Negative Even Grade mKdV Hierarchy and its Soliton Solutions

In this paper we discuss the algebraic construction of the mKdV hierarchy in terms of an affine Lie algebra (s) over capl(2). An interesting novelty araises from the negative even grade sector of the affine algebra leading to nonlinear integro-differential equations admiting non-trivial vacuum configuration. These solitons solutions are constructed systematically from generalization of the dressing method based on non zero vacua. The sub-hierarchies admiting such class of solutions are classified.

Dressing approach to the nonvanishing boundary value problem for the AKNS hierarchy

We propose an approach to the nonvanishing boundary value problem for integrable hierarchies based on the dressing method. Then we apply the method to the AKNS hierarchy. The solutions are found by introducing appropriate vertex operators that takes into account the boundary conditions.

Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

THE REDUCTIVE PERTURBATION METHOD AND THE KORTEWEG-DE VRIES HIERARCHY

By using the reductive perturbation method of Taniuti with the introduction of an infinite sequence of slow time variables tau(1), tau(3), tau(5), ..., we study the propagation of long surface-waves in a shallow inviscid fluid. The Korteweg-de Vries (KdV) equation appears as the lowest order amplitude equation in slow variables. In this context, we show that, if the lowest order wave amplitude zeta(0) satisfies the KdV equation in the time tau(3), it must satisfy the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1), With n = 2, 3, 4,.... AS a consequence of this fact, we show with an explicit example that the secularities of the evolution equations for the higher-order terms (zeta(1), zeta(2),...) of the amplitude can be eliminated when zeta(0) is a solitonic solution to the KdV equation. By reversing this argument, we can say that the requirement of a secular-free perturbation theory implies that the amplitude zeta(0) satisfies the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1) This essentially means that the equations of the KdV hierarchy do play a role in perturbation theory. Thereafter, by considering a solitary-wave solution, we show, again with an explicit, example that the elimination of secularities through the use of the higher order KdV hierarchy equations corresponds, in the laboratory coordinates, to a renormalization of the solitary-wave velocity. Then, we conclude that this procedure of eliminating secularities is closely related to the renormalization technique developed by Kodama and Taniuti.

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.

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.