1,720,979 research outputs found
Poincare-einstein holography for forms via conformal geometry in the bulk
No full textWe study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. We solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. We also develop a product formula for solving these asymptotic problems in general. The central tools of our approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale. From this, we obtain a map from existing solutions to new ones that exchanges Dirichlet and Neumann boundary conditions. Together, the scale tractor and exterior structure extend the solution generating algebra of Gover and Waldron to a conformally invariant, Poincaré-Einstein calculus on (tractor) differential forms. This calculus leads to explicit holographic formulæ for all the higher order conformal operators on weighted differential forms, differential complexes, and Q-operators of Branson and Gover (2005). This complements the results of Aubry and Guillarmou where associated conformal harmonic spaces parametrise smooth solutions
Developing a tractor calculus on null-infinity of Minkowski space
No full textFull Text is available to authenticated members of The University of Auckland only.In the usual construction of conformal tractor calculus on a pseudo-Riemannian manifold, there is an assumption of nondegeneracy of the metric. So if we were to lift this assumption, we would need to redefine the tractor machinery. This is of particular interest in the study of the asymptotics of space-times, which have metrics that are not positive-definite. These space-times are often modelled as compactified manifolds, with boundary I , referred to as null-infinity, which has the structure of a conformal manifold with a degenerate direction. Then if we want to study conformally invariant objects on I , we are inclined to develop this new tractor calculus. This is done in [13]. with the motivation of modelling the geometry of gravitational waves. We aim to adapt this definition into a more familiar setting by studying the Minkowski case and defining tractor machinery in relation to the ambient tractor bundle
Invariant differential operators in conformal geometry
No full textFull text is available to authenticated members of The University of Auckland only.We develop a universal and algorithmic construction of invariant differential operators between irreducible bundles in conformal geometry. The classification of such operators in the flat case is well-known in terms of representation theory. The main result of the thesis is a construction of curved analogues of these. We obtain curved analogues in every case save for an exception which exists in every pattern in every even dimension. The operators are described via explicit formulae in tractor calculus. These are closely related to the usual “V-formulae” for invariant operators in Riemannian geometry. The construction follows Eastwood’s curved translation principle which we implement in the conformal tractor calculus. We work in both real and complex setting and for all signatures. Further, we use the developed calculus to study one class of these operators - the conformal Killing operator on forms - in detail. We construct invariant prolongations of the corresponding systems of partial differential equations. Using these, we obtain information about the solution space. In particular, we develop a helicity raising and lowering construction in the general setting, and also on conformally Einstein manifolds
Twisted Milnor torsion for finite group actions
No full textWe define an equivariant twisted Milnor torsion as a metric on the equivariant determinant line of the twisted Thom-Smale complex for finite group actions. The cochain twisting the differential is a twisting element for the A∞-structure induced by a homotopy transfer
along the Laudenbach-de Rham quasi-isomorphism. We define an equivariant twisted Reidemeister
torsion, the simplicial counterpart of the Milnor metric, by generating a twisting
cochain for the simplicial complex using the Gugenheim-de Rham A∞-quasi-isomorphism,
extending a definition of Mathai and Wu. Under a variation of the metric on the flat vector
bundle, we derive an anomaly formula for the equivariant twisted Milnor metric from
the results of Bismut and Zhang. We use the adiabatic spectral sequence to compare the
twisted Reidemeister torsion at the unit element with the twisted analytic torsion, showing
that these are equal on odd-dimensional closed manifolds with a unimodular local system.
We conclude by highlighting the analytic difficulty with defining an equivariant twisted
analytic torsion
Fourier and Gegenbauer expansions for fundamental solutions of the Laplacian and powers in Rd and Hd
No full textWe compute fundamental solutions and associated Fourier cosine series for the Laplacian (and its powers) in Euclidean space Rd and in hyperbolic space Hd by introducing natural coordinate systems. More specific, this is done as follows. We prove parameter derivative formulae for certain associated Legendre functions. We derive closed-form expressions of normalized fundamental solutions for powers of the Laplacian in Rd and compute Fourier expansions for these fundamental solutions in terms of natural angles in axisymmetric subgroup type coordinate systems. We give azimuthal and separation angle Fourier expansions for pure hyperspherical coordinate systems, as well as Fourier expansions in mixed Euclidean-hyperspherical coordinate systems. Using azimuthal Fourier expansions compared with Gegenbauer polynomial expansions of fundamental solutions for powers of the Laplacian, we construct multi-summation addition theorems in pure hyperspherical subgroup type coordinate systems. We give some examples of multi-summation addition theorems for a certain sub-class of pure hyperspherical coordinate systems in Rd for d ∈ {3, 4, . . .}. We also give an example of a logarithmic multi-summation addition theorem, namely that for an unnormalized fundamental solution for powers of the Laplacian in R4. In the d-dimensional hyperboloid model of hyperbolic geometry Hd, we compute spherically symmetric normalized fundamental solutions for the Laplace-Beltrami operator. Finally, we also compute Fourier expansions for unnormalized fundamental solutions for this space in two and three dimensions
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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