Supersymmetry and the KdV equations for integrable hierarchies with a half-integer gradation

Supersymmetry is formulated for integrable models based on the sl(2 1) loop algebra endowed with a principal gradation. The symmetry transformations which have half-integer grades generate supersymmetry. The sl(2 1) loop algebra leads to N=2 supersymmetric mKdV and sinh-Gordon equations. The corresponding N=1 mKdV and sinh-Gordon equations are obtained via reduction induced by twisted automorphism. Our method allows for a description of a non-local symmetry structure of supersymmetric integrable models. © 2003 Elsevier B.V. All rights reserved.

Perceptions of laypersons and orthodontists regarding the buccal corridor in long- and short-face individuals

Objective: To determine the perception of orthodontists and laypersons regarding the size of the dark spaces in the buccal corridors and how that affects smile esthetics in individuals with long and short faces.Materials and Methods: Images of eight smiling individuals were modified to create five sizes of dark spaces in the buccal corridors (2%, 10%, 15%, 22%, and 28%) and were submitted to a group of laypersons and a group of orthodontists.Results: Laypersons were more critical in their evaluation than orthodontists. Laypersons could not distinguish the gradation of dark spaces in the buccal corridor unless it was very plain. Orthodontists perceived this gradation beginning at 15%. Female evaluators were more critical than male evaluators in both groups.Conclusions: The presence or absence of dark spaces in the buccal corridors has little influence over smile esthetics. While this aspect must be considered in the orthodontic diagnosis, there is no justification for expanding the buccal corridor to eliminate dark spaces unless they are very evident. (Angle Orthod. 2011;81:86-90.)

Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems

We associate to an arbitrary Z-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer-Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given.

Solitons from dressing in an algebraic approach to the constrained KP hierarchy

The algebraic matrix hierarchy approach based on affine Lie sl(n) algebras leads to a variety of 1 + 1 soliton equations. By varying the rank of the underlying sl(n) algebra as well as its gradation in the affine setting, one encompasses the set of the soliton equations of the constrained KP hierarchy.The soliton solutions are then obtained as elements of the orbits of the dressing transformations constructed in terms of representations of the vertex operators of the affine sl(n) algebras realized in the unconventional gradations. Such soliton solutions exhibit non-trivial dependence on the KdV (odd) time flows and KP (odd and even) time Bows which distinguishes them From the conventional structure of the Darboux-Backlund-Wronskian solutions of the constrained KP hierarchy.

Supersymmetry for integrable hierarchies on loop superalgebras

An algebraic approach is employed to formulate N = 2 supersymmetry transformations in the context of integrable systems based on loop superalgebras sl(p + 1, p), p >= 1, with homogeneous gradation. We work with extended integrable hierarchies, which contain supersymmetric AKNS and Lund-Regge sectors. We derive the one-soliton solution for p = 1 which solves positive and negative evolution equations of the N = 2 supersyrnmetric model.

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)

Affine Toda systems coupled to matter fields

We investigate higher grading integrable generalizations of the affine Toda systems, where the flat connections defining the models take values in eigensubspaces of an integral gradation of an affine Kac-Moody algebra, with grades varying from l to -l (l > 1). The corresponding target space possesses nontrivial vacua and soliton configurations, which can be interpreted as particles of the theory, on the same footing as those associated to fundamental fields. The models can also be formulated by a hamiltonian reduction procedure from the so-called two-loop WZNW models. We construct the general solution and show the classes corresponding to the solitons. Some of the particles and solitons become massive when the conformal symmetry is spontaneously broken by a mechanism with an intriguing topological character and leading to a very simple mass formula. The massive fields associated to nonzero grade generators obey field equations of the Dirac type and may be regarded as matter fields. A special class of models is remarkable. These theories possess a U(1 ) Noether current, which, after a special gauge fixing of the conformal symmetry, is proportional to a topological current. This leads to the confinement of the matter field inside the solitons, which can be regarded as a one-dimensional bag model for QCD. These models are also relevant to the study of electron self-localization in (quasi-)one-dimensional electron-phonon systems.

Higher grading conformal affine Toda theory and (generalized) sine-Gordon/massive Thirring duality

Some properties of the higher grading integrable generalizations of the conformal affine Toda systems are studied. The fields associated to the non-zero grade generators are Dirac spinors. The effective action is written in terms of the Wess-Zumino-Novikov-Witten (WZNW) action associated to an affine Lie algebra, and an off-critical theory is obtained as the result of the spontaneous breakdown of the conformal symmetry. Moreover, the off-critical theory presents a remarkable equivalence between the Noether and topological currents of the model. Related to the off-critical model we define a real and local lagrangian provided some reality conditions are imposed on the fields of the model. This real action model is expected to describe the soliton sector of the original model, and turns out to be the master action from which we uncover the weak-strong phases described by (generalized) massive Thirring and sine-Gordon type models, respectively. The case of any (untwisted) affine Lie algebra furnished with the principal gradation is studied in some detail. The example of s^l(n) (n = 2, 3) is presented explicitly. © SISSA/ISAS 2003.

Protocolo de exame físico para a coluna toracolombar de equinos

Thoracolumbar injuries represent a challenge to the veterinarian that seeks to eliminate the pain, reinstitute the athletic use of the horse and minimize economic losses. The percentage of lost training days due to orthopedic conditions in race horses is of 72.1% and within those conditions is back pain, whicht represents from 4.35% to 20% of the lameness cases. The present study searched to establish a protocol based on score points for the thoracolumbar physical exam, by which it is able to determine the possible affected areas and the seriousness of the injuries. Along with the physical exam, it was performed an ultrasonographic exam of the thoracolumbar region to characterize and classify the injuries found, as to accompany its evolution after treatment. It was observed a clear reduction in the physical exam score sum in all animals between the exam days being that the exam of most of the animals presented a zero score at 60 days after the treatment. Relating the evolution of the clinical exam with the ultrasonography image tests, there was a positive association between the reduction score in the severity scale and the evolution of the ultrasonographic image of the evaluated structures. Thus, it can be concluded that gradation of the physical exam showed to be efficient and allowed the monitoring of the clinical evolution, as the answer of the injuries to the suggested treatment. Besides that, the results showed that 60 days is the ideal time for the first reevaluation of the animal after the treatment.

The algebraic structure behind the derivative nonlinear Schrödinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of an Ŝℓ2Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows. The equivalence between the latter and the massive Thirring model is also explicitly demonstrated. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation. © 2013 IOP Publishing Ltd.

Correlação entre a densidade microvascular sanguínea e linfática e a proliferação celular no carcinoma epidermóide de assoalho bucal e língua

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Gente sem sorte: os mulatos no Brasil colonial

Pós-graduação em História - FCHS

Relações entre aquisição da percepção auditiva e aprendizagem da ortografia: consoantes soantes em questão

We compared the relationships between acquisition of auditory perception and the acquisition of sonorant consonants spelling in children of the first two grades of elementary school. The comparison was based on a procedure of identifying and writing the same set of words that presented phonological contrasts between them. As to the results, it was found: (1) gradation in the acquisition of subclasses within a larger class; (2) matches and mismatches between the two types of task; (3) increased adjustments in spelling and more mismatches in auditory perception with increasing enrollment. This set of results indicates, therefore, the complexity of the relationships between the acquisition of auditory perception and the acquisition of spelling, since, once contacted, their journey together at the same time promotes links and outcomes between them.

The anuran calling repertoire in the light of social context

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