On the Uniqueness of the Fock Quantization of the Dirac Field in the Closed FRW Cosmology

The Fock quantization of free fields propagating in cosmological backgrounds is in general not unambiguously defined due to the non-stationarity of the spacetime. For the case of a scalar field in cosmological scenarios it is known that the criterion of unitary implementation of the dynamics serves to remove the ambiguity in the choice of Fock representation (up to unitary equivalence). Here, applying the same type of arguments and methods previously used for the scalar field case, we discuss the issue of the uniqueness of the Fock quantization of the Dirac field in the closed FRW spacetime proposed by D'Eath and Halliwell.Comment: 11 page

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Collaborative learning advancing international students: a multidisciplinary approach

Universities are making great efforts in order to improve their rates in terms of internationalization. With the rise of international mobility, among students, new challenges are emerging on the high education system. In this sense, this paper aims to show some key strategies in terms of teaching methodologies that Universities should follow forward to a better internationalization performance. It is based on the case of University of Beira Interior in Portugal, in a multidisciplinary approach, which involves scholars from the Department of Civil Engineering and Architecture, and from the Department of Mathematics, teaching at the Civil Engineering studies. The main research questions of this paper are the following: are the currently used teaching methodologies prepared to accommodate international students who have different standards of proficiency whether in terms of language or in basic knowledge of mathematics? Which are the challenges of high education system, in order to improve the performance of international students, engaging them as part of a collaborative learning approach? The conclusions show that there is the need of following new teaching methodologies in a more collaborative approach, in order to promote the integration of international students.info:eu-repo/semantics/publishedVersio

Bicontactual hypermaps

Doutoramento em MatemáticaEsta tese dedica-se ao estudo de hipermapas regulares bicontactuais, hipermapas com a propriedade que cada hiperface contacta só com outras duas hiperfaces. Nos anos 70, S. Wilson classificou os mapas bicontactuais e, em 2003, Wilson e Breda d’Azevedo classificaram os hipermapas bicontactuais no caso não-orientável. Quando esta propriedade é transferida para hipermapas origina três tipos de bicontactualidade, atendendo ao modo como as duas hiperfaces aparecem à volta de uma hiperface fixa: edge-twin, vertextwin and alternate (dois deles são o dual um do outro). Um hipermapa topológico é um mergulho celular de um grafo conexo trivalente numa superfície compacta e conexa tal que as células são 3-coloridas. Ou de maneira mais simples, um hipermapa pode ser visto como um mapa bipartido. Um hipermapa orientado regular é um triplo ordenado consistindo num conjunto finito e dois geradores, que são permutações (involuções) do conjunto tal que o grupo gerado por eles, chamado o grupo de monodromia, actua regularmente no conjunto. Nesta tese, damos uma classificação de todos os hipermapas orientados regulares bicontactuais e, para completar, reclassificamos, usando o nosso método algébrico, os hipermapas não-orientáveis bicontactuais.This thesis is devoted to the study of bicontactual regular hypermaps, hypermaps with the property that each hyperface meets only two others. In the seventies, S. Wilson classified the bicontactual maps and, in 2003, Wilson and Breda d’Azevedo classified the bicontactual non-orientable hypermaps. When this property is transferred for hypermaps it gives rise to three types of bicontactuality, according as the two hyperfaces appear around a fixed hyperface: edge-twin, vertex-twin and alternate (two of which are dual of each other). A topological hypermap is a cellular embedding of a connected trivalent graph into a compact and connected surface such that the cells are 3-colored. Or simply, a hypermap can be seen as a bipartite map. A regular oriented-hypermap is an ordered triple, consisting of a finite set and two generators, which are permutations of the set, such that the group generate by them, called monodromy group, acts regularly on the set. In this thesis, we give a classification of all bicontactual regular orientedhypermaps and, for completion, we reclassify, using our algebraic method, the bicontactual non-orientable hypermaps

Teaching methodologies in civil engineering: a multidisciplinary approach

Nowadays universities are rethinking their teaching methodologies not only in order to adapt to the use of new technologies, such as the ICT (information and communication technologies) or the GIS (Geographic Information Systems) but also in order to advance the international students towards a multidisciplinary approach. Thus, this article is the result of a multidisciplinary approach gathering scholars from Portugal and Romania, presenting a set of several teaching methodologies used on the domains of civil engineering. It is based on the experience of the University of Beira Interior (UBI) in Portugal and the Faculty of Constructions, Cadastre and Architecture of the University of Oradea (UO) in Romania. Among other descriptions, the conclusions show that there are several different and common aspects in between the Portuguese and the Romanian experiences. Regarding the common aspects there is the need of finding new teaching methodologies in order to consider the different backgrounds of the international students coming from several countries and continents, having diverse high educational systems. Thus, the international students are encouraged to work together and to actively participate in the development, presentation and discussion of their scientific findings.info:eu-repo/semantics/publishedVersio

Research methodologies focused on urban planning and mathematical issues

This article aims to present an interdisciplinary approach about the research methodologies used at the civil engineering research field, in the domains of urban planning and mathematics. Actually, there are some similarities in between the research process features of urban planning and mathematics. In fact, these both scientific subjects follow analogous tasks in their research process, which have the same starting point with the definition of the research problem and the final phase, based on the proposed solution. It joins scholars from the department of civil engineering and architecture, experts in spatial analysis and scholars form the department of mathematics of the University of Beira Interior. Two case studies will be presented as examples of the application of these methodological approaches, both of them focused on the urban planning researches, associated with postgraduate teachings, one is related to a PhD thesis and the other one relates to a master degree dissertation.info:eu-repo/semantics/publishedVersio

Comments on Mathematical Aspects of the Biró–Néda Model

We address two mathematical aspects of the Biró–Néda dynamical model, recently applied in the statistical analysis of several and varied complex phenomena. First, we show that a given implicit assumption ceases to be valid outside the most simple and common cases, and we analyze the consequences thereof, in what the formulation of the model and probability conservation is concerned. Second, we revisit the transient behavior in the case of a constant reset rate and a constant or linear growth rate, improving on a previous analysis by including more general initial conditions

Comments on Mathematical Aspects of the Biró–Néda Model

We address two mathematical aspects of the Biró–Néda dynamical model, recently applied in the statistical analysis of several and varied complex phenomena. First, we show that a given implicit assumption ceases to be valid outside the most simple and common cases, and we analyze the consequences thereof, in what the formulation of the model and probability conservation is concerned. Second, we revisit the transient behavior in the case of a constant reset rate and a constant or linear growth rate, improving on a previous analysis by including more general initial conditions

On chirality groups and regular coverings of regular oriented hypermaps

summary:We prove that if the Walsh bipartite map $\mathcal {M}=\mathcal {W}(\mathcal {H})$ of a regular oriented hypermap $\mathcal {H}$ is also orientably regular then both $\mathcal {M}$ and $\mathcal {H}$ have the same chirality group, the covering core of $\mathcal {M}$ (the smallest regular map covering $\mathcal {M}$) is the Walsh bipartite map of the covering core of $\mathcal {H}$ and the closure cover of $\mathcal {M}$ (the greatest regular map covered by $\mathcal {M}$) is the Walsh bipartite map of the closure cover of $\mathcal {H}$. We apply these results to the family of toroidal chiral hypermaps $(3,3,3)_{b,c}=\mathcal {W}^{-1}\{6,3\}_{b,c}$ induced by the family of toroidal bipartite maps $\{6,3\}_{b,c}$