Vertex theorems for capillary drops on support planes

We consider a capillary drop that contacts several planar bounding walls so as to produce singularities (vertices) in the boundary of its free surface. It is shown under various conditions that when the number of vertices is less than or equal to three, then the free surface must be a portion of a sphere. These results extend the classical theorem of H. Hopf on constant mean curvature immersions of the sphere. The conclusion of sphericity cannot be extended to more than three vertices, as we show by examples

How far can it be argued that rationality of modernity creates a dehumanised and disenchanted self?

This essay seeks to discover just how far it can be argued that rationality of modernity can do so by focusing on various theorists and their position on the subject. Max Weber is a key philosopher whose perspective is considered throughout the discourse of the essay on topics such as secularisation, capitalism, formal rationality, bureaucracy and ‘iron cages’ which imprison the self. Ritzer’s theory of ‘McDonaldization’ is also considered, arguing that his specific tenets of control and efficiency lead to dehumanisation. This is concurred by Bryman and his postulations of ‘emotional labour’. Marxist theory is also accounted for, around the subject of reification; the transformation of the consciousness of a human into an object. The extreme depths of the argument surrounding the rationality of modernity are presented through applying the theories to the nature of the Nazi Holocaust. Finally, consideration is given as to how to re-humanise and re-enchant the self through postmodernist observation and a case study on the power of community