Further results on the inverse along an element in semigroups and rings

In this paper, we introduce a new notion in a semigroup $S$ as an extension of Mary's inverse. Let $a,d\in S$. An element $a$ is called left (resp. right) invertible along $d$ if there exists $b\in S$ such that $bad=d$ (resp. $dab=b$) and $b\leq_\mathcal{L}d$ (resp. $b\leq_\mathcal{R}d$). An existence criterion of this type inverse is derived. Moreover, several characterizations of left (right) regularity, left (right) $\pi$-regularity and left (right) $*$-regularity are given in a semigroup. Further, another existence criterion of this type inverse is given by means of a left (right) invertibility of certain elements in a ring. Finally we study the (left, right) inverse along a product in a ring, and, as an application, Mary's inverse along a matrix is expressed.

The inverse along a product and its applications

In this paper, we study the recently defined notion of the inverse along an element. An existence criterion for the inverse along a product is given in a ring. As applications, we present the equivalent conditions for the existence and expressions of the inverse along a matrix.

An alternative educational indicator for classifying secondary schools in Portugal

The purpose of this paper aims at carrying out a study in the area of Statistics for classifying Portuguese Secondary Schools (both mainland and islands: “Azores” and “Madeira”), taking into account the results achieved by their students in both national examinations and internal assessment. The main according consists of identifying groups of schools with different performance levels by considering the sub-national public and private education systems’ as well as their respective geographic location. For this, we developed an alternative educational indicator for the so-called Secondary Education indicator rankings released since 2001 by the Portuguese media.

Recurrence relations for Clifford algebra-valued orthogonal polynomials

The theory of orthogonal polynomials of one real or complex variable is well established as well as its generalization for the multidimensional case. Hypercomplex function theory (or Clifford analysis) provides an alternative approach to deal with higher dimensions. In this context, we study systems of orthogonal polynomials of a hypercomplex variable with values in a Clifford algebra and prove some of their properties.

Thin films composed of gold nanoparticles dispersed in a dielectric matrix: the influence of the host matrix on the optical and mechanical responses

Gold nanoparticles were dispersed in two different dielectric matrices, TiO2 and Al2O3, using magnetron sputtering and a post-deposition annealing treatment. The main goal of the present work was to study how the two different host dielectric matrices, and the resulting microstructure evolution (including both the nanoparticles and the host matrix itself) promoted by thermal annealing, influenced the physical properties of the films. In particular, the structure and morphology of the nanocomposites were correlated with the optical response of the thin films, namely their localized surface plasmon resonance (LSPR) characteristics. Furthermore, and in order to scan the future application of the two thin film system in different types of sensors (namely biological ones), their functional behaviour (hardness and Young's modulus change) was also evaluated. Despite the similar Au concentrations in both matrices (~ 11 at.%), very different microstructural features were observed, which were found to depend strongly on the annealing temperature. The main structural differences included: (i) the early crystallization of the TiO2 host matrix, while the Al2O3 one remained amorphous up to 800 °C; (ii) different grain size evolution behaviours with the annealing temperature, namely an almost linear increase for the Au:TiO2 system (from 3 to 11 nm), and the approximately constant values observed in the Au:Al2O3 system (4–5 nm). The results from the nanoparticle size distributions were also found to be quite sensitive to the surrounding matrix, suggesting different mechanisms for the nanoparticle growth (particle migration and coalescence dominating in TiO2 and Ostwald ripening in Al2O3). These different clustering behaviours induced different transmittance-LSPR responses and a good mechanical stability, which opens the possibility for future use of these nanocomposite thin film systems in some envisaged applications (e.g. LSPR-biosensors).

In vitro anti-Candida activity of Glycyrrhiza glabra L.

The severity and frequency of opportunistic fungal infections still growing, concomitantly to the increasing rates of antimicrobial drugs resistance. Natural matrices have been used over years due to its multitude of health benefits, including antifungal potential. Thus, the present work aims to evaluate the anti-Candida potential of the phenolic extract and individual phenolic compounds of Glycyrrhiza glabra L. (licorice), by disc diffusion assay, followed by determination of the minimal inhibitory concentration (MIC) and minimal fungicidal concentration (MFC) for both planktonic cells and biofilms. Licorice extract evidenced inhibitory potential against the nineteen tested Candida strains, but no pronounced effect was observed by testing the most abundant individual phenolic compounds. Candida tropicalis strains were the most sensible, followed by Candida glabrata, Candida parapsilosis and, then, Candida albicans. Lower MIC and MFC values were achieved to C. glabrata and C. tropicalis, which confirms its susceptibility to licorice extract; however, for C. tropicalis strains a higher variability was observed. Anti-biofilm potential was also achieved, being most evident in some C. glabrata and C. tropicalis strains. In general, a twice concentration of the MIC was necessary for planktonic cells to obtain a similar potential to that one observed for biofilms. Thus, an upcoming approach for new antifungal agents, more effective and safer than the current ones, is stablished; notwithstanding, further studies are necessary in order to understand its mechanism of action, as also to assess kinetic parameters.

School governance and academic excellence: the representations of distinguished students in an annual award of excellence

Within a research project on «academic excellence in the state school», this paper is a contribution to the sociological reflection on the cultural and organisational characteristics of the school and its relationship with the academic success of students. The data we present stem from a case study underway at a secondary school in the north of Portugal, referring to the universe of students that since 2003 have distinguished themselves for achieving grades equal to or greater than 18 (on a scale of 0 to 20) and have thus been included in the school’s Framework of Excellence. From a contextual approach to this educational practice, we focused on the cultural characteristics of the school/subject as analytical support for the study of school and non-school dimensions in their mutual connections. To this end, we used the information from document analysis and data collected from a questionnaire survey administered to more than two-thirds of the students included in the above-mentioned Framework of Excellence. Subsequently, we will use the data from this survey to understand the extent to which academic excellence is perceived as an indivisible social construction of the school’s political and organisational matrix, particularly in terms of the educational and teaching guidelines adopted by the management body. We will conclude by questioning the meaning of the school’s management policies regarding the emphasis on educational outcomes, with particular focus on the representations of excellent students in the processes of school leadership, teaching organisation, school merit and justice.

A new perspective of students allocation satisfaction in engineering courses in Portugal

Publicado em "AIP Conference Proceedings" Vol. 1648

Forecasting time series combining Holt-Winters and bootstrap approaches

Publicado em "AIP Conference Proceedings", Vol. 1648

The role of automatic shape and position recognitionin streamlining manufacturing

The main features of most components consist of simple basic functional geometries: planes, cylinders, spheres and cones. Shape and position recognition of these geometries is essential for dimensional characterization of components, and represent an important contribution in the life cycle of the product, concerning in particular the manufacturing and inspection processes of the final product. This work aims to establish an algorithm to automatically recognize such geometries, without operator intervention. Using differential geometry large volumes of data can be treated and the basic functional geometries to be dealt recognized. The original data can be obtained by rapid acquisition methods, such as 3D survey or photography, and then converted into Cartesian coordinates. The satisfaction of intrinsic decision conditions allows different geometries to be fast identified, without operator intervention. Since inspection is generally a time consuming task, this method reduces operator intervention in the process. The algorithm was first tested using geometric data generated in MATLAB and then through a set of data points acquired by measuring with a coordinate measuring machine and a 3D scan on real physical surfaces. Comparison time spent in measuring is presented to show the advantage of the method. The results validated the suitability and potential of the algorithm hereby proposed

On simple bounds for eigenvalues of symmetric tridiagonal matrices

How much can be said about the location of the eigenvalues of a symmetric tridiagonal matrix just by looking at its diagonal entries? We use classical results on the eigenvalues of symmetric matrices to show that the diagonal entries are bounds for some of the eigenvalues regardless of the size of the off-diagonal entries. Numerical examples are given to illustrate that our arithmetic-free technique delivers useful information on the location of the eigenvalues.

Differential activation of the default mode network in jet lagged individuals

Long-term exposure to transmeridian flights has been shown to impact cognitive functioning. Nevertheless, the immediate effects of jet lag in the activation of specific brain networks have not been investigated. We analyzed the impact of short-term jet lag on the activation of the default mode network (DMN). A group of individuals who were on a transmeridian flight and a control group went through a functional magnetic resonance imaging acquisition. Statistical analysis was performed to test for differences in the DMN activation between groups. Participants from the jet lag group presented decreased activation in the anterior nodes of the DMN, specifically in bilateral medial prefrontal and anterior cingulate cortex. No areas of increased activation were observed for the jet lag group. These results may be suggestive of a negative impact of jet lag on important cognitive functions such as introspection, emotional regulation and decision making in a few days after individuals arrive at their destination.

TP perturbation of TN matrices and totally positive directions

Here, we define and consider (linear) TP-directions and TP-paths for a totally nonnegative matrix, in an effort to more deeply understand perturbation of a TN matrix to a TP matrix. We give circumstances in which a TP-direction exists and an example to show that they do not always exist. A strategy to give (nonlinear) TP-paths is given (and applied to this example). A long term goal is to understand the sparsest TP-perturbation for application to completion problems.

Occupational stress and coping among portuguese military police officers

This study describes the professional experience of military police officers from the Portuguese Republican National Guard (N = 95). We focused on the main sources and consequences of stress and the coping strategies used to deal with stress. The evaluation protocol included one closed-ended question and four open-ended questions. Data analysis of meaningful text segments was conceptually based and data categorization followed deductive content analysis. Results allowed the identification of 483 meaning units. Factors intrinsic to the job and the relationships at work were the main stressors referred by participants. The consequences of stressors were evident at an individual level, affecting family, psychological, and physical/health domains. The coping strategies used to deal with the main source of stress in the professional career were focused on problem solving (e.g., active confrontation) and emotional regulation (e.g., situation acceptance). Practical implications and future avenues of research with these professionals are discussed.

Cylindrically symmetric models of gravitational collapse to black holes: a short review

We survey results about exact cylindrically symmetric models of gravitational collapse in General Relativity. We focus on models which result from the matching of two spacetimes having collapsing interiors which develop trapped surfaces and vacuum exteriors containing gravitational waves. We collect some theorems from the literature which help to decide a priori about eventual spacetime matchings. We revise, in more detail, some toy models which include some of the main mathematical and physical issues that arise in this context, and compute the gravitational energy flux through the matching boundary of a particular collapsing region. Along the way, we point out several interesting open problems.