RESUMO
The propagation of nonlinear shallow water waves over a random seabed is studied. A bathymetry which fluctuates randomly from a constant mean adds multiple scattering to resonant interactions and harmonic generation. By the method of multiple scales, nonlinear evolution equations for the harmonic amplitudes are derived. Effects of multiple scattering are shown to be represented by certain linear damping terms with complex coefficients related to the correlation function of the seabed disorder. For any finite number of harmonics, an equation governing the total wave energy is derived. By numerical solution of the amplitude equations, the effects of spatial attenuation (localization) on harmonic generation are studied.
RESUMO
BACKGROUND: Impairments in work productivity and daily activities contribute to the burden of rheumatoid arthritis (RA). It is thus essential to use an instrument assessing both work and daily activity impairments when studying the full impact of RA on individuals. The Work Productivity and Activity Impairment (WPAI) questionnaire is such an instrument. OBJECTIVE: This study aims to linguistically validate the RA-specific WPAI (WPAI:RA) instrument in 20 new languages and to assess its content validity for individuals with RA. METHODS: The linguistic validation of the questionnaire followed a standard methodology that included comprehension test interviews (n = 5 individuals with RA per language) to assess the relevance, understanding and acceptability of the WPAI:RA. Content validity of the instrument was simultaneously investigated. RESULTS: Comprehension testing showed that the WPAI:RA questionnaire was well understood similarly across countries; minor changes were made to ensure fidelity to the original concepts and for ease of comprehension. The majority of interviewees (66/93) considered its content comprehensive and appropriate to measure their ability to work and perform daily activities. CONCLUSION: The WPAI:RA questionnaire is now linguistically validated in 20 new languages [Czech (Czech Republic), Dutch (Belgium), English (Canada and UK), French (Belgium, Canada and France), German (Germany), Hungarian (Hungary), Italian (Italy), Polish (Poland), Portuguese (Brazil), Romanian (Romania), Russian (Russia and Ukraine), Spanish (Argentina, Mexico, Spain and US) and Ukrainian (Ukraine)]. The WPAI:RA questionnaire shows good content validity. It can thus be used in multi-country clinical trials to assess RA-related impact on the patients' ability to work and perform daily activities.