A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory

The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower semicontinuous function defined on a Banach space, through an approach based on an abstract notion of subdifferential operator, and taking into account the “smoothness” of the Banach space. Here, we give (Theorem 1) an extension in a metric setting, based on the notion of slope from [11] and coercivity is considered in a generalized sense, inspired by [9]; our result allows to recover, for example, the coercivity result of [19], where a weakened version of the Palais-Smale condition is used. Our main tool (Proposition 1) is a consequence of Ekeland’s variational principle extending [12, Corollary 3.4], and deals with a function f which is, in some sense, the “uniform” Γ-limit of a sequence of functions.

Autoethnography : critical appreciation of an emerging art

In this article, the author discusses how she applied autoethnography in a study of the design of hypermedia educational resources and shows how she addressed problematic issues related to autoethnographic legitimacy and representation. The study covered a 6-year period during which the practitioner’s perspective on the internal and external factors influencing the creation of three hypermedia CD-ROMs contributed to an emerging theory of design. The author highlights the interrelationship between perception and reality as vital to qualitative approaches and encourages researchers to investigate their reality more fully by practicing the art of autoethnography.

Enhancing the trust of location acquisition systems for critical applications and location-based security services

This paper identifies a number of critical infrastructure applications that are reliant on location services from cooperative location technologies such as GPS and GSM. We show that these location technologies can be represented in a general location model, such that the model components can be used for vulnerability analysis. We perform a vulnerability analysis on these components of GSM and GPS location systems as well as a number of augmentations to these systems.