An elementary proof of the uniqueness of the solutions of linear odes

In this note, we present an elementary proof of the uniqueness of the solutions of the initial value problems of linear ordinary differential equations (odes)

Lyapunov, metric and flag spectra

We introduce the \emph{metric spectrum}, which measures the exponential rate of approximation to an isolated invariant set of points starting in its stable set, and relate it to the Lyapunov spectrum. We determine the metric spectrum of each Morse component of the finest Morse decomposition of a linear induced flow on a generalized flag manifold

Existence of complete Lyapunov functions for semiflows on separable metric spaces

The aim of this short note is to show how to construct a complete Lyapunov function of a semiflow by using a complete Lyapunov function of its time-one map. As a byproduct we assure the existence of complete Lyapunov functions for semiflows on separable metric spaces

Internet addiction and loneliness among children and adolescents in the education setting: an empirical pilot study

Research into various behavioural addictions has shown that such behaviour can negatively impact psychological wellbeing. One behavioural addiction that has been increasingly studied empirically is that of Internet Addiction (IA). Despite general consensus concerning the negative effects of IA on mental health and other indices of physical and psychosocial health, little research has been done in child and adolescent populations in specific contexts. The main objectives of this study were to (i) investigate the extent of problems caused by IA in children and adolescents, (ii) determine the socio-demographic and behavioural characteristics of children and adolescents with IA, and (iii) to provide a model capable of predicting IA in the educational context among the target population. A total of 131 Portuguese school children and adolescents participated in this study. Results indicated a relatively high incidence of IA in the sample (13%). Additionally, the correlational analyses revealed associations between IA and loneliness, social loneliness, and other variables related to the educational context. Results demonstrated that IA could be predicted using a model encompassing three variables (i.e., weekly Internet usage, loneliness, and classroom behaviour). Overall, the present findings corroborated results from other studies and added to the behavioural addiction literature by examining a younger cohort than previous empirical studies