1,721,042 research outputs found
Adams' Inequality with the Exact Growth Condition in R4
No full textAdams' inequality is an extension of the Trudinger-Moser inequality to the case when the Sobolev space considered has more than one derivative. The goal of this paper is to give the optimal growth rate of the exponential-type function in Adams' inequality when the problem is considered in the whole space R4
Trudinger-Moser Inequalities with the Exact Growth Condition in R<sup>N</sup> and Applications
Get PDFIn a recent paper [19], the authors obtained a sharp version of the Trudinger-Moser inequality in the whole space R2, giving necessary and sufficient conditions for the boundedness and the compactness of general nonlinear functionals in W 1, 2(R2). We complete this study showing that an analogue of the result in [19] holds in arbitrary dimensions N ≥2. We also provide an application to the study of the existence of ground state solutions for quasilinear elliptic equations in RN
Time quasi-periodic vortex patches of Euler equation in the plane
Get PDFWe prove the existence of time quasi-periodic vortex patch solutions of the
2-Euler equations in , close to uniformly rotating Kirchhoff
elliptical vortices, with aspect ratios belonging to a set of asymptotically
full Lebesgue measure. The problem is reformulated into a quasi-linear
Hamiltonian equation for a radial displacement from the ellipse. A major
difficulty of the KAM proof is the presence of a zero normal mode frequency,
which is due to the conservation of the angular momentum. The key novelty to
overcome this degeneracy is to perform a perturbative symplectic reduction of
the angular momentum, introducing it as a symplectic variable in the spirit of
the Darboux-Carath\'eodory theorem of symplectic rectification, valid in finite
dimension. This approach is particularly delicate in a infinite dimensional
phase space: our symplectic change of variables is a nonlinear modification of
the transport flow generated by the angular momentum itself. This is the first
time such an idea is implemented in KAM for PDEs. Other difficulties are the
lack of rotational symmetry of the equation and the presence of
hyperbolic/elliptic normal modes. The latter difficulties -- as well as the
degeneracy of a normal frequency -- are absent in other vortex patches problems
which have been recently studied using the formulation introduced in this
paper.Comment: 88 page
Higher order Adams' inequality with the exact growth condition
No full textAdams' inequality is the complete generalization of the TrudingerâMoser inequality to the case of Sobolev spaces involving higher order derivatives. The failure of the original form of the sharp inequality when the problem is considered on the whole space (Formula presented.) served as a motivation to investigate in the direction of a refined sharp inequality, the so-called Adams' inequality with the exact growth condition. Due to the difficulties arising in the higher order case from the lack of direct symmetrization techniques, this refined result is known to hold on first- and second-order Sobolev spaces only. We extend the validity of Adams' inequality with the exact growth to higher order Sobolev spaces
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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