Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

We consider the Hamiltonian reduction of the two-loop Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra script Ĝ. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-Abelian generalizations of the conformal affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ-functions, which are defined for any integrable highest weight representation of script Ĝ, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed. We also introduce what we call the two-loop Virasoro algebra, describing extended symmetries of the two-loop WZNW models.

Affine Lie algebraic origin of constrained KP hierarchies

An affine sl(n + 1) algebraic construction of the basic constrained KP hierarchy is presented. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and it is shown that these approaches are equivalent. The model is recognized to be the generalized non-linear Schrödinger (GNLS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Bäcklund transformations and interpolate between GNLS and multi-boson KP-Toda hierarchies. Our construction uncovers the origin of the Toda lattice structure behind the latter hierarchy. © 1995 American Institute of Physics.

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.

Tau-functions and dressing transformations for zero-curvature affine integrable equations

The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras g. Their common feature is that they have some special vacuum solutions corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of g; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of g. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail. © 1997 American Institute of Physics.

A new rain-operated seed dispersal mechanism in Bertolonia mosenii (Melastomataceae), a Neotropical rainforest herb

Although widespread among fungi, lichens, liverworts, and mosses, seed dispersal mechanisms operated by rain are unusual among flowering plants. Generally speaking, two mechanisms are involved in seed dispersal by rains: the splash-cup and the springboard. Here we describe a new seed dispersal mechanism operated by rain in a Neotropical rainforest herb Bertolonia mosenii Cogniaux (Melastomataceae). The study was carried out at the lowland Atlantic rainforest, southeastern Brazil. We experimentally demonstrate that rain is necessary to release the seeds from the capsules through what we call squirt-corner seed dispersal mechanism: when a raindrop strikes the mature fruit, the water droplet forces the seeds outward to the angles (corners) of the triangular capsule and the seeds are released. As far as we know squirt-corner represents a new rain-operated seed dispersal mechanism, and a novel seed dispersal mode both for Melastomataceae and for flowering plants from Neotropical forests.

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.

Differential fruit consumption of two Melastomataceae by birds in Serra da Mantiqueira, southeastern Brazil

In this study we report on the consumption of two syntopic Melastomataceae species by birds in a lower montane forest in Monte Verde, southeastern Brazil. The species of frugivores were identified and characterized by their methods of capture and consumption of fruits. We also provide information on abundance, phenology of plants and fruit characteristics of the two Melastomataceae species. The 13 observed species of birds formed two statistically distinct frugivorous groups with taxonomic and behavioral differences. Five of seven bird species that fed on L. aff. sublanata fruits belong to the subfamily Thraupinae and most fruits were mashed before swallowed. Four of the eight bird species that visited M. cinerascens belong to the subfamily Turdinae and all fruits were swallowed whole. Only two bird species were common visitors of both Melastomataceae species. Our findings show that fruits of the two Melastomataceae species with similar morphological characteristics were exploited differently by frugivorours birds.

SEM studies on the leaf indumentum of six Melastomataceae species from Brazilian Cerrado

The wide diversity of their trichomes, which vary from simple unicellular to very complex structures, is a remarkable characteristic in Melastomataceae. This paper characterizes the leaf indumentum of Miconia albicans (Sw.) Triana, M. chamissois Naudin, M. fallax DC., M. ligustroides (DC.) Naudin, Microlepis oleaefolia (DC.) Triana and Rhynchanthera dichotoma DC., typical species from Brazilian cerrado. Samples collected from the median third of young and mature leaf blades were processed following the usual scanning electron microscopy techniques (SEM). We observed ten morphological types of trichomes and four of emergences. With five different types, four of which are reported for the first time, Rhynchanthera dichotoma is the species that presents the most diverse indumenta. A mixed type of trichome formed by a glandular and a branched non-glandular portion called lateral-gland was observed in M. ligustroides. Such non-glandular portion presents different degrees of development. A correlation is suggested between the stage of development of the non-glandular portion and the exposition to light of these lateral gland on young leaves.

Produção de sementes e comportamento germinativo de Tibouchina clavata (Pers.) Wurdack. (Melastomataceae)

In the process of riverine forest restoration, increasing emphasis has been given to the study of herbaceous and shrub species. However, for many of these we still lack basic knowledge, such as reproduction biology. Therefore, the objective of this study was to characterize the production, seed germination and reproductive capacity of Tibouchina clavata (Pers.) Wurdack., a species of wide distribution in wetlands. Fruits were collected from different mother trees located on the southern coast of São Paulo state and, after processing, were subjected to germination under constant temperatures of 25 and 30°C, and alternated temperatures of 25-30°C in the first essay, and at 15, 20, 25, 30, 35, 40°C in another essay, and at 25 °C with presence or absence of light. 10 plants were marked and, in each one, the number of fruits per plant and seed number per fruit were determined to characterize their reproductive capacity. The species germinates over a wide temperature range (15 to 35 °C), and the optimum temperature was in the range of 20 to 30 °C. Seed didn't germinate at 40 °C and could be characterized as being of absolute positive photoblastism. In general, there were over 1600 seeds per fruit and 85.000 seeds per plant. The high seed yield, coupled with good germination percentage demonstrated that this is a species with high reproductive potential.

Utilização de reguladores vegetais na propagação vegetativa de clidemia blepharodes DC. e C. Suffruticosa O. Berg (Melastomataceae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Observer-based control design for switched affine systems and applications to DC-DC converters

This paper deals with the problem of establishing a state estimator for switched affine systems. For that matter, a modification on the Luenberger observer is proposed, the switched Luenberger observer, whose idea is to design one output gain matrix for each mode of the original system. The efficiency of the proposed method relies on a simplification on estimation error which is proved always valid, guaranteeing the estimation error to asymptotically converge to zero, for any initial state and switching law. Next, a dynamic output-dependent switching law is formulated. Then, design methodologies using linear matrix inequalities are proposed, which, to the authors's knowledge, have not yet been applied to this problem. Finally, observers for DC-DC converters are designed and simulated as application examples. © 2013 Brazilian Society for Automatics - SBA.

Relação de custo/benefício na interação entre a aranha Peucetia flava (Oxyopidae) e a planta Rhynchanthera dichotoma (Melastomataceae)

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

Estudo da germinação de sementes de Tibouchina mutabilis (Vell.) Cogn. (Melastomataceae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Avaliação da atividade antiulcerogênica dos extratos e frações das folhas de Mouriri elliptica Mart. (Melastomataceae) e Byrsonima basiloba A. Juss. (Malpighiaceae)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Efeito da (-)-epicatequina presente nas folhas Mouriri pusa Gardin. (Melastomataceae) na prevenção e tratamento de colite ulcerativa em ratos

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