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Local Blaschke-Kakutani ellipsoid characterization and Banach's isometric subspaces problem
No full textWe prove the following local version of Blaschke-Kakutani's characterization of ellipsoids: Let V be a finite-dimensional real vector space, B subset of V a convex body with 0 in its interior, and 2 <= k < dim Van integer. Suppose that the body B is contained in a cylinder based on the cross-section B boolean AND X for every k-plane X from a connected open set of linear k-planes in V. Then in the region of V swept by these k-planes B coincides with either an ellipsoid, or a cylinder over an ellipsoid, or a cylinder over a k-dimensional base. For k = 2 and k = 3 we obtain as a corollary a local solution to Banach's isometric subspaces problem: If all cross-sections of B by k-planes from a connected open set are linearly equivalent, then the same conclusion as above holds. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).Funding
This work was supported by the Russian Science Foundation under Grant 21-11-00040. The second author was supported by the Engineering and Physical Sciences Research 24 S. Ivanov et al. / Journal of Functional Analysis 289 (2025) 111063 Council [EP/S021590/1], The EPSRC Centre for Doctoral Training in Geometry and Number Theory (The London School of Geometry and Number Theory), University College London.
Acknowledgments
The authors are grateful to the anonymous referee for prompting us to write Remark 1.5
Banach's isometric subspace problem in dimension four
Get PDFWe prove that if all intersections of a convex body
with 3-dimensional linear subspaces are linearly equivalent then is a
centered ellipsoid. This gives an affirmative answer to the case of the
following question by Banach from 1932: Is a normed vector space whose
-dimensional linear subspaces are all isometric, for a fixed , necessarily Euclidean?
The dimensions and is the first case where the question was
unresolved. Since the -sphere is parallelizable, known global topological
methods do not help in this case. Our proof employs a differential geometric
approach.Comment: 25 pages, v2: minor corrections and text improvement
A note on abelian envelopes
No full textThis is a short note bridging the gap between two notions of universal abelian categories associated to exact categories, namely, Rump\u27s quotient categories and Bodzenta-Bondal\u27s abelian envelopes. The established connection allows us to draw several easy conclusions, in particular, we answer some (baisc) questions raised by Bodzenta and Bondal.minor correction
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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