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Topological entropy of a sequence of monotone maps on circles
Yujun Zhu,Jinlian Zhang,Lianfa He 대한수학회 2006 대한수학회지 Vol.43 No.2
In this paper, we prove that the topological entropy of a sequence of equi-continuous monotone maps $f_{1,\infty}=\{f_i\}_{i=1}^{\infty}\;$ on circles is $\;h(f_{1,\infty})=\limsup\limits_{n\rightarrow\infty}\frac{1}{n}\log\prod\limits_ {i=1}^{n}|\deg f_{i}|.$ As applications, we give the estimation of the entropies for some skew products on annular and torus. We also show that a diffeomorphism $f$ on a smooth $2$-dimensional closed manifold and its extension on the unit tangent bundle have the same entropy.
TOPOLOGICAL ENTROPY OF A SEQUENCE OF MONOTONE MAPS ON CIRCLES
Zhu Yuhun,Zhang Jinlian,He Lianfa Korean Mathematical Society 2006 대한수학회지 Vol.43 No.2
In this paper, we prove that the topological entropy of a sequence of equi-continuous monotone maps $f_{1,\infty}={f_i}\;\infty\limits_{i=1}$on circles is $h(f_{1,\infty})={\frac{lim\;sup}{n{\rightarrow}\infty}}\;\frac 1 n \;log\;{\prod}\limits_{i=1}^n|deg\;f_i|$. As applications, we give the estimation of the entropies for some skew products on annular and torus. We also show that a diffeomorphism f on a smooth 2-dimensional closed manifold and its extension on the unit tangent bundle have the same entropy.
Linfen Xu,Ling liu,Xiaoyan Zhao,Jinyu Lin,Shaohan Xu,Jinlian He,Debin Jiang,Yong Xia The Korean Electrochemical Society 2023 Journal of electrochemical science and technology Vol.14 No.1
The effective detection of human chorionic gonadotropin (HCG) is considerably important for the clinical diagnosis of both of early pregnancy and nonpregnancy-related diseases. In this work, a simple and sensitive electrochemical sandwich-type immunosensing platform was designed by synthesizing b-cyclodextrin (CD) functionalized graphene (CD/GN) hybrid as simultaneously sensing platform and signal transducer coupled with rhodamine b (RhB) as probe. In brief, GN offers large surface area and high conductivity, while CD exhibits superior host-guest recognition capability, thus the primary antibody (Ab1) of HCG can be bound into the cavities of CD/GN to form stable Ab1/CD/GN inclusion complex; meanwhile, the secondary antibody (Ab2) and RhB can also enter into the cavities, producing RhB/Ab2/CD/GN complex. Then, by using Ab1/CD/GN as sensing platform and RhB/Ab2/CD/GN as signal transducer (in which RhB was signal probe), a simple sandwich-type immunosensor was constructed. Under the optimum parameters, the designed immunosensor exhibited a considerable low analytical detection of 1.0 pg mL<sup>-1</sup> and a wide linearity of 0.002 to 10.0 ng mL<sup>-1</sup> for HCG, revealing the developed sandwich-type electrochemical immunosensing platform offered potential real applications for the determination of HCG.