1,721,260 research outputs found
A multiplicity result for Euler–Lagrange orbits satisfying the conormal boundary conditions
No full textIn this paper, we study the multiplicity problem for Euler–Lagrange orbits that satisfy the conormal boundary conditions for a suitable class of reversible Lagrangian functions on compact manifolds. Such a class contains, e.g. the energy function of reversible Finsler metrics that satisfy a convexity condition on the boundary
A multiplicity result for orthogonal geodesic chords in Finsler disks
Full text linkIn this paper, we study the existence and multiplicity problems for orthogonal Finsler geodesic chords in a manifold with boundary which is homeomorphic to a N-dimensional disk. Under a suitable assumption, which is weaker than convexity, we prove that, if the Finsler metric is reversible, then there are at least N orthogonal Finsler geodesic chords that are geometrically distinct. If the reversibility assumption does not hold, then there are at least two orthogonal Finsler geodesic chords with different values of the energy functional
Brake orbits for Hamiltonian systems of the classical type via geodesics in singular Finsler metrics
Full text linkWe consider Hamiltonian functions of the classical type, namely, even and convex with respect to the generalized momenta. A brake orbit is a periodic solution of Hamilton’s equations such that the generalized momenta are zero on two different points. Under mild assumptions, this paper reduces the multiplicity problem of the brake orbits for a Hamiltonian function of the classical type to the multiplicity problem of orthogonal geodesic chords in a concave Finslerian manifold with boundary. This paper will be used for a generalization of a Seifert’s conjecture about the multiplicity of brake orbits to Hamiltonian functions of the classical type
Optimally controlled steady-states for multi-input underactuated linear systems
No full textIn this paper the problem of optimizing the regulation of a weakly dual redundant plant with multiple actuators is addressed. When the system is underactuated, only a subset of the outputs can be independently controlled. In this regard, the main objective of the paper pertains the optimization of the steady-state performance of the plant. A connection between the overall optimal input and the inputs that provide a perfect reference tracking of the full controllable square subsystems is established. The proposed control scheme is validated by the simulation experiment of a tracking problem for a three mass coupled system
On the relative category in the brake orbits problem
Full text linkIn this paper we show how the notion of the Lusternik–Schni- relmann relative category can be used to study a multiplicity problem for brake orbits in a potential well which is homeomorphic to the N-dimen- sional unit disk. The estimate of the relative category of the set of chords with endpoints on the (N − 1)-unit sphere was shown to the third author by Fadell and Husseini while he was visiting the University of Wisconsin at Madison
Mixing properties of erasing interval maps
Full text linkWe study the measurable dynamical properties of the interval map generated by the model-case erasing substitution rho, defined by rho (00) = empty word, rho (01) = 1, rho (10) = 0, rho (11) = 01. We prove that, although the map is singular, its square preserves the Lebesgue measure and is strongly mixing, thus ergodic, with respect to it. We discuss the extension of the results to more general erasing maps
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
Reachability and stabilization of scheduled steady-states for LPV single-input systems
No full textThe aim of this work is characterizing the class of LPV systems that admit steady-state trajectories depending exclusively on the scheduling parameter. In particular, it will be shown that only certain parameter dependent steady-state profiles are admissible and can be reached by means of a suitable control input. Furthermore, the asymptotic stability and the stabilization of such steady-states is investigated using Lyapunov-based techniques. Extensive numerical simulations illustrate and corroborate the theoretical results. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved
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