179,441 research outputs found
Invariance of the distributional curvature of the cone under smooth diffeomorphisms
No full textAn explicit calculation is carried out to show that the distributional curvature of a 2-cone, calculated by Clarke et al (Clarke C J S, Vickers J A and Wilson J P 1996 Class. Quantum Grav. 13 2485-98), using Colombeau's new generalized functions is invariant under nonlinear Coo coordinate transformations
Jonathan Vickers and Kerri Pratt
No full text2014 Jonathan Vickers Award winner Kerri Pratt, her work and circumstances relating to the award
Sheaves of nonlinear generalized functions and manifold-valued distributions
No full textThis paper is part of an ongoing program to develop a theory of generalized differential geometry. We consider the space G[X,Y] of Colombeau generalized functions defined on a manifold X and taking values in a manifold Y. This space is essential in order to study concepts such as flows of generalized vector fields or geodesics of generalized metrics. We introduce an embedding of the space of continuous mappings C(X,Y) into G[X,Y] and study the sheaf properties of
G[X,Y]. Similar results are obtained for spaces of generalized vector bundle homomorphisms. Based on these constructions we propose the definition of a space D'[X,Y] of distributions on X taking values in Y. D'[X,Y] is realized as a quotient of a certain subspace of G[X,Y
On the Geroch-Traschen class of metrics
No full textWe compare two approaches to semi-Riemannian metrics of low regularity. The maximally 'reasonable' distributional setting of Geroch and Traschen is shown to be consistently contained in the more general setting of nonlinear distributional geometry in the sense of Colombea
Support: Can it be a value creation strategy for positive marketing?
No full textIn pursuit of improving people's wellbeing and engaging in positive marketing, this paper addresses the application of Vickers' Appreciation System to deepen our understanding of how people comprehend their environment and respond to improve their situation. The paper highlights how companies can collaboratively engage in people's appreciation and support them in fulfilling their needs
A global theory of algebras of generalized functions II: tensor distributions
No full textWe extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby obtain a universal algebra of generalized tensor fields canonically containing the space of distributional tensor fields. The canonical embedding of distributional tensor fields also commutes with the Lie derivative. This construction provides the basis for applications of algebras of generalized functions in nonlinear distributional geometry and, in particular, to the study of spacetimes of low differentiability in general relativity
Reducing DCO registrations through electronic matching of cancer registry data and routine hospital data
No full textFrom twelve months after its original publication, this work is licensed under the Creative Commons Attribution-NonCommercial-Share Alike 3.0 Unported License.
To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0
The Penrose singularity theorem in regularity C^{1,1}
No full textWe extend the validity of the Penrose singularity theorem to spacetime metrics of regularity C^{1,1}. The proof is based on regularization techniques, combined with recent results in low regularity causality theor
Inflation targeting in practice: the UK experience
No full textIn this speech (given at the CFSresearch conference on the Implementation of Price Stability held at the Bundesbank Frankfurt am Main, 10. - 12. Sept 1998), John Vickers discusses theoretical and practical issues relating to inflation targeting as used in the United Kingdom doing the past six years. After outlining the role of the Bank s Monetary Policy Committee, he considers the Committee s task from a theoretical perspective, beforediscussing the concept and measurement of domestically generated inflation
Green operators in low regularity spacetimes and quantum field theory
No full textIn this paper we develop the mathematics required in order to provide a description of the observables for quantum fields on low-regularity spacetimes. In particular we consider the case of a massless scalar field φ on a globally hyperbolic spacetime M with C1,1 metric g. This first entails showing that the (classical) Cauchy problem for the wave equation is well-posed for initial data and sources in Sobolev spaces and then constructing low-regularity advanced and retarded Green operators as maps between suitable function spaces. In specifying the relevant function spaces we need to control the norms of both φ and gφ in order to ensure that g ◦ G± and G± ◦ g are the identity maps on those spaces. The causal propagator G = G+ − G− is then used to define a symplectic form ω on a normed space V(M) which is shown to be isomorphic to ker(g). This enables one to provide a locally covariant description of the quantum fields in terms of the elements of quasi-local C∗-algebras
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