1,720,958 research outputs found
On the defect of compactness in Banach spaces
No full textConcentration compactness methods improve convergence for bounded sequences in Banach spaces beyond the weak-star convergence provided by the Banach–Alaoglu theorem. A further improvement of convergence, known as profile decomposition, is possible up to defect of compactness, a series of “elementary concentrations” defined relative to the action of some group of linear isometric operators. This note presents a general profile decomposition for uniformly convex and uniformly smooth Banach spaces, generalizing the result of one of the authors (S.S.) for Sobolev spaces and of the other (C.T. jointly with I. Schindler) for general Hilbert spaces. Unlike in the Hilbert space case, profile decomposition is based not on weak convergence, but on a different mode of convergence, called polar convergence, which coincides with weak convergence if and only if the norm satisfies the known Opial condition, used in the context of fixed point theory for nonexpansive mapsLes méthodes de la concentration compacité permettent l’amélioration de la convergence des (sous-)suites bornées dans les espaces de Banach au-delà de la convergence faible étoile fournie par le théorème de Banach–Alaoglu. Une amélioration de convergence est possible en tenant compte de l’action d’un groupe d’isométries. P.-L. Lions a étudié ce type d’amélioration dans des espaces de fonctions spécifiques avec les groupes des translations et des dilatations. Une analyse complète en décomposition en profils (des suites bornées) pour les espace de Sobolev ̇
W1,p(RN)avec les groupes des translations et dilatations a été établie par un des auteurs (S.S.). L’autre auteur (avec I. Schindler) a démontré l’existence d’une décomposition en profils semblable dans un espace d’Hilbert général sur lequel agit un groupe d’isométrie satisfaisant certaines hypothèses. Ce cadre général a permis d’établir des décompositions en profils avec d’autres groupes d’isométries tels que des isométries sur des variétés sous-riemanniennes, des dilatations logarithmiques pour des espaces d’Orlicz et le groupe galiléen pour étudier l’équation de Schrödinger non linéaire (T. Tao). Ce travail généralise la décomposition en profils pour un espace de Banach uniformément convexe et uniformément régulier. Nous introduisons une autre définition de convergence faible, dite convergence polaire. La convergence polaire coïncide avec la convergence faible si et seulement si la norme satisfait à la condition d’Opial, utilisée pour la théorie du point fixe dans le cas des applications non expansives. La convergence polaire xkx est caractérisée par la dualité (xk−x)∗0. Dans les espaces de Besov et de Triebel–Lizorkin (qui contiennent les espaces de Lebesgue et Sobolev), la condition d’Opial est satisfaite pour des normes équivalentes via la décomposition de Littlewood–Paley, ce qui donne une décomposition en profils avec un reste qui tend vers 0 en norme pour des suites bornées des espaces correspondants
Concentration analysis in Banach spaces
Full text linkThe concept of a profile decomposition formalizes concentration compactness arguments on the functional-analytic level, providing a powerful refinement of the Banach-Alaoglu weak-star compactness theorem. We prove existence of profile decompositions for general bounded sequences in uniformly convex Banach spaces equipped with a group of bijective isometries, thus generalizing analogous results previously obtained for Sobolev spaces and for Hilbert spaces. Profile decompositions in uniformly convex Banach spaces are based on the notion of Delta-convergence by Lim [Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60 (1976) 179-182] instead of weak convergence, and the two modes coincide if and only if the norm satisfies the well-known Opial condition, in particular, in Hilbert spaces and l(p)-spaces, but not in L-p(R-N), p not equal 2 Delta-convergence appears naturally in the context of fixed point theory for non-expansive maps. The paper also studies the connection of Delta-convergence with the Brezis-Lieb lemma and gives a version of the latter without an assumption of convergence a.
On weak convergence in metric spaces
No full textThis note gives an exposition of various extensions of the notion
of weak convergence to metric spaces. They are motivated by applications,
such as existence of xed points of non-expansive maps, and analysis of the
defect of compactness relative to gauge groups in Banach spaces, where weak
convergence is generally less useful than respectively, asymptotic centers in [14]
and polar convergence in a preliminary version of [35]). The note compares
notions of convergence of weak type found in literature, in particular the notion
of -convergence introduced by Lim in [25], polar convergence introduced by
the authors, and the modes of convergence of weak type introduced by Jost
[20], Sosov [36] and Monod [28] in Hadamard spaces. Some applications of
polar convergence, such as the existence of xed points for nonexpansive maps
and a suitable variant of the Brezis-Lieb Lemma are produced
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
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe 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
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
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