Curso de matematica para economistas, Capitulos I e II: funções, algebra linear e aplicações

Os autores objetivam, com este trabalho preliminar, bem como com aqueles que lhe darão continuidade, na sequência de composição de um livro de matemática para economistas, registrar as suas experiências ao longo dos últimos anos ministrando cadeiras de matemática nos cursos de pós-graduação em economia da Fundação Getúlio Vargas, da UFF (Universidade Federal Fluminense) e da PUC-RJ. Reveste-se de constante repetição em tais cursos a discussão sobre que pontos abordar, bem como com qual grau de profundidade, e em que ordem. É neste sentido que os autores esperam, com a sequência didática que aqui se inicia, trazer alguma contribuição para o assunto.

Ideais separatistas e autonomia política: depoimentos sobre a criação do estado do Tocantins

O presente trabalho analisa a criação do estado do Tocantins, através da divisão doestado de Goiás. Essa análise tem relação com as articulações políticas bem como ohistórico de atividades desenvolvidas para a divisão da região. Os líderes separatistas emsuas respectivas épocas como Lysias Rodrigues, Feliciano Machado Braga e José WilsonSiqueira Campos são estudados de maneira mais enfática levando-se em conta que suasações tiveram relevância e conhecimento em âmbito nacional. A questão da Marcha paraOeste através da intenção de ocupar os espaços vazios do sertão brasileiro se desenvolvecomo tema de extrema importância para o entendimento do trabalho. Como marco dessa"interiorização", o estudo das cidades-capitais projetadas como forma de introduzir amodernidade nos sertões também é levantada. Sendo assim, Goiânia, Brasília e Palmasaparecem como instrumentos para a formação da identidade de um povo. Com base nisso, asentrevistas feitas com representantes da região do Tocantins ganham valor principal por setratar de uma espécie de testemunhas da história.

Derivações de Shamsuddin simples de K[X1,...,Xn] e ideais maximais cíclicos à esquerda da álgebra de Weyl An(k)

Seja K um corpo de característica zero e seja An(K) a n-ésima Álgebra de Weyl sobre K. Neste trabalho, discutimos a existência de ideais maximais à esquerda de An (K) gerados por operadores de ordem 1. Primeiramente, estabelecemos uma relação entre derivações simples de K[X1: ..., Xn] e ideais principais maximais à esquerda de Ân(K). Para n> 2, caracterizamos as derivações de Shamsuddin de K[X1, ..., Xn] que são simples. Depois, mostrámos que se d é uma derivação de Shamsuddin simples de K[X1, ..., Xn], então existe 9 E K[X1, ..., Xn] tal que Ân.(d+g) é um ideal maximal principal à esquerda.

Ideais primos e ideais fechados em anéis de polinômios

Este trabalho tem por objetivo estudar os ideais primos do anel de polinômios R[X], com R um anel primo, não necessariamente comutativo. Para tanto, introduzimos o conceito de ideais principais fechados em R[X], que permite caracterizar os ideais primos como contração de ideais de Q[X] sendo definidos por polinômios mônicos irredutíveis de C[X], onde Q é o anel de quocientes µa direita de Martindale de R e C é o centro de Q, que é um corpo.

Ativismo judicial e materialização das políticas públicas infanto-juvenis na constituição da república: Fixação de planos ideais de atuação para os atores do Sistema de Garantia de Direitos (SGD)

The research arose from the necessity of showing ways to be followed by the actors of the System Guaranteeing Rights of the Child and Adolescent (SGD), regarding the implementation of rights for young people, because the legislation in force in Brazil is currently considered a model around the world and, paradoxically, the fundamental rights of children and adolescents are not met, even with the constitutionally guaranteed priority. Thus, the study investigates the fundamentality rights for young people, enshrined in the Constitution of the Republic, as well as the ways of effectiveness of these rights through the actions of actors of the System Guaranteeing Rights, especially the judiciary. Focusing realized, studying theories of fundamental rights, especially Structuring a Theory of Law (Strukturiende Rechtslehre), Friedrich Müller, who emphasizes the need for analysis of social reality in the application of the rule of law. Study also the public budget and public policies concerning children and adolescents, with emphasis on preparation of budget laws and the process of discussion, deliberation, choice and implementation of public policies for children and teenagers. It then presents the typical functions of the members of System Guaranteeing Rights, as well as prepare a plan for optimum performance for each of the actors, with emphasis on analysis of the implementation of public policies at the municipal level. Finally, it analyzes the theory of separation of three powers, and discusses the positive and negative factors for judicial intervention, concluding that the Courts can consider the action activist, from finding the omission of the Executive and legislative branches, as regards the implementation of the rights of children and adolescents, as well as the rights of children and young people are not realized in most cases, due to the omission of actors of the System Guaranteeing Rights

Ideais formativos de homem da emissora de Educação Rural de Caicó (Rio Grande do Norte, 1963-1978)

Under the aegis of the third diocese bishop of Caicó, Dom Manuel Tavares de Araújo, the Broadcasting Station of Rural Education of that city was founded, in May 1 s" 1963 with the ideal of being then an educational city, preferentially for youths and adults, rural meu and women of the arca of Seridó in Rio Grande do Norte state. In the year of its 40th birthday (2003), we began the investigation of that radio station choosing as study object its educational and formative programming, in the inc1usion of the first fifteen years of its existence (1963-1978), period that reaches the official inauguration of the Radio Station and the end of the bishopric of its fOllllder as Bishop of Caicó. Elucidating and showing Man's formative ideaIs longed by that Catholic educational broadcasting station, underlying to its radiophonic programming, such as the idealization for it reached, is the objective of this Doctorate work. It was considered pertinent to discover the guidelines that historically have permeated the Social Doçtrine of the Catholic Church addressing its aggiornamento, especially in what concerns to the employment of the modern ways of communication for the distance with the aim of evangelizing and educating. In arder to understand the ideaIs of the investigated educational Radio, we have delimited the research to the thematic Catholic Church, means of social communication and base education. In face of the study object and the aim to be reached it was appealed, methodologically, to the notion of cultural action present in Certeau (1995), and to the understanding of educational formation backgrounded fIam the modern thinkers that discuss it. Such frame references have allowed us to analyze in a wider spectrum tl)e programming broadcasted on the air by the sound wavys of that educ(itional Çatholic Radio, as well as, the very acts of cultural idealizations that has orientated it in its foundations. The thesis here defended is that. the Radio, at procJaiming itself as a broadcasting station of rural education directed preferably to the rural sertanejo countrymen, without neglecting its admitted ends, has surpassed them in its overall range. It was identified an articulate approach of its programmatic modules with the guid,elines emanateq from the Catholic Teaching about the use of the. means of social communication. At conceiving, establishin,g and executing an ec1ectic programmatic and div,ersified grating, the Rural Radio of Caicó has transcended to a strict human-Christian formation to request the development of the human, spiritual and cQrporaldimensions, jointly. With suchprogramming, it addressed to the seridoenses as real meu and women inserted in the "sertanej.o" environment with effective structural and existential problems of alI types, induding the hunger, the thirst, the syndical organization, the cQoperativism, the colIective modero work and the absence of universalizing school education. Its radiophonic transmissions, I}lled by the demands of an enlarged, open, dialogic and responsible communication, wheneIllbracing dedicated modules to religious and catechetical emissions, to the entertainment, to the radiojoumalism, to the country root culture, and to the school education of b se for the modality of the School and of the radiophonic classes, subsumed to ideaIs that longed for the formation of a multifaceted and pluridimensional sertanejo Man; of men and women that, without abjuring the Catholicism, were able to understand, to dialogued and to live together with the general demands of a society in progressive mutation, whose economical, social, cultural and educational demands it IDade themselves to be felt through the sertão potiguar of the Serido region, equal way of the intemationalized world

Some experiments with high order compact methods using a computer algebra software - Part I

We consider a procedure for obtaining a compact fourth order method to the steady 2D Navier-Stokes equations in the streamfunction formulation using the computer algebra system Maple. The resulting code is short and from it we obtain the Fortran program for the method. To test the procedure we have solved many cavity-type problems which include one with an analytical solution and the results are compared with results obtained by second order central differences to moderate Reynolds numbers. (c) 2005 Elsevier B.V. All rights reserved.

Some experiments with high order compact methods using a computer algebra software - Part II (non-uniform grid)

We generalize a procedure proposed by Mancera and Hunt [P.F.A. Mancera, R. Hunt, Some experiments with high order compact methods using a computer algebra software-Part 1, Appl. Math. Comput., in press, doi: 10.1016/j.amc.2005.05.015] for obtaining a compact fourth-order method to the steady 2D Navier-Stokes equations in the streamfunction formulation-vorticity using the computer algebra system Maple, which includes conformal mappings and non-uniform grids. To analyse the procedure we have solved a constricted stepped channel problem, where a fine grid is placed near the re-entrant corner by transformation of the independent variables. (c) 2006 Elsevier B.V. All rights reserved.

Deformations of N=2 superconformal algebra and supersymmetric two-component Camassa-Holm equation

This paper is concerned with a link between central extensions of N = 2 superconformal algebra and a supersymmetric two-component generalization of the Camassa-Holm equation. Deformations of superconformal algebra give rise to two compatible bracket structures. One of the bracket structures is derived from the central extension and admits a momentum operator which agrees with the Sobolev norm of a co-adjoint orbit element. The momentum operator induces, via Lenard relations, a chain of conserved Hamiltonians of the resulting supersymmetric Camassa-Holm hierarchy.

Mass generation from Lie algebra extensions

Applied to the electroweak interactions, the theory of Lie algebra extensions suggests a mechanism by which the boson masses are generated without resource to spontaneous symmetry breaking. It starts from a gauge theory without any additional scalar field. All the couplings predicted by the Weinberg-Salam theory are present, and a few others which are nevertheless consistent within the model.

Lorentz-violating dilatations in momentum space and some extensions on nonlinear actions of Lorentz-algebra-preserving systems

We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the corresponding deformed symmetries are presented with particular emphasis on deformed dilatation transformations. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided in order to preserve the Lorentz algebra. Two distinct cases are considered: a deformed dilatation transformation with a spacelike preferred direction and a very special relativity embedding with a lightlike preferred direction. In both analysis we consider the possibility of introducing quantum deformations of the corresponding symmetries such that the spacetime coordinates can be reconstructed and the particular form of the real space-momentum commutator remains covariant. Eventually feasible experiments, for which the nonlinear Lorentz dilatation effects here pointed out may be detectable, are suggested.

Discretizing the deformation parameter in the su(q)(2) quantum algebra

Inspired in recent works of Biedenham [1, 2] on the realization of the q-algebra su(q)(2), We show in this note that the condition [2j + 1](q) = N-q(j) = integer, implies the discretization of the deformation parameter alpha, where q = e(alpha). This discretization replaces the continuum associated to ct by an infinite sequence alpha(1), alpha(2), alpha(3),..., obtained for the values of j, which label the irreps of su(q)(2). The algebraic properties of N-q(j) are discussed in some detail, including its role as a trace, which conducts to the Clebsch-Gordan series for the direct product of irreps. The consequences of this process of discretization are discussed and its possible applications are pointed out. Although not a necessary one, the present prescription is valuable due to its algebraic simplicity especially in the regime of appreciable values of alpha.

Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CURRENT-ALGEBRA OF SUPER WZNW MODELS

We derive the current algebra of supersymmetric principal chiral models with a Wess-Zumino term. At the critical point one obtains two commuting super-affine Lie algebras as expected, but, in general, them are intertwining fields connecting both right and left sectors, analogously to the bosonic case. Moreover, in the present supersymmetric extension we have a quadratic algebra, rather than an affine Lie algebra, due to the mixing between bosonic and fermionic fields; the purely fermionic sector displays an affine Lie algebra as well.