1,720,960 research outputs found
Completely exceptional 2nd order PDEs via conformal geometry and BGG resolution
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The moment map on the space of symplectic 3d Monge-Ampère equations
Full text linkFor any 2nd order scalar PDE in one unknown function, we construct, by means of the characteristics of , a contact sub-bundle of the underlying contact manifold J1, consisting of conic varieties, called the contact cone structure associated with . We then focus on symplectic Monge-Ampère equations in 3 independent variables, that are naturally parametrized, over C, by the projectivization of the 14-dimensional irreducible representation of the simple Lie group Sp(6, C). The associated moment map allows to define a rational map from the space of symplectic 3D Monge-Ampère equations to the projectivization of the space of quadratic forms on a 6-dimensional symplectic vector space. We study the relationship between the variety , herewith called the co-characteristic variety of , and the contact cone structure of a 3D Monge -Ampère equation , by obtaining a complete list of mutually non-equivalent quadratic forms on a 6-dimensional symplectic space
Geometry of Lagrangian Grassmannians and nonlinear PDEs
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Lowest degree invariant second-order PDEs over rational homogeneous contact manifolds
No full text For each simple Lie algebra [Formula: see text] (excluding, for trivial reasons, type [Formula: see text]), we find the lowest possible degree of an invariant second-order PDE over the adjoint variety in [Formula: see text], a homogeneous contact manifold. Here a PDE [Formula: see text] has degree [Formula: see text] if [Formula: see text] is a polynomial of degree [Formula: see text] in the minors of [Formula: see text], with coefficient functions of the contact coordinate [Formula: see text], [Formula: see text], [Formula: see text] (e.g., Monge–Ampère equations have degree 1). For [Formula: see text] of type [Formula: see text] or [Formula: see text], we show that this gives all invariant second-order PDEs. For [Formula: see text] of types [Formula: see text] and [Formula: see text], we provide an explicit formula for the lowest-degree invariant second-order PDEs. For [Formula: see text] of types [Formula: see text] and [Formula: see text], we prove uniqueness of the lowest-degree invariant second-order PDE; we also conjecture that uniqueness holds in type [Formula: see text]. </jats:p
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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