1,721,003 research outputs found
Heir-equations for partial differential equations: a 25-year review
Full text linkHeir-equations were found by iterating the nonclassical symmetry method.
Apart inheriting the same Lie symmetry algebra of the original partial differential
equation, and thus yielding more (and different) symmetry solutions
than expected, the heir-equations are connected to conditional Lie-Baecklund
symmetries, and generalized conditional symmetries; moreover they solve the
inverse problem, namely a special solution corresponds to the nonclassical symmetry.
A review of 25-year work is presented, and open problems are brought
forward
Magnetohydrodynamics and deep mixing in evolved stars. I. two- and three-dimensional analytical models for the asymptotic giant branch
No full textThe advection of thermonuclear ashes by magnetized domains emerging near the H shell was suggested to explain asymptotic giant branch (AGB) star abundances. Here we verify this idea quantitatively through exact MHD models. Starting with a simple two-dimensional (2D) geometry and in an inertia frame, we study plasma equilibria avoiding the complications of numerical simulations. We show that below the convective envelope of an AGB star, variable magnetic fields induce a natural expansion, permitted by the almost ideal MHD conditions, in which the radial velocity grows as the second power of the radius. We then study the convective envelope, where the complexity of macroturbulence allows only for a schematic analytical treatment. Here the radial velocity depends on the square root of the radius. We then verify the robustness of our results with 3D calculations for the velocity, showing that for both studied regions the solution previously found can be seen as a planar section of a more complex behavior, in which the average radial velocity retains the same dependency on the radius found in 2D. As a final check, we compare our results to approximate descriptions of buoyant magnetic structures. For realistic boundary conditions, the envelope crossing times are sufficient to disperse in the huge convective zone any material transported, suggesting magnetic advection as a promising mechanism for deep mixing. The mixing velocities are smaller than for convection but larger than for diffusion and adequate for extra mixing in red giants. © 2014. The American Astronomical Society
Ordinary differential equations invariant under two-variable Moebius transformations
Full text linkWe consider two Möbius transformations that map two variables, compute their invariants and describe the ordinary differential equations that are kept invariant under these transformations
On differential equations invariant under two-variable Moebius transformations
Full text linkWe compute invariants for the two-variable M ̈obius transformation. In particular we are interested in partial differential equations in two dependent and two independent variables that are kept invariant under this transformation
Minimally superintegrable systems in flat three-dimensional space are also linearizable
No full textThis article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in M. C. Nucci and R. Campoamor-Stursberg. Minimally superintegrable systems in flat three-dimensional space are also linearizable. J Math Phys. 63 (2022), no. 12, 123510, and may be found at https://doi.org/10.1063/5.0086431.It is shown that all minimally superintegrable Hamiltonian systems in a three-dimensional flat space derived in the work of Evans [Phys. Rev. A 41, 5666–5676 (1990)] possess hidden symmetries leading to their linearization.Ministerio de Ciencia e InnovaciónDepto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasInstituto de Matemática Interdisciplinar (IMI)TRUEpu
Generalized symmetries, first integrals, and exact solutions of chains of differential equations
Full text linkNew integrability properties of a family of sequences of ordinary differential equations, which contains the Riccati and Abel chains as the most simple sequences, are studied. The determination of n generalized symmetries of the nth-order equation in each chain provides, without any kind of integration, n-1 functionally independent first integrals of the equation. A remaining first integral arises by a quadrature by using a Jacobi last multiplier that is expressed in terms of the preceding equation in the corresponding sequence. The complete set of n first integrals is used to obtain the exact general solution of the nth-order equation of each sequence. The results are applied to derive directly the exact general solution of any equation in the Riccati and Abel chains
Quantization of the dynamics of a particle on a double cone by preserving Noether symmetries
Full text linkThe classical quantization of the motion of a free particle and that of an harmonic oscillator on a double cone are achieved by a quantization scheme [M. C. Nucci, Theor. Math. Phys. 168 (2011) 994], that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger equation. The result is different from that given in [K. Kowalski, J. Rembielński, Ann. Phys. 329 (2013) 146]. A comparison of the different outcomes is provided
Superintegrable systems in non-Euclidean plane: Hidden symmetries leading to linearity
Full text linkNineteen classical superintegrable systems in two-dimensional non-Euclidean spaces are shown to possess hidden symmetries leading to their linearization. They are the two Perlick systems [Ballesteros et al., Classical Quantum Gravity 25, 165005 (2008)], the Taub-NUT system [Ballesteros et al., SIGMA 7, 048 (2011)], and all the 17 superintegrable systems for the four types of Darboux spaces as determined by Kalnins et al. [J. Math. Phys. 44, 5811-5848 (2003)]
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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