Lagrangian Curves in a 4-dimensional affine symplectic space

Lagrangian curves in R4 entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify La- grangrian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in R4 and determine Lagrangian geodesic

Systemic arterial compliance following ultra-marathon

There is a growing interest in training for and competing in race distances that exceed the marathon; however, little is known regarding the vascular effects of participation in such prolonged events, which last multiple consecutive hours. There exists some evidence that cardiovascular function may be impaired following extreme prolonged exercise, but at present, only cardiac function has been specifically examined following exposure to this nature of exercise. The primary purpose of this study was to characterize the acute effects of participation in an ultra-marathon on resting systemic arterial compliance. Arterial compliance and various resting cardiovascular indices were collected at rest from 26 healthy ultra-marathon competitors using applanation tonometry (HDI CR-2000) before and after participation in a mountain trail running foot race ranging from 120-195 km which required between 20-40 continuous hours (31.2±6.8 h) to complete. There was no significant change in small artery compliance from baseline to post race follow-up (8.5±3.4-7.7±8.2 mL/mmHgx100, p=0.65), but large artery compliance decreased from 16.1±4.4 to 13.5±3.8 mL/mmHgx10 (p=0.003). Participation in extreme endurance exercise of prolonged duration was associated with acute reductions in large artery compliance, but the time course of this effect remains to be elucidated