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Local and nonlocal solvable stuctures in the reduction of ODEs
No full textSolvable structures, likewise solvable algebras of local
symmetries, can be used to integrate scalar ODEs by quadratures.
Solvable structures, however, are particularly suitable for the
integration of ODEs with a lack of local symmetries. In fact,
under regularity assumptions, any given ODE always admits solvable
structures even though finding them in general could be a very
difficult task. In practice a noteworthy simplification may come
by computing solvable structures which are adapted to some
admitted symmetry algebra. In this paper we consider solvable
structures adapted to local and nonlocal symmetry algebras of any
order (i.e., classical and higher). In particular we introduce the
notion of nonlocal solvable structure
Ricci flat metrics with bidimensional null orbits. I. General aspects and nonabelian case
No full textApplications of solvable structures to the nonlocal symmetry-reduction of ODEs
No full textAn application of solvable structures to the reduction of ODEs with a lack of local symmetries is given. Solvable structures considered here are all defined in a nonlocal extension, or covering space,
of a given ODE. Examples of the reduction procedure are provided
Nonlocal interpretation of [lambda]-symmetries
No full textA reduction method of ODEs not possessing Lie point symmetries makes use of
the so called -symmetries. These symmetries are not standard
symmetries, nevertheless for any given -symmetry of an ODE one can always reconstruct nonlocal symmetries of %
. As a consequence, using these nonlocal symmetries, the -symmetry
reduction method follows from the standard method of symmetry reduction by
differential invariants
Symmetries and first integrals for non-variational equations
Full text linkFor a class of exterior ideals, we present a method associating first integrals of the characteristic distributions to symmetries of the ideal. The method is applied, under some assumptions, to the study of first integrals of ordinary differential equations and first order partial differential equations as well as to the determination of first integrals for integrable distributions of vector fields
On the geometry of twisted symmetries: Gauging and coverings
Full text linkWe consider the theory of twisted symmetries of differential equations, in particular λ and μ-symmetries, and discuss their geometrical content. We focus on their interpretation in terms of gauge transformations on the one hand, and of coverings on the other one
Generalised symmetries of partial differential equations via complex transformations
No full textWe consider two systems of real analytic partial differential equations, related by a holomorphic contact map H. We study how the generalised symmetries of the first equation are mapped into those of the second one, and determine under which conditions on H such a map is invertible. As an application of these results, an example of physical interest is discussed
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
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