The Galois theory of the lemniscate

This article studies the Galois groups that arise from division points of the lemniscate. We compute these Galois groups two ways: first, by class field theory, and second, by proving the irreducibility of lemnatomic polynomials, which are analogs of cyclotomic polynomials. We also discuss Abel's theorem on the lemniscate and explain how lemnatomic polynomials relate to Chebyshev polynomials.Comment: The revised version adds four references and some historical remarks. We also note that a special case of Theorem 4.1 appears in Lemmermeyer's Reciprocity Law

A fast and portable Re-Implementation of Piskunov and Valenti's Optimal-Extraction Algorithm with improved Cosmic-Ray Removal and Optimal Sky Subtraction

We present a fast and portable re-implementation of Piskunov and Valenti's optimal-extraction algorithm (Piskunov & Valenti, 2002} in C/C++ together with full uncertainty propagation, improved cosmic-ray removal, and an optimal background-subtraction algorithm. This re-implementation can be used with IRAF and most existing data-reduction packages and leads to signal-to-noise ratios close to the Poisson limit. The algorithm is very stable, operates on spectra from a wide range of instruments (slit spectra and fibre feeds), and has been extensively tested for VLT/UVES, ESO/CES, ESO/FEROS, NTT/EMMI, NOT/ALFOSC, STELLA/SES, SSO/WiFeS, and finally, P60/SEDM-IFU data.Comment: 23 pages, 12 figure

Multipole Expansions of Aggregate Charge: How Far to Go?

Aggregates immersed in a plasma or radiative environment will have charge distributed over their extended surface. Previous studies have modeled the aggregate charge using the monopole and dipole terms of a multipole expansion, with results indicating that the dipole-dipole interactions play an important role in increasing the aggregation rate and altering the morphology of the resultant aggregates. This study examines the effect that including the quadrupole terms has on the dynamics of aggregates interacting with each other and the confining electric fields in laboratory experiments. Results are compared to modeling aggregates as a collection of point charges located at the center of each spherical monomer comprising the aggregate.Comment: 6 page

Building the Future Students’ Blended Learning Experiences from Current Research Findings

Original article can be found at: http://www.ejel.org/index.htm Copyright Electronic Journal of e-LearningBetween March 2007 and February 2009, the Joint Information Systems Committee (JISC) funded a Learners’ Journeys project at the University of Hertfordshire. This was part of their second phase of investment in research into the Learners’ Experiences through their E-Learning Programme and was known as LXP2. STROLL (STudent Reflections On Lifelong e-Learning), as the Learners’ Journeys project was known, researched into the experiences of current undergraduate students in Higher Education (HE) and Further Education (FE) primarily through a series of diaries constructed by student volunteers. Using video and audio recording to capture students’ own reflections on their learning and their use of technology over the 2 year period the project data has offered many reflections from students on their use of technology for both learning and leisure. Building on this and other recent research data, the authors now suggest that for many HE students, technology has become a ubiquitous part of their lives to the extent that they may own or access regularly multiple items of personal technology that are used interchangeably for learning and leisure, including their computers and their mp3 players.Peer reviewe

Correction for Gonzalez et al., "Migraines Are Correlated with Higher Levels of Nitrate-, Nitrite-, and Nitric Oxide-Reducing Oral Microbes in the American Gut Project Cohort".

[This corrects the article DOI: 10.1128/mSystems.00105-16.]

Migraines Are Correlated with Higher Levels of Nitrate-, Nitrite-, and Nitric Oxide-Reducing Oral Microbes in the American Gut Project Cohort.

Nitrates, such as cardiac therapeutics and food additives, are common headache triggers, with nitric oxide playing an important role. Facultative anaerobic bacteria in the oral cavity may contribute migraine-triggering levels of nitric oxide through the salivary nitrate-nitrite-nitric oxide pathway. Using high-throughput sequencing technologies, we detected observable and significantly higher abundances of nitrate, nitrite, and nitric oxide reductase genes in migraineurs versus nonmigraineurs in samples collected from the oral cavity and a slight but significant difference in fecal samples. IMPORTANCE Recent work has demonstrated a potentially symbiotic relationship between oral commensal bacteria and humans through the salivary nitrate-nitrite-nitric oxide pathway (C. Duncan et al., Nat Med 1:546-551, 1995, http://dx.doi.org/10.1038/nm0695-546). Oral nitrate-reducing bacteria contribute physiologically relevant levels of nitrite and nitric oxide to the human host that may have positive downstream effects on cardiovascular health (V. Kapil et al., Free Radic Biol Med 55:93-100, 2013, http://dx.doi.org/10.1016/j.freeradbiomed.2012.11.013). In the work presented here, we used 16S rRNA Illumina sequencing to determine whether a connection exists between oral nitrate-reducing bacteria, nitrates for cardiovascular disease, and migraines, which are a common side effect of nitrate medications (U. Thadani and T. Rodgers, Expert Opin Drug Saf 5:667-674, 2006, http://dx.doi.org/10.1517/14740338.5.5.667)

Conformational transformations induced by the charge-curvature interaction at finite temperature

The role of thermal fluctuations on the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular aggregates may undergo transformation to polygonal shape. The transition occurs both in the case of hardening and softening charge-bending interaction. In the former case the charge and curvature are smoothly distributed along the chain while in the latter spontaneous kink formation is initiated. The transition to a non-circular conformation is analogous to the phase transition of the second kind.Comment: 23 pages (Latex), 10 figures (Postscript), 2 biblio file (bib-file and bbl-file