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- On the Uniqueness of the Fock Quantization of the Dirac Field in the Closed FRW CosmologyPublication . Cortez, Jerónimo; Inácio, Ilda; Martín-Benito, Mercedes; Velhinho, JoséThe 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.
- Convertible subspaces that arise from different numberings of the vertices of a graphPublication . Cruz, Henrique F. Da; Inácio, Ilda; Serôdio, RogérioIn this paper, we describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing ± signs. These subspaces can arise from different numberings of the vertices of a graph. With this numbering process, we obtain some well-known sequences of integers. For instance, in the case of a path of length n, we prove that the number of these subspaces is the (n + 1)th Fibonacci number.
- Convertible Subspaces of Hessenberg-Type MatricesPublication . Cruz, Henrique F. Da; Rodrigues, Ilda Inácio; Serôdio, Rogério; Simões, A. M.; Velhinho, JoseWe describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing ± signs. An explicit characterization of convertible Hessenberg-type matrices is presented. We conclude that convertible matrices with the maximum number of nonzero entries can be reduced to a basic set.
- Teaching methodologies in civil engineering: a multidisciplinary approachPublication . Virtudes, Ana L.; Rodrigues, Ilda Inácio; Santos, Bertha; Pop, MariaNowadays 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.
- Research methodologies focused on urban planning and mathematical issuesPublication . Virtudes, Ana L.; Rodrigues, Ilda Inácio; Sá, João Paulo Costa e; Azevedo, Henrique Oliveira de; Simões, Alberto; Serôdio, RogérioThis 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.
- Collaborative learning advancing international students: a multidisciplinary approachPublication . Virtudes, Ana L.; Rodrigues, Ilda Inácio; Cavaleiro, VictorUniversities 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.
- VI Workshop on Computational Data Analysis and Numerical Methods: Book of AbstractsPublication . Simões, A. M.; Nunes, Célia; Inácio, Ilda; Grilo, Luis; Carapau, FernandoThis Workshop takes place at the University of Beira Interior, located in the beautiful city of Covilhã, Portugal. The host institution, as well as the Polytechnic Institute of Tomar and the University of Évora have committed themselves tothis challenge, hoping that the final result may exceed the expectations of the participants ,sponsors and organizers. [...]