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.

Development of procedures for the design, optimization and manufacturing of customized orthopaedic and trauma implants: Geometrical/anatomical modelling from 3D medical imaging

Tese de Doutoramento (Programa Doutoral em Engenharia Biomédica)

Reforço de ligações tradicionais de madeira

Dissertação de mestrado integrado em Engenharia Civil

Polyphenols and sugars recovery from autohydrolysis of pineapple waste

[Excerpt] The aim of this research was to evaluate the influence of temperature, time and mass/ volume ratio on the release of sugars and polyphenols using an autohydrolysis procedure from pineapple waste. A Box-Bhenken design was used with three factors (time, temperature and mass/volume ratio) and three levels was used. All treatments were performed in triplicate. Nine central points were used. For autohydrlosysis treatments, an oil bath was used [1]. After autohydrolysis, liquid phases or hydrolysates were analyzed for glucose and fructose concentration by high performance liquid chromatography (HPLC) [2]. The FolinCiocalteu assay was used to measure total polyphenols of hydrolysates [3] and HPLC to identify these molecules [4]. (...)