ATTEMPTS TO DEFINE QUASI-INTEGRABILITY

In this paper we discuss some ideas on how to define the concept of quasi-integrability. Our ideas stem from the observation that many field theory models are "almost" integrable; i.e. they possess a large number of "almost" conserved quantities. Most of our discussion will involve a certain class of models which generalize the sine-Gordon model in (1 + 1) dimensions. As will be mentioned many field configurations of these models look like those of the integrable systems and so appear to be close to those in integrable model. We will then attempt to quantify these claims looking in particular, both analytically and numerically, at field configurations with scattering solitons. We will also discuss some preliminary results obtained in other models.

Quantum solitons in the XXZ model with staggered external magnetic field

The 1-D 1/2-spin XXZ model with staggered external magnetic field, when restricting to low field, can be mapped into the quantum sine-Gordon model through bosonization: this assures the presence of soliton, antisoliton and breather excitations in it. In particular, the action of the staggered field opens a gap so that these physical objects are stable against energetic fluctuations. In the present work, this model is studied both analytically and numerically. On the one hand, analytical calculations are made to solve exactly the model through Bethe ansatz: the solution for the XX + h staggered model is found first by means of Jordan-Wigner transformation and then through Bethe ansatz; after this stage, efforts are made to extend the latter approach to the XXZ + h staggered model (without finding its exact solution). On the other hand, the energies of the elementary soliton excitations are pinpointed through static DMRG (Density Matrix Renormalization Group) for different values of the parameters in the hamiltonian. Breathers are found to be in the antiferromagnetic region only, while solitons and antisolitons are present both in the ferromagnetic and antiferromagnetic region. Their single-site z-magnetization expectation values are also computed to see how they appear in real space, and time-dependent DMRG is employed to realize quenches on the hamiltonian parameters to monitor their time-evolution. The results obtained reveal the quantum nature of these objects and provide some information about their features. Further studies and a better understanding of their properties could bring to the realization of a two-level state through a soliton-antisoliton pair, in order to implement a qubit.

Conceito de educação musical de Zoltan Kodály e teoria de aprendizagem musical de Edwin Gordon: uma abordagem comparativa

Escrever um artigo que, sem a pretensão de ser exaustivo, apontasse semelhanças no modo de pensar a Educação e a Aprendizagem Musicais de Kodály e Gordon, tornou-se para mim uma necessidade quase compulsiva, depois de frequentar o Seminário promovido pela APEM e ministrado pelo próprio Prof. Gordon nos dias 3 e 4 de Novembro de 1995.

In oboedientia, sine proprio, et in castitate, sub clausura: a ordem de Santa Clara em Portugal (séc. xiii-xiv)

Dissertação apresentada para cumprimento dos requisitos necessários à obtenção do grau de Doutor em História (Especialidade em História Económica e Social Medieval)

ESTRATÉGIA REPRODUTIVA E ALGUNS ASPECTOS DEMOGRÁFICOS DO CAMARÃO Palaemonetes carteri GORDON, 1935 NA AMAZONIA CENTRAL, RIO NEGRO

A ecologia do camarão Palaemonetes carteri Gordon, 1935 (Decapoda: Palaemonidae) foi estudada através de coletas mensais, realizadas de janeiro 1989 até maio 1990, na região de Manaus. P. carteri vive na liteira submersa dos igarapés de terra firme em áreas baixas inundadas periodicamente pelas enchentes dos rios. A estratégia de reprodução e a dinâmica da razão sexual foram estudados na base dos 4,441 indivíduos coletados. P. carteri mostrou um dimorfismo sexual do comprimento, as fêmeas sendo maiores que os machos. O período de reprodução foi restrito a enchente e a cheia das águas. O número de ovos por fêmea variou entre 5 e 39, sem nenhuma correlação com o tamanho das fêmeas. A razão sexual mostrou uma predominância de fêmeas sem nenhuma variação sazonal significativa.