Smoothing Property for Schrödinger Equations¶with Potential Superquadratic at Infinity

We prove a smoothing property for one dimensional time dependent Schr?dinger equations with potentials which satisfy at infinity, k≥ 2. As an application, we show that the initial value problem for certain nonlinear Schr?dinger equations with such potentials is L ₂ well-posed. We also prove a sharp asymptotic estimate of the L ^p -norm of the normalized eigenfunctions of H=−Δ+V for large energy. Dedicated to Jean-Michel Combes on the occasion of his Sixtieth Birthday Received: 10 October 2000 / Accepted: 29 March 2001     

Distortions of videofiberoscopy imaging: Reconsideration and correction

An analysis was made of the optical distortion of a lens system of a fiberscope and the distortion related to lens-object angles and lens-object distances used in laryngeal flexible endoscopic examinations. The optical distortion was systematic and, therefore, could be corrected through computer processing once the calibration was made. Similarly, the distortion related to the lens-object angle and distance varied systematically depending on distance and angle and, therefore, could be predicted if those parameters were measured simultaneously. The correction of those distortions of videofiberoscopic image is demonstrated, and a procedure for recording and measuring laryngeal images that minimizes measurement error due to those distortions is suggested.