Jung-Chao Ban

Publications (4)0 Total impact

• Article: Measures of the full Hausdorff dimension for a general Sierpi\'{n}ski carpet

  Jung-Chao Ban, Chih-Hung Chang, Ting-Ju Chen
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  ABSTRACT: The measure of the full dimension for a general Sierpi\'{n}ski carpet is studied. In the first part of this study, we give a criterion for the measure of the full Hausdorff dimension of a Sierpi\'{n}ski carpet. Meanwhile, it is the conditional equilibrium measure of zero potential with respect to some Gibbs measure $\nu_{\alpha}$ of matrix-valued potential $\alpha\mathbf{N}$ (defined later). On one hand, this investigation extends the result of [17] without condition \textbf{(H)}. On the other hand, it provides a checkable condition to ensure the existence and uniqueness of the measure of the full Hausdorff dimension for a general Sierpi\'{n}ski carpet. In the second part of this paper we give a criterion for the Markov projection measure and estimate its number of steps by means of the induced matrix-valued potential. The results enable us to answer some questions which arise from [1] and [4] on the projection measure and factors.
  06/2012;
• Article: The Complexity of Permutive Cellular Automata.

  Jung-Chao Ban, Chih-Hung Chang, Ting-Ju Chen, Mei-Shao Lin
  J. Cellular Automata. 01/2011; 6:385-397.
• Article: On the Monotonicity of Entropy for Multilayer Cellular Neural Networks.

  Jung-Chao Ban, Chih-Hung Chang
  I. J. Bifurcation and Chaos. 01/2009; 19:3657-3670.
• Article: On the Dense Entropy of Two-Dimensional Inhomogeneous Cellular Neural Networks.

  Jung-Chao Ban, Chih-Hung Chang
  I. J. Bifurcation and Chaos. 01/2008; 18:3221-3231.