Unlinked Embedded Graphs

This paper is a self-contained development of an invariant of graphs embedded in three-dimensional Euclidean space using the Jones polynomial and skein theory. Some examples of the invariant are computed. An unlinked embedded graph is one that contains only trivial knots or links. Examples show that the invariant is sufficiently powerful to distinguish some different unlinked embeddings of the same graph.

Trivial Jensen measures without regularity

In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point.

Spectral synthesis and topologies on ideal spaces for Banach *-algebras

This paper continues the study of spectral synthesis and the topologies τ∞ and τr on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a finite extension of an abelian group then τr is Hausdorff on the ideal space of L1(G) if and only if L1(G) has spectral synthesis, which in turn is equivalent to G being compact. The result is applied to nilpotent groups, [FD]−-groups, and Moore groups. An example is given of a non-compact, non-abelian group G for which L1(G) has spectral synthesis. It is also shown that if G is a non-discrete group then τr is not Hausdorff on the ideal lattice of the Fourier algebra A(G).

Spectral synthesis for Banach Algebras II

This paper continues the study of spectral synthesis and the topologies tau-infinity and tau-r on the ideal space of a Banach algebra, concentrating particularly on the class of Haagerup tensor products of C*-algebras. For this class, it is shown that spectral synthesis is equivalent to the Hausdorffness of tau_infinity. Under a weak extra condition, spectral synthesis is shown to be equivalent to the Hausdorffness of tau_r.

Endomorphisms of Banach algebras of infinitely differentiable functions

In this note we study the endomorphisms of certain Banach algebras of infinitely differentiable functions on compact plane sets, associated with weight sequences M. These algebras were originally studied by Dales, Davie and McClure. In a previous paper this problem was solved in the case of the unit interval for many weights M. Here we investigate the extent to which the methods used previously apply to general compact plane sets, and introduce some new methods. In particular, we obtain many results for the case of the closed unit disc. This research was supported by EPSRC grant GR/M31132

Futuretalk: one small step towards a Chronolinguistics

In the area of linguistics and language teaching, science fiction is useful in very many ways. An obvious way is that it sets up many complex and rich worlds and outlines the sorts of adjustments that language must make in those contexts. It thus draws a strong link between language and context; it shows how the construction of reality is largely a matter of language; and it speculates on where we are linguistically heading. It is a useful mirror on language development. Extrapolating the dialects of the future has been the province of science fiction in the last century. Though few SF writers are professional linguists, their method in general tends to take a holistic view of form, meaning and social context. Characters in science fiction are not individuals but are 'everyman' tokens, and the language they use symbolises the culture they inhabit. Linguistic extrapolation in science fiction thus treats language both as the technology of communication and as an index of social change. In this paper, I argue that predicting the language of the future, though extremely difficult, is possible. I call this new discipline chronolinguistics, and I set out the draft principles and parameters of a chronolinguistics, based on the future languages speculated by John Brunner, Russell Hoban, William Gibson, Greg Bear, Neal Stephenson and Iain M.Banks.

La ventriloquia y el otro in El hablador de Vargas Llosa

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From "Rational Utopia" to "Will-to-Utopia". On the "Post-modern" Turn in the Recent Work of Agnes Heller

Agnes Heller recently described her position as 'postmodernist', suggesting a move from a political radical to a politically liberal or 'neoconservative' position. The aim of this paper is to assess the degree to which Heller can still be regarded as a radical political thinker through an evaluation of her work on autonomy, democracy and contingency all of which remain key concepts in her thinking about the political. We find in each case that whilst many of the motifs of her critical Marxist period recur in her recent work, they are losing their oppositional or 'negative' character in the sense that making these motifs operational would require changes to the structure or functioning of liberal-capitalism. Whils remaining in some sense a radical thinker Heller has moved from the advocacy of a 'rational utopia' to a form of theorising which I describe as 'will-to-utopia': radical at the surface yet conservative at the core.

The hybrid library: a view from the UK

This paper aims to provide an overview of digital library development in the UK, concentrating on the eLib (Electronic Libraries) programme. It also discusses the idea of the Hybrid Library and considers how it fits into current electronic library developments. The paper is divided into the following areas. First, it summarises the background to the eLib programme and discusses some of its preliminary findings. It then discusses the concept of the Hybrid Library, followed by a summary of the of the current eLib (phase 3) projects which include hybrid library development projects. Finally, it identifies a number of common themes between the different projects which are currently being investigated.

The changing role of subject librarians in academic libraries

Discusses the roles that subject librarians (or 'subject specialists') play in contemporary UK academic libraries. Argues that subject librarians, who still form a significant grouping of senior staff in most UK academic libraries, continue to have a significant role to play in the delivery of library services and that applies to both traditional and electronic library services. Discusses the traditional role of subject librarians and analyzes the way in which this role is changing. Those areas where the changing responsibilities are extensions of traditional roles into new areas are pinpointed, together with examples of where subject librarians are performing new roles and adopting new ways of working. Areas where the changing role of subject librarians can be specifically identified include: greater emphasis on liaison with users; advocacy of the collections; adopting new roles; dealing with user enquiries in new ways; working with technical staff; selecting electronic library materials; carrying out more information skills training; having a greater involvement in the implementation of educational technology; team working and project working. Presents practical examples based on experiences at Nottingham university and other UK research libraries. The redesign and relaunch of Nottingham University Library Web site is described to illustrate many of these points.

Motivation in action: A process model of L2 motivation

As part of a long-term project aimed at designing classroom interventions to motivate language learners, we have searched for a motivation model that could serve as a theoretical basis for the methodological applications. We have found that none of the existing models we considered were entirely adequate for our purpose for three reasons: (1) they did not provide a sufficiently comprehensive and detailed summary of all the relevant motivational influences on classroom behaviour; (2) they tended to focus on how and why people choose certain courses of action, while ignoring or playing down the importance of motivational sources of executing goal-directed behaviour; and (3) they did not do justice to the fact that motivation is not static but dynamically evolving and changing in time, making it necessary for motivation constructs to contain a featured temporal axis. Consequently, partly inspired by Heckhausen and Kuhl's 'Action Control Theory', we have developed a new 'Process Model of L2 Motivation', which is intended both to account for the dynamics of motivational change in time and to synthesise many of the most important motivational conceptualisations to date. In this paper we describe the main components of this model, also listing a number of its limitations which need to be resolved in future research.

Hexagonal patterns in finite domains

In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the possible patterns. In finite rectangular domains, it is shown that a regular hexagonal pattern cannot occur if the aspect ratio is rational. In practice, it is found experimentally that in a rectangular region, patterns of irregular hexagons are often observed. This work analyses the geometry and dynamics of irregular hexagonal patterns. These patterns occur in two different symmetry types, either with a reflection symmetry, involving two wavenumbers, or without symmetry, involving three different wavenumbers. The relevant amplitude equations are studied to investigate the detailed bifurcation structure in each case. It is shown that hexagonal patterns can bifurcate subcritically either from the trivial solution or from a pattern of rolls. Numerical simulations of a model partial differential equation are also presented to illustrate the behaviour.