Stably free modules over virtually free groups

Let $F_m$ be the free group on $m$ generators and let $G$ be a finite nilpotent group of non square-free order; we show that for each $m\ge 2$ the integral group ring ${\bf Z}[G\times F_m]$ has infinitely many stably free modules of rank 1.Comment: 9 pages. The final publication is available at http://www.springerlink.com doi:10.1007/s00013-012-0432-

The prediction and management of aquatic nitrogen pollution across Europe: an introduction to the Integrated Nitrogen in European Catchments project (INCA)

Excess nitrogen in soils, fresh water, estuarine and marine systems contributes to nutrient enrichment in key ecosystems throughout Europe, often leading to detrimental environmental impacts, such as soil acidification or the eutrophication of water bodies. The Integrated Nitrogenmodel for European Catchments (INCA) project aims to develop a generic version of the Integrated Nitrogen in Catchments (INCA) model to simulate the retention and transport of nitrogen within river systems, thereby providing a tool to aid the understanding of nitrogen dynamics and for river-basin management/policy-making. To facilitate the development of the model, 10 partners have tested the INCA model with data collected in study sites located in eight European countries as part of the INCA project. This paper summarises the key nitrogen issues within Europe, describes the main aims and methodology of the INCA project, and sets the project in the context of the current major research initiatives at a European level.</p> <p style='line-height: 20px;'><b>Keywords: </b>Europe, European Union, nitrogen, nitrate, ammonium, river basin management, modelling, water chemistry, acidification, eutrophication, Water Framework Directive, INCA

On the Discovery of Monocular Rivalry by Tscherning in 1898:Translation and Review

Monocular rivalry was named by Breese in 1899. He made prolonged observation of superimposed orthogonal gratings; they fluctuated in clarity with either one or the other grating occasionally being visible alone. A year earlier, Tscherning observed similar fluctuations with a grid of vertical and horizontal lines and with other stimuli; we draw attention to his prior account. Monocular rivalry has since been shown to occur with a wide variety of superimposed patterns with several independent rediscoveries of it. We also argue that Helmholtz described some phenomenon other than monocular rivalry in 1867

Multi-component measurements of the Jefferson Lab energy recovery linac electron beam using optical transition and diffraction radiation

High brightness electron accelerators, such as energy recovery linacs (ERL), often have complex particle distributions that can create difficulties in beam transport as well as matching to devices such as wigglers used to generate radiation from the beam. Optical transition radiation (OTR), OTR interferometry (OTRI) and optical diffraction-transition radiation interferometry (ODTRI) have proven to be effective tools for diagnosing both the spatial and angular distributions of charged particle beams. OTRI and ODTRI have been used to measure rms divergences and optical transverse phase space mapping has been demonstrated using OTRI. In this work we present the results of diagnostic experiments using OTR and ODR conducted at the Jefferson Laboratory 115 MeV ERL which show the presence of two separate components within the spatial and angular distributions of the beam. By assuming a correlation between the spatial and angular features we estimate an rms emittance value for each of the two components.Comment: 25 pages, 10 figures; accepted for publication in PRSTAB; minor formatting errors correcte

Observation and Modeling of the Solar Transition Region: II. Solutions of the Quasi-Static Loop Model

In the present work we undertake a study of the quasi-static loop model and the observational consequences of the various solutions found. We obtain the most general solutions consistent with certain initial conditions. Great care is exercised in choosing these conditions to be physically plausible (motivated by observations). We show that the assumptions of previous quasi-static loop models, such as the models of Rosner, Tucker and Vaiana (1978) and Veseckey, Antiochos and Underwood (1979), are not necessarily valid for small loops at transition region temperatures. We find three general classes of solutions for the quasi-static loop model, which we denote, radiation dominated loops, conduction dominated loops and classical loops. These solutions are then compared with observations. Departures from the classical scaling law of RTV are found for the solutions obtained. It is shown that loops of the type that we model here can make a significant contribution to lower transition region emission via thermal conduction from the upper transition region.Comment: 30 pages, 3 figures, Submitted to ApJ, Microsoft Word File 6.0/9

Searching for the earliest galaxies in the 21 cm forest

We use a model developed by Xu et al. (2010) to compute the 21 cm line absorption signatures imprinted by star-forming dwarf galaxies (DGs) and starless minihalos (MHs). The method, based on a statistical comparison of the equivalent width (W_\nu) distribution and flux correlation function, allows us to derive a simple selection criteria for candidate DGs at very high (z >= 8) redshift. We find that ~ 18% of the total number of DGs along a line of sight to a target radio source (GRB or quasar) can be identified by the condition W_\nu < 0; these objects correspond to the high-mass tail of the DG distribution at high redshift, and are embedded in large HII regions. The criterion W_\nu > 0.37 kHz instead selects ~ 11% of MHs. Selected candidate DGs could later be re-observed in the near-IR by the JWST with high efficiency, thus providing a direct probe of the most likely reionization sources.Comment: 8 pages, 3 figures. Accepted for publication in Science in China Series

All-optical switching and strong coupling using tunable whispering-gallery-mode microresonators

We review our recent work on tunable, ultrahigh quality factor whispering-gallery-mode bottle microresonators and highlight their applications in nonlinear optics and in quantum optics experiments. Our resonators combine ultra-high quality factors of up to Q = 3.6 \times 10^8, a small mode volume, and near-lossless fiber coupling, with a simple and customizable mode structure enabling full tunability. We study, theoretically and experimentally, nonlinear all-optical switching via the Kerr effect when the resonator is operated in an add-drop configuration. This allows us to optically route a single-wavelength cw optical signal between two fiber ports with high efficiency. Finally, we report on progress towards strong coupling of single rubidium atoms to an ultra-high Q mode of an actively stabilized bottle microresonator.Comment: 20 pages, 24 figures. Accepted for publication in Applied Physics B. Changes according to referee suggestions: minor corrections to some figures and captions, clarification of some points in the text, added references, added new paragraph with results on atom-resonator interactio

Prognostic value of lymph node ratio and extramural vascular invasion on survival for patients undergoing curative colon cancer resection

There was no study funding. We are grateful to Tony Rafferty (Tailored Information for the People of Scotland, TIPs) for providing survival data.Peer reviewedPublisher PD