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- 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.
- 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.