Semigrupos numéricos

Um semigrupo numérico é um submonoide de (N, +) tal que o seu complementar em N é finito. Neste trabalho estudamos alguns invariantes de um semigrupo numérico S tais como: multiplicidade, dimensão de imersão, número de Frobenius, falhas e conjunto Apéry de S. Caracterizamos uma apresentação minimal para um semigrupo numérico S e descrevemos um método algorítmico para determinar esta apresentação. Definimos um semigrupo numérico irredutível como um semigrupo numérico que não pode ser expresso como intersecção de dois semigrupos numéricos que o contenham propriamente. A finalizar este trabalho, estudamos os semigrupos numéricos irredutíveis e obtemos a decomposição de um semigrupo numérico em irredutíveis. ABSTRACT: A numerical semigroup is a submonoid of (N, +) such that its complement of N is finite. ln this work we study some invariants of a numerical semigroup S such as: multiplicity, embedding dimension, Frobenius number, gaps and Apéry set of S. We characterize a minimal presentation of a numerical semigroup S and describe an algorithmic procedure which allows us to compute a minimal presentation of S. We define an irreducible numerical semigroup as a numerical semigroup that cannot be expressed as the intersection of two numerical semigroups properly containing it. Concluding this work, we study and characterize irreducible numerical semigroups, and describe methods for computing decompositions of a numerical semigroup into irreducible numerical semigroups.

The Worldhood of the Cinematic Image

A close analysis of the specifically cinematographic procedure in Akira Kurosawa’s ‘Dream’ Crows reveals it as an articulated and insightful philosophical statement, endowed with general relevance concerning ‘natural’ perception, phenomenological Erlebnis, mechanical image and aesthetic rapture. The antagonism between the Benjaminian lineage of a mechanical irreducibility of the cinematic image to anthropocentric categories, and the Cartesian tradition of a film-philosophy still relying on the equally irreducible structure of the intentional act, be it the one of a deeply embodied and enworlded counsciousness, in accounting for the essential structure of film and spectator (and their relation), i.e., the antagonism between the decentering primacy of the image and the self-centered primacy of perception, cannot be settled through a simple Phenomenological shift from occularcentric, intentional counsciousness to its embodyment ‘in-the-world’ as yet another carrier of intentionality. Still it remains to be explained what is it in the mechanical image that is able to so deeply affect the human flesh, and conversely, to what features in the human bodily experience is its mechanical other, the fascinating image, so successfuly adressing? It should be expected from the anti-Cartesianism of both the early and the late Merleau-Ponty the textual support for an approach to the essential condition of passivity in movie watching, that would be convergent with Benjamin. The Chapter ‘Le sentir’, in Phénoménologie de la perception, will offer us the proper guide to elucidate what we are already perceiving and conceiving in Kurosawa’s film, where the ex-static phenomenological body of the aesthetical contemplator ‘enters the frame’ like the Benjaminian surgeon enters the body and like the painter - and always already like our deepest level of ‘sensing’, previously to any act of cousciousness - ‘just looses himself in the scene before him’. The Polichinello secret of cinema watching is nonetheless too evident to be seen, and that is where Phenomenological description and reduction are still required.