, that the cosmic ray sky is non isotropic but also that the power spectrum is not an appropriate tool to represent its anisotropies, whatever the sky coverage available. We apply the method to simulations of the Pierre Auger Observatory, reconstructing an input power spectrum with the Southern site only and with both Northern and Southern ones. Finally, we show the improvement that a full-sky observatory brings to test an isotropic distribution, and we discuss the sensitivity of the Pierre Auger Observatory to large scale anisotropies.Comment: 16 pages, 6 figures, version accepted for publication by JCA

Mean curvature flow in a Ricci flow background

Following work of Ecker, we consider a weighted Gibbons-Hawking-York functional on a Riemannian manifold-with-boundary. We compute its variational properties and its time derivative under Perelman's modified Ricci flow. The answer has a boundary term which involves an extension of Hamilton's Harnack expression for the mean curvature flow in Euclidean space. We also derive the evolution equations for the second fundamental form and the mean curvature, under a mean curvature flow in a Ricci flow background. In the case of a gradient Ricci soliton background, we discuss mean curvature solitons and Huisken monotonicity.Comment: final versio

Local light-ray rotation

We present a sheet structure that rotates the local ray direction through an arbitrary angle around the sheet normal. The sheet structure consists of two parallel Dove-prism sheets, each of which flips one component of the local direction of transmitted light rays. Together, the two sheets rotate transmitted light rays around the sheet normal. We show that the direction under which a point light source is seen is given by a Mobius transform. We illustrate some of the properties with movies calculated by ray-tracing software.Comment: 9 pages, 6 figure

The ALTO project at IPN Orsay

In order to probe neutron rich radioactive noble gases produced by photo-fission, a PARRNe1 experiment (Production d'Atomes Radioactifs Riches en Neutrons) has been carried out at CERN. The incident electron beam of 50 MeV was delivered by the LIL machine: LEP Injector Linac. The experiment allowed to compare under the same conditions two production methods of radioactive noble gases: fission induced by fast neutrons and photo-fission. The obtained results show that the use of the electrons is a promising mode to get intense neutron rich ion beams. Thereafter, the success of this photo-fission experiment, a conceptual design for the installation at IPN Orsay of a 50 MeV electron accelerator close to the PARRNe-2 device has been worked out: ALTO Project. This work has started within a collaboration between IPNO, LAL and CERN groups.Comment: 14 pages, pdf file, International School-Seminar on Heavy-Ion Physics 7 (2002

The Treatment of Cesium Ore by Sulfur Chloride and Chlorine

A Southern Rhodesian cesium ore containing essentially pollucite was chlorinated by a gaseous mixture of sulfur chloride and chlorine at temperatures between 500 and 700°C. The reaction products consisted principally of SiCl4, AlCl3, CsCl, and CsCl • A1Cl3. Under favorable conditions for chlorination, 17 wt % of the ore remained unreacted. The optimum conditions were the fixed bed reactor used in this study were chlorination at 650°C for 4.5 hr with an ore particle size that passes a 150 mesh sieve

Manifolds with 1/4-pinched flag curvature

We say that a nonnegatively curved manifold $(M,g)$ has quarter pinched flag curvature if for any two planes which intersect in a line the ratio of their sectional curvature is bounded above by 4. We show that these manifolds have nonnegative complex sectional curvature. By combining with a theorem of Brendle and Schoen it follows that any positively curved manifold with strictly quarter pinched flag curvature must be a space form. This in turn generalizes a result of Andrews and Nguyen in dimension 4. For odd dimensional manifolds we obtain results for the case that the flag curvature is pinched with some constant below one quarter, one of which generalizes a recent work of Petersen and Tao