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Heights of points with bounded ramification
Get PDFLet be an elliptic curve defined over a number field with fixed
non-archimedean absolute value of split-multiplicative reduction, and let
be an associated Latt\`es map. Baker proved in 2003 that the N\'eron-Tate
height on is either zero or bounded from below by a positive constant, for
all points of bounded ramification over . In this paper we make this bound
effective and prove an analogue result for the canonical height associated to
. We also study variations of this result by changing the reduction type of
at . This will lead to examples of fields such that the N\'eron-Tate
height on non-torsion points in is bounded from below by a positive
constant and the height associated to gets arbitrarily small on . The
same example shows, that the existence of such a lower bound for the
N\'eron-Tate height is in general not preserved under finite field extensions.Comment: There was an error in the proof of the former Lemma 5.8. This false
lemma and the former Theorem 5.9 have been deleted in this versio
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
A Note on Extensions of ℚtr
No full textIn this note we investigate the behaviour of the absolute logarithmic Weil-height h on extensions of the field ℚtr of totally real numbers. It is known that there is a gap between 0 and the next smallest value of h on ℚtr, whereas in ℚtr(i) there are elements of arbitrarily small positive height. We prove that all elements of small height in any finite extension of ℚtr already lie in ℚtr(i). This leads to a positive answer to a question of Amoroso, David and Zannier, if there exists a pseudo algebraically closed field with the mentioned height gap
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News on quadratic polynomials
Get PDFMany problems in mathematics have remained unsolved because of missing links between mathematical disciplines, such as algebra, geometry, analysis, or number theory. Here we introduce a recently discovered result concerning quadratic polynomials, which uses a bridge between algebra and analysis. We study the iterations of quadratic polynomials, obtained by computing the value of a polynomial for a given number and feeding the outcome into the exact same polynomial again. These iterations of polynomials have interesting applications, such as in fractal theory
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
On Narkiewicz’s property (P)
No full textNon UBCUnreviewedAuthor affiliation: University of BaselPostdoctora
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
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