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 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.

Emotional aspects of childhood career development: importance and future agenda

Childhood is a central period for career and social-emotional development. However, the literature covering childhood career development and the role of emotions in careers is scarce. In this article, we advocate for the consideration of emotions in childhood career development. Emotional aspects of children’s career exploration, key-figures and interests, as well as of childhood antecedents of lifelong career processes are presented. Relations between childhood emotion, behavior, functioning and learning are also presented. Conclusions center on a call for focused study of the role of emotion in childhood career development and how such an agenda will advance the literature.

Poly(ester-urethane) scaffolds: effect of structure on properties and osteogenic activity of stem cells

The present study aimed to investigate the effect of structure (design and porosity) on the matrix stiffness and osteogenic activity of stem cells cultured on poly(ester-urethane) (PEU) scaffolds. Different three-dimensional (3D) forms of scaffold were prepared from lysine-based PEU using traditional salt-leaching and advanced bioplotting techniques. The resulting scaffolds were characterized by differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), scanning electron microscopy (SEM), mercury porosimetry and mechanical testing. The scaffolds had various pore sizes with different designs, and all were thermally stable up to 300â °C. In vitrotests, carried out using rat bone marrow stem cells (BMSCs) for bone tissue engineering, demonstrated better viability and higher cell proliferation on bioplotted scaffolds compared to salt-leached ones, most probably due to their larger and interconnected pores and stiffer nature, as shown by higher compressive moduli, which were measured by compression testing. Similarly, SEM, von Kossa staining and EDX analyses indicated higher amounts of calcium deposition on bioplotted scaffolds during cell culture. It was concluded that the design with larger interconnected porosity and stiffness has an effect on the osteogenic activity of the stem cells.