1,720,987 research outputs found
Undefined Jacobi last multiplier? Complete symmetry group!
No full textThe Jacobi last multiplier has an intimate association with the symmetries of differential equations.
We present four examples in which the inability to obtain a last multiplier using the method of Lie itself provides
us with information.We show that the three representations of the complete symmetry group of the linear harmonic
oscillator can be obtained by searching for Jacobi last multipliers: they correspond to the Lie point symmetries
that have zero determinant, thus far regarded as a useless case. The point is emphasized using the examples of the
Volterra–Verhulst–Pearl equation, the Kepler problem and a scalar equation of fourth order
Lie Groups and Quantum Mechanics
No full textMathematical modelling should present a consistent description of physical phenomena.
We illustrate an inconsistency with two Hamiltonians—the standard Hamiltonian and
an example found in Goldstein—for the simple harmonic oscillator and its quantisation.
Both descriptions are rich in Lie point symmetries and so one can calculate many Jacobi
Last Multipliers and therefore Lagrangians. The Last Multiplier provides the route to the
resolution of this problem and indicates that the great debate about the quantisation of
dissipative systems should never have occurred
Some Lagrangians for systems without a Lagrangian
No full textWe demonstrate how to construct many different Lagrangians for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71-128) not to have a Lagrangian. Following Bateman's dictum (1931 Phys. Rev. 38 815-9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational principle
Classical integrals as quantum mechanical differential operators: a comparison with the symmetries of the Schrödinger Equation
No full textSuperintegrable systems are characterised by the possession of many symmetries and integrals. We use the simple harmonic oscillator as an example and examine the relationship between the Noetherian integrals of a given Lagrangian as quantum operators and the Lie symmetries of the corresponding Schr ̈odinger Equation
Complete symmetry group and nonlocal symmetries for some two-dimensional evolution equations
No full textAbstractThe complete symmetry group of an 1+1 evolution equation of maximal symmetry has been demonstrated to be represented by the six-dimensional Lie algebra of point symmetries sl(2,R)⊕sW, where W is the three-dimensional Heisenberg–Weyl algebra. We construct a complete symmetry group of a 1+2 evolution equation ut=(F(u)ux)y for some functions F using the point symmetries admitted by the equation. The 1+2 equation is not completely specifiable by point symmetries alone for some specific functions F. We make use of Ansätze already reported by Myeni and Leach [S.M. Myeni, P.G.L. Leach, Nonlocal symmetries and complete symmetry groups of evolution equations, J. Nonlinear Math. Phys. 13 (2006) 377–392] which provide a route to the determination of the required generic nonlocal symmetries necessary to supplement the point symmetries for the complete specification of these 1+2 evolution equations. Further we find that taking some suitable linear combination of Lie point symmetries helps to optimise the procedure of specifying the equation. A general result concerning the number of symmetries required to form a complete symmetry group of evolution is presented in the Conclusion
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
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