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This paper deals with a nonlinear string-beam system describing the torsional-vertical oscillations of a suspension bridge. We consider the initial-boundary value problem and study the existence and uniqueness question. We assume time independent right hand sides, but allow quite general nonlinear terms. Using the Faedo-Galerkin method we prove the existence of a unique solution on an arbitrary large time interval.

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Background and Aims. Obstructive sleep apnoea is a potentially serious sleep disorder associated with the risk of cardiovascular disease. It is treated with continuous airway pressure (CPAP) but this is not always successful. Unsuccessful cases should be treated by bilevel positive airway pressure (BiPAP). The aim of this study was to determine whether common respiratory parameters and/or body mass index (BMI) can be used to predict the probability CPAP failure and hence start such patients on BiPAP from the outset. Methods. A sample of patients treated by CPAP for OSAS was evaluated a retrospective cohort study. The data measured in sleep monitoring of the successfully treated group and of the group where CPAP had failed were compared. Subsequently, the predictive abilities of BMI, Apnoea Index (AI), Apnoea-Hypopnea Index (AHI), percentage of sleep time in less than 90% oxygen saturation (T90), average oxygen saturation over the duration of sleep (SaO2) and average desaturation per hour of sleep (ODI) were assessed with respect to CPAP failure, both individually and in combination. Results. A sample of 479 patients was included in the study. All of the recorded variables except AI were significantly associated with failure of CPAP and their ability to predict the failure ranged from poor to moderate. Since there was significant correlation among all the variables measured a two-variable prediction model combining T90 and BMI produced no significant improvement in the quality of CPAP failure prediction. Conclusions. BMI was a significant predictor of CPAP failure although it was slightly less predictive than T90. The set of monitored variables included in our study does not allow for CPAP failure to be predicted with clinically relevant reliability.