Abstract. We consider the one-dimensional focusing nonlinear Schrödinger equation (NLS) with a delta potential and even initial data. The problem is equivalent to the solution of the initial/boundary problem for NLS on a half-line with Robin boundary conditions at the origin. We follow the method of Bikbaev and Tarasov which utilizes a Bäcklund transformation to extend the solution on the half-line to a solution of the NLS equation on the whole line. We study the asymptotic stability of the stationary 1-soliton solution of the equation under perturbation by applying the nonlinear steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou. Our work strengthens, and extends, earlier work on the problem by Holmer and Zworski.
Benzenethiol-and 1,4-benzenedithiol-adsorbed Si(111)-7 × 7 surfaces were studied by using scanning tunneling microscopy and synchrotron radiation photoemission spectroscopy, which showed that benzenethiol molecules were adsorbed on Si adatoms with upright structures and 1,4benzenedithiol molecules on two adjacent Si adatoms with a bridging structure. At the initial stage, the adsorptions can be understood by a dissociative process between sulfur and hydrogen on the Si atoms. Here, sulfur bonds to the electrophilic adatoms while hydrogen bonds to neighboring nucleophilic restatoms. On the other hand, this adsorption mechanism during the initial stage does not apply at higher exposures of molecules, as is noticed from the photoemission spectra.
This article introduces a time-domain-based artificial intelligence (AI) radar system for gesture recognition using 33-GS/s direct sampling technique. High-speed sampling using a time-extension method allows AI learning to be applied to a time-domain radar signal reflecting information on both dynamic and static gestures, and thus can recognize not only dynamic but also static gestures. The Vernier clock generators and high-speed active samplers applied with the time-extension technique makes sampling at 33 GS/s possible. A 1-D convolutional neural network and long short-term memory are employed for both static and dynamic gestures and recognition rates of 93.2% and 90.5% are obtained, respectively. The radar system is implemented using a 65-nm CMOS process with a power consumption of 95 mW.
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