TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.

On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.

Some examples of nil Lie algebras

Generalizing Petrogradsky`s construction, we give examples of infinite-dimensional nil Lie algebras of finite Gelfand-Kirillov dimension over any field of positive characteristic.

ON SPECIALITY OF BINARY-LIE ALGEBRAS

In the present work, binary-Lie, assocyclic, and binary (-1,1) algebras are studied. We prove that, for every assocyclic algebra A, the algebra A(-) is binary-Lie. We find a simple non-Malcev binary-Lie superalgebra T that cannot be embedded in A(-s) for an assocyclic superalgebra A. We use the Grassmann envelope of T to prove the similar result for algebras. This solve negatively a problem by Filippov (see [1, Problem 2.108]). Finally, we prove that the superalgebra T is isomorphic to the commutator superalgebra A(-s) for a simple binary (-1,1) superalgebra A.

Group algebras of torsion groups and Lie nilpotence

Let * be an involution of a group algebra FG induced by an involution of the group G. For char F not equal 2, we classify the torsion groups G with no elements of order 2 whose Lie algebra of *-skew elements is nilpotent.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

Solução da equação advectivo-difusiva utilizando regras para manipulação de exponenciais de operadores diferenciais e simetrias de Lie : aplicações em engenharia ambiental

Vários métodos analíticos, numéricos e híbridos podem ser utilizados na solução de problemas de difusão e difusão-advecção. O objetivo deste trabalho é apresentar dois métodos analíticos para obtenção de soluções em forma fechada da equação advectivo-difusiva em coordenadas cartesianas que descreve problemas de dispersão de poluentes na água e na atmosfera. Um deles é baseado em regras de manipulação de exponenciais de operadores diferenciais, e o outro consiste na aplicação de simetrias de Lie admitidas por uma equação diferencial parcial linear. Desenvolvem-se regras para manipulação de exponenciais de operadores diferenciais de segunda ordem com coeficientes constantes e para operadores advectivo-difusivos. Nos casos em que essas regras não podem ser aplicadas utiliza-se uma formulação para a obtenção de simetrias de Lie, admitidas por uma equação diferencial, via mapeamento. Define-se um operador diferencial com a propriedade de transformar soluções analíticas de uma dada equação diferencial em novas soluções analíticas da mesma equação. Nas aplicações referentes à dispersão de poluentes na água, resolve-se a equação advectivo-difusiva bidimensional com coeficientes variáveis, realizando uma mudança de variáveis de modo a reescrevê-la em termos do potencial velocidade e da função corrente correspondentes ao respectivo escoamento potencial, estendendo a solução para domínios de contornos arbitrários Na aplicação referente ao problema de dispersão de poluentes na atmosfera, realiza-se uma mudança de variáveis de modo a obter uma equação diferencial parcial com coeficientes constantes na qual se possam aplicar as regras de manipulação de exponenciais de operadores diferenciais. Os resultados numéricos obtidos são comparados com dados disponíveis na literatura. Diversas vantagens da aplicação das formulações apresentadas podem ser citadas, a saber, o aumento da velocidade de processamento, permitindo a obtenção de solução em tempo real; a redução da quantidade de memória requerida na realização de operações necessárias para a obtenção da solução analítica; a possibilidade de dispensar a discretização do domínio em algumas situações.

Ribeira, técnica versus natureza: transformações em prol de um projeto de modernização (1860-1932)

The necessity of the insertion of the capital of Rio Grande do Norte in the world-wide commercial scene and its claim as the seat of political power, in ends of nineteenth and beginning of twentieth century, determined the direction of urban interventions undertaken by government to restructure the city. In that matter, there were several actions of improvements and embellishment in Natal, which had, as a starting point, the adequacy works of the port, located in the Ribeira quarter, with the aim of ending the physical isolation that reinforced its economic stagnation. Besides the problems faced in the opening bar of the Potengi River, and would complement the required improvements, other barriers demonstrate the tension established between the physic-geographic field and the man: the flooded and slope which connected Cidade Alta and Ribeira the first two quarters of the city.The execution of these works demanded knowledge whose domain and application it was for engineering. But, how the actions done for the engineers, in sense to transform natural areas into constructed spaces made possible the intentional conformation of the quarter of the Ribeira in a commercial and politician-administrative center, in the middle of the XIX century and beginning of the XX? Understand, therefore, the employment effects of technology on the physical-geographical Ribeira, is the objective of this work that uses theoretical and methodological procedures of Urban Environmental History, by analyzing the relationship between the environment and the man, mediated by knowledge and use of technologies. The documental research was used, as primary sources, the Messages of the Provincial Assembly Government that later became the Legislative Assembly of Rio Grande do Norte reports and articles on specialized publications, in addition to local newspapers. The work is structured in five chapters. First, some comments about Urban Environmental History (Chapter 1) supplemented with analysis of the conceptual construction of nature in the Contemporary Era and its application in the city (chapter 02), the following chapters (03 and 04) deal with the rise of engineers as a active group in the Brazilian government frameworks and their vision about the nature inside the urban environment and it is studied how the professional technicians dealt with the improvement work of the harbor and in the shock with the natural forces. Other works that would complement this "project" of modernization and had had natural obstacles to be removed the Ribeira flood and slope constitute the subject of the fifth chapter. Finally, some final considerations retake the initial discussions aiming an association between the technique and the nature as junction elements inside the process of constitution of a Modern Natal

Helminthological screening of free-ranging grey brocket deer Mazama gouazoubira Fischer, 1817 (Cervidae: Odocoileini) from Brazilian Pantanal wetlands, with considerations on Pygarginema verrucosa (Molin, 1860) Kadenatzii, 1948 (Spirocercidae: Ascaropsinae)

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

Leptospira spp. antibodies in captive coatis (Nasua nasua Storr, 1780) (Carnivora: Procyonidae)

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

Predação de morcegos (Phyllostomidae) pela cuíca d’água Chironectes minimus (Zimmermann, 1780) (Didelphimorphia, Didelphidae) e uma breve revisão de predação em Chiroptera

Bats are predated for some of vertebrates and invertebrates. Some opportunistic species preys these animals' prisoners in nests during procedures of capture in field. This study records the predation of Carollia perspicillata (Linnaeus, 1758) and Sturnira lilium (E. Geoffroy, 1810) for Chironectes minimus (Zimmermann, 1780) on riparian forest of the brook Talhadinho belonging of the São Paulo, São Paulo, Southeast Brazil, and also presents a lifting previous of mammalian what they present the same one behavior opportunistic predatory, discussing measures simple to avoid this type of predation.