[應用數學系] 國科會研究計畫 2022-08
多重整數系統之遍歴理論 班榮超
[應用數學系] 國科會研究計畫 2021-08
自由群上子平移的熵研究 班榮超
[應用數學系] 國科會研究計畫 2021-08
整合研究：動態系統的不變量、拓樸性質及分類問題研究—多重平移系統的Lipschitz等價問題 班榮超
[應用數學系] 專書/專書篇章 2019-02
Measures of the full Hausdorff dimension for sofic affine-invariant sets on T^2 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Chen, Ting-Ju
[應用數學系] 專書/專書篇章 2014-11
Tracking Mean Field Dynamics by Synchronous Computations of Recurrent Multilayer Perceptrons 班榮超 ; Ban, Jung-Chao ; Wu, Jiann-Ming ; Wu, Chun-Chang
[應用數學系] 專書/專書篇章 2013-01
On the Structure of Two-Layer Cellular Neural Networks 班榮超 ; Ban, Jung-Chao ; Lin, Song-Sun
[應用數學系] 會議論文 2011-04
Complexity of two dimensional multi-layer cellular neural networks 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Hu, Wen-Guei ; Lin, Song-Sun
[應用數學系] 期刊論文 2025-06
Thermodynamic formalism and large deviation principle of multiplicative Ising models 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lai, Guan-Yu
[應用數學系] 期刊論文 2025-06
Hausdorff dimensions of affine multiplicative shifts 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lai, Guan-Yu ; Liao, Lingmin
[應用數學系] 期刊論文 2025-06
Hausdorff dimensions of irreducible Markov hom tree-shifts 班榮超 ; Ban, Jung-Chao ; Lai, Guan-Yu ; Wu, Yu-Liang
[應用數學系] 期刊論文 2025-06
The strip entropy approximation of Markov tree-shifts 班榮超 ; Ban, Jung-Chao ; Lai, Guan-Yu ; Tsai, Cheng-Yu
[應用數學系] 期刊論文 2025-05
Entropy of axial products on N^d and trees 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lai, Guan-Yu
[應用數學系] 期刊論文 2025-05
Projected spread models 班榮超 ; 洪芷漪 ; Ban, Jung-Chao ; Hong, Jyy-I ; Tsai, Cheng-Yu ; Wu, Yu-Liang
[應用數學系] 期刊論文 2025-04
Positioned spread models: A mathematical analysis of the topological and random population systems 班榮超 ; 洪芷漪 ; Ban, Jung-Chao ; Hong, Jyy-I ; Tsai, Cheng-Yu
[應用數學系] 期刊論文 2025-03
On the topological pressure of axial product on trees 班榮超 ; Ban, Jung-Chao ; Wu, Yu-Liang
[應用數學系] 期刊論文 2025-01
Survival properties and spread rates in non-autonomous spread models 班榮超 ; 洪芷漪 ; Ban, Jung-Chao ; Hong, Jyy-I ; Tsai, Cheng-Yu ; Tsou, Chu-Yang
[應用數學系] 期刊論文 2024-05
Hausdorff dimension of multidimensional multiplicative subshifts 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lai, Guan-Yu
[應用數學系] 期刊論文 2024-04
On mixing properties of Markov tree-shifts 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Huang, Nai-Zhu ; Lai, Guan-Yu
[應用數學系] 期刊論文 2024-03
Large deviation principle of multiplicative Ising models on Markov-Cayley trees 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Zhang, Zongfan
[應用數學系] 期刊論文 2024-02
Topological entropy and sequence entropy for hom tree-shifts on unexpandable trees 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Hu, Wen-Guei ; Lai, Guan-Yu ; Wu, Yu-Liang
[應用數學系] 期刊論文 2023-12
On the escape rate of subshifts of finite type and 2-multiplicative integer systems on N^d 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lai, Guan-Yu
[應用數學系] 期刊論文 2023-08
An analogue of topological sequence entropy for Markov hom tree-shifts 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Hu, Wen-Guei ; Lai, Guan-Yu ; Wu, Yu-Liang
[應用數學系] 期刊論文 2023-06
Boundary complexity and surface entropy of 2-multiplicative integer systems on N^d 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lai, Guan-Yu
[應用數學系] 期刊論文 2023-06
Topological and random spread models with frozen symbols 班榮超 ; 洪芷漪 ; Ban, Jung-Chao ; Hong, Jyy-I ; Tsai, Cheng-Yu ; Wu, Yu-Liang
[應用數學系] 期刊論文 2023-05
Decidability of CPC-irreducibility of subshifts of finite type over free groups 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Wu, Yu-Liang
[應用數學系] 期刊論文 2023-04
The entropy of multiplicative subshifts on trees 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Zhang, Zongfan
[應用數學系] 期刊論文 2023-02
Mathematical analysis of topological and random m-order spread models 洪芷漪 ; 班榮超 ; Hong, Jyy-I ; Ban, Jung-Chao ; Wu, Yu-Liang
[應用數學系] 期刊論文 2023-01
Commutativity of entropy for nonautonomous systems on trees 班榮超 ; Ban, Jung-Chao ; Huang, Nai-Zhu
[應用數學系] 期刊論文 2023-01
Large deviation principle of nonconventional ergodic averages 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lai, Guan-Yu
[應用數學系] 期刊論文 2022-10
Spread rates of spread models with frozen symbols 洪芷漪 ; 班榮超 ; Hong, Jyy-I ; Ban, Jung-Chao ; Wu, Yu-Liang
[應用數學系] 期刊論文 2022-09
Topological entropy for shifts of finite type over Z and trees 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Hu, Wen-Guei ; Wu, Yu-Liang
[應用數學系] 期刊論文 2021-12
Stem and topological entropy on Cayley trees 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Wu, Yu-Liang ; Wu, Yu-Ying
[應用數學系] 期刊論文 2021-10
Characterization and Topological Behavior of Homomorphism Tree-Shifts 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Hu, Wen-Guei ; Lai, Guan-Yu
[應用數學系] 期刊論文 2021-09
Mathematical analysis of spread models: From the viewpoints of deterministic and random cases 班榮超 ; 洪芷漪 ; Ban, Jung-Chao ; Hong, Jyy-I ; Chang, Chih-Hung ; Wu, Yu-Liang
[應用數學系] 期刊論文 2021-09
Large deviation principle of multidimensional multiple averages on Nd 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lai, Guan-Yu
[應用數學系] 期刊論文 2021-08
On structure of topological entropy for tree-shifts of finite type 班榮超 ; Ban, Jung-Chao ; Chih-HungChang ; Wen-GueiHu ; Yu-LiangWu
[應用數學系] 期刊論文 2021-06
On the topological entropy of subshifts of finite type on free semigroups 班榮超 ; Ban, Jung-Chao ; Chan, Chih-Hung
[應用數學系] 期刊論文 2021-06
Verification of mixing properties in two-dimensional shifts of finite type 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lin, Song-Sun ; Lin, Yin-Heng
[應用數學系] 期刊論文 2021-02
On the entropy of multidimensional multiplicative integer subshifts 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lai , Guan-Yu
[應用數學系] 期刊論文 2020-07
Characterization for entropy of shifts of finite type on Cayley trees 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2020-07
Entropy Dimension of Shift Spaces on Monoids 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Huang, Nai-Zhu
[應用數學系] 期刊論文 2020-06
Characterization for entropy of shifts of finite type on Cayley trees 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2020-06
Entropy Dimension of Shift Spaces on Monoids 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Huang, Nai-Zhu
[應用數學系] 期刊論文 2020-06
Entropy Dimension of Shifts of Finite Type on Free Groups 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2020-04
Complexity of Shift Spaces on Semigroups 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Huang, Yu-Hsiung
[應用數學系] 期刊論文 2019-11
Topologically Mixing Properties of Multiplicative Integer System 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Hu, Wen-Guei ; Lai, Guan-Yu ; Wu, Yu-Liang
[應用數學系] 期刊論文 2019-10
Decidability of Irreducible tree shifts of finite type 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Huang, Nai-Zhu ; Wu, Yu-Liang
[應用數學系] 期刊論文 2019-06
Entropy bifurcation of neural networks on Cayley trees 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Huang, Nai-Zhu
[應用數學系] 期刊論文 2019-05
Complexity of neural networks on Fibonacci-Cayley tree 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2019-05
Pattern generation problems arising in multiplicative integer systems 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lin, Song-Sun
[應用數學系] 期刊論文 2018-05
Measure of the full Hausdorff dimension for sofic affine-invariant sets on T^2 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Chen, Ting-Ju
[應用數學系] 期刊論文 2017-11
Mixing properties of tree-shifts 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2017-06
Tree-shifts: The entropy of tree-shifts of finite type 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2017-06
簡單通往複雜之路 班榮超 ; Ban, Jung-Chao
[應用數學系] 期刊論文 2017-05
Tree-shifts: Irreducibility, mixing, and the chaos of tree-shifts 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2016-07
When are two multi-layer cellular neural networks the same? 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2016-06
淺談動力系統中的禍福相倚 班榮超 ; Ban, Jung-Chao
[應用數學系] 期刊論文 2016-03
Solution Structure of Multi-layer Neural Networks with Initial Condition 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2016-02
The spatial complexity of inhomogeneous multi-layer neural networks 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2015-08
Neural network equations and symbolic dynamics 班榮超 ; Ban, Jung-Chao
[應用數學系] 期刊論文 2015-07
On the structure of multi-layer cellular neural networks: complexity between two layers 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2015-01
Realization problem of multi-layer cellular neural networks 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2014-12
The multifractal spectra for the recurrence rates of beta-transformations 班榮超 ; Ban, Jung-Chao ; Li, Bing
[應用數學系] 期刊論文 2014-05
Dimension spectrum for sofic systems 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Lin, Mei-Shao ; Chen, Ting-Ju
[應用數學系] 期刊論文 2013-12
Inhomogeneous lattice dynamical systems and the boundary effect 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2013-11
Hausdorff Dimension of Multi-Layer Neural Networks 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2013-07
The layer effect on multi-layer cellular neural networks 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2013-01
Diamond in multi-layer cellular neural networks 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2013-01
On the Quantitative Behavior of the Linear Cellular Automata. 班榮超 ; Ban, Jung-Chao ; Akin, Hassan ; Chang, Chih-Hung
[應用數學系] 期刊論文 2013-01
The learning problem of multi-layer neural networks 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2013-01
Zeta functions for two-dimensional shifts of finite type 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lin, Song-Sun ; Lin, Yin-Heng
[應用數學系] 期刊論文 2012-04
On the structure of multi-layer cellular neural networks 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Lin, Song-Sun
[應用數學系] 期刊論文 2011-05
Factor map, diamond and density of pressure functions 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2011-01
The Complexity of Permutive Cellular Automata 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Chen, Ting-Ju ; Lin, Mei-Shao
[應用數學系] 期刊論文 2010-03
Zeta function for two-dimensional subshift of finite type 班榮超 ; Ban, Jung-Chao ; Hu, Wen-Guei ; Lin, Song-Sun ; Lin, Yin-Heng
[應用數學系] 期刊論文 2010-01
The dimensions of a non-conformal repeller and an average conformal repeller 班榮超 ; Ban, Jung-Chao ; Cao, Yong-Luo ; Hu, Hu-Yi
[應用數學系] 期刊論文 2009-11
On the monotonicity of entropy for multilayer cellular neural networks 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2009-09
Mixing property and entropy conjugacy of Z2 subshift of finite type: a case study 班榮超 ; Ban, Jung-Chao ; Lin, Szu-Yu ; Lin, Yin-Heng
[應用數學系] 期刊論文 2009-09
The Hausdorff dimension of average conformal repellers under random perturbation 班榮超 ; Ban, Jung-Chao ; Cao, Yong-Luo ; Zhao, Yun
[應用數學系] 期刊論文 2009-06
Pullback and forward attractors for dissipative lattice dynamical systems with additive noises 班榮超 ; Ban, Jung-Chao ; Hsu, Cheng-Hsiung ; Lin, Yin-Heng ; Yang, Tzi-Sheng
[應用數學系] 期刊論文 2009-05
The topological pressure of linear cellular automata 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2009-01
Spatial complexity in multi-layer cellular neural networks 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung ; Lin, Song-Sun ; Lin, Yin-Heng
[應用數學系] 期刊論文 2008-11
On the dense entropy of two-dimensional inhomogeneous cellular neural networks 班榮超 ; Ban, Jung-Chao ; Chang, Chih-Hung
[應用數學系] 期刊論文 2007-09
Patterns generation and spatial entropy in two-dimensional lattice models 班榮超 ; Ban, Jung-Chao ; Lin, Song-Sun ; Lin, Yin-Heng
[應用數學系] 期刊論文 2005-08
Patterns generation and transition matrices in multi-dimensional lattice models 班榮超 ; Ban, Jung-Chao ; Lin, Song-Sun
[應用數學系] 期刊論文 2004-07
The devil’s staircase dimensions and measure-theoretical entropy of maps with horizontal gap 班榮超 ; Ban, Jung-Chao ; Lin, Song-Sun
[應用數學系] 期刊論文 2003-01
Devil`s staircase of gap maps 班榮超 ; Ban, Jung-Chao ; Hsu, Cheng-Hsiung ; Lin, Song-Sun
[應用數學系] 期刊論文 2002-03
Spatial disorder of cellular neural networks—with biased term 班榮超 ; Ban, Jung-Chao ; Lin, Song-Sun ; Hsu, Cheng-Hsiung
[應用數學系] 期刊論文 2001-08
Spatial disorder of CNN—with asymmetric output function 班榮超 ; Ban, Jung-Chao ; Chien, Kai-Ping ; Lin, Song-Sun ; Hsu, Cheng-Hsiung
[應用數學系] 期刊論文 2001-06
Exact number of mosaic patterns in cellular neural networks 班榮超 ; Ban, Jung-Chao ; Lin, Song-Sun ; Shih, Chih-Wen 
