Covering Dimension of C*-Algebras and 2-Coloured Classification

Peer reviewed

Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.

Influence of cephalometric characteristics on the occlusal success rate of Class II malocclusions treated with 2-and 4-premolar extraction protocols

Introduction: The objectives of this investigation were to compare the initial cephalometric characteristics of complete Class II Division 1 malocclusions treated with 2 or 4 premolar extractions and to verify their influence on the occlusal success rate of these treatment protocols. Methods: A sample of 98 records from patients with complete Class II Division 1 malocclusion was divided into 2 groups with the following characteristics: group 1 consisted of 55 patients treated with 2 maxillary first premolar extractions at an initial mean age of 13.07 years; group 2 included 43 patients treated with 4 premolar extractions, with an initial mean age of 12.92 years. Initial and final occlusal statuses were evaluated on dental casts with Grainger`s treatment priority index (TPI), and the initial cephalometric characteristics were obtained from the pretreatment cephalograms. The initial cephalometric characteristics and the initial and final occlusal statuses of the groups were compared with the t test. A multiple regression analysis was used to evaluate the influence of all variables in the final TPI. Results: The 2-premolar extraction protocol provided a statistically smaller TPI and consequently a better occlusal success rate than the 4-premolar extraction protocol. The 4-premolar extraction group had statistically smaller apical base lengths, more vertical facial growth patterns, and greater hard- and soft-tissue convexities at pretreatment than the 2-premolar extraction group. However, the multiple regression analysis showed that only the extraction protocol was significantly associated with the final occlusal status. Conclusions: The initial cephalometric characteristics of the groups did not influence the occlusal success rate of these 2 treatment protocols.

Application of the maximum entropy method to the (2 + 1)D four-fermion model

We investigate spectral functions extracted using the maximum entropy method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma, and massive pseudoscalar meson; our results confirm the Goldstone nature of the π and permit an estimate of the meson binding energy. We have, however, seen no signal of σ→ππ decay as the chiral limit is approached. In the symmetric phase we observe a resonance of nonzero width in qualitative agreement with analytic expectations; in addition the ultraviolet behavior of the spectral functions is consistent with the large nonperturbative anomalous dimension for fermion composite operators expected in this model.

Contributo para a validação de uma escala pediátrica, Peabody Developmental Motor Scale-2 (versão portuguesa)

Mestrado em Fisioterapia

Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics

We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a Cr diffeomorphism f of a surface, are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.

The impact of banks dimension on profitability, sustainability and efficiency: An analysis for the Iberian financial system

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics

Fractal Dimension in Quantifying Experimental-Pulmonary-Hypertension-Induced Cardiac Dysfunction in Rats

Abstract Background: Right-sided heart failure has high morbidity and mortality, and may be caused by pulmonary arterial hypertension. Fractal dimension is a differentiated and innovative method used in histological evaluations that allows the characterization of irregular and complex structures and the quantification of structural tissue changes. Objective: To assess the use of fractal dimension in cardiomyocytes of rats with monocrotaline-induced pulmonary arterial hypertension, in addition to providing histological and functional analysis. Methods: Male Wistar rats were divided into 2 groups: control (C; n = 8) and monocrotaline-induced pulmonary arterial hypertension (M; n = 8). Five weeks after pulmonary arterial hypertension induction with monocrotaline, echocardiography was performed and the animals were euthanized. The heart was dissected, the ventricles weighed to assess anatomical parameters, and histological slides were prepared and stained with hematoxylin/eosin for fractal dimension analysis, performed using box-counting method. Data normality was tested (Shapiro-Wilk test), and the groups were compared with non-paired Student t test or Mann Whitney test (p < 0.05). Results: Higher fractal dimension values were observed in group M as compared to group C (1.39 ± 0.05 vs. 1.37 ± 0.04; p < 0.05). Echocardiography showed lower pulmonary artery flow velocity, pulmonary acceleration time and ejection time values in group M, suggesting function worsening in those animals. Conclusion: The changes observed confirm pulmonary-arterial-hypertension-induced cardiac dysfunction, and point to fractal dimension as an effective method to evaluate cardiac morphological changes induced by ventricular dysfunction.

Hopf bifurcation for degenerate singular points of multiplicity 2n-1 in dimension 3

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The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-Algebras

We prove that the Cuntz semigroup is recovered functorially from the Elliott invariant for a large class of C¤-algebras. In particular, our results apply to the largest class of simple C¤-algebras for which K-theoretic classification can be hoped for. This work has three significant consequences. First, it provides new conceptual insight into Elliott's classification program, proving that the usual form of the Elliott conjecture is equivalent, among Z-stable algebras, to a conjecture which is in general substantially weaker and for which there are no known counterexamples. Second and third, it resolves, for the class of algebras above, two conjectures of Blackadar and Handelman concerning the basic structure of dimension functions on C¤-algebras. We also prove in passing that the Kuntz-Pedersen semigroup is recovered functorially from the Elliott invariant for all simple unital C¤-algebras of interest.

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.

Monopoles in arbitrary dimension

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The normative dimension of social life from a second-person perspective

This thesis argues that insofar as we want to account for the normative dimension of social life, we must be careful to avoid construing that normative dimension in such a way as to exclude that which the second-person perspective reveals is important to social life and our ability to participate in it.¦The second-person perspective reveals that social life ought to be understood as a mix or balance of the regular and the irregular, where, in addition, those one interacts with are always to some extent experienced as other in a way that is neither immediately, nor perhaps ultimately, understandable. For persons to be able to participate in social life, conceived of in this way, they must have abilities that allow them to be, to some extent, hesitant and tentative in their relations with others, and thus tolerant of ambiguity, uncertainty and unpredictability, and responsive to and capable of learning from the otherness of others in the course of interacting with them.¦Incorporating the second-person perspective means we have to make some changes to the way we think about the normative in general, and the normative dimension of social life in particular. It does not mean giving up on the distinction between the normative and the regular - that continues to be fundamentally important but it does mean not excluding, as part of social life and as worthy of explanation, all that which is irregular. A radical way of putting it would be to say that there must be a sense in which the irregular is part of the normative. A less radical way, and the way adopted by this thesis, is to say that any account of the normative dimension of social life must not be such as to exclude the importance of irregularity from social life. This will mean 1) not characterising conventions, norms and rules as determinants of appropriateness and inappropriateness; 2) not thinking of them as necessary; 3) not thinking of them as necessarily governing minds; and 4) not thinking of them as necessarily shared.¦-¦L'argument principal de la thèse est que, pour rendre compte de la dimension normative de la vie sociale, il faut veiller à ne pas exclure la perspective de la deuxième personne - une perspective importante pour comprendre la vie sociale et la capacité requise pour y participer.¦Cette perspective nous permet d'imaginer la vie sociale comme un mélange ou un équilibre entre le régulier et l'irrégulier, l'interaction entre des individus pouvant être appréhendée comme l'expérience de chaque personne avec «l'autre» d'une manière qui n'est pas immédiatement compréhensible, et qui ne peut pas, peut-être, être ultimement comprise. Pour participer à la vie sociale, l'on doit avoir la capacité de rester hésitant et «réactif» dans ses relations avec les autres, de rester ouvert à leur altérité et de tolérer l'ambiguïté, l'incertitude et l'imprévisibilité des interactions sociales.¦Adopter une perspective «à la deuxième personne» conduit à une autre manière de penser la normativité en général, et la dimension normative de la vie sociale en particulier. Cela ne veut pas dire qu'il faut abandonner la distinction entre le normatif et le régulier - une distinction qui garde une importance fondamentale - mais qu'il faut reconnaître l'irrégulier comme faisant partie de la vie sociale et comme étant digne, en tant que tel, d'être expliqué. Une conception radicale pourrait même concevoir l'irrégulier comme faisant partie intégrante de la normativité. Une approche moins radicale, qui est celle adoptée dans cette thèse, est de dire que tout compte-rendu de la dimension normative de la vie sociale doit prendre en considération l'importance de l'irrégularité dans la vie sociale. Une telle approche implique que les conventions, normes et règles (1) ne déterminent pas ce qui est approprié ou inapproprié; (2) ne sont pas toujours nécessaires ; (3) ne gouvernent pas le fonctionnement de l'esprit ; et (4) ne sont pas nécessairement partagées.