1,721,002 research outputs found
Symmetry and singularity properties of the generalised Kummer–Schwarz and related equations
No full textAbstractWe examine the generalised Kummer–Schwarz equation and some of its generalisations from the viewpoints of symmetry and singularity analyses. We determine the Complete Symmetry Group of the general equation and show that different forms of the fourth-order representative illustrate the three possible classes of Laurent series to be expected in the course of the singularity analysis
Equivalence classes of second-order ordinary differential equations with only a three-dimensional Lie algebra of point symmetries and linearisation
No full textAbstractThere are seven equivalence classes of second-order ordinary differential equations possessing only three Lie point symmetries and hence not linearisible by means of a point transformation. We examine the representatives of these classes for linearisibility by means of other types of transformation. In particular we compare the potential for linearisibility and the possession of the Painlevé property. The complete symmetry group is realised in the standard algebra for each of the equivalence classes
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
Noether's Theorem and Symmetry
Full text linkIn Noether's original presentation of her celebrated theorem of 1918, allowances were made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon the derivatives of the dependent variable(s), the so-called generalized, or dynamical, symmetries. A similar allowance is to be found in the variables of the boundary function, often termed a gauge function by those who have not read the original paper. This generality was lost after texts such as those of Courant and Hilbert or Lovelock and Rund confined attention to only point transformations. In recent decades, this diminution of the power of Noether's Theorem has been partly countered, in particular, in the review of Sarlet and Cantrijn. In this Special Issue, we emphasize the generality of Noether's Theorem in its original form and explore the applicability of even more general coefficient functions by allowing for nonlocal terms. We also look at the application of these more general symmetries to problems in which parameters or parametric functions have a more general dependence upon the independent variables
Heat polynomials and Lie point symmetries
No full textAbstractThe classical heat polynomials are polynomial solutions of the heat equation. We demonstrate the generation of such polynomials through the medium of the group theoretical properties of the equation. A generalised procedure for the generation of polynomial solutions is presented and this is extended to the construction of related polynomials
On the Uniqueness of the Schwarzian and Linearisation by Nonlocal Contact Transformation
No full textAbstractWe investigate the uniqueness of the Schwarzian from a group theoretic point of view. The Kummer–Schwarz equation, obtained from the Schwarzian, is also analysed for its group properties. Related equations (arising in the study of geodesic curves on a surface of constant curvature) are constructed. These equations are generalised by reducing the symmetry imposed. The unique generalisation is linearised under a nonlocal contact transformation
The Algebraic Structure of the First Integrals of Third-Order Linear Equations
No full textAbstractWe use the Lie theory of extended groups to analyse the first integrals of scalar third-order linear ordinary differential equations. The analysis reveals three natural classes for which the equation has four, five, or seven symmetries. We show that each class has first integrals with a specific number of symmetries. Illustrative examples of each class are given. Comparison is made with the integrals of nonlinear equations
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