We investigate the regularity of the marginals onto hyperplanes for sets of finite perimeter. We prove, in particular, that if a set of finite perimeter has log-concave marginals onto a.e. hyperplane then the set is convex.

Previous studies have suggested that the timing of puberty might have an impact on the adult skeleton. What composite of bone structure could be affected by the timing of puberty is unknown at present. In this study, we evaluated the relationship between age at menarche and bone cortex geometry at the distal radius. Using peripheral quantitative computed tomography, we determined total area of ...

In the plane, the way to enclose the most area with a given perimeter and to use the shortest perimeter to enclose a given area, is always to use a circle. If we replace the plane by a regular tiling of it, and construct polyforms i.e. shapes as sets of tiles, things become more complicated. We need to redefine the area and perimeter measures, and study the consequences carefully. A spiral cons...

Perimeter surveillance is one of the major applications of sensor networks. The perimeter represents the physical extent of the region to be monitored and depending on the application, it is required to sense the intrusion enter the monitored region or leave from the monitored region of the object being monitored. In this paper, the problem of identifying the perimeter of the wireless network’s...

Modeling generic size features of delamination, such as area or length, has long been considered in the literature for damage prognosis composites through specific models describing state evolution with load cycles time. However, delamination shape never considered, despite that it holds important information diagnosis and prognosis, including area, its center, perimeter, useful structural safe...

The number of essentially different square polyominoes of order n and minimum perimeter p(n) is enumerated.