1,721,044 research outputs found
On some strong Poincaré inequalities on Riemannian models and their improvements
Full text linkWe prove second and fourth order improved Poincaré type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part of the gradient or of the laplacian, they can be seen as stronger versions of the classical Poincaré inequality. We show that such inequalities hold true on model manifolds as well, under suitable curvature assumptions and sharpness of some constants is also discussed
Improved multipolar Poincaré–Hardy inequalities on Cartan–Hadamard manifolds
Full text linkWe prove a family of improved multipolar Poincaré–Hardy inequalities on Cartan–Hadamard manifolds. For suitable configurations of poles, these inequalities yield an improved multi- polar Hardy inequality and an improved multipolar Poincaré inequality such that the critical unipolar singular mass is reached at any pole
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Full text link“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
Full text linkWe 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
On the first frequency of reinforced partially hinged plates
No full textWe consider a partially hinged rectangular plate and its normal modes. The dynamical properties of the plate are influenced by the spectrum of the associated eigenvalue problem. In order to improve the stability of the plate, we place a certain amount of denser material in appropriate regions. If we look at the partial differential equation appearing in the model, this corresponds to insert a suitable weight coefficient inside the equation. A possible way to locate such regions is to study the eigenvalue problem associated to the aforementioned weighted equation. In this paper, we focus our attention essentially on the first eigenvalue and on its minimization in terms of the weight. We prove the existence of minimizing weights inside special classes and we try to describe them together with the corresponding eigenfunctions
An optimal improvement for the Hardy inequality on the hyperbolic space and related manifolds
Full text linkWe prove optimal improvements of the Hardy inequality on the hyperbolic space. Here, optimal means that the resulting operator is critical in the sense of Devyver, Fraas, and Pinchover (2014), namely the associated inequality cannot be further improved. Such inequalities arise from more general, optimal ones valid for Laplacian shifted by a constant , a problem that had been studied in Berchio, Ganguly, and Grillo (2017) only when is the bottom of the spactrum of the Laplacian. A different, critical and new inequality on the hyperbolic space, locally of Hardy type, is also shown. Such results have in fact greater generality since they are proved on general Cartan-Hadamard manifolds under curvature assumptions, possibly depending on the point. Existence/nonexistence of extremals for the related Hardy-Poincaré inequalities are also proved using concentration-compactness technique and a Liouville comparison theorem. As applications of our inequalities, we obtain an improved Rellich inequality and we derive a quantitative version of Heisenberg-Pauli-Weyl uncertainty principle for the shifted Laplacian
On the first frequency of reinforced partially hinged plates
Full text linkWe consider a partially hinged rectangular plate and its normal modes. The dynamical properties of the plate are influenced by the spectrum of the associated eigenvalue problem. In order to improve the stability of the plate, we place a certain amount of denser material in appropriate regions. If we look at the partial differential equation appearing in the model, this corresponds to insert a suitable weight coefficient inside the equation. A possible way to locate such regions is to study the eigenvalue problem associated to the aforementioned weighted equation. In this paper, we focus our attention essentially on the first eigenvalue and on its minimization in terms of the weight. We prove the existence of minimizing weights inside special classes and we try to describe them together with the corresponding eigenfunctions
The fractional porous medium equation on the hyperbolic space
Full text linkWe consider a nonlinear degenerate parabolic equation of porous medium type, whose diffusion is driven by the (spectral) fractional Laplacian on the hyperbolic space. We provide existence results for solutions, in an appropriate weak sense, for data belonging either to the usual Lp spaces or to larger (weighted) spaces determined either in terms of a ground state of the laplacian, or of the (fractional) Green’s function. For such solutions, we also prove different kind of smoothing effects, in the form of quantitative L1- L∞ estimates. To the best of our knowledge, this seems the first time in which the fractional porous medium equation has been treated on non-compact, geometrically non-trivial examples
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