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Jacobi's last multiplier and the complete symmetry group of the Euler-Poinsot system
No full textThe symmetry approach to the determination of Jacobi's last multiplier is inverted to provide a source of additional symmetries for the EulerPoinsot system. These addtional symmetries are nonlocal. They provide the symmetries for the representation of the complete symmetry group of the system
Symmetry analysis of and first integrals for the continuum Heisenberg spin chain
No full textDaniel et al. [6] analysed the singularity structure of the continuum limit of the one-dimensional anisotropic Heisenberg spin chain in a transverse field and determined the conditions under which the system is nonintegrable and exhibits chaos. We investigate the governing differential equations for symmetries and find the associated first integrals. Our results complement the results of Daniel et al
The harmony in the Kepler and related problems
No full textThe technique of reduction of order developed by Nucci [J. Math. Phys. 37, 1772-1775 (1996)] is used to produce nonlocal symmetries in addition to those reported by Krause [J. Math. Phys. 35, 5734-5748 (1994)] in his study of the complete symmetry group of the Kepler problem. The technique is shown to be applicable to related problems containing a drag term which have been used to model the motion of low altitude satellites in the Earth's atmosphere and further generalizations. A consequence of the application of this technique is the demonstration of the group theoretical relationship between the simple harmonic oscillator and the Kepler and related problems
The determination of nonlocal symmetries by the technique of reduction of order
No full textAutonomous systems of ordinary differential equations can be rewritten as systems of first order ordinary differential equations and one of the dependent variables chosen as a new independent variable. Some of the variables are eliminated to give a mixed system of first and second order equations for which the determination of point symmetries can be automated without having to make an Ansatz on the detailed structure of the symmetry. Because the coefficient function for the original independent variable appears only as its derivative in the reduced system, symmetries which are nonlocal in this variable become local symmetries of the reduced system and can be computed algorithmically
Symmetry, singularities and integrability in complex dynamics V: Complete symmetry groups of certain relativistic spherically symmetric systems
No full textSymmetry, singularities and integrability in complex dynamics V: Complete symmetry groups of certain relativistic spherically symmetric systems
No full textWe show that the concept of complete symmetry group introduced by Krause (J. Math. Phys. 35 (1994), 5734-5748) in the context of the Newtonian Kepler problem has wider applicability, extending to the relativistic context of the Einstein equations describing spherically symmetric bodies with certain conformal Killing symmetries. We also provide a simple demonstration of the nonuniqueness of the complete symmetry group
On the Hojman conservation quantities in Cosmology
No full textAbstractWe discuss the application of the Hojman's Symmetry Approach for the determination of conservation laws in Cosmology, which has been recently applied by various authors in different cosmological models. We show that Hojman's method for regular Hamiltonian systems, where the Hamiltonian function is one of the involved equations of the system, is equivalent to the application of Noether's Theorem for generalized transformations. That means that for minimally-coupled scalar field cosmology or other modified theories which are conformally related with scalar-field cosmology, like f(R) gravity, the application of Hojman's method provide us with the same results with that of Noether's Theorem. Moreover we study the special Ansatz. ϕ(t)=ϕ(a(t)), which has been introduced for a minimally-coupled scalar field, and we study the Lie and Noether point symmetries for the reduced equation. We show that under this Ansatz, the unknown function of the model cannot be constrained by the requirement of the existence of a conservation law and that the Hojman conservation quantity which arises for the reduced equation is nothing more than the functional form of Noetherian conservation laws for the free particle. On the other hand, for f(T) teleparallel gravity, it is not the existence of Hojman's conservation laws which provide us with the special function form of f(T) functions, but the requirement that the reduced second-order differential equation admits a Jacobi Last multiplier, while the new conservation law is nothing else that the Hamiltonian function of the reduced equation
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
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