11 documents found, page 1 of 2
Bounds for the zeros of unilateral octonionic polynomials
Serôdio, Rogério; Beites, P. D.; Vitória, JoséIn the present work it is proved that the zeros of a unilateral octo- nionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic ...
Bounds for the zeros of unilateral octonionic polynomials
Serôdio, Rogério; Beites, P. D.; Vitoria, JoséIn the present work it is proved that the zeros of a unilateral octo- nionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic ...
Convertible subspaces that arise from different numberings of the vertices of a...
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)...
Eigenvalues of matrices related to the octonions
Serôdio, Rogério; Beites, P. D.; Vitoria, JoseA pseudo real matrix representation of an octonion, which is based on two real matrix represen- tations of a quaternion, is considered. We study how some operations defined on the octonions change the set of eigenvalues of the matrix obtained if these operations are performed after or before the matrix representation. The established results could be of particular interest to researchers working on estimation a...
Higher education methodologies: from urban planning to mathematical issues
Virtudes, Ana L.; Rodrigues, Ilda; Simões, A. M.; Serôdio, RogérioThis article will be focused on higher education learning and teaching methodologies, based on the experience of the Master Degree in Civil Engineering at the University of Beira Interior, in Covilhã (Portugal). It aims to present the results of the practises used by scholar of urban planning and mathematical issues, both regarding the civil engineering research field. Actually, there are some similarities in b...
Data’s Hidden Data: Qualitative Revelations of Sports Efficiency Analysis broug...
Campaniço, Ana Teresa; Valente, António; Serôdio, Rogério; Escalera, SérgioIn the study of effectiveness and efficiency of an athlete’s performance, intelligent systems can be applied on qualitative approaches and their performance metrics provide useful information on not just the quality of the data, but also reveal issues about the observational criteria and data collection context itself. 2000 executions of two similar exercises, with different levels of complexity, were collected...
Research methodologies focused on urban planning and mathematical issues
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 st...
Intersection of a Double Cone and a Line in the Split-Quaternions Context
Serôdio, Rogério; Beites, P. D.; Vitoria, JoseThis is a work on an application of the real split-quaternions to Spatial Analytic Geometry. Concretely, the intersection of a double cone and a line, which can be the empty set, a point, two points or a line, is studied in the real split-quaternions setting.
Convertible Subspaces of Hessenberg-Type Matrices
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.
Conjugacy and geometry II : moore-penrose inverse and feet of the perpendiculars
Costa, C.; Martins, Fernando M. L.; Serôdio, Rogério; Tadeu, Pedro; Vincente, M. A. Facas; Vitória, JoséIn this paper on space geometry, generalized inverses are used in the study of distances. Three cases are considered: distance from a point to a plane, distance from a point to a line and distance between two skew lines. Moore-Penrose inverses occur in the expressions of the feet of the perpendiculars and in the representation of the vectors materializing the distances. The results of this kind of problems fit ...