Browsing by Author "Shieh, SF"

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Cellular neural networks: Space-dependent template, mosaic patterns and spatial chaos
(2002-08-01)
Juang, J
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Shieh, SF
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Turyn, L
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應用數學系
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Department of Applied Mathematics
We consider a Cellular Neural Network (CNN) with a bias term in the integer lattice Z(2) on the plane Z(2). We impose a space-dependent coupling (template) appropriate for CNN in the hexagonal lattice on Z(2). Stable mosaic patterns of such CNN are completely characterized. The spatial entropy of a (p(1), p(2))-translation invariant set is proved to be well-defined and exists. Using such a theorem, we are also able to address the complexities of resulting mosaic patterns.
Eigenvalue problems for one-dimensional discrete Schrodinger operators with symmetric boundary conditions
(2001-11-19)
Juang, J
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Lin, WW
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Shieh, SF
;
應用數學系
;
Department of Applied Mathematics
In this paper, we investigate the one-dimensional discrete Schrodinger equation with general, symmetric boundary conditions. Our results primarily concern the number of energy states lying in the wells.
On the spatial entropy of two-dimensional golden mean
(2004-01-01)
Juang, J
;
Shieh, SF
;
應用數學系
;
Department of Applied Mathematics
The aim of this paper is to derive a sharper lower bound for the spatial entropy of two-dimensional golden mean.
The spatial entropy of two-dimensional subshifts of finite type
(2000-12-01)
Juang, JQ
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Lin, SS
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Shieh, SF
;
Lin, WW
;
應用數學系
In this paper, two recursive formulas for computing the spatial entropy of two-dimensional subshifts of finite type are given. The exact entropy of a nontrivial example arising in cellular neural networks is obtained by using such formulas. We also establish some general theory concerning the spatial entropy of two-dimensional subshifts of finite type. In particular, we show that if either of the transition matrices is rank-one, then the associated exact entropy can be explicitly obtained. The generalization of our results to higher dimension can be similarly obtained. Furthermore, these formulas can be used numerically for estimating the spatial entropy.