Matemática e Estatística | Capítulos/artigos em livros internacionais / Book chapters/papers in international books
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- Analysis in weak systemsPublication . Fernandes, António M.; Ferreira, Fernando; Ferreira, GildaThe authors survey and comment their work on weak analysis. They describe the basic set-up of analysis in a feasible second-order theory and consider the impact of adding to it various forms of weak Konig's lemma. A brief discussion of the Baire categoricity theorem follows. It is then considered a strengthening of feasibility obtained (fundamentally) by the addition of a counting axiom and showed how it is possible to develop Riemann integration in the stronger system. The paper finishes with three questions in weak analysis.
- Area-preserving diffeomorphisms from the C1-StandpointPublication . Bessa, MárioMore than thirty years have passed since Newhouse (Am. J. Math. 99:1061–1087, 1977) published a dichotomy on C1 area-preserving diffeomorphisms. Here we revisit some central results on surface conservative C1-diffeomorphisms by presenting, in particular, a new proof of Newhouse’s theorem and also by proving some, although folklore, not yet proved results on this setting. We intend that this exposition can be used by a large audience as an introduction to the concept of dominated splitting and its relevance to the theory of C1-stability of area-preserving diffeomorphisms.
- Asymptotic statistical results: theory and practicePublication . Kitsos, Christos P.; Oliveira, AmilcarThe target of this paper is to discuss the existent difference of Asymptotic Theory in Statistics comparing to Mathematics. There is a need for a limiting distribution in Statistics, usually the Normal one. Adopting the sequential principle the first-order autoregression model and the stochastic approximation are referred for their particular interest for asymptotic results.
- Challenges and opportunities for island tourist destinations: the case of the Island of Sal, Cape VerdePublication . Neves, Gilberto A.; Nunes, Catarina S.; Fernandes, Paula OdeteThe Tourism Area Life Cycle destination goes through different phases from its exploration until its decline or rejuvenation. The knowledge about these different phases allows the improvement of investment decisions by the private sector or by the government, in a context of challenges and opportunities. The main objective of this study was to verify in which phase the Island of Sal and Cape Verde were at an individual and competitive level during the period 2010-2018, considering the Tourism Development Index (TDI). To calculate the TDI, destinations with the same ‘sun and beach’ market were chosen, such as the Dominican Republic, Morocco, Tunisia and the Canary Islands, because they compete for the same European market and their geographical proximity to this market; data from government and non-government sources were used. It was concluded that the Island of Sal is in the Development phase, the same phase as that of Cape Verde. As for competitiveness, they are in the exploration and stagnation phase, both needing to increase the TDI to 48% and 43%, respectively to reach the involvement phase. For the calculation of the TDI, data from Cape Verde can be used to analyse the Sal Island index and vice versa. Strategic policies must be considered in the long term, incorporating information on the relative positions of direct competitors and unexpected events such as COVID 19, which can be seen as an opportunity to diversify the offer, create new segments and discover new inbound markets.
- Convergence to equilibria of solutions to the coagulation-fragmentation equationsPublication . Costa, Fernando Pestana daThe Coagulation-Fragmentation equations are a model for the dynamics of cluster growth and consist of a countable number of non-locally coupled ordinary differential equations, modelling the concentration of the various clusters. The framework for the study of these equations is to see them as a nonlinear ODE in an appropriate infinite dimensional Banach space. A number of results about existence, uniqueness, density conservation, and asymptotic behaviour of solutions have been obtained in recent years. In the present paper we review some of the more recent results on the asymptotic behaviour of solutions as time tends to infinity. We pay special attention to the different behaviour of solutions in the weak-star and in the strong topologies of the phase space. This distinction can be interpreted in terms of a dynamic phase transition in the physical system modelled by the equations. It is shown that a balance between the relative strength of coagulation and fragmentation is crucial for that distinct behaviour to take place.
- Fractional boson gas and fractional poisson measure in infinite dimensionsPublication . Oliveira, Maria João; Mendes, Rui VilelaAs a consequence of Haag’s theorem, to obtain a non-trivial theory, one either works with a non-Fock representation or with a Fock representation in a finite volume. Calculations in the Fock representation taking the N,V→ ∞limit with the ratio N/V=ρ fixed, show the equivalence of the free Boson gas and the infinite-dimensional Poisson measure. The N/V limit provides a way to deal with non-trivial infinite systems using the Fock representation. However, by the very nature of the fixed ρ density limit, it is unable to deal with systems with density fluctuations, a shortcoming that is solved by the use of reducible functionals. A particularly interesting reducible functional is the one associated to the infinite-dimensional fractional Poisson measure which we recall in this work.
- A fuzzy patient model in anaesthesiaPublication . Nunes, Catarina S.; Mahfouf, M.; Linkens, D. A.Balanced anaesthesia introduces the problem of drug interactions. In this article, the effect concentrations of anaesthetic and analgesic are used to model the pharmacodynamic interactions of the two drugs on the cardiovascular parameters, and on the auditory evoked potentials. An adaptive network-based fuzzy inference system is used to model the different signals. A stimulus model is used to establish the effects of surgical stimulus on the cardiovascular parameters. This model, is constructed into a Mamdani type of fuzzy model, using the anaesthetist knowledge described by fuzzy IF-THEN rules. Clinical data is used to construct the patient model.
- Garch models for drug effects on patient heart rate, during general anaesthesiaPublication . Brás, Susana; Nunes, Catarina S.; Amorim, PedroA model that can describe the effect of anaesthetic drugs on patient’s heart rate (HR) is of great importance when considering haemodynamic stability under surgery. A Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model was used to model HR considering the effect concentrations of the anaesthetic propofol and the analgesic remifentanil, using the clinical data of 16 patients. The model was able to capture the HR trend in all 16 patients with very small errors throughout the surgical time. A correlation was found between the GARCH parameters and patient baseline characteristics, leading to the possibility a patient adjusted adaptive model.
- Generic hamiltonian dynamical systems: an overviewPublication . Bessa, Mário; Dias, João LopesWe present for a general audience the state of the art on the generic properties of C 2 Hamiltonian dynamical systems.
- Global dynamics of generic 3-flowsPublication . Araújo, Vítor; Bessa, Mário; Pacífico, Maria JoséIn this chapter we present some results from the generic viewpoint, either for C 1 flows on 3-manifolds, or for C1 conservative flows on 3-manifolds. This means that we present some properties satisfied by a generic subset of all vector fields in compact 3-manifolds in the C1 topology.
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