839 resultados para Sobolev spaces
Resumo:
Lean principles create highly efficient healthcare facilities by maximising the clinical value of every part of a facility and by removing everything else. In order that clinical accommodation can be used for a diverse set of functions including unexpected tasks and processes that haven’t even been invented, they have to be big. But somewhat surprisingly, whole facilities tend to shrink in terms of gross floor areas by disposing of non-clinical spaces when designed using Lean principles. And with the whole unit – the building costs shrink too. Using examples from the UK and the USA, this talk explores the unexpected solutions and improved outcomes when designers use a Lean approach to design.
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Knowledge economy seeks its nourishment from diversity and dissemination of ideas and creativity of its talent base. This has led to the acknowledgement of place making as a major strategy to attract and retain the knowledge base into the emerging knowledge and innovation spaces. The study seeks to explore the adoption of place making in this context. Literature and practice provide information to understand the evolution of various spatial typologies and the specialised role of place making in such locations. This helps in determining the key facilitators of place making. The paper takes an interdisciplinary approach and develops an integrated conceptual framework considering dimensions and facilitators of place making. Through the lens of the framework, best practices across Europe—i.e., Cambridge Science Park (UK), 22@Barcelona (Spain), Arabianranta (Finland), Strijp-S (Netherlands), and Digital Hub (Ireland)—are scrutinised to highlight various approaches to place making. The findings provide insights and a discussion into the interplay of form, function, image and underlying processes in globally emerging spatial typologies of contemporary knowledge and innovation spaces.
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Renewable energy is commonly considered a technological addition to urban environments. By contrast, this PhD used a holistic approach to develop a design framework for integrating local electricity production into the ecological function and cultural use of public space. The framework addresses social engagement related to public interaction, and economic engagement related to the estimated quantity of electricity produced, in conjunction with environmental engagement related to the embodied energy required to construct the renewable energy infrastructure. The outcomes will contribute to social and environmental change by engaging society, enriching the local economy and increasing social networks.
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Social media analytics is a rapidly developing field of research at present: new, powerful ‘big data’ research methods draw on the Application Programming Interfaces (APIs) of social media platforms. Twitter has proven to be a particularly productive space for such methods development, initially due to the explicit support and encouragement of Twitter, Inc. However, because of the growing commercialisation of Twitter data, and the increasing API restrictions imposed by Twitter, Inc., researchers are now facing a considerably less welcoming environment, and are forced to find additional funding for paid data access, or to bend or break the rules of the Twitter API. This article considers the increasingly precarious nature of ‘big data’ Twitter research, and flags the potential consequences of this shift for academic scholarship.
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The current growth of Kathmandu Valley has been malignant in many ways which suggests a decline of public realm in the city. As the current efforts for planning and design of public open space exhibit numerous problems related to both physical and social aspects of city building, this book examines the shortcomings with contemporary urban development from urban planning and design point of view and attempts to suggest methods to overcome such shortcomings based on the study of historic urban squares. This book identifies the inherent urban design qualities of the historic urban squares in order to learn from them and also attempts to put forward the principles and guidelines for contemporary public space design based on such findings.
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In the developed world, we feel the effects of "digital disruption" in our experiences of the spaces of retail, hospitality, entertainment, finance, arts and culture, and even healthcare. This disruption can take many forms: augmentation of physical experience with a digital complement such as the use of a bespoke mobile application to navigate an art museum, ordering food on digital tablets in a restaurant, recording our health data to share with a doctor. We also rate and review our experiences of a wide range of services and share these opinions with diverse others via the social web.
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This article argues identifying as lesbian, gay, bisexual, transgender, intersex, queer and/or questioning (LGBTIQ) in rural spaces can produce specific types of policing experiences. While some literature examines the experiences of LGBTIQ people with police, very little has focused on how rurality explicitly shapes these experiences. This is significant considering research highlights how rurality can be connected to pronounced experiences of homophobia and trans-phobia. The article highlights examples from three research projects that explored: LGBTIQ young people's interactions with police; LGBTI people's interactions with police liaison services; and LGBTIQ-identifying police officers. The examples demonstrate the need for further research to examine how policing “happens” with rural LGBTIQ people to ensure more accountable policing policies and practice, and to highlight the complexities of localized, rural policing contexts that can both support and marginalize LGBTIQ people.
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The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
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A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.
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The topic of this dissertation is the geometric and isometric theory of Banach spaces. This work is motivated by the known Banach-Mazur rotation problem, which asks whether each transitive separable Banach space is isometrically a Hilbert space. A Banach space X is said to be transitive if the isometry group of X acts transitively on the unit sphere of X. In fact, some weaker symmetry conditions than transitivity are studied in the dissertation. One such condition is an almost isometric version of transitivity. Another investigated condition is convex-transitivity, which requires that the closed convex hull of the orbit of any point of the unit sphere under the rotation group is the whole unit ball. Following the tradition developed around the rotation problem, some contemporary problems are studied. Namely, we attempt to characterize Hilbert spaces by using convex-transitivity together with the existence of a 1-dimensional bicontractive projection on the space, and some mild geometric assumptions. The convex-transitivity of some vector-valued function spaces is studied as well. The thesis also touches convex-transitivity of Banach lattices and resembling geometric cases.
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The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.
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This thesis consists of three articles on Orlicz-Sobolev capacities. Capacity is a set function which gives information of the size of sets. Capacity is useful concept in the study of partial differential equations, and generalizations of exponential-type inequalities and Lebesgue point theory, and other topics related to weakly differentiable functions such as functions belonging to some Sobolev space or Orlicz-Sobolev space. In this thesis it is assumed that the defining function of the Orlicz-Sobolev space, the Young function, satisfies certain growth conditions. In the first article, the null sets of two different versions of Orlicz-Sobolev capacity are studied. Sufficient conditions are given so that these two versions of capacity have the same null sets. The importance of having information about null sets lies in the fact that the sets of capacity zero play similar role in the Orlicz-Sobolev space setting as the sets of measure zero do in the Lebesgue space and Orlicz space setting. The second article continues the work of the first article. In this article, it is shown that if a Young function satisfies certain conditions, then two versions of Orlicz-Sobolev capacity have the same null sets for its complementary Young function. In the third article the metric properties of Orlicz-Sobolev capacities are studied. It is usually difficult or impossible to calculate a capacity of a set. In applications it is often useful to have estimates for the Orlicz-Sobolev capacities of balls. Such estimates are obtained in this paper, when the Young function satisfies some growth conditions.
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In this paper I conduct a Foucauldian discourse analysis of a political speech given by Brendon Nelson in 2006 when the Australian Minister for Defence in the Howard Coalition Government. The speech connects conceptualisations of terror, globalization, education and literacy as part of a whole of government security strategy. The analysis examines this speech as an example of a liberal way of governing the conduct of diverse and unpredictable populations. My analysis suggests that the apparatus of government has been strategically used in order to biopolitically contain the rise of complex social forces and protect a set of homogenous cultural values. The purposes of education and uses of literacy are seen as instruments for the inscription of a coded set of values understood to be synonymous with civil society.