This paper studies the eigentime and related issues in the fractal network corresponding to the Sierpiński fractal antenna.The access time or hitting time H(i,j)is the expected number of steps before node j is visite...This paper studies the eigentime and related issues in the fractal network corresponding to the Sierpiński fractal antenna.The access time or hitting time H(i,j)is the expected number of steps before node j is visited,starting from node i.The eigentime of G is the expectation of H(i,j)for all i,j∈G.Classical eigenvalue method let H(i,i)=0.However,when studying the random walk behavior of electrons in fractal networks corresponding to fractal antennas,it is nec-essary to consider the time when electrons leave a certain node and first return to that node(self return time).This paper adopts two research methods-the eigenvalue method based on spectral theory and the Markov chain method based on stochastic process theory-to obtain the modified in-trinsic time,and demonstrates through an example that the difference between the classical intrin-sic time and the modified intrinsic time is precisely due to the self return time.This paper shows the applications of fractal networks in modern communications.The research results are expected to provide a theoretical basis for the design and performance optimization of fractal antennas.展开更多
The weighted self-similar network is introduced in an iterative way.In order to understand the topological properties of the self-similar network,we have done a lot of research in this field.Firstly,according to the s...The weighted self-similar network is introduced in an iterative way.In order to understand the topological properties of the self-similar network,we have done a lot of research in this field.Firstly,according to the symmetry feature of the self-similar network,we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix.Then,we obtain eigenvalues of the Laplacian matrix from these two successive generations.Finally,we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix.展开更多
基金supported by the Young Talent Fund of Association for Science and Technology in Shaanxi,China,un-der grant No.20230513.
文摘This paper studies the eigentime and related issues in the fractal network corresponding to the Sierpiński fractal antenna.The access time or hitting time H(i,j)is the expected number of steps before node j is visited,starting from node i.The eigentime of G is the expectation of H(i,j)for all i,j∈G.Classical eigenvalue method let H(i,i)=0.However,when studying the random walk behavior of electrons in fractal networks corresponding to fractal antennas,it is nec-essary to consider the time when electrons leave a certain node and first return to that node(self return time).This paper adopts two research methods-the eigenvalue method based on spectral theory and the Markov chain method based on stochastic process theory-to obtain the modified in-trinsic time,and demonstrates through an example that the difference between the classical intrin-sic time and the modified intrinsic time is precisely due to the self return time.This paper shows the applications of fractal networks in modern communications.The research results are expected to provide a theoretical basis for the design and performance optimization of fractal antennas.
基金supported by the Natural Science Foundation of China(Nos.11671172)。
文摘The weighted self-similar network is introduced in an iterative way.In order to understand the topological properties of the self-similar network,we have done a lot of research in this field.Firstly,according to the symmetry feature of the self-similar network,we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix.Then,we obtain eigenvalues of the Laplacian matrix from these two successive generations.Finally,we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix.
