On a class of linearizable Monge-Amp\`ere equations

Monge-Amp\`ere equations of the form, $u_{xx}u_{yy}-u_{xy}^2=F(u,u_x,u_y)$ arise in many areas of fluid and solid mechanics. Here it is shown that in the special case $F=u_y^4f(u, u_x/u_y)$, where $f$ denotes an arbitrary function, the Monge-Amp\`ere equation can be linearized by using a sequence of Amp\`ere, point, Legendre and rotation transformations. This linearization is a generalization of three examples from finite elasticity, involving plane strain and plane stress deformations of the incompressible perfectly elastic Varga material and also relates to a previous linearization of this equation due to Khabirov [7]

First Results From the Large Binocular Telescope: Deep Photometry of New dSphs

This contribution describes photometry for two Galactic dSphs obtained with the Large Binocular Telescope to a magnitude of ~25.5. Using the Large Binocular Camera, a purpose-built wide-field imager for the LBT, we have examined the structure and star formation histories of two newly-discovered Local Group members, the Hercules dSph and the Leo T dSph/dIrr system. We have constructed a structural map for the Hercules system using three-filter photometry to V ~ 25.5. This is the first deep photometry for this system, and it indicates that Hercules is unusually elongated, possibly indicating distortion due to the Galactic tidal field. We have also derived the first star formation history for the Leo T system, and find that its oldest population of stars (age ~ 13 Gyr) were relatively metal-rich, with [Fe/H] ~ -1.5.Comment: Four pages, two figures. To appear in the proceedings of "Galaxies in the Local Volume", Astrophysics and Space Science, editors B. Koribalski and H. Jerje

Electrodynamics of quasi-two-dimensional BEDT-TTF charge transfer salts

We consider the millimeter-wave electrodynamics specific to quasi-two-dimensional conductors and superconductors based on the organic donor molecule BEDT-TTF. Using realistic physical parameters, we examine the current polarizations that result for different oscillating (GHz) electric and magnetic field polarizations. We show that, in general, it is possible to discriminate between effects (dissipation and dispersion) due to in-plane and interlayer ac currents. However, we also show that it is not possible to selectively probe any single component of the in-plane conductivity tensor, and that excitation of interlayer currents is strongly influenced by the sample geometry and the electromagnetic field polarization.Comment: 5 pages including 3 figures Minor correction to figure

The abundance of an invasive freshwater snail Tarebia granifera (Lamarck, 1822) in the Nseleni River, South Africa

The invasive freshwater snail Tarebia granifera (Lamarck, 1822) was first reported in South Africa in 1999 and it has become widespread across the country, with some evidence to suggest that it reduces benthic macroinvertebrate biodiversity. The current study aimed to identify the primary abiotic drivers behind abundance patterns of T. granifera, by comparing the current abundance of the snail in three different regions, and at three depths, of the highly modified Nseleni River in KwaZulu-Natal, South Africa. Tarebia granifera was well established throughout the Nseleni River system, with an overall preference for shallow waters and seasonal temporal patterns of abundance. Although it is uncertain what the ecological impacts of the snail in this system are, its high abundances suggest that it should be controlled where possible and prevented from invading other systems in the region

Exercise-induced respiratory muscle work: Effects on blood flow, fatigue and performance

This is the post print version of this article. The official published version can be obtained from the link below.In healthy subjects, heavy intensity endurance exercise places substantial demands on the respiratory muscles as breathing frequency, ventilation and the work of breathing rise over time. In the highly trained subject working at high absolute work rates, the ventilatory demand often causes varying degrees of expiratory flow limitation, sometimes accompanied by lung hyperinflation and, therefore, increased elastic work of breathing. Time-dependant increases in effort perceptions for both dyspnea and limb discomfort accompany these increased ventilatory demands. Similar responses to endurance exercise but at much lower exercise intensities also occur in patients with COPD and CHF. Note that these responses significantly influence exercise performance times in both health and disease. This effect was demonstrated by the marked reductions in the rate of rise of effort perceptions and the enhanced exercise performance times elicited by unloading the respiratory muscles using pressure support ventilation or proportional assist mechanical ventilation. In healthy fit subjects, unloading the inspiratory work of breathing by about one half increased performance by an average of 14% (Harms et al. 2000), and in CHF and COPD patients performance time more than doubled with respiratory muscle unloading (O’Donnell et al. 2001). Why are effort perceptions of limb discomfort markedly reduced and exercise performance increased when the respiratory muscles are unloaded? Our hypothesis is shown in Fig. 1

Whole egg consumption and cortical bone in healthy children

Eggs contain bioactive compounds thought to benefit pediatric bone. This cross-sectional study shows a positive link between childhood egg intake and radius cortical bone. If randomized trials confirm our findings, incorporating eggs into children's diets could have a significant impact in preventing childhood fractures and reducing the risk of osteoporosis. INTRODUCTION: This study examined the relationships between egg consumption and cortical bone in children. METHODS: The cross-sectional study design included 294 9-13-year-old black and white males and females. Three-day diet records determined daily egg consumption. Peripheral quantitative computed tomography measured radius and tibia cortical bone. Body composition and biomarkers of bone turnover were assessed using dual-energy X-ray absorptiometry and ELISA, respectively. RESULTS: Egg intake was positively correlated with radius and tibia cortical bone mineral content (Ct.BMC), total bone area, cortical area, cortical thickness, periosteal circumference, and polar strength strain index in unadjusted models (r = 0.144-0.224, all P < 0.050). After adjusting for differences in race, sex, maturation, fat-free soft tissue mass (FFST), and protein intakes, tibia relationships were nullified; however, egg intake remained positively correlated with radius Ct.BMC (r = 0.138, P = 0.031). Egg intake positively correlated with total body bone mineral density, BMC, and bone area in the unadjusted models only (r = 0.119-0.224; all P < 0.050). After adjusting for covariates, egg intake was a positive predictor of radius FFST (β = 0.113, P < 0.050) and FFST was a positive predictor of Ct.BMC (β = 0.556, P < 0.050) in path analyses. There was a direct influence of egg on radius Ct.BMC (β = 0.099, P = 0.035), even after adjusting for the mediator, FFST (β = 0.137, P = 0.020). Egg intake was positively correlated with osteocalcin in both the unadjusted (P = 0.005) and adjusted (P = 0.049) models. CONCLUSION: If the positive influence of eggs on Ct.BMC observed in this study is confirmed through future randomized controlled trials, whole eggs may represent a viable strategy to promote pediatric bone development and prevent fractures