A two-parameter model of Hermitian matrices in zero-dimensional space is solved in the large-N limit. A very interesting phase diagram and a spontaneous magnetisation are exhibited.

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An optical scanning technique of dactylogram (fingerprint) has been developed by using plural LED's with different wavelength as emitting elements and a color CCD or CMOS area image sensor as receiving element. Owing to the R/G/B filters built in that color area image sensor, if the above LED's have wave lengths corresponding to those peak sensing wavelengths of the R/G/B outputs of that color area image sensor, and if the above mentioned LED's are installed to emit light on the surface of finger from different directions, then it will be effective to get a 3D picture by using a single color area image sensor. Moreover, the time needed to obtain a 3D picture is only that for single exposure.Thanks to the inherent nature of 3D picture, the sharpness of border of the ridges of a fingerprint in the picture is greatly enhanced. This simplifies the data transmission. Besides, by a simple signal processing of those output waveforms of the color area image sensor, the security against counterfeiting in fingerprint identification can be easily ensured. These features are essential for fingerprint authentication in INTERNET environment and E-Commerce environments.