background: pancreatitis is a serious complication of endoscopic retrograde cholangiopancreatography (ercp) and may cause significant morbidity and even death. there is no effective prophylactic intervention for patients with average risk yet. this study aims to investigate preventive effect of aggressive hydration for post-ercp pancreatitis. materials and methods: in a double-blind controlled ...

We characterize the perimeter-minimizing double bubbles on all flat two-tori and, as corollaries, on the flat infinite cylinder and the flat infinite strip with free boundary. Specifically, we show that there are five distinct types of minimizers on flat two-tori, depending on the areas to be enclosed.

The classical isoperimetric inequality in R3 states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 120.