OALib Journal期刊

ISSN: 2333-9721



匹配条件: “Katherine Borthwick” ,找到相关结果约2716条。
Abriendo la historia, abriendo la ense anza. Una aproximación al proyecto OpenLIVES
Katherine Borthwick,Pedro García-Guirao
Caracteres : Estudios Culturales y Críticos de la Esfera Digital , 2012,
Abstract: The OpenLIVES project (Learning Insights from the Voices of émigrés) will digitise and publish materials documenting the experiences of Spanish migrants especially to France, Germany and the UK during the decade of 50s, 60s and 70s and returning migrants to Spain, repurposing this data as open educational resources. Such primary research data on migration has potential relevance to a wide range of academic disciplines including history, politics, economics, sociology, etc. and is of ongoing interest and debate in the wider world. The project will demonstrate that a set of research data collected using an ethnographic methodology for a specific purpose can be used in a range of ways within humanities and social science disciplines. The data and open education resources will be released, in the first instance using the community repository for the humanities, Humbox, developed with funding from JISC by the University of Southampton.
Upper and lower bounds on resonances for manifolds hyperbolic near infinity
David Borthwick
Mathematics , 2007,
Abstract: For a conformally compact manifold that is hyperbolic near infinity and of dimension $n+1$, we complete the proof of the optimal $O(r^{n+1})$ upper bound on the resonance counting function, correcting a mistake in the existing literature. In the case of a compactly supported perturbation of a hyperbolic manifold, we establish a Poisson formula expressing the regularized wave trace as a sum over scattering resonances. This leads to an $r^{n+1}$ lower bound on the counting function for scattering poles.
Sharp geometric upper bounds on resonances for surfaces with hyperbolic ends
David Borthwick
Mathematics , 2010,
Abstract: We establish a sharp geometric constant for the upper bound on the resonance counting function for surfaces with hyperbolic ends. An arbitrary metric is allowed within some compact core, and the ends may be of hyperbolic planar, funnel, or cusp type. The constant in the upper bound depends only on the volume of the core and the length parameters associated to the funnel or hyperbolic planar ends. Our estimate is sharp in that it reproduces the exact asymptotic constant in the case of finite-area surfaces with hyperbolic cusp ends, and also in the case of funnel ends with Dirichlet boundary condtiions.
Scattering theory for conformally compact metrics with variable curvature at infinity
David Borthwick
Mathematics , 2000,
Abstract: We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular, generalized eigenfunctions exhibit L^2 decay in directions where the asymptotic curvature is sufficiently negative. The scattering matrix is shown to be a pseudodifferential operator. For generic frequency in this part of the continuous spectrum, we give an explicit construction of the resolvent kernel.
Sharp upper bounds on resonances for perturbations of hyperbolic space
David Borthwick
Mathematics , 2009,
Abstract: For certain compactly supported metric and/or potential perturbations of the Laplacian on $\mathbb{H}^{n+1}$, we establish an upper bound on the resonance counting function with an explicit constant that depends only on the dimension, the radius of the unperturbed region in $\mathbb{H}^{n+1}$, and the volume of the metric perturbation. This constant is shown to be sharp in the case of scattering by a spherical obstacle.
Distribution of resonances for hyperbolic surfaces
David Borthwick
Mathematics , 2013,
Abstract: We study the distribution of resonances for geometrically finite hyperbolic surfaces of infinite area by countting resonances numerically. The resonances are computed as zeros of the Selberg zeta function, using an algorithm for computation of the zeta function for Schottky groups. Our particular focus is on three aspects of the resonance distribution that have attracted attention recently: the fractal Weyl law, the spectral gap, and the concentration of decay rates.
Scattering theory and deformations of asymptotically hyperbolic metrics
David Borthwick
Mathematics , 1997,
Abstract: For an asymptotically hyperbolic metric on the interior of a compact manifold with boundary, we prove that the resolvent and scattering operators are continuous functions of the metric in the appropriate topologies.
Nearly Kahlerian Embeddings of Symplectic Manifolds
David Borthwick,Alejandro Uribe
Physics , 1998,
Abstract: Given an integral symplectic manifold, we construct a family of "coherent state" maps into complex projective space. The maps are built from sections of the tensor powers of a hermitian line bundle whose curvature is a multiple of the symplectic form. We show that this family is an almost-complex version of the Kodiara embedding. That is, the maps are embeddings which are approximately pseudo-holomorphic.
A local quantum version of the Kolmogorov theorem
D. Borthwick,S. Graffi
Physics , 2004, DOI: 10.1007/s00220-005-1299-4
Abstract: Consider in $L^2 (\R^l)$ the operator family $H(\epsilon):=P_0(\hbar,\omega)+\epsilon Q_0$. $P_0$ is the quantum harmonic oscillator with diophantine frequency vector $\om$, $Q_0$ a bounded pseudodifferential operator with symbol holomorphic and decreasing to zero at infinity, and $\ep\in\R$. Then there exists $\ep^\ast >0$ with the property that if $|\ep|<\ep^\ast$ there is a diophantine frequency $\om(\ep)$ such that all eigenvalues $E_n(\hbar,\ep)$ of $H(\ep)$ near 0 are given by the quantization formula $E_\alpha(\hbar,\ep)= {\cal E}(\hbar,\ep)+\la\om(\ep),\alpha\ra\hbar +|\om(\ep)|\hbar/2 + \ep O(\alpha\hbar)^2$, where $\alpha$ is an $l$-multi-index.
Did a 1-dimensional magnet detect a 248-dimensional Lie algebra?
David Borthwick,Skip Garibaldi
Physics , 2010,
Abstract: About a year ago, a team of physicists reported in Science that they had observed "evidence for E8 symmetry" in the laboratory. This expository article is aimed at mathematicians and explains the chain of reasoning connecting measurements on a quasi-1-dimensional magnet with a 248-dimensional Lie algebra.

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