Homotopy minimal period self-maps on flat manifolds

This paper studies the homotopical minimal period set for self-maps on flat manifolds. We introduce a new invariant: the density of the homotopical minimal period set in the natural numbers. Some conditions on self-maps and flat manifolds are obtained so that the corresponding density is positive. © 2013 Elsevier Inc

Vitamin D and calcium: what do we need to know?

This chapter provides a summary of the literature including results from large trials, meta-analyses, and recent major recommendations. Two well-accepted and recent recommendations include those from the Agency for Health Research and Quality on calcium and vitamin D supplementation and from the Institute of Medicine\u27s dietary reference intakes for calcium and vitamin D. This review suggests that there is strong evidence for synergistic roles of calcium and vitamin D in maintaining bone health in postmenopausal women, but the correlation between vitamin D alone and bone health is overall inconclusive