Recently economic time series models have been developed largely. One direction is nonstationary and long range dependent models. The other is nonlinear models. This paper make a brief survay on new models along these directions. And some problems to be sloved in future are listed.

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Multi-stability and bifurcations in 2 or 3 coupled nonlinear oscillators are described based on the coupled equations of van der Pol and Rayleigh types. For the 2-coupled oscillators, relative stability between in-phase and anti-phase modes is discussed in relation to the connection parameters between the oscillators. It is shown that the effect of frustration among the oscillators becomes important when the number of the oscillators becomes more than three. Relative stability between the different modes based on these theoretical consideration is discussed in comparison with the actual experimental results with salt-water oscillator and oscillatory chemical reaction.

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This article focuses on mathematical aspects of computer vision, emphasizing the fact that many mathematically interesting facts are found through the process of designing and implementing practical engineering systems. This viewpoint is illustrated by analyzing the reliability of 3-D reconstruction from two images by stereo. First, the camera imaging is modeled as perspective projection, and the geometry of stereo is mathematically defined. It is shown that by introducing a model of image noise and applying statistical optimization, the 3-D positions of feature points are optimally reconstructed and their covariance matrices are quantitatively evaluated. Finally, related mathematically interesting topics are described from an engineering perspective.

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