Acclimatization improves submaximal exercise economy at 5533m

We tested whether the better subjective exercise tolerance perceived by mountaineers after altitude acclimatization relates to enhanced exercise economy. Thirty-two mountaineers performed progressive bicycle exercise to exhaustion at 490 m and twice at 5533 m (days 6–7 and day 11), respectively, during an expedition to Mt. Muztagh Ata. Maximal work rate (Wmax) decreased from mean ± SD 356 ± 73 watts at 490 m to 191 ± 49 watts and 193 ± 45 watts at 5533 m, days 6–7 and day 11, respectively; corresponding maximal oxygen uptakes (VO2max) were 50.7 ± 9.5, 26.3 ± 5.6, 24.7 ± 7.0 mL/min/kg (P = 0.0001 5533 m vs 490 m). On days 6–7 (5533 m), VO2 at 75% Wmax (152 ± 37 watts) was 1.75 ± 0.45 L/min, oxygen saturation 68 ± 8%. On day 11 (5533 m), at the same submaximal work rate, VO2 was lower (1.61 ± 0.47 L/min, P < 0.027) indicating improved net efficiency; oxygen saturation was higher (74 ± 7%, P < 0.0004) but ratios of VO2 to work rate increments remained unchanged. On day 11, mountaineers climbed faster from 4497 m to 5533 m than on days 5–6 but perceived less effort (visual analog scale 50 ± 15 vs 57 ± 20, P = 0.006) and reduced symptoms of acute mountain sickness. We conclude that the better performance and subjective exercise tolerance after acclimatization were related to regression of acute mountain sickness and improved submaximal exercise economy because of lower metabolic demands for non-external work-performing functions.

Self-adjoint extensions for confined electrons: From a particle in a spherical cavity to the hydrogen atom in a sphere and on a cone

In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at the wall of the cavity. In this paper, we study this situation in detail both for a free particle and for a hydrogen atom centered in a spherical cavity. For appropriate values of the self-adjoint extension parameter, the bound states localized at the wall resonate with the standard hydrogen bound states. We also examine the accidental symmetry generated by the Runge–Lenz vector, which is explicitly broken in a spherical cavity with general Robin boundary conditions. However, for specific radii of the confining sphere, a remnant of the accidental symmetry persists. The same is true for an electron moving on the surface of a finite circular cone, bound to its tip by a 1/r1/r potential.