Sphere-foliated minimal and constant mean curvature hypersurfaces in product spaces

In this paper, we prove that minimal hypersurfaces when $n\geq 3$ and nonzero constant mean curvature hypersurfaces when $n\geq2$ foliated by spheres in parallel horizontal hyperplanes in ${\mathbb{H}}^n \times \mathbb{R}$ must be rotationally symmetric.Comment: This article is to appear in Bull. Korean Math. Soc. in 201

The Use of Pivot Point in Ship Handling for Safer and More Accurate Ship Manoeuvring

The size of ships has increased notably over recent decades. The size of harbours and ports has however not grown in proportion. As a result ship manoeuvring in harbours and ports has become more problematic, and more of an art than a science. The ‘pivot point’ concept can be useful in analysing slow ship manoeuvring and has therefore been widely adopted by practitioners and training institutions. As a result many practitioners now routinely plan con-fined manoeuvring using the ‘pivot point’ concept. Traditionally the ‘pivot point’ concept has been defined in a number of contradictory and inaccurate ways leading to confusion and mystification. As a result many practitioners and trainers often rely on intuition to bridge the gap between reality and their flawed understanding of theory. In this presentation the theoretical aspect of the pivot point is reviewed and correct definitions put forward and applied to basic and ‘special’ ship’s manoeuvres