A gap in the spectrum of the Neumann-Laplacian on a periodic waveguide

We will study the spectral problem related to the Laplace operator in a singularly perturbed periodic waveguide. The waveguide is a quasi-cylinder with contains periodic arrangement of inclusions. On the boundary of the waveguide we consider both Neumann and Dirichlet conditions. We will prove that provided the diameter of the inclusion is small enough in the spectrum of Laplacian opens spectral gaps, i.e. frequencies that does not propagate through the waveguide. The existence of the band gaps will verified using the asymptotic analysis of elliptic operators.Comment: 26 pages, 6 figure

An international comparison of occupational health guidelines for the management of mental disorders and stress-related psychological symptoms

Background We compared available guidelines on the management of mental disorders and stress-related psychological symptoms in an occupational healthcare setting and determined their development and reporting quality. Methods To identify eligible guidelines, we systematically searched National Guideline Clearinghouse, Guidelines International Network Library and PubMed. Members of the International Commission on Occupational Health (ICOH), were also consulted. Guidelines recommendations were compared and reporting quality was assessed using the AGREE II instrument. Results Of 2126 titles retrieved, 14 guidelines were included: 1 Japanese, 2 Finnish, 2 Korean, 2 British and 7 Dutch. Four guidelines were of high-reporting quality. Best described was the Scope and Purpose, and the poorest described were competing interests (Editorial independence) and barriers and facilitators for implementation (Applicability). Key recommendations were often difficult to identify. Most guidelines recommend employing an inventory of symptoms, diagnostic classification, performance problems and workplace factors. All guidelines recommend specific return-to-work interventions, and most agreed on psychological treatment and communication between involved stakeholders. Discussion Practice guidelines to address work disability due to mental disorders and stress-related symptoms are available in various countries around the world, however, these guidelines are difficult to find. To promote sharing, national guidelines should be accessible via established international databases. The quality of the guideline's developmental process varied considerably. To increase quality and applicability, guideline developers should adopt a common structure for the development and reporting of their guidelines, for example Appraisal of Guidelines for Research and Evaluation (AGREE) criteria. Owing to differences in social systems, developers can learn from each other through reviews of this kind