Invariant manifolds for singularly perturbed linear functional differential equations

AbstractThe existence of “slow” and “fast” manifolds, and of invariant manifolds approaching the manifold of orbits of the degenerate system, is discussed for singularly perturbed systems of linear retarded functional differential equations (FDE). It is shown that these manifolds exist only in very degenerate situations and, consequently, the geometry of the flow of singularly perturbed ordinary differential equations does not generalize to FDEs

Restrictions on the flows of functional differential equations in neighborhoods of singularities

The paper is a report on the work of Faria and Magalhaes regarding possible restrictions on the flows defined by scalar retarded Functional Differential Equations(FOEs), locally around certain simple singularities, when compared with the possible flows of Ordinary Differential Equations (ODEs) with the same singularities

Democracy and the Body Politic : From Sovereign Power to Indeterminacy

As a political technology, camps materialize the ominous potential of modern democracy understood as sovereign power. Indeed, although one usually associates the massive projects of segregation, reeducation and extermination carried out in and through camps to the totalitarian regimes of the 20th century, the more puzzling truth is that the reasoning justifying them is not incompatible with the concept of popular sovereignty. The popular collective subject in whose name divine-right monarchs were deposed, and whose constituent power brought forth new, more egalitarian political institutions, can also turn out to be a force that closes in on itself and fosters a quest for transparent, homogeneous identity that does not shy away from employing the most ruthless coercive means. In this paper, I turn to Claude Lefort’s concept of indeterminacy as an alternative reading of the modern democratic endeavour that preserves a self-critical awareness of democracy’s ominous side. My contention is that Lefort’s concept proves to be fruitful in two ways. On the one hand, it allows us to grasp why the camp – and, for that matter, the populist strongman – is an ever-present possibility of democratic politics. On the other hand, and most importantly, it equips us with the tools to challenge these sovereigntist drifts from a specifically democratic perspective.Non peer reviewe

Promise and Failure : Nationalism in the Interwar Thought of Carl Schmitt and Eric Voegelin

This article analyses the role played by the concept of nation in the interwar writings of Carl Schmitt (1888-1985) and Eric Voegelin (1901-1985). It contends that, although these conservative thinkers were drawn in different ways to the anti-progressive potential of nationalist ideas, the centre of their political and theoretical horizons in that period is occupied by the problems of political unity and authority. Therefore, their nationalism is fundamentally determined by, and instrumental to, their adherence to a monistic and authoritarian conception of the state. This, in turn, leads them to embrace, though not without some reservations, the solutions put forward by the emergent far-right 'strongmen' to the interwar crisis of liberal democracy. Each author tested in his own way the porous borders between conservatism, nationalism, and fascism - a topic whose scholarly and political relevance is far from being exhausted.Peer reviewe

The Legitimacy of Modern Democracy

By re-examining the political thought of Max Weber, Carl Schmitt and Hans Kelsen, this book offers a reflection on the nature of modern democracy and the question of its legitimacy. Pedro T. Magalhães shows that present-day elitist, populist and pluralist accounts of democracy owe, in diverse and often complicated ways, an intellectual debt to the interwar era, German-speaking, scholarly and political controversies on the problem(s) of modern democracy. A discussion of Weber’s ambivalent diagnosis of modernity and his elitist views on democracy, as they were elaborated especially in the 1910s, sets the groundwork for the study. Against that backdrop, Schmitt’s interwar political thought is interpreted as a form of neo-authoritarian populism, whereas Kelsen evinces robust, though not entirely unproblematic, pluralist consequences. In the conclusion, the author draws on Claude Lefort’s concept of indeterminacy to sketch a potentially more fruitful way than can be gleaned from the interwar German discussions of conceiving the nexus between the elitist, populist and pluralist faces of modern democracy. The Legitimacy of Modern Democracy will be of interest to political theorists, political philosophers, intellectual historians, theoretically oriented political scientists, and legal scholars working in the subfields of constitutional law and legal theory

Seismic vulnerability of churches in Faial and Pico islands, Azores

Earthquakes represent one of the main cause of serious damage and loss of historic and architectural heritage. Interventions to preserve these building should start with a careful knowledge and assessment of their seismic vulnerability, in order to support any needed retrofitting and strengthening measures. This paper proposes a procedure to register and diagnose of the level of damage on churches after the occurrence of an earthquake, and also to assess the seismic vulnerability of this type of construction. This procedure was applied to sixteen churches in the Azores islands which were hit by the July 9th 1998 earthquake. Belfries of church towers are elements with a particular seismic vulnerability. For this reason, and based on the Italian methodology proposed by the Linee Guida (2006), it is applied to belfries of two churches from Pico (Azores), a simplified mechanical model for assessment of seismic vulnerability of this type of structures

Methodological nationalism and migration studies : historical and contemporary perspectives

This chapter approaches the issue of methodological nationalism in the social sciences from both a historical and a contemporary perspective, with particular emphasis on migration studies. First, it offers a historical overview of the problem and delves into its early intellectual history by examining Eric Voegelin’s reflections on ‘national minds’ in the interwar period This anticipates many questions and challenges that future critics of methodological nationalism would consider to be central. Second, we examine the persistence of nation-state-centred concepts and methods in the context of migration and refugee studies. Third, the chapter discusses different conceptual tools for overcoming the insufficiencies of methodological nationalism, weighing both their fruitfulness and their limits. Notwithstanding the ineradicability of nation-state-centred frameworks in social science as well as in the self-perceptions of migrant populations, we show that it is possible to conceive of both ‘community’ and ‘knowledge’ in non-national terms to investigate the possibilities of knowledge produced through experiences of displacement.Peer reviewe

CP asymmetry from hadronic charm rescattering in B± → π−π+π± decays at the high mass region

A model for the $B^\pm \to \pi^-\pi^+\pi^\pm$ decay amplitude is proposed to study the large CP violation observed at the high mass region of the Dalitz plane. A short distance $b \to u$ amplitude with the weak phase $\gamma$ is considered together with the contribution of a hadronic charm loop and a s-wave $D\bar{D}\to \pi\pi$ rescattering. In the model, the $\chi_c^0$ appears as a narrow resonant state of the $D\bar D$ system below threshold. It is introduced in an unitary two channel S-matrix model of the coupled $D\bar D$ and $\pi\pi$ channels, where the $\chi_c^0$ complex pole in $D\bar D$ channel shows its signature in the off-diagonal matrix element and in the associated $D\bar{D}\to \pi\pi$ transition amplitude. The strong phase of the resulting decay amplitude has a sharp sign change at the $D\bar D$ threshold, changing the sign of the CP asymmetry, as it is observed in the data. We conclude that the hadronic charm loop and rescattering mechanism are relevant to the broadening of the CP asymmetry around the $\chi_c^0$ resonance in the $\pi\pi$ channel. This novel mechanism provides a possible interpretation of the CP asymmetry defier experimental result presented by the LHCb collaboration for the $B^\pm \to \pi^-\pi^+\pi^\pm$ decay in the high mass region

Field behavior of an Ising model with aperiodic interactions

We derive exact renormalization-group recursion relations for an Ising model, in the presence of external fields, with ferromagnetic nearest-neighbor interactions on Migdal-Kadanoff hierarchical lattices. We consider layered distributions of aperiodic exchange interactions, according to a class of two-letter substitutional sequences. For irrelevant geometric fluctuations, the recursion relations in parameter space display a nontrivial uniform fixed point of hyperbolic character that governs the universal critical behavior. For relevant fluctuations, in agreement with previous work, this fixed point becomes fully unstable, and there appears a two-cycle attractor associated with a new critical universality class.Comment: 9 pages, 1 figure (included). Accepted for publication in Int. J. Mod. Phys.