Large Time Existence for Thin Vibrating Plates

We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system as $h\to 0$ is either the nonlinear von K\'arm\'an plate equation or the linear fourth order Germain-Lagrange equation. In the case of the linear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation

The fundamental left-right asymmetry in the Germanic verb cluster

Cinque (2005, 2009, 2014a) observes that there is an asymmetry in the possible ordering of dependents of a lexical head before versus after the head. A reflection on some of the concepts needed to develop Cinque’s ideas into a theory of neutral word order reveals that dependents need to be treated separately by class. The resulting system is applied to the problem of word order in the Germanic verb cluster. It is shown that there is an extremely close match between theoretically derived expectations for clusters made up of auxiliaries, modals, causative ‘let’, a main verb, and verbal particles. The facts point to the action of Cinque’s fundamental left-right asymmetry in language in the realm of the verb cluster. At the same time, not all verb clusters fall under Cinque’s generalization, which, therefore, argues against treating all cases of restructuring uniformly

Thin vibrating plates: long time existence and convergence to the von Kármán plate equations

The asymptotic behavior of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness h of the plate tends to zero. We discuss the long time existence and convergence to solutions of the time-dependent von Kármán and linear plate equation under appropriate scalings of the applied force and of the initial values in terms of h

Clinical evaluation of cochlear implant sound coding taking into account conjectural masking functions, MP3000™.

Efficacy of the SPEAK and ACE coding strategies was compared with that of a new strategy, MP3000™, by 37 European implant centers including 221 subjects. The SPEAK and ACE strategies are based on selection of 8-10 spectral components with the highest levels, while MP3000 is based on the selection of only 4-6 components, with the highest levels relative to an estimate of the spread of masking. The pulse rate per component was fixed. No significant difference was found for the speech scores and for coding preference between the SPEAK/ACE and MP3000 strategies. Battery life was 24% longer for the MP3000 strategy. With MP3000 the best results were found for a selection of six components. In addition, the best results were found for a masking function with a low-frequency slope of 50 dB/Bark and a high-frequency slope of 37 dB/Bark (50/37) as compared to the other combinations examined of 40/30 and 20/15 dB/Bark. The best results found for the steepest slopes do not seem to agree with current estimates of the spread of masking in electrical stimulation. Future research might reveal if performance with respect to SPEAK/ACE can be enhanced by increasing the number of channels in MP3000 beyond 4-6 and it should shed more light on the optimum steepness of the slopes of the masking functions applied in MP3000