The group inverse of a product

In this paper, we characterize the existence and give an expression of the group inverse of a product of two regular elements by means of a ring unit.

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.

The influence of fibre orientation on the post-cracking tensile behaviour of steel fibre reinforced self-compacting concrete

Adding fibres to concrete provides several advantages, especially in terms of controlling the crack opening width and propagation after the cracking onset. However, distribution and orientation of the fibres toward the active crack plane are significantly important in order to maximize its benefits. Therefore, in this study, the effect of the fibre distribution and orientation on the post-cracking tensile behaviour of the steel fibre reinforced self-compacting concrete (SFRSCC) specimens is investigated. For this purpose, several cores were extracted from distinct locations of a panel and were subjected to indirect (splitting) and direct tensile tests. The local stress-crack opening relationship (σ-w) was obtained by modelling the splitting tensile test under the finite element framework and by performing an Inverse Analysis (IA) procedure. Afterwards the σ-w law obtained from IA is then compared with the one ascertained directly from the uniaxial tensile tests. Finally, the fibre distribution/orientation parameters were determined adopting an image analysis technique.

Thin panels of cement composites reinforced with recycled fibres for the shear strengthening of reinforced concrete elements

A new technique was developed for producing thin panels of a cement based material reinforced with relatively high content of steel fibres originated from the industry of tyre recycling. Flexural tests with notched and un-notched specimens were carried out to characterize the mechanical properties of this Fibre Reinforced Cement Composite (FRCC) and the results are presented and discussed. The values of the fracture mode I parameters of the developed FRCC were determined by performing inverse analysis with test results obtained in three point notched beam bending tests. To appraise the potentialities of these FRCC panels for the increase of the shear capacity of reinforced (RC) beams, numerical research was performed on the use of developed FRCC panel for shear reinforcement by applying the panels in the lateral faces of RC beams deficiently reinforced in shear.

Tensile stress–crack width law for steel fibre reinforced self-compacting concrete obtained from indirect (splitting) tensile tests

In this work, the fracture mode I parameters of steel fibre reinforced self-compacting concrete (SFRSCC) were derived from the numerical simulation of indirect splitting tensile tests. The combined experimental and numerical research allowed a comparison between the stress-crack width (σ - w) relationship acquired straightforwardly from direct tensile tests, and the σ - w response derived from inverse analysis of the splitting tensile tests results. For this purpose a comprehensive nonlinear 3D finite element (FE) modeling strategy was developed. A comparison between the experimental results obtained from splitting tensile tests and the corresponding FE simulations confirmed the good accuracy of the proposed strategy to derive the σ – w for these composites. It is concluded that the post-cracking tensile laws obtained from inverse analysis provided a close relationship with the ones obtained from the experimental uniaxial tensile tests.

Recycled steel fibre reinforced concrete failing in bending and in shear

Recent research is showing that the addition of Recycled Steel Fibres (RSF) from wasted tyres can decrease significantly the brittle behaviour of cement based materials, by improving its toughness and post-cracking resistance. In this sense, Recycled Steel Fibre Reinforced Concrete (RSFRC) seems to have the potential to constitute a sustainable material for structural and non-structural applications. To assess this potential, experimental and numerical research was performed on the use of RSFRC in elements failing in bending and in beams failing in shear. The values of the fracture mode I parameters of the developed RSFRC were determined by performing inverse analysis with test results obtained in three point notched beam bending tests. To assess the possibility of using RSF as shear reinforcement in Reinforced Concrete (RC) beams, three point bending tests were executed with three series of RSFRC beams flexurally reinforced with a relatively high reinforcement ratio of longitudinal steel bars in order to assure shear failure for all the tested beams. By performing material nonlinear simulations with a computer program based on the finite element method (FEM), the applicability of the fracture mode I crack constitutive law derived from the inverse analysis is assessed for the prediction of the behaviour of these beams. The performance of the formulation proposed by RILEM TC 162 TDF and CEB-FIP 2010 for the prediction of the shear resistance of fibre reinforced concrete elements was also evaluated.

A model to simulate the moment-rotation and crack width of FRC members reinforced with longitudinal bars

The present work describes a model for the determination of the moment–rotation relationship of a cross section of fiber reinforced concrete (FRC) elements that also include longitudinal bars for the flexural reinforcement (R/FRC). Since a stress–crack width relationship (σ–w)(σ–w) is used to model the post-cracking behavior of a FRC, the σ–w directly obtained from tensile tests, or derived from inverse analysis applied to the results obtained in three-point notched beam bending tests, can be adopted in this approach. For a more realistic assessment of the crack opening, a bond stress versus slip relationship is assumed to simulate the bond between longitudinal bars and surrounding FRC. To simulate the compression behavior of the FRC, a shear friction model is adopted based on the physical interpretation of the post-peak compression softening behavior registered in experimental tests. By allowing the formation of a compressive FRC wedge delimited by shear band zones, the concept of concrete crushing failure mode in beams failing in bending is reinterpreted. By using the moment–rotation relationship, an algorithm was developed to determine the force–deflection response of statically determinate R/FRC elements. The model is described in detail and its good predictive performance is demonstrated by using available experimental data. Parametric studies were executed to evidence the influence of relevant parameters of the model on the serviceability and ultimate design conditions of R/FRC elements failing in bending.

Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem

Tunnel engineering – influence of the type and the quantity of measurements in the back analysis of geomechanical parameters

The monitoring data collected during tunnel excavation can be used in inverse analysis procedures in order to identify more realistic geomechanical parameters that can increase the knowledge about the interested formations. These more realistic parameters can be used in real time to adapt the project to the real structure in situ behaviour. However, monitoring plans are normally designed for safety assessment and not especially for the purpose of inverse analysis. In fact, there is a lack of knowledge about what types and quantity of measurements are needed to succeed in identifying the parameters of interest. Also, the optimisation algorithm chosen for the identification procedure may be important for this matter. In this work, this problem is addressed using a theoretical case with which a thorough parametric study was carried out using two optimisation algorithms based on different calculation paradigms, namely a conventional gradient-based algorithm and an evolution strategy algorithm. Calculations were carried for different sets of parameters to identify several combinations of types and amount of monitoring data. The results clearly show the high importance of the available monitoring data and the chosen algorithm for the success rate of the inverse analysis process.

Methodology for real-time adaptation of tunnels support using the observational method

The observational method in tunnel engineering allows the evaluation in real time of the actual conditions of the ground and to take measures if its behavior deviates considerably from predictions. However, it lacks a consistent and structured methodology to use the monitoring data to adapt the support system in real time. The definition of limit criteria above which adaptation is required are not defined and complex inverse analysis procedures (Rechea et al. 2008, Levasseur et al. 2010, Zentar et al. 2001, Lecampion et al. 2002, Finno and Calvello 2005, Goh 1999, Cui and Pan 2012, Deng et al. 2010, Mathew and Lehane 2013, Sharifzadeh et al. 2012, 2013) may be needed to consistently analyze the problem. In this paper a methodology for the real time adaptation of the support systems during tunneling is presented. In a first step limit criteria for displacements and stresses are proposed. The methodology uses graphics that are constructed during the project stage based on parametric calculations to assist in the process and when these graphics are not available, since it is not possible to predict every possible scenario, inverse analysis calculations are carried out. The methodology is applied to the “Bois de Peu” tunnel which is composed by two tubes with over 500 m long. High uncertainty levels existed concerning the heterogeneity of the soil and consequently in the geomechanical design parameters. The methodology was applied in four sections and the results focus on two of them. It is shown that the methodology has potential to be applied in real cases contributing for a consistent approach of a real time adaptation of the support system and highlight the importance of the existence of good quality and specific monitoring data to improve the inverse analysis procedure.

End-of-day dryness, corneal sensitivity and blink rate in contact lens wearers

Purpose: To study the relationship among the variables intensity ofthe end-of-day (EOD) dryness, corneal sensitivity and blink rate in soft contact lens (CL) wearers. Methods: Thirty-eight soft CL wearers (25 women and 13 men; mean age 27.1 ± 7.2 years) were enrolled. EOD dryness was assessed using a scale of 0–5 (0, none to 5, very intense). Mechanical and thermal (heat and cold) sensitivity were measured using a Belmonte’s gas esthesiometer. The blink rate was recorded using a video camera while subjects were wearing a hydrogel CL and watching a film for 90 min in a controlled environmental chamber. Results: A significant inverse correlation was found between EOD dryness and mechanical sensitivity (r: −0.39; p = 0.02); however, there were no significant correlations between EOD dryness and thermal sensitivity. A significant (r: 0.56; p < 0.001) correlation also was observed between EOD dryness and blink rate, but no correlations were found between blink rate and mechanical or thermal sensitivity. Conclusions: CL wearers with higher corneal sensitivity to mechanical stimulation reported more EOD dryness with habitual CL wear. Moreover, subjects reporting more EOD dryness had an increased blink rates during wear of a standard CL type. The increased blink rate could act to improve the ocular surface environment and relieve symptoms

Cultura, liderança e resultados escolares: uma abordagem a partir das representações dos alunos do ensino secundário

Grande parte dos estudos produzidos sobre a liderança escolar tem incidido na análise da relação entre os processos de liderança, a aprendizagem e o sucesso. Embora esta convergência de enfoque (liderança/sucesso) encubra abordagens teóricas, disciplinares e metodológicas muito diferenciadas, é evidente a presença de uma perspetiva unidirecional, mais focada nas políticas e nas práticas de liderança e menos na forma como estas são entendidas pelos alunos. Neste artigo, propomos um enfoque invertido, focado nas representações dos alunos sobre os processos de liderança. Do ponto de vista metodológico, recorremos aos dados recolhidos no âmbito de quatro estudos de caso realizados em escolas/agrupamentos com ensino secundário, resultantes da administração de um inquérito por questionário e da realização de focus group a alunos com resultados académicos de excelência e a alunos não incluídos neste nível de desempenho. Elegemos como referência analítica um estudo de caso de longa duração, a partir do qual colocamos em confronto os dados recolhidos nos outros três contextos estudados. Os resultados deste estudo apontam para a existência de relações e diferenças significativas entre a cultura organizacional da escola e os estilos de liderança, sendo destacada a importância do papel do Diretor na condução do ideário de excelência da escola.

Determination of the top-quark pole mass using t(t)over-bar+1-jet events collected with the ATLAS experiment in 7 TeV pp collisions

The normalized differential cross section for top-quark pair production in association with at least one jet is studied as a function of the inverse of the invariant mass of the tt¯+1-jet system. This distribution can be used for a precise determination of the top-quark mass since gluon radiation depends on the mass of the quarks. The experimental analysis is based on proton--proton collision data collected by the ATLAS detector at the LHC with a centre-of-mass energy of 7 TeV corresponding to an integrated luminosity of 4.6 fb−1. The selected events were identified using the lepton+jets top-quark-pair decay channel, where lepton refers to either an electron or a muon. The observed distribution is compared to a theoretical prediction at next-to-leading-order accuracy in quantum chromodynamics using the pole-mass scheme. With this method, the measured value of the top-quark pole mass, mpolet, is: mpolet =173.7 ± 1.5 (stat.) ± 1.4 (syst.) +1.0−0.5 (theory) GeV. This result represents the most precise measurement of the top-quark pole mass to date.

Sistema de posicionamento baseado em redes de sensores sem fios

Dissertação de mestrado integrado em Engenharia Eletrónica Industrial e Computadores