Closed-Form transformation between geodetic and ellipsoidal coordinates

We present formulas for direct closed-form transformation between geodetic coordinates(Φ, λ, h) and ellipsoidal coordinates (β, λ, u) for any oblate ellipsoid of revolution.These will be useful for those dealing with ellipsoidal representations of the Earth's gravityfield or other oblate ellipsoidal figures. The numerical stability of the transformations for nearpolarand near-equatorial regions is also considered

Mixed cinetic control of calcite dissolution

Calcite dissolution experiments performed with a rotating disc apparatus reveal that at low pH ( . 5.5) the dissolution is independent of the H+-concentration and controlled by mixed kinetics, where the chemical reaction is first order. The transition from H+-independence to -dependence occurs where H+ penetrate the diffusion boundary layer and first reach the surface. The pH at which this occurs depends on the nature of the calcite reactant, solution composition and the hydrodynamics of the system. The mixed kinetic treatment shows to be compatible with previous empirical rate dependencies.Des expériences de dissolution de la calcite montrent qu'à pH faible ( 5) , la dissolution est indépendante de la concentration en H et est contrôlée par des cinétiques mixtes, où la réaction chimique est prépondérante. La transition entre les deux systèmes se produit lorsque les H pénètrent la couche de diffusion et atteignent la surface. Le pH à ce moment dépend de la nature de la calcite, de la composition et de l'hydrodynamique du système. Les expériences à cinétique mixte sont compatibles avec les taux de dissolution prévus empiriquement .Sjöberg E.L. Mixed cinetic control of calcite dissolution. In: Pétrologie des altérations et des sols. Vol. I : Pétrologie expérimentale. Colloque international du CNRS, Paris 4-7 juillet 1983. Strasbourg : Institut de Géologie – Université Louis-Pasteur, 1983. pp. 119-126. (Sciences Géologiques. Mémoire, 71

Heterogeneous contributions of change in population distribution of body mass index to change in obesity and underweight

From 1985 to 2016, the prevalence of underweight decreased, and that of obesity and severe obesity increased, in most regions, with significant variation in the magnitude of these changes across regions. We investigated how much change in mean body mass index (BMI) explains changes in the prevalence of underweight, obesity, and severe obesity in different regions using data from 2896 population-based studies with 187 million participants. Changes in the prevalence of underweight and total obesity, and to a lesser extent severe obesity, are largely driven by shifts in the distribution of BMI, with smaller contributions from changes in the shape of the distribution. In East and Southeast Asia and sub-Saharan Africa, the underweight tail of the BMI distribution was left behind as the distribution shifted. There is a need for policies that address all forms of malnutrition by making healthy foods accessible and affordable, while restricting unhealthy foods through fiscal and regulatory restrictions. © Copyright