2 resultados para elastica
em CentAUR: Central Archive University of Reading - UK
Resumo:
We conducted the first molecular phylogenetic study of Ficus section Malvanthera (Moraceae; subgenus Urostigma) based on 32 Malvanthera accessions and seven outgroups representing other sections of Ficus subgenus Urostigma. We used DNA sequences from the nuclear ribosomal internal and external transcribed spacers (ITS and ETS), and the glyceraldehyde-3-phosphate dehydrogenase (G3pdh) region. Phylogenetic analysis using maximum parsimony, maximum likelihood and Bayesian methods recovered a monophyletic section Malvanthera to the exclusion of the rubber fig, Ficus elastica. The results of the phylogenetic analyses do not conform to any previously proposed taxonomic subdivision of the section and characters used for previous classification are homoplasious. Geographic distribution, however, is highly conserved and Melanesian Malvanthera are monophyletic. A new subdivision of section Malvanthera reflecting phylogenetic relationships is presented. Section Malvanthera likely diversified during a period of isolation in Australia and subsequently colonized New Guinea. Two Australian series are consistent with a pattern of dispersal out of rainforest habitat into drier habitats accompanied by a reduction in plant height during the transition from hemi-epiphytic trees to lithophytic trees and shrubs. In contradiction with a previous study of Pleistodontes phylogeny suggesting multiple changes in pollination behaviour, reconstruction of changes in pollination behaviour on Malvanthera, suggests only one or a few gains of active pollination within the section. (C) 2008 Elsevier Inc. All rights reserved.
Resumo:
This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.