75 research outputs found
Continuous Truth II: Reflections
Abstract. In the late 1960s, Dana Scott first showed how the Stone-Tarski topological interpretation of Heytingâs calculus could be extended to model intuitionistic analysis; in particular Brouwerâs continuity prin-ciple. In the early â80s we and others outlined a general treatment of non-constructive objects, using sheaf modelsâconstructions from topos theoryâto model not only Brouwerâs non-classical conclusions, but also his creation of ânew mathematical entitiesâ. These categorical models are intimately related to, but more general than Scottâs topological model. The primary goal of this paper is to consider the question of iterated extensions. Can we derive new insights by repeating the second act? In Continuous Truth I, presented at Logic Colloquium â82 in Florence, we showed that general principles of continuity, local choice and local com-pactness hold in the gros topos of sheaves over the category of separable locales equipped with the open cover topology. We touched on the question of iteration. Here we develop a more gen-eral analysis of iterated categorical extensions, that leads to a reflection schema for statements of predicative analysis. We also take the opportunity to revisit some aspects of both Continuous Truth I and Formal Spaces (Fourman & Grayson 1982), and correct two long-standing errors therein
Homebuyers and the representation of spatial markets by information providers
Purpose â The purpose of this paper is to renew a research agenda considering the impact that information providersâ processes are having on the housing market; in particular to develop a research agenda around the role of the Internet in shaping householdsâ perceptions of the spatial nature of housing markets. Design/methodology/approach â This paper reviews the existing literature. It uses preliminary extensive survey findings about the role of the Internet in housing search to hypothesise ways in which households may be affected by this transition. Findings â Not applicable â other than evidence for the growth in the importance of the Internet in shaping householdsâ housing search. Practical implications â First, the academy needs to readdress the theory surrounding information acquisition and use insights from economics, sociology and psychology to understand these processes. Second, local authorities and academics should analyse the impact of Internet use on housing market boundaries (and the profound subsequent impact on policy traction). Third, estate agents should reconsider the role of the Internet in shaping housing markets and provide a critical response to the large property search engines. Originality/value â This paper reviews the literature and explores the necessity of a renewed interest in research on the role of information sources in framing and constraining housing search behaviour
A Reduction Theorem for the KripkeâJoyal Semantics: Forcing Over an Arbitrary Category can Always be Replaced by Forcing Over a Complete Heyting Algebra
Dynamics of an Unbounded Interface Between Ordered Phases
We investigate the evolution of a single unbounded interface between ordered
phases in two-dimensional Ising ferromagnets that are endowed with
single-spin-flip zero-temperature Glauber dynamics. We examine specifically the
cases where the interface initially has either one or two corners. In both
examples, the interface evolves to a limiting self-similar form. We apply the
continuum time-dependent Ginzburg-Landau equation and a microscopic approach to
calculate the interface shape. For the single corner system, we also discuss a
correspondence between the interface and the Young tableau that represents the
partition of the integers.Comment: 9 pages, 11 figures, 2-column revtex4 format. V2: references added
and discussion section expanded slightly. Final version for PRE. V3: A few
small additional editorial change
Materializing digital collecting: an extended view of digital materiality
If digital objects are abundant and ubiquitous, why should consumers pay for, much less collect them? The qualities of digital code present numerous challenges for collecting, yet digital collecting can and does occur. We explore the role of companies in constructing digital consumption objects that encourage and support collecting behaviours, identifying material configuration techniques that materialise these objects as elusive and authentic. Such techniques, we argue, may facilitate those pleasures of collecting otherwise absent in the digital realm. We extend theories of collecting by highlighting the role of objects and the companies that construct them in materialising digital collecting. More broadly, we extend theories of digital materiality by highlighting processes of digital material configuration that occur in the pre-objectification phase of materialisation, acknowledging the role of marketing and design in shaping the qualities exhibited by digital consumption objects and consequently related consumption behaviours and experiences
Microflares and the Statistics of X-ray Flares
This review surveys the statistics of solar X-ray flares, emphasising the new
views that RHESSI has given us of the weaker events (the microflares). The new
data reveal that these microflares strongly resemble more energetic events in
most respects; they occur solely within active regions and exhibit
high-temperature/nonthermal emissions in approximately the same proportion as
major events. We discuss the distributions of flare parameters (e.g., peak
flux) and how these parameters correlate, for instance via the Neupert effect.
We also highlight the systematic biases involved in intercomparing data
representing many decades of event magnitude. The intermittency of the
flare/microflare occurrence, both in space and in time, argues that these
discrete events do not explain general coronal heating, either in active
regions or in the quiet Sun.Comment: To be published in Space Science Reviews (2011
An Observational Overview of Solar Flares
We present an overview of solar flares and associated phenomena, drawing upon
a wide range of observational data primarily from the RHESSI era. Following an
introductory discussion and overview of the status of observational
capabilities, the article is split into topical sections which deal with
different areas of flare phenomena (footpoints and ribbons, coronal sources,
relationship to coronal mass ejections) and their interconnections. We also
discuss flare soft X-ray spectroscopy and the energetics of the process. The
emphasis is to describe the observations from multiple points of view, while
bearing in mind the models that link them to each other and to theory. The
present theoretical and observational understanding of solar flares is far from
complete, so we conclude with a brief discussion of models, and a list of
missing but important observations.Comment: This is an article for a monograph on the physics of solar flares,
inspired by RHESSI observations. The individual articles are to appear in
Space Science Reviews (2011
Some remarks on extending bar induction
Contains fulltext :
128988.pdf (publisher's version ) (Open Access
A correction to âconcepts of general topology in constructive mathematics and in sheavesâ
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