Spectral and weak polynomial completeness for the porduct of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F , satisfying the following property: for every monic polynomial f(x) = xn + an-1xn-1 + … +a1x + aο over F, with a root in F and aο = (-1)n det(AB), there are nonsingular matrices X, Y ϵ Fnxn such that X A X-1 Y BY-1 has characteristic polynomial f (x). © 2014 © 2014 Taylor & Francis.

The K-Th derivatives of the immanant and the X-symmetric power of an operator

In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.

The norm of the K- Th derivative of the X-symmetric power of an operator

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained.

Crossing balanced and stair nested desings

Balanced nesting is the most usual form of nesting and originates, when used singly or with crossing of such sub-models, orthogonal models. In balanced nesting we are forced to divide repeatedly the plots and we have few degrees of freedom for the first levels. If we apply stair nesting we will have plots all of the same size rendering the designs easier to apply. The stair nested designs are a valid alternative for the balanced nested designs because we can work with fewer observations, the amount of information for the different factors is more evenly distributed and we obtain good results. The inference for models with balanced nesting is already well studied. For models with stair nesting it is easy to carry out inference because it is very similar to that for balanced nesting. Furthermore stair nested designs being unbalanced have an orthogonal structure. Other alternative to the balanced nesting is the staggered nesting that is the most popular unbalanced nested design which also has the advantage of requiring fewer observations. However staggered nested designs are not orthogonal, unlike the stair nested designs. In this work we start with the algebraic structure of the balanced, the stair and the staggered nested designs and we finish with the structure of the cross between balanced and stair nested designs.

Periodic paths on nonautonomous graphs

We define nonautonomous graphs as a class of dynamic graphs in discrete time whose time-dependence consists in connecting or disconnecting edges. We study periodic paths in these graphs, and the associated zeta functions. Based on the analytic properties of these zeta functions we obtain explicit formulae for the number of n-periodic paths, as the sum of the nth powers of some specific algebraic numbers.

Congruences on monoids of transformations preserving the orientation on a finite chain

Journal of Algebra, 321 (2009), p. 743–757

On divisors of pseudovarieties generated by some classes of full transformation semigroups

Algebra Colloquium, 15 (2008), p. 581–588

LSP communication in a digital age: the outcomes of teaching and learning in tertiary education

This paper discusses the changes brought by the communication revolution in teaching and learning in the scope of LSP. Its aim is to provide an insight on how teaching which was bi-dimensional, turned into a multidimensional system, gathering other complementary resources that have transformed, in a incredibly short time, the ways we receive share and store information, for instance as professionals, and keep in touch with our peers. The increasing rise of electronic publications, the incredible boom of social and professional networks, search engines, blogs, list servs, forums, e-mail blasts, Facebook pages, YouTube contents, Tweets and Apps, have twisted the way information is conveyed. Classes ceased to be predictable and have been empowered by digital platforms, innumerous and different data repositories (TILDE, IATE, LINGUEE, and so many other terminological data banks) that have definitely transformed the academic world in general and tertiary education in particular. There is a bulk of information to be digested by students, who are no longer passive but instead responsible and active for their academic outcomes. The question is whether they possess the tools to select only what is accurate and important for a certain subject or assignment, due to that overflow? Due to the reduction of the number of course years in most degrees, after the implementation of Bologna and the shrinking of the curricula contents, have students the possibility of developing critical thinking? Both teaching and learning rely on digital resources to improve the speed of the spreading of knowledge. But have those changes been effective to promote really communication? Furthermore, with the increasing Apps that have already been developed and will continue to appear for learning foreign languages, for translation among others, will the students feel the need of learning them once they have those Apps. These are some the questions we would like to discuss in our paper.

Host cell adhesion to Schistosoma mansoni larvae in the peritoneal cavity of naive mice: histological and scanning electron microscopic studies

Cercariae of Schistosoma mansoni inoculated into the peritoneal cavity of naive mice induced host cell adhesion to their surface, but after 90 minutes the number of adherent cells sharply decreased. The cell detachment is progressive and simultaneous to the cercaria-schistosomule transformation. The histological study showed mainly neutrophils in close contact with the larvae. Mononuclear cells and some eosinophils were occasionally seen surrounding the adherent neutrophils. The scanning electron microscopy showed cells displaying twisted microvilli and several microplicae contacting or spreading over the larval surface, and larvae completely surrounded by clusters of cells. These results suggest that the neutrophils recognize molecules on the cercarial surface which induce their spreading

On derivatives and norms of generalized matrix functions and respective symmetric powers

In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th xi-symmetric tensor power of an operator and a matrix, when xi is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tensor power.

Spectral and weak polynomial completeness for the product of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).

Weakly spectrally complete pair of matrices

Let and be matrices over an algebraically closed field. Let be elements of such that and . We give necessary and sufficient condition for the existence of matrices and similar to and, respectively, such that has eigenvalues.

The impact of an online mathematics education project (MATACTIVA) on higher education students

The Online Mathematics Education Project (MatActiva) is an exciting new initiative which aims to support and enhance mathematics education. The project is led by the Institute of Accounting and Administration of Porto (ISCAP), part of the Polytechnic Institute of Porto (IPP). It provides innovative resources and carefully constructed materials around themes such as Elementary Mathematics, Calculus, Algebra, Statistics and Financial Mathematics to help support and inspire students and teachers of mathematics. The goal is to increase mathematical understanding, confidence and enjoyment, enrich the mathematical experience of each person, and promote creative and imaginative approaches to mathematics. Furthermore the project can be used to deliver engaging and effective mathematics instruction through the flipped classroom model. This paper also presents the findings of a large survey, whose propose was to study the student’s reaction to the project.

Congruences on monoids of order-preserving or order-reversing transformations on a finite chain

Glasgow Mathematical Journal, nº 47 (2005), pg. 413-424

Solvable monoids with commuting idempotents

International Journal of Algebra and Computation, 15, nº 3 (2005), p. 547-570