REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

Hamiltonian hierarchy of pseudo-potentials

The general structure of the Hamiltonian hierarchy of the pseudo-Coulomb and pseudo-Harmonic potentials is constructed by the factorization method within the supersymmetric quantum mechanics (SQMS) formalism. The excited states and spectra of eigenfunctions of the potentials are obtained through the generation of the members of the hierarchy. It is shown that the extra centrifugal term added to the Coulomb and Harmonic potentials maintain their exact solvability.

Analytic hierarchy prioritisation of new product development activities for electronics manufacturing

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A hierarchy of adaptive (X)over-bar control charts

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Territorial behaviour and dominance hierarchy of Anthracothorax nigricollis Vieillot 1817 (Aves: Trochilidae) on food resources

Dominant species are those which delimit and defend territories from other individuals of the same or different species. Subordinate species are those which, furtive and sneakily, use sources of nectar from other individuals. This study aimed to describe the aggressive interactions between species of hummingbirds, define which species are dominant and which are subordinate, investigate if the sharing of resources occurs during the visits, and compare the behaviour of the dominant species in different strata (tree, arbustive and herbaceous). The species observed interacting with Anthracothorax nigricollis Vieillot 1817 were Phaethornis pretrei Lesson and Delattrer 1839, Thalurania furcata Gmelin 1788, and Polytmus guainumbi Pallas 1764. Nine behavioural acts grouped into four categories were identified and described. The dominant species is A. nigricollis (with 0.9 of the attacks), followed by T. furcata (with 0.07) and P. pretrei (with 0.03). The resource sharing was seen only in the shrub layer, in C. surinamensis, in which there was intraspecific and interspecific sharing. A. nigricollis showed higher interspecific toleration, T. furcata (0.27) and P. pretrei (0.55) than intraspecific A. nigricollis (0.18). The frequency of occurrence of behaviours expressed by A. nigricollis in the three vegetation strata differed significantly.

Boussinesq solitary-wave as a multiple-time solution of the Korteweg-de Vries hierarchy

We study the Boussinesq equation from the point of view of a multiple-time reductive perturbation method. As a consequence of the elimination of the secular producing terms through the use of the Korteweg-de Vries hierarchy, we show that the solitary-wave of the Boussinesq equation is a solitary-wave satisfying simultaneously all equations of the Korteweg-de Vries hierarchy, each one in an appropriate slow time variable. © 1995 American Institute of Physics.

The Korteweg-de Vries hierarchy and long water-waves

By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion, we show that the Korteweg-de Vries hierarchy equations do play a role in the description of such waves. Finally, we show that this procedure of eliminating secularities is closely related to the renormalization technique introduced by Kodama and Taniuti. © 1995 American Institute of Physics.

The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation

We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity-free perturbation theory, we show that the well known N-soliton dynamics of the shallow water wave equation, in the particular case of α = 2β, can be reduced to the N-soliton solution that satisfies simultaneously all equations of the Korteweg-de Vries hierarchy.

Inside-out vs. standard vein graft to repair a sensory nerve in rats

Nerve regeneration in a sensory nerve was obtained by the application of different techniques: inside-out vein graft (IOVG group) and standard vein graft (SVG group). These techniques provide a good microenvironment for axon regeneration in motor nerves, but their efficiency for regeneration of sensory nerves is controversial. The saphenous nerve was sectioned and repaired by the inside-out and standard vein graft techniques in rats. After 4, 12, and 20 weeks the graft and the distal stump were observed under electron microscopy. In each studied period, the pattern, diameters, and thickness of the myelin sheaths of the regenerated axons were measured in the graft and distal stump. A comparative study about the regenerated nerve fibers by these two different techniques was performed. Regenerated nerve fibers were prominent in both vein grafts 4 weeks after the surgical procedures. On the other hand, in the distal stump, regenerated nerve fibers were observed only from 12 weeks. In both inside-out vein graft and standard vein graft statistical difference was not observed about the diameters and thickness of the myelinated fibers after 20 weeks. On the other hand, the inside-out group had greater regenerated axon number when compared to the standard group. There is a capillary invasion in both graft and distal stump, especially in the IOVG group. The regenerated axons follow these capillaries all the time like satellite microfascicles. After 20 weeks, the diameters of regenerated fibers repaired by the standard vein graft technique were closer to the normal fibers compared to the inside-out vein graft. On the other hand, the pattern of these regenerated axons was better in the IOVG group.

Dominance hierarchy in different stages of development in colonies of the primitively eusocial wasp Mischocyttarus cerberus styx (Hymenoptera, Vespidae)

In primitively eusocial insect societies, reproductive division of labor is established by dominance-submission interactions which determine a linear dominance hierarchy. As previously observed for other species, in Mischocyttarus cerberus styx (Hymenoptera, Vespidae), the dominant female is the main egg layer. Most of her attacks were to the females directly beneath in the rank establishing a hierarchy. During the pre-emergence stage, the hierarchy was already defined and in the post-emergence stage, pre-male substage, the frequency of dominance interactions were strong but the hierarchy was still maintained by the first-ranked female. In the decline stage there were many neutral individuals which could be the reproductives of a new colony.

Dominance hierarchy in different stages of development in colonies of the primitively eusocial wasp Mischocyttarus cassununga (Hymenoptera, Vespidae)

Seven colonies of Mischocyttarus cassununga were studied under field conditions at Universidade Federal de Juiz de Fora, MG, in southeastern Brazil: in pre-emergence, post-emergence and decline stages, during 145.8 hours. Dominance interactions among the females were quantified to verify the dynamics of succession in the social hierarchy of the colonies. Early pre-emergence colonies present more intense aggressive interactions than late pre-emergence ones, because the females are engaged in securing the role of main egg layer in the nest. In post-emergence (pre-male) colonies the dominance hierarchy is more defined and the frequency of dominance and subordination behaviors were lower than in pre-emergence stages: most of the agonistic behaviors are restricted to the first ranked females (potentially queens) and the subordinate individuals play the role of workers in the nests. In the post-emergence, post-male, and decline stages the hierarchy is still maintained by the aggressive behaviors of the 1st-ranked female but because the presence of males and future nest foundresses these interactions are not well defined in a linear way.