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.

Career barriers influencing career success: A focus on academics’ perceptions and experiences

Purpose – Few research has addressed the factors that undermine people’s subjective perceptions of career success. Hence, the purpose of this paper is to further illuminate the issue of career barriers in perceptions of career success for a specific group of professionals: academics. Design/methodology/approach – This study adopts an interpretative-social constructionist methodology. Complementarily, it was employed a phenomenological method in data gathering and analysis – with the use of in-depth interviews and a theme analysis. The research was undertaken with a group of 87 Portuguese academics of both sexes and in different stages of their academic careers. Findings – The findings pinpoint the existence of multi-level barriers encountered by the academics when trying to succeed in their careers. The interviewees mentioned particularly the organizational-professional career barriers pertaining to three general themes: poor collegiality and workplace relationships; the lack of organizational support and employment precariousness; and the career progression standards and expectations. At the individual life cycle level the interviewees referred to the theme of finding balance; at the same time, the gender structure was also a theme mentioned as an important career barrier in career success, particularly by the women interviewed. Research limitations/implications – One of the limitations of this research is related to the impossibility of generalizability of its findings for the general population. Nevertheless, the researcher provides enough detail that grants the reader with the ability to judge of its similarity to other research contexts. Practical implications – This research highlights the role played by distinct career barriers for a specific professional group: academics. This has implications for higher education policy-makers and for human resources managers in higher education institutions. Originality/value – The current study extends the literature on career success by offering detailed anecdotal evidence on how negative work experiences might hinder career success. This research shows that to understand career barriers to success it is useful to consider multi-level factors: organizational-level factors (e.g. poor collegiality and workplace relationships); individual-level factors (e.g. life-cycle factors such as age/career stage); and structural-level factors (e.g. gender).

Refinement in hybridised institutions

Hybrid logics, which add to the modal description of transition structures the ability to refer to specific states, offer a generic framework to approach the specification and design of reconfigurable systems, i.e., systems with reconfiguration mechanisms governing the dynamic evolution of their execution configurations in response to both external stimuli or internal performance measures. A formal representation of such systems is through transition structures whose states correspond to the different configurations they may adopt. Therefore, each node is endowed with, for example, an algebra, or a first-order structure, to precisely characterise the semantics of the services provided in the corresponding configuration. This paper characterises equivalence and refinement for these sorts of models in a way which is independent of (or parametric on) whatever logic (propositional, equational, fuzzy, etc) is found appropriate to describe the local configurations. A Hennessy–Milner like theorem is proved for hybridised logics.