谢宾斯基垫片上的尺度因子
The Scaling Factor on the Sierpinski Gasket
摘要:
本文将给出关于谢宾斯基垫片上尺度因子计算方法的综述。我们主要介绍等权条件下谢宾斯基垫片尺度因子的两种求法。一是用Δ-Y变换,另外一种则是用经典微积分中关于极值部分的理论。
Abstract: In this paper, we give a statement of the computing method of scaling factor on the Sierpinski gasket. We will introduce two methods in computing the scaling factor under equal-weighted condition. One is by Δ-Y Transformation. The other one is using extreme values in classical calculus theory.
参考文献
[1]
|
Kigami, J. (1989) A harmonic calculus on the Sierpinski spaces. Japan Journal of Applied Mathematics, 8, 259-290.
|
[2]
|
Kigami, J. (1993) Harmonic calculus on p.c.f. self-similar sets. Transactions of American Mathematical Society, 335, 721-755.
|
[3]
|
Kigami, J. (2001) Analysis on fractals. Cambridge University Press, Cam-bridge.
|
[4]
|
Lindstrøm, T. (1990) Brownian motion on nested fractal. Memory of American Mathematical Society, 420.
|
[5]
|
Strichartz, R.S. (2000) Taylor approximations on Sierpinski gasket type fractals. Journal of Functional Analysis, 174, 76-127.
|
[6]
|
Strichartz, R.S. (2006) Differential equations on fractals: A tutorial. Princeton University press, Princeton.
|
[7]
|
张永照, 杨万明, 张淑艳 (1995) 电阻形联接与形联接等效变换的简单推导. 大学物理, 3, 18-19.
|
[8]
|
过祥龙, 张毓麟 (1997) Sierpinski电阻网络等效电阻的研究. 大学物理, 4, 8-10.
|
[9]
|
郭慧丽 (2001) Sierpinski变形电阻网络等效阻值的研究. 甘肃高师学报, 2, 27-28.
|
[10]
|
李建新 (2005) 一类n级嵌套的三角形电阻网络的研究. 安阳工学院学报, 13, 58-60.
|
[11]
|
孙亚萍 (2011) Δ-Y变换在数学中的应用. 硕士论文, 南京审计学院, 南京.
|
[12]
|
潘新月 (2013) 谢宾斯基垫片上尺度因子的求法. 硕士论文, 南京审计学院, 南京.
|