A mathematical model is described for estimating changes in plasma 25-hydroxyvitamin D (25(OH)D) levels throughout the year as a consequence of varying the oral intake of vitamin D and the behaviour outdoors of white British adults resident in different regions of the UK. The model yields seasonal and geographical patterns of 25(OH)D concentrations that agree closely with observational studies....

We further investigate the dimensional duality (D-duality) proposed in arXiv:0705.0550 by mainly focusing on the properties of D-branes in this background. We derive the world-sheet correspondence of static D-branes, and discuss the fate of non-static D-branes from the world-sheet viewpoint. The quantum string production with or without D-branes is also studied from the time-like Liouville theo...