Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

On the critical periods of perturbed isochronous centers

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A relative double commutant theorem for hereditary sub-C*-algebras

We prove a double commutant theorem for hereditary subalgebras of a large class of C*-algebras, partially resolving a problem posed by Pedersen[8]. Double commutant theorems originated with von Neumann, whose seminal result evolved into an entire field now called von Neumann algebra theory. Voiculescu proved a C*-algebraic double commutant theorem for separable subalgebras of the Calkin algebra. We prove a similar result for hereditary subalgebras which holds for arbitrary corona C*-algebras. (It is not clear how generally Voiculescu's double commutant theorem holds.)

Maximal C*-algebras of quotients and injective envelopes of C*-algebras

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The ‘Global Dimension’ of Contemporary Politics. An Argument for Taking ‘Global’ Seriously

Recent years have seen a striking proliferation of the term ‘global’ in public and political discourse. The popularity of the term is a manifestation of the fact that there is a widespread notion that contemporary social reality is ‘global’. The acknowledgment of this notion has important political implications and raises questions about the role played by the idea of the ‘global’ in policy making. These questions, in turn, expose even more fundamental issues about whether the term ‘global’ indicates a difference in kind, even an ontological shift, and, if so, how to approach it. This paper argues that the notion of ‘global’, in other words the ‘global dimension’, is a significant aspect of contemporary politics that needs to be investigated. The paper argues that in the globalization discourse of International Studies ‘global’ is ‘naturalized’, which means that it is taken for granted and assumed to be self-evident. The term ‘global’ is used mainly in a descriptive way and subsumed under the rubric of ‘globalization’. ‘Global’ tends to be equated with transnational and/or world-wide; hence, it addresses quantitative differences in degree but not (alleged) differences in kind. In order to advance our understanding of contemporary politics, ‘global’ needs to be taken seriously. This means, firstly, to understand and to conceptualize ‘global’ as a social category; and, secondly, to uncover ‘global’ as a ‘naturalized’ concept in the Political and International Studies strand of the globalization discourse in order to rescue it for innovative new approaches in the investigation of contemporary politics. In order to do so, the paper suggests adopting a strong linguistic approach starting with the analysis of the word ‘global’. Based on insights from post-structuralism as well as cognitive and general constructivist perspectives it argues that a frame-based corpus linguistic analysis offers the possibility of investigating the collective/social meaning(s) of global in order to operationalize them for the analysis of the ‘global dimension’ of contemporary politics.

A Computable general equilibrium approach to hypothetical extractions and missing links

Identifying key sectors or key locations in an interconnected economy is of paramount importance for improving policy planning and directing economic strategy. Hence the relevance of categorizing them and hence the corresponding need of evaluating their potential synergies in terms of their global economic thrust. We explain in this paper that standard measures based on gross outputs do not and cannot capture the relevant impact due to self- imposed modeling limitations. In fact, common gross output measures will be systematically downward biased. We argue that an economy wide Computable General Equilibrium (CGE) approach provides a modeling platform that overcomes these limitations since it provides (i) a more comprehensive measure of linkages and (ii) an alternate way of accounting for links' relevance that is in consonance with standard macromagnitudes in the National Income and Product Accounts.

L’experiència dels darrers vint anys: una anàlisi comparativa de les cerimònies olímpiques

Article publicat a Papers: revista de sociologia (no. 38, 1992), que presenta una reflexió sobre el significat cultural dels Jocs Olímpics i compara les cerimònies de Los Angeles'84 i Seül'88 en perspectiva als Jocs de Barcelona'92.

Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.

On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities

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Variational inequalities in Hilbert spaces with measures and optimal stopping problems

We study the existence theory for parabolic variational inequalities in weighted L2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coeficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.

Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

We give sufficient conditions for existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.

Orthogonal systems in finite grahps

To a finite graph there corresponds a free partially commutative group: with the given graph as commutation graph. In this paper we construct an orthogonality theory for graphs and their corresponding free partially commutative groups. The theory developed here provides tools for the study of the structure of partially commutative groups, their universal theory and automorphism groups. In particular the theory is applied in this paper to the centraliser lattice of such groups.

Contribució de Pietro Mengoli al concepte de límit a través d'una teoria de les quasi proporcions

El treball de recerca que aquí es presenta és l’estudi dels tres primers "elementa" de la "Geometriae Speciosae Elementa" (Bolonya, 1659) de Pietro Mengoli (1625-1686), que fou possiblement el deixeble més original de Bonaventura Cavalieri (1598-1647). En aquesta obra Mengoli desenvolupa un nou mètode per calcular quadratures utilitzant una teoria numèrica anomenada de “quasi proporcions”. Mengoli fonamenta les quasi proporcions en la teoria de proporcions del llibre cinquè dels "Elements" d’Euclides, a la qual hi afegeix unes nocions originals: raó “quasi nul•la”, “quasi infinita” i “quasi un nombre”. Una exhaustiva anàlisi d’aquesta teoria demostra l’originalitat de l’obra de Mengoli tant pel que fa a la seva forma d’exposició com pel que fa al seu contingut.

Músiques del món: anàlisi per a la selecció i l'establiment de criteris per un repertori a l'escola

Aquest treball s'emmarca dins un projecte que planteja la incorporació de les audicions de músiques del món a les aules d’infantil i primària. Aquest projecte consta de diferents fases; la que aquí s’exposa comença situant el concepte de músiques del món i l’aportació que comporta la seva inclusió en el currículum, es presenta l’elaboració d'una selecció d'obres juntament amb el procés que ha comportat -es parteix de 528 peces, s'amplia amb 106 a la tercera etapa del procés, per arribar a una selecció final de 19 audicions- i es defineixen els criteris que s'han anat delimitant al llarg del procés per fer aquesta selecció: vivencials, musicals, geogràfics i didàctics

La vigència dels valors olímpics en el discurs periodístic: anàlisi del tractament informatiu dels Jocs Olímpics d’Atlanta a “El Periódico de Catalunya”

Document publicat com a part de la col·lecció Working Papers, que es va presentar a l’Assignatura Campus de la Universitat Autònoma de Barcelona (UAB) “Esport, Olimpisme i Cultura Contemporània”, durant el curs 1996/1997. Amb aquesta recerca l’autor pretén descobrir el sistema de valors que es difon a la premsa, concretament a &i&El Periódico de Catalunya&/i&, per analitzar el grau en què els mitjans de comunicació propicien o neguen els valors olímpics que indica el mateix Comitè Olímpic Internacional (COI) en la seva Carta Olímpica.