1,720,982 research outputs found
On the reduction theory of the Nijenhuis operator and its applications to Gel'fand-Dikii equations, Proc.Iutam-Isimm Symposium on Modern Developments in Analitical Mechanics, ATTI ACC.SCIENZE DI TORINO, Suppl.Vol.117
No full textThe aim of this paper is twofold: to develop the basic elements of the reduction theory of the Nijenhuis operators, and to explicitly construct the recursion operator of the general Gelfand-Dickii equations. To deal with the first problem, the geometric properties of the Nijenhuis operator are pointed out: they mainly concern a remarkable integrable distribution defined by such operators. The two “reduction theorems” presented in the paper give the conditions allowing to obtain a reduced kernel-free Nijenhuis operator either on any fixed leaf or on the space of the leaves of this distribution, respectively. In the second part of the paper, a remarkable class of matrix Nijenhuis operators is introduced, depending on an arbitrary matrix with constant entries; the recursion operator of the Gelfand-Dickii equations is then obtained as a particular application of the reduction theory to this class of operators
A geometrical characterization of integrable Hamiltonian systems through the theory of Poisson-Nijenhuis manifolds, Quaderno S/19, Dipartimento di Matematica dell'Universita' di Milano
No full textIn this report (172 pages, with 4 appendices) we introduce the concept of Posson-Nijenhuis (PN) manifold and we show that the integrable Hamiltonian systems are the "fundamental fields" of such manifolds. In particular, we expl;icitly construct a simple model of infinite-dimensional PN manifold and we show that it gives rise to the Gelfand-Dickey equations. The many advantages of the present approach seem to be its conceptual simplicity and the property of being systematic. The different equations are obtained as different reductions of a single PN structure, performed over special submanifolds picked out by the geometry of the PN manifold itself
Old and new results on recursion operators: an algebraic approach to KP equation
No full textFrom the MR review by L.C. Li: "The main goal of the present work is to develop a theory of recursion operators for the KP equation. The authors begin by presenting an abstract version of one-dimensional KdV theory and introduce what they call a "KdV bichain''. The theory is then extended to two space dimensions by introducing an extra derivation. As application, the KP chain is obtained as a reduction of the two-dimensional KdV bichain.
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
REDUCTION TECHNIQUES FOR INFINITE-DIMENSIONAL HAMILTONIAN-SYSTEMS - SOME IDEAS AND APPLICATIONS
No full textIn the language of tensor analysis on differentaible manifolds we present a reduction method of integrability structures, and apply it to recover some well-known hierarchies of integrable nonlinear evolution equations. The main object dealt with in the paper is the Poisson-Nijenhuis manifold, both in global and in local form: both formulations turn out to be useful, either for theoretical developments or for the applications
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