A Conley-type decomposition of the strong chain recurrent set

For a continuous flow on a compact metric space, the aim of this paper is to prove a Conley-type decomposition of the strong chain recurrent set. We first discuss in details the main properties of strong chain recurrent sets. We then introduce the notion of strongly stable set as an invariant set which is the intersection of the $\omega$-limits of a specific family of nested and definitively invariant neighborhoods of itself. This notion strengthens the one of stable set; moreover, any attractor results strongly stable. We then show that strongly stable sets play the role of attractors in the decomposition of the strong chain recurrent set; indeed, we prove that the strong chain recurrent set coincides with the intersection of all strongly stable sets and their complementaries

The generalized recurrent set, explosions and Lyapunov functions

We consider explosions in the generalized recurrent set for homeomorphisms on a compact metric space. We provide multiple examples to show that such explosions can occur, in contrast to the case for the chain recurrent set. We give sufficient conditions to avoid explosions and discuss their necessity. Moreover, we explain the relations between explosions and cycles for the generalized recurrent set. In particular, for a compact topological manifold with dimension greater or equal $2$, we characterize explosion phenomena in terms of existence of cycles. We apply our results to give sufficient conditions for stability, under $\mathscr{C}^0$ perturbations, of the property of admitting a continuous Lyapunov function which is not a first integral

Tax systems and tax reforms in Latin America: country studies

This paper is part of a wider research concerning taxation systems an reforms carried on ar the Departemnt of Pubic economics of the Uiversity of Pavia -I taly. These country studies refer to Argentina, Brazil, Chile, Costa Rica, Colombia, Mexico, Paraguay and Uruguay and are due to eminent native esperts. The papers depict and discuss the tax systems ad reforms in the aforementioned countries since the early 1990 to 2006.Tax Systems; Tas reofoerms; Latin American countries

The Role of Environment on the Formation of Early-Type Galaxies

(Abridged) We present a detailed study of the stellar populations of a volume-limited sample of early-type galaxies from SDSS, across a range of environments -- defined as the mass of the host dark matter halo. The stellar populations are explored through the SDSS spectra, via projection onto a set of two spectral vectors determined from Principal Component Analysis. We find the velocity dispersion of the galaxy to be the main driver behind the different star formation histories of early-type galaxies. However, environmental effects are seen to play a role (although minor). Galaxies populating the lowest mass halos have stellar populations on average ~1Gyr younger than the rest of the sample. The fraction of galaxies with small amounts of recent star formation is also seen to be truncated when occupying halos more massive than 3E13Msun. The sample is split into satellite and central galaxies for a further analysis of environment. Satellites are younger than central galaxies of the same stellar mass. The younger satellite galaxies in 6E12Msun halos have stellar populations consistent with the central galaxies found in the lowest mass halos of our sample (i.e. 1E12Msun). This result is indicative of galaxies in lower mass halos being accreted into larger halos.Comment: 11 pages, 10 figures. Accepted for publication in MNRA

The generalized recurrent set, explosions and Lyapunov functions

We consider explosions in the generalized recurrent set for homeomorphisms on a compact metric space. We provide multiple examples to show that such explosions can occur, in contrast to the case for the chain recurrent set. We give sufficient conditions to avoid explosions and discuss their necessity. Moreover, we explain the relations between explosions and cycles for the generalized recurrent set. In particular, for a compact topological manifold with dimension greater or equal 2, we characterize explosion phenomena in terms of existence of cycles. We apply our results to give sufficient conditions for stability, under C 0 perturbations, of the property of admitting a continuous Lyapunov function which is not a first integral

BC2L-C N-Terminal Lectin Domain Complexed with Histo Blood Group Oligosaccharides Provides New Structural Information

International audienceLectins mediate adhesion of pathogens to host tissues, filling in a key role in the first steps of infection. Belonging to the opportunistic pathogen Burkholderia cenocepacia, BC2L-C is a superlectin with dual carbohydrate specificity, believed to mediate cross-linking between bacteria and host cells. Its C-terminal domain binds to bacterial mannosides while its N-terminal domain (BCL2-CN) recognizes fucosylated human epitopes. BC2L-CN presents a tumor necrosis factor alpha (TNF-α) fold previously unseen in lectins with a novel fucose binding mode. We report, here, the production of a novel recombinant form of BC2L-CN (rBC2L-CN2), which allowed better protein stability and unprecedented co-crystallization with oligosaccharides. Isothermal calorimetry measurements showed no detrimental effect on ligand binding and data were obtained on the binding of Globo H hexasaccharide and l-galactose. Crystal structures of rBC2L-CN2 were solved in complex with two blood group antigens: H-type 1 and H-type 3 (Globo H) by X-ray crystallography. They provide new structural information on the binding site, of importance for the structural-based design of glycodrugs as new antimicrobials with antiadhesive properties

Birkhoff attractors of dissipative billiards

We study the dynamics of dissipative billiard maps within planar convex domains. Such maps have a global attractor. We are interested in the topological and dynamical complexity of the attractor, in terms both of the geometry of the billiard table and of the strength of the dissipation. We focus on the study of an invariant subset of the attractor, the so-called Birkhoff attractor. On the one hand, we show that for a generic convex table with "pinched" curvature, the Birkhoff attractor is a normally contracted manifold when the dissipation is strong. On the other hand, for a mild dissipation, we prove that generically the Birkhoff attractor is complicated, both from the topological and the dynamical point of view.Comment: 48 pages, 10 figure

La conoscenza di architettura, città e paesaggio: "Il Progetto Logico di Rilievo" in una sperimentazione metodologica

Non si parla come si pensa, ma si pensa come si parla: ciò induce a dire che come il flusso del pensiero segue la sintassi della lingua madre, così il pensiero formale, sia esso interpretativo o propositivo, segue l'impianto geometrico. La Geometria è di fatto un sistema assiomatico che, se modernamente lo si è compreso come puramente formale, nella realtà dei comuni mortali nasce e rimane materiale: un vero "a priori" kantiano. Ora, le ragioni del "volere geometrico" che pervade la vita delle civiltà può avere svariate ragioni che scomodano svariate discipline: a noi può bastare la duplice considerazione che vede la Geometria tanto come mezzo per giustificare scelte formali attraverso sicure relazioni tra entità, quanto il filo logico che rende comprensibile e comunicabile una idea anche di pura fantasia. Il nostro contributo intende dimostrare, quanto sia utile ancora e sempre, dalla tradizione alla contemporaneità, la conoscenza della Geometria nelle sue varie forme. You do not speak as you think, but you think as you speak: this means that as the flow of thought follows our language syntax, so the formal thinking, whether purposeful or interpretational, follows the geometric layout. Geometry is an axiomatic system that, if modernly it is purely formal, in ordinary life remains material: a true Kantian "a priori". Geometry pervades the civilized people's life; we can take into consideration two aspects: firstly, the Geometry justify formal choices through fixed relationships between entities; secondly, Geometry makes understandable and communicable ideas. Our contribution aims to demonstrate how Geometry, from tradition to modernity, is still useful in its various form