1,720,963 research outputs found
Integrability, analyticity, isochrony, equilibria, small oscillations, and Diophantine relations: results from the stationary Burgers hierarchy
No full textAn isochronous system is introduced by modifying the Nth ODE of the stationary Burgers hierarchy, and then, by investigating its behaviour near its equilibria, neat Diophantine relations are identified, involving (well-known) polynomials of arbitrary degree having integer zeros, or equivalently matrices the determinants of which yield such polynomials. The basic idea to arrive at such relations is not new, but the specific application reported in this paper is new, and it is likely to open the way to several analogous new findings
Tridiagonal matrices, orthogonal polynomials and Diophantine relations: I
No full textIt is well known that the eigenvalues of tridiagonal matrices can be identified with the zeros of polynomials satisfying three-term recursion relations and being therefore members of an orthogonal set. A class of such polynomials is identified some of which feature zeros given by simple formulae involving integer numbers. In the process certain neat formulae are also obtained, which perhaps deserve to be included in standard compilations, since they involve classical polynomials such as the Jacobi polynomials and other 'named' polynomials
Proof of certain Diophantine conjectures and identification of remarkable classes of orthogonal polynomials
No full textCertain Diophantine conjectures are proven, and to do so certain remarkable classes of orthogonal polynomials are identified, yielding additional Diophantine findings
Polynomials defined by three-term recursion relations and satisfying a second recursion relation: connection with discrete integrability, remarkable (often Diophantine) factorizations
No full textIn this paper (as in previous ones) we identify and investigate polynomials p(n)((nu)) (x) featuring at least one additional parameter nu besides their argument x and the integer n identifying their degree. They are orthogonal (provided the parameters they generally feature fit into appropriate ranges) inasmuch as they are defined via standard three-term linear recursion relations; and they are interesting inasmuch as they obey a second linear recursion relation involving shifts of the parameter nu and of their degree n, and as a consequence, for special values of the parameter nu, also remarkable factorizations, often having a Diophantine connotation. The main focus of this paper is to relate our previous machinery to the standard approach to discrete integrability, and to identify classes of polynomials featuring these remarkable properties
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
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