Integrability vs supersymmetry: Poisson structures of the pohlmeyer reduction

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Supersymmetry flows, semi-symmetric space sine-Gordon models and the Pohlmeyer reduction

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On negative flows of the AKNS hierarchy and a class of deformations of a bihamiltonian structure of hydrodynamic type

A deformation parameter of a bihamiltonian structure of hydrodynamic type is shown to parametrize different extensions of the AKNS hierarchy to include negative flows. This construction establishes a purely algebraic link between, on the one hand, two realizations of the first negative flow of the AKNS model and, on the other, two-component generalizations of Camassa-Holmand Dym-type equations. The two-component generalizations of Camassa-Holm- and Dym-type equations can be obtained from the negative-order Hamiltonians constructed from the Lenard relations recursively applied on the Casimir of the first Poisson bracket of hydrodynamic type. The positive-order Hamiltonians, which follow froth the Lenard scheme applied on the Casimir of the second Poisson bracket of hydrodynamic type, are shown to coincide with the Hamiltonians of the AKNS model. The AKNS Hamiltonians give rise to charges conserved with respect to equations of motion of two-component Camassa-Holm- and two-component Dym-type equations.

Congruent spatial and temporal foraging by a dominant ant (Hym., Formicidae) and its replacement in an assemblage in a large urban structure in southeastern Brazil

At fixed bail stations in a large institutional setting in Brazil, the temporal and spatial pattern of usage of the dominant species of ant was studied. The ant Crematogaster cf. magnifica, was found in 91% of sampling points. These studies were conducted using the same points as a previous study of tile then dominant ant. Monomorium pharaonis, which was found to have declined from 93% to 3% spatial point occupation. The frequency of point usage during this study was significantly different from the Poisson distribution for both species, indicating non-random use of space. Crematogaster cf. magnifica was significantly more spatially exclusive than had been documented for M. pharaonis, and the probability of points originally occupied by M. pharaonis later becoming occupied by C. cf. magnifica was in excess of 90%. Temporal bait exploitation patterns of the two species did not differ. These data demonstrate that structural ant communities can change over time without human intervention, although short- term stability is characteristic of the urban dominant ants in subtropical Brazil.