In this paper we study the limit as p →∞ of minimizers of the fractional W -norms. In particular, we prove that the limit satisfies a non-local and non-linear equation. We also prove the existence and uniqueness of solutions of the equation. Furthermore, we prove the existence of solutions in general for the corresponding inhomogeneous equation. By making strong use of the barriers in this cons...

This paper outlines and contextualises some current findings of an on-going investigation begun in 2009 at the Visual Effects Research Lab (VERL). The three-year project links the worlds of film, art, technology and computer science. In sharing methodologies and promoting cross-, transand inter-disciplinary understanding the project is beginning to challenge established notions of visual though...

The comments above (see below for who made them and when) represent one type of thinking about infinity. There are other types, as we will see, and they all create difficulties for students, philosophers and even mathematicians. The purpose of this article is to show how a particular theory about how people come to understand mathematics, APOS Theory, can be helpful in understanding the thinkin...

These notes discuss sets, mappings between sets, and the notion of countably infinite. This material supplements the lecture on countably and uncountably infinite sets in the EE 503 probability class. The material is useful because probability theory is defined over abstract sets, probabilities are defined as measures on subsets, and random variables are defined by mappings from an abstract set...

We generalize Penrose’s notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Lifshitz and Schrödinger spaces (proposed as AdS/CFT duals of nonrelativistic f...

In this article I concentrate on three issues. First, Graham Oppy’s treatment of the relationship between the concept of infinity and Zeno’s paradoxes lay bare several porblems that must be dealt with if the concept of infinity is to do any intellectual work in philosophy of religion. Here I will expand on some insightful remarks by Oppy in an effort ot adequately respond to these problems. Sec...

Within the context of the standard model of rationality within economic modelling we show the existence of a utility function that rationalises a demand correspondence, hence completely characterizes the associated preference structure, by taking a dense demand sample. This resolves the problem of revealed preferences under some very mild assumptions on the demand correspondence which are close...

We consider the high-frequency Helmholtz equation with a given source term, and a small absorption parameter α > 0. The high-frequency (or: