843 resultados para Sobolev Spaces Besov Spaces Carnot Groups Sub-Laplacians


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The Irish border has been described as a ‘natural’ cultural divide between the island's two dominant indigenous ethno-national communities. However, an examination of key resources of ethno-national group culture - religion, sport and language - provides evidence to challenge this representation. Moreover, in the post-1994 period of conflict transformation, evidence is also presented to support the proposition that the Irish border region has developed into a cultural space in which Irish nationalist and Ulster unionist ethno-national communities can explore cultural differences and commonalities through cross-border, cross-community contact and communication in small group encounters. This space underpins the reconfiguration of the border from barrier to political bridge between North and South. European Union (EU) Peace programmes for Ireland, beginning in 1995, provided the support for a cross-border approach to escaping the cage of ethno-national conflict in Northern Ireland. However, post-2004 EU enlargement signalled the beginning of the end for EU Peace funding and severe economic recession has undermined the expectation of British-Irish intergovernmental intervention to support cross-border partnerships and their work. Therefore, the outlook for the sustainability of this cross-border cultural space is gloomy with potentially deleterious consequences for the continued reconfiguration of the border from barrier to bridge.

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In this paper, we present new methods for constructing and analysing formulations of locally reacting surfaces that can be used in finite difference time domain (FDTD) simulations of acoustic spaces. Novel FDTD formulations of frequency-independent and simple frequency-dependent impedance boundaries are proposed for 2D and 3D acoustic systems, including a full treatment of corners and boundary edges. The proposed boundary formulations are designed for virtual acoustics applications using the standard leapfrog scheme based on a rectilinear grid, and apply to FDTD as well as Kirchhoff variable digital waveguide mesh (K-DWM) methods. In addition, new analytic evaluation methods that accurately predict the reflectance of numerical boundary formulations are proposed. numerical experiments and numerical boundary analysis (NBA) are analysed in time and frequency domains in terms of the pressure wave reflectance for different angles of incidence and various impedances. The results show that the proposed boundary formulations structurally adhere well to the theoretical reflectance. In particular, both reflectance magnitude and phase are closely approximated even at high angles of incidence and low impedances. Furthermore, excellent agreement was found between the numerical boundary analysis and the experimental results, validating both as tools for researching FDTD boundary formulations.

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The context for this paper is a teacher education program for adult literacy practitioners at Queen’s University Belfast in Northern Ireland. This paper describes and reflects on the use of arts-based approaches to enhance these practitioners’ conceptualizations of literacy, presenting their arts-based responses and their evaluations of the methods and their contrasting definitions of literacy at the start and the end of the course. The discussion raises questions about the inclusion of visual literacy in adult literacy teacher education programmes.

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Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.

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A question central to modelling and, ultimately, managing food webs concerns the dimensionality of trophic niche space, that is, the number of independent traits relevant for determining consumer-resource links. Food-web topologies can often be interpreted by assuming resource traits to be specified by points along a line and each consumer's diet to be given by resources contained in an interval on this line. This phenomenon, called intervality, has been known for 30 years and is widely acknowledged to indicate that trophic niche space is close to one-dimensional. We show that the degrees of intervality observed in nature can be reproduced in arbitrary-dimensional trophic niche spaces, provided that the processes of evolutionary diversification and adaptation are taken into account. Contrary to expectations, intervality is least pronounced at intermediate dimensions and steadily improves towards lower- and higher-dimensional trophic niche spaces.

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The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

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We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

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The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property A has in fact the property. Some further ideas on the problem of whether or not amenability (in this setting) implies property A are discussed.

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The contemporary dominance of visuality has turned our understanding of space into a mode of unidirectional experience that externalizes other sensual capacities of the body while perceiving the built environment. This affects not only architectural practice but also architectural education when an introduction to the concept of space is often challenging, especially for the students who have limited spatial and sensual training. Considering that an architectural work is not perceived as a series of retinal pictures but as a repeated multi-sensory experience, the problem definitions in the design studio need to be disengaged from the dominance of a ‘focused vision’ and be re-constructed in a holistic manner. A method to address this approach is to enable the students to refer to their own sensual experiences of the built environment as a part of their design processes. This paper focuses on a particular approach to the second year architectural design teaching which has been followed in the Department of Architecture at Izmir University of Economics for the last three years. The very first architectural project of the studio and the program, entitled ‘Sensing Spaces’, is conducted as a multi-staged design process including ‘sense games, analyses of organs and their interpretations into space’. The objectives of this four-week project are to explore the sense of space through the design of a three-dimensional assembly, to create an awareness of the significance of the senses in the design process and to experiment with re-interpreted forms of bodily parts. Hence, the students are encouraged to explore architectural space through their ‘tactile, olfactory, auditory, gustative and visual stimuli’. In this paper, based on a series of examples, architectural space is examined beyond its boundaries of structure, form and function, and spatial design is considered as an activity of re-constructing the built environment through the awareness of bodily senses.

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Reprinted in Trevor Barnes and Derek Gregory (eds), Reading Human Geography: The Poetics and Politics of Inquiry, (London: Arnold, 1997), pp. 27-48