4 resultados para Twisted affine superalgebras

em Instituto Politécnico do Porto, Portugal


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It has been shown that in reality at least two general scenarios of data structuring are possible: (a) a self-similar (SS) scenario when the measured data form an SS structure and (b) a quasi-periodic (QP) scenario when the repeated (strongly correlated) data form random sequences that are almost periodic with respect to each other. In the second case it becomes possible to describe their behavior and express a part of their randomness quantitatively in terms of the deterministic amplitude–frequency response belonging to the generalized Prony spectrum. This possibility allows us to re-examine the conventional concept of measurements and opens a new way for the description of a wide set of different data. In particular, it concerns different complex systems when the ‘best-fit’ model pretending to be the description of the data measured is absent but the barest necessity of description of these data in terms of the reduced number of quantitative parameters exists. The possibilities of the proposed approach and detection algorithm of the QP processes were demonstrated on actual data: spectroscopic data recorded for pure water and acoustic data for a test hole. The suggested methodology allows revising the accepted classification of different incommensurable and self-affine spatial structures and finding accurate interpretation of the generalized Prony spectroscopy that includes the Fourier spectroscopy as a partial case.

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This paper discusses the changes brought by the communication revolution in teaching and learning in the scope of LSP. Its aim is to provide an insight on how teaching which was bi-dimensional, turned into a multidimensional system, gathering other complementary resources that have transformed, in a incredibly short time, the ways we receive share and store information, for instance as professionals, and keep in touch with our peers. The increasing rise of electronic publications, the incredible boom of social and professional networks, search engines, blogs, list servs, forums, e-mail blasts, Facebook pages, YouTube contents, Tweets and Apps, have twisted the way information is conveyed. Classes ceased to be predictable and have been empowered by digital platforms, innumerous and different data repositories (TILDE, IATE, LINGUEE, and so many other terminological data banks) that have definitely transformed the academic world in general and tertiary education in particular. There is a bulk of information to be digested by students, who are no longer passive but instead responsible and active for their academic outcomes. The question is whether they possess the tools to select only what is accurate and important for a certain subject or assignment, due to that overflow? Due to the reduction of the number of course years in most degrees, after the implementation of Bologna and the shrinking of the curricula contents, have students the possibility of developing critical thinking? Both teaching and learning rely on digital resources to improve the speed of the spreading of knowledge. But have those changes been effective to promote really communication? Furthermore, with the increasing Apps that have already been developed and will continue to appear for learning foreign languages, for translation among others, will the students feel the need of learning them once they have those Apps. These are some the questions we would like to discuss in our paper.

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We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.

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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.