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摘要翻译：
文献[1]和[2]研究了距离正则网络的有效电阻的计算，其中第一篇是基于网络的分层和与网络相关的Stieltjes函数计算的，而后一篇是基于Christoffel-Darboux恒等式给出了有效电阻的递推公式。本文研究了伪距离正则网络[21]或QD型网络的有效电阻的估计，利用这些网络的分层，证明了给定节点如$\alpha$和所有属于同一层的节点对$\alpha$($R_{\alpha\beta^{(m)}}$，$\beta$对$\alpha$)的有效电阻是相同的。然后，基于谱技术，根据与网络相关的第一和第二正交多项式，给出了有效电阻$R_{\alpha\beta_{(m)}}$使得$L_{-1}_{\alpha\alpha}=L_{-1}_{\beta\beta}$（使得网络相对于它们对称的节点）的解析公式，其中$L_{-1}$是网络的拉普拉斯的伪逆。从距离正则网络中，网络的所有节点$alpha,beta$均满足$l^{-1}_{alpha\alpha}=l^{-1}_{beta\beta}$这一事实出发，利用给出的公式直接计算了$m=1,2,..,d$($d$为网络直径与层数相同）的有效电阻$r_{alpha\beta}$。
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英文标题：
《Evaluation of effective resistances in pseudo-distance-regular resistor
networks》
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作者：
M. A. Jafarizadeh, R. Sufiani, S. Jafarizadeh
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：Other Condensed Matter 其他凝聚态物质
分类描述：Work in condensed matter that does not fit into the other cond-mat classifications
在不适合其他cond-mat分类的凝聚态物质中工作
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英文摘要：
In Refs.[1] and [2], calculation of effective resistances on distance-regular networks was investigated, where in the first paper, the calculation was based on the stratification of the network and Stieltjes function associated with the network, whereas in the latter one a recursive formula for effective resistances was given based on the Christoffel-Darboux identity. In this paper, evaluation of effective resistances on more general networks called pseudo-distance-regular networks [21] or QD type networks \cite{obata} is investigated, where we use the stratification of these networks and show that the effective resistances between a given node such as $\alpha$ and all of the nodes $\beta$ belonging to the same stratum with respect to $\alpha$ ($R_{\alpha\beta^{(m)}}$, $\beta$ belonging to the $m$-th stratum with respect to the $\alpha$) are the same. Then, based on the spectral techniques, an analytical formula for effective resistances $R_{\alpha\beta^{(m)}}$ such that $L^{-1}_{\alpha\alpha}=L^{-1}_{\beta\beta}$ (those nodes $\alpha$, $\beta$ of the network such that the network is symmetric with respect to them) is given in terms of the first and second orthogonal polynomials associated with the network, where $L^{-1}$ is the pseudo-inverse of the Laplacian of the network. From the fact that in distance-regular networks, $L^{-1}_{\alpha\alpha}=L^{-1}_{\beta\beta}$ is satisfied for all nodes $\alpha,\beta$ of the network, the effective resistances $R_{\alpha\beta^{(m)}}$ for $m=1,2,...,d$ ($d$ is diameter of the network which is the same as the number of strata) are calculated directly, by using the given formula.
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PDF链接：
https://arxiv.org/pdf/707.257
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