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by Heinz-Otto Kreiss * and Shiu Hong Lui**
No full textIntroduction We consider partial differential equations of the form u t = P (x; @ @x )u + "f (x; t; u; u x ; : : :) + F (x; t); u(x; 0) = u 0 (x): (1:1) We assume that F and its derivatives decay like 1=(t + 1) q for some suitable q ? 0 and we want to investigate under what conditions lim t!1 ju(\Delta; t)j 1 = 0: (1:2) We shall use the following concepts. Definition 1.1. If (1.2) holds uniformly for 0 " " 0 ; " 0 ? 0;<F29
Singular value decay for solutions of Sylvester equations
No full textA Sylvester equation is an operator equation of the form . A fact that has been proven multiple times before, see \cite{penzl2000eigenvalue,sabino2006solution}, is that if has low rank, then and satisfying certain conditions imply has a low rank approximation. Another set of conditions was given by Beckermann and Townsend in 2019, \cite{beckermann2019bounds}, where they impose the conditions that and are both normal, and have disjoint and well-separated spectra. In this thesis, we explore cases where the normality condition can be relaxed. Our main tool is unitary operator dilations, whereby one can realize a given operator as the corner of a unitary operator acting on a bigger space. The basic problem becomes the lifting of the original Sylvester equation to a new one involving the unitary dilation. This is reminiscent of the so-called intertwining dilation theorem, but it requires a completely new analysis as we require additional conditions if we wish to be able to guarantee the solution has a low rank approximation.
Our main result states that if we trade in normality of for a norm condition on and , then we can unitarily dilate . This in turn allows us to conclude that has a low rank approximation provided our condition is satisfied, is normal, and has low rank. Due to the similarity in the conditions for the theorem by Beckermann and Townsend and the conditions required to solve a Sylvester equation quickly using algorithms such as the alternating direction implicit (ADI) method, our dilation method also allows us to show the ADI method does not require too many iterations without requiring to be normal.October 202
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
Rayleigh-Bénard simulation using the gas-kinetic Bhatnagar-Gross-Krook scheme in the incompressible limit
No full textDispelling 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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