Nonassociative structures and 3-Sasakian homogeneous manifolds

The 3-Sasakian homogeneous spaces are certain contact manifolds whose geometric structure is very well codified in Lie theoretical terms. This fact can be used to find interesting invariant affine connections, with nice properties or special holonomies. The more fruitful results arise in the particular case of the 7-dimensional 3-Sasakian homogeneous manifolds, that is, the corresponding sphere and the Aloff-Wallach space, although the target is to find a good connection independently of the dimension. A nonassociative structure related to Lie algebras appears through this study, that one of symplectic triple system. In particular the curvature of an affine connection can be written by means of the binary and ternary products in this triple system. Also, for some distinguished connections, the holonomy algebra can be described in a unified form, what helps to find a suitable candidate for a best affine connection adapted to the geometry of the 3-Sasakian manifold, which necessarily will have nonzero torsion.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Gradings on Lie Algebras: main results and tools

The aim of this talk is not to provide an explicit and complete classification of the gradings on simple finite-dimensional Lie algebras, complex and real, simply because the topic is too wide. Thus, we have selected some of the keys of the classification up to equivalence, with emphasis on the complex field case.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Octonions and exceptional Lie algebras

It is well known that octonions (both real and complex) are very involved in the structure of the exceptional Lie algebras. We will explore several aspects of this relationship: how octonions provide models of the exceptional Lie algebras, coordinatizating them by means of structurable algebras. This plays an important role in the description of their inner ideals, and, in turn, these appear naturally in certain point-line geometries. In general, these constructions are related to gradings over the integers. We will use also the octonions and related structures to approach gradings on exceptional Lie algebras but over finite groups. Contrary to the situation above, these gradings are related to semisimple elements, and the nice symmetry behind the constructions is reflected in the corresponding Lie groups and in Particle Physics.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Option Valuation As an Expectation in The Complex Domain: The Black-Scholes Case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call.european call, fourier transform, generalized function, laplace transform, error function.

Term structure of interest rate. european financial integration.

In this paper we estimate, analyze and compare the term structures of interest rate in six different countries, during the period 1992-2004. We apply Nelson and Siegel model to obtain them with a weekly frequency. Four European Monetary Union countries, Spain, France, Germany and Italy are included. UK is also included as a European country, but not integrated in the Monetary Union. Finally US completes the analysis. The goal is to determine the differences in the shape of curves between these countries. Likewise, we can determinate the most usual term structure shapes that appear in every country.Term structure of interest rate, parsimonious models, level parameter, slope parameter, European interest rate.

A utopia europeia em O Brasil: país do futuro de Zweig

The publication in 1941 of Stefan Zweig’s Brazil. A Land of the Future (Brasilien. Ein Land der Zukunft) was met both with great enthusiasm and harsh criticisms. Many reviewers thought that Zweig’s view of the country was too exotic, naive, idealistic, utopian, and even the result of the propaganda efforts carried out by the Vargas administration. In an attempt to understand and bridge the gap between Zweig’s idea of Brazil and the country’s «reality», this article analyzes the text hand in hand with Zweig’s memoirs and other of his non-fiction works from the perspective of his utopian thinking and ethical commitment to the notions of freedom, peace, cosmopolitanism, tolerance, and common understanding.A publicação em 1941 de Brasil, um país do futuro (Brasilien. Ein Land der Zukunft), de Stefan Zweig, foi recebida com um grande entusiasmo e com as críticas mais duras. Muitos críticos pensaram que a visão que Zweig tinha do país era exótica, ingênua, idealista e utópica demais, refletindo até o resultado dos esforços de propaganda realizados pelo governo Vargas. Na tentativa de compreender e preencher o vazio entre a ideia que Zweig tinha do Brasil e a «realidade» do país, este artigo analisa o texto junto com as memorias de Zweig e outros trabalhos de não-ficção a partir da perspetiva do seu pensamento utópico e do compromisso ético das noções de liberdade, paz, cosmopolitismo, tolerância e entendimento comum

La inocencia de Verena : la querella por el control de la voz en Las bostonianas de Henry James

Las Bostonianas, de Henry James, es una de aquellas piezas literarias cuya naturaleza tiende a la ambigüedad, a la resistencia a las interpretaciones reduccionistas. Hoy en día, la perspectiva de los estudios de género nos permite ir más allá de tales interpretaciones, accediendo al corazón del texto, a aquello que le da coherencia, para poder dar cuenta de sus equívocos más notorios. Así, la primera parte de este artículo está dedicada al análisis del personaje principal de la historia, Verena Tarrant, en cuanto a figura vacía de lo extraordinario y atrapada bajo un sinfín de discursos ideológicos que le dan cuerpo, otorgándole una identidad artificial. En consecuencia, la auténtica Verena queda, paradójicamente, silenciada; su voz, su don, sirve únicamente para expresar los deseos proyectados por los demás personajes. En la segunda parte del artículo, y en un movimiento hacia la esfera de lo público, se lleva a cabo una interpretación alegórica de Verena y de las dinámicas de deseo que giran a su alrededor. Este nuevo nivel de análisis nos lleva a desambiguar el texto, ofreciendo una clave interpretativa del mismo basada en el principio del personaje como representante de una determinada ideología o conjunto de valores. Finalmente, el artículo concluye con la visión de James de una sociedad distópica, vacilante entre dos corrientes ideológicas que están, a su vez, lejos de justificar la realidad a la que aluden.Henry James' The Bostonians is one of those literary works whose nature tends towards ambiguity and resistance to reductionist interpretations. Today, the gender studies' perspective allows us to surpass such interpretations, and to access the text's core -what holds it together- so as to explain its primary opacities. Thus, the first part of this article is dedicated to the analysis of the story's main character, Verena, as a figure void of the extraordinary and trapped in an unending number of ideological discourses which, in turn, shape her as a constructed identity. Consequently, Verena's self is left silenced; paradoxically, her voice, her gift, is exclusively used to communicate the wishes projected by other characters. The second part of the article, which moves from the private to the public sphere, is an attempt to allegorically interpret Verena and the dynamics of desire which surround her. This second level of analysis will facilitate a reading of the text as less ambiguous, offering an interpretative key based on the notion of character as the spokesperson of a given ideology or set of values. Finally, the article concludes with James' vision of a dystopic society, hesitant between two ideological alternatives which are far from justifying the reality to which they refer