Higher-Order Corrections for the Deflection of Light around a Massive Object. Diagonal PadéApproximants and Ray-Tracing Algorithms

From the Schwarzschild metric we obtain the higher-order terms for the deflection of light around a massive object using the Lindstedt-Poincaré method to solve the equation of motion of a photon around the stellar object. The asymptotic series obtained by this method was obtained up to order 20 in the expansion parameter, and was found to better approximate the numerical solution with higher order terms—a property that can’t be taken for granted for any asymptotic series. Additionally, we obtain diagonal Padé approximants from the perturbation expansion, and we show how these are a better fit for the numerical data than the original formal Taylor series. Furthermore, we use these approximants in ray-tracing algorithms to model the bending of light around massive objects.

Gone with the wind： Seasonal trends in foraging movement directions for a central-place forager

Lesser kestrels Falco naumanni are migratory central-place foragers that breed in dynamic arable landscapes. After arriving from migration, kestrels have no knowledge of the distribution of crops, and consequently prey, around their colony. The energy demand of pairs increases as breeding season progresses, but at the same time prey abundance, and their knowledge on prey distribution, also increases. Wind can have a strong influence on flight cost and kestrels should try to reduce energy expendi- ture when possible. When prey abundance is low, kestrels have little knowledge of prey distribution, and pairs have no chicks, they could reduce foraging flight cost by leaving the colony with tailwinds. When prey is abundant, knowledge on prey distribu- tion has increased, and chick demand is high, kestrels should fly to the most favorable foraging patches. We analyzed foraging trips directions in a lesser kestrel colony along the breeding season and in relation to wind speed and direction. We recorded 664 foraging trips from 19 individuals using GPS-dataloggers. We found that outward flights direction changed from uniform to a concentrated distribution along the season, as prey abundance and individual experience increased. We also found a temporal trend in the angular difference between outward flights and wind directions, with low values early in the season and then increa- sing as expected, but again low values at the end, contrary to expectation. Results suggest changes in kestrels foraging strategy along the season in relation to wind. Kestrels depart more with tailwinds in exploratory flights early in the season, while there is a spurious coincidence in direction to preferred foraging patches and dominant wind direction at the end [Current Zoology 60 （5）： 604-615, 2014].

Appendiceal endometriosis differentially diagnosed from acute appendicitis

Endometriosis is a common disease in premenopausal women involving pelvic organs specially. Howeverendometriosis that affects the appendix is rarely seen except appendiceal endometriosis that mimics acute appendicitis. In a patient with acute appendicitis we diagnosed and operated on, histopathological examination of the appendix revealed appendiceal endometriosis which caused symptoms.