Expansive algebraic actions of countable abelian groups

This paper gives an algebraic characterization of expansive actions of countable abelian groups on compact abelian groups. This naturally extends the classification of expansive algebraic $\mathbb{Z}^d$-actions given by Schmidt using complex varieties. Also included is an application to a natural class of examples arising from unit subgroups of integral domains

Volumetric visualization of 3D data

In recent years, there has been a rapid growth in the ability to obtain detailed data on large complex structures in three dimensions. This development occurred first in the medical field, with CAT (computer aided tomography) scans and now magnetic resonance imaging, and in seismological exploration. With the advances in supercomputing and computational fluid dynamics, and in experimental techniques in fluid dynamics, there is now the ability to produce similar large data fields representing 3D structures and phenomena in these disciplines. These developments have produced a situation in which currently there is access to data which is too complex to be understood using the tools available for data reduction and presentation. Researchers in these areas are becoming limited by their ability to visualize and comprehend the 3D systems they are measuring and simulating

The taxicab locus of Apollonius: promoting exploratory routes to the punchline using rich undergraduate tasks

A key motivational tactic in undergraduate mathematics teaching is to launch topics with fundamental questions that originate from surprising or remarkable phenomena. Nonetheless, constructing a sequence of tasks that promotes students' own routes to resolving such questions is challenging. This note aims to address this challenge in two ways. First, to illustrate the motivational tactic, the taxicab manifestation of a locus attributed to Apollonius is introduced and a natural question arising from comparison with the analogous Euclidean locus is considered, namely, does the taxicab locus of Apollonius ever coincide with a taxicab circle? Second, a companion sequence of rich undergraduate tasks is elaborated using theoretical design principles, with the tasks culminating in this fundamental geometric question. This note therefore provides a design approach that can be replicated in undergraduate teaching contexts based around similarly motivating mathematical phenomena

A natural boundary for the dynamical zeta function for commuting group automorphisms

Abstract. For an action α of Z d by homeomorphisms of a compact metric space, D. Lind introduced a dynamical zeta function and conjectured that this function has a natural boundary when d � 2. In this note, under the assumption that α is a mixing action by continuous automorphisms of a compact connected abelian group of finite topological dimension, it is shown that the upper growth rate of periodic points is zero and that the unit circle is a natural boundary for the dynamical zeta function. 1

Indisciplinarity as social form: challenging the distribution of the sensible in the visual arts

The concept of ‘the distribution of the sensible’, sometimes translated as ‘partition’ or ‘division’, arguably underpins all of Jacques Rancière’s work, though is only directly articulated in one of his later works ‘The Politics of Aesthetics’ (2004). This concept has quickly gained currency in the discourses surrounding cutting edge contemporary art biennales, and Rancière himself has become the ‘philosophe du jour’ for the progressive or radical artist. However, one rarely hears his name uttered in conversations concerning Graphic Design practice, either inside or outside of the academy. For Rancière, ‘the distribution of the sensible’ refers to implicit conventions, laws, social structures, modes of consciousness, the function to separate individuals or social stratas from each other, preventing participation in the creation of a common world. This system enables, legitimises, and authorizes some, whilst at the same time stultifying, disabling, and censoring other. For Rancière, this distribution operates at a meta-level, across both the political and aesthetic realms. Thought in this way, Rancière’s philosophy politicises aesthetics and even aestheticises politics, though not in the sense that Benjamin meant. Through a reading of Rancière’s philosophy, this paper will interrogate a specific aspect of the ‘the distribution of the sensible’ in operation within the arts, particularly their institutionalized forms in the universities and the creative industries. I wish to argue that it is the specific effects of this distribution, rather than the physical properties of the work, or qualities of the human creative labour, which separates Graphic Design from Art; which designate Graphic Design as not art; that creates certain institutional accolades. As a speculative proposition, this paper proceeds from the Rancièrian presumption that a creative ‘community of equals’,beyond disciplinary antagonisms, heirarchization, and seprations, is at least a possibility, and tries to imagine what the creative industries would look like if we proceed from this assumption. I reintroduce Rancière’s use of the term ‘indisciplinarity’ here to suggest that collaboration between Graphic Design and Fine Art is both possible and the necessary characteristic of a truly egalitarian democratic society