Three-body clusters are studied in the algebraic cluster model. Particular attention is paid to the case of three identical particles. It is shown in a geometrical analysis that the harmonic oscillator, the deformed oscillator and the oblate symmetric top are contained as special solutions. An application of the oblate top limit to the nucleus 12 C suggests that the low-lying spectrum can be de...

Capacitive Micro-machined Ultrasonic Transducers (CMUTs) are the ultrasonic devices which produce better features in contrast to piezoelectric transducers. The intrinsic parameter of CMUT varies with the variation in geometrical dimension of the device. The cavity height and the radius of the CMUT with circular membrane is varied in the lumped parallel plate model for its impact on the paramete...

In the probabilistic topic models, the quantity of interest—a lowrank matrix consisting of topic vectors—is hidden in the text corpus matrix, masked by noise, and the Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank matrix and the singular vectors of the text corpus matrix are usually complicated a...

We present a simple model for the friction of two solid bodies moving against each other. In a self consistent way we can obtain the dependence of the macro-scopic friction force as a function of the driving velocity, the normal force and the ruggedness of the surfaces in contact. Our results are discussed in the context of friction laws used in earthquake models.