Level sets of functions and symmetry sets of smooth surface sections

We prove that the level sets of a real C^s function of two variables near a non-degenerate critical point are of class C^[s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at hyperbolic points or elliptic points, and in particular at umbilic points. We also analyse the cases coming from degenerate critical points, corresponding to elliptic cusps of Gauss on a surface, where the differentiability is now reduced to C^[s/4]. However in all our applications to symmetry sets of families of plane curves, we assume the C^infty smoothness.Comment: 15 pages, Latex, 6 grouped figures. The final version will appear in Mathematics of Surfaces. Lecture Notes in Computer Science (2005

Demonstration of Niobium Tin in 218 MHz Low-beta Quarter Wave Accelerator Cavity

A 218 MHz quarter wave niobium cavity has been fabricated for the purpose of demonstrating Nb3Sn technology on a low-beta accelerator cavity. Niobiumtin has been established as a promising next generation SRF material, but development has focused primarily in high-beta elliptical cell cavities. This material has a significantly higher TC than niobium, allowing for design of higher frequency quarter wave cavities (that are subsequently smaller) as well as for significantly lowered cooling requirements (possibly leading to cryocooler based designs). The fabrication, initial cold testing, and Nb3Sn coating are discussed as well as test plans and details of future applications.Comment: 21st Intl Conf Radio Frequency Superconductivity (SRF 2023

REDRISK: reduction of the virus risk in shellfish harvesting areas

Filter feeding bivalve shellfish can accumulate human pathogenic bacteria and viruses if grown in sewage-contaminated waters. Current consumer protection legislation relies on classification of harvesting areas based on their sanitary quality, using E coli as an indicator of sewage contamination. Advances in viral monitoring have shown that E coli can underestimate the extent of the contamination. The most common cause of gastroenteritis associated with shellfish is norovirus, commonly known as winter vomiting virus. The REDRISK project was undertaken to investigate the main environmental factors that cause viral contamination in shellfish. The REDRISK project is part of a EU research pillar with parallel research being undertaken in the UK, France and Spain. A recently developed technique to quantify norovirus in shellfish, real-time PCR, has been used in the REDRISK project. Clew Bay, in Co. Mayo was chosen as the study area in Ireland. The bay is generally considered to have good water quality but with certain areas subject to intermittent sewage contamination. The cooperation of local producers and organisations such as the Clew Bay Marine Forum and the Native Oyster Co-op greatly helped the project. The project was divided into a two-phased approach. Phase one involved the identification of contamination sources impacting the bay through a sanitary survey and selection of appropriate sites for further study. Results of the first phase of this study were presented previously at this forum (Keaveney, et al 2006) and the characteristics of the sites selected for study and locations within the bay are shown in table 1 and figure 1 respectively. The second phase of the project focused on monitoring environmental conditions and microbiological levels in shellfish to identify environmental conditions leading to viral contamination. This paper reports the finding of this monitoring

Dyspnea affective response: comparing COPD patients with healthy volunteers and laboratory model with activities of daily living

Background: Laboratory-induced dyspnea (breathing discomfort) in healthy subjects is widely used to study perceptual mechanisms, yet the relationship between laboratory-induced dyspnea in healthy volunteers and spontaneous dyspnea in patients with chronic lung disease is not well established. We compared affective responses to dyspnea 1) in COPD patients vs. healthy volunteers (HV) undergoing the same laboratory stimulus; 2) in COPD during laboratory dyspnea vs. during activities of daily living (ADL). Methods: We induced moderate and high dyspnea levels in 13 COPD patients and 12 HV by increasing end-tidal CO2 (PETCO2) during restricted ventilation, evoking air hunger. We used the multidimensional dyspnea profile (MDP) to measure intensity of sensory qualities (e.g., air hunger (AH) and work/effort (W/E)) as well as immediate discomfort (A1) and secondary emotions (A2). Ten of the COPD subjects also completed the MDP outside the laboratory following dyspnea evoked by ADL. Results: COPD patients and HV reported similar levels of immediate discomfort relative to sensory intensity. COPD patients and HV reported anxiety and frustration during laboratory-induced dyspnea; variation among individuals far outweighed the small differences between subject groups. COPD patients reported similar intensities of sensory qualities, discomfort, and emotions during ADL vs. during moderate laboratory dyspnea. Patients with COPD described limiting ADL to avoid greater dyspnea. Conclusions: In this pilot study, we found no evidence that a history of COPD alters the affective response to laboratory-induced dyspnea, and no difference in affective response between dyspnea evoked by this laboratory model and dyspnea evoked by ADL

(In)finite extent of stationary perfect fluids in Newtonian theory

For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the corresponding stationary Newton-Euler system). Under more restrictive conditions, we can also exclude the presence of "hollow" configurations. Our main result, which does not assume axial symmetry, uses the virial theorem as the key ingredient and generalises a known result in the static case. In the axially symmetric case stronger results are obtained and examples are discussed.Comment: Corrections according to the version accepted by Ann. Henri Poincar

Interior Weyl-type Solutions of the Einstein-Maxwell Field Equations

Static solutions of the electro-gravitational field equations exhibiting a functional relationship between the electric and gravitational potentials are studied. General results for these metrics are presented which extend previous work of Majumdar. In particular, it is shown that for any solution of the field equations exhibiting such a Weyl-type relationship, there exists a relationship between the matter density, the electric field density and the charge density. It is also found that the Majumdar condition can hold for a bounded perfect fluid only if the matter pressure vanishes (that is, charged dust). By restricting to spherically symmetric distributions of charged matter, a number of exact solutions are presented in closed form which generalise the Schwarzschild interior solution. Some of these solutions exhibit functional relations between the electric and gravitational potentials different to the quadratic one of Weyl. All the non-dust solutions are well-behaved and, by matching them to the Reissner-Nordstr\"{o}m solution, all of the constants of integration are identified in terms of the total mass, total charge and radius of the source. This is done in detail for a number of specific examples. These are also shown to satisfy the weak and strong energy conditions and many other regularity and energy conditions that may be required of any physically reasonable matter distribution.Comment: 21 pages, RevTex, to appear in General Relativity and Gravitatio

Jasmonate promotes auxin-induced adventitious rooting in dark-grown Arabidopsis thaliana seedlings and stem thin cell layers by a cross-talk with ethylene signalling and a modulation of xylogenesis

Background: Adventitious roots (ARs) are often necessary for plant survival, and essential for successful micropropagation. In Arabidopsis thaliana dark-grown seedlings AR-formation occurs from the hypocotyl and is enhanced by application of indole-3-butyric acid (IBA) combined with kinetin (Kin). The same IBA + Kin-treatment induces AR-formation in thin cell layers (TCLs). Auxin is the main inducer of AR-formation and xylogenesis in numerous species and experimental systems. Xylogenesis is competitive to AR-formation in Arabidopsis hypocotyls and TCLs. Jasmonates (JAs) negatively affect AR-formation in de-etiolated Arabidopsis seedlings, but positively affect both AR-formation and xylogenesis in tobacco dark-grown IBA + Kin TCLs. In Arabidopsis the interplay between JAs and auxin in AR-formation vs xylogenesis needs investigation. In de-etiolated Arabidopsis seedlings, the Auxin Response Factors ARF6 and ARF8 positively regulate AR-formation and ARF17 negatively affects the process, but their role in xylogenesis is unknown. The cross-talk between auxin and ethylene (ET) is also important for AR-formation and xylogenesis, occurring through EIN3/EIL1 signalling pathway. EIN3/EIL1 is the direct link for JA and ET-signalling. The research investigated JA role on AR-formation and xylogenesis in Arabidopsis dark-grown seedlings and TCLs, and the relationship with ET and auxin. The JA-donor methyl-jasmonate (MeJA), and/or the ET precursor 1-aminocyclopropane-1-carboxylic acid were applied, and the response of mutants in JA-synthesis and -signalling, and ET-signalling investigated. Endogenous levels of auxin, JA and JA-related compounds, and ARF6, ARF8 and ARF17 expression were monitored. Results: MeJA, at 0.01 μM, enhances AR-formation, when combined with IBA + Kin, and the response of the early-JA-biosynthesis mutant dde2–2 and the JA-signalling mutant coi1–16 confirmed this result. JA levels early change during TCL-culture, and JA/JA-Ile is immunolocalized in AR-tips and xylogenic cells. The high AR-response of the late JA-biosynthesis mutant opr3 suggests a positive action also of 12-oxophytodienoic acid on AR-formation. The crosstalk between JA and ET-signalling by EIN3/EIL1 is critical for AR-formation, and involves a competitive modulation of xylogenesis. Xylogenesis is enhanced by a MeJA concentration repressing AR-formation, and is positively related to ARF17 expression. Conclusions: The JA concentration-dependent role on AR-formation and xylogenesis, and the interaction with ET opens the way to applications in the micropropagation of recalcitrant species