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三维MANDELBROT渗流下临界形态 被引量:1

Lower State of Mandelbrot's Percolation Process in Three Dimension
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摘要 本文研究了三维andelbrot渗流下临界形态,证明了渗流函数θ(p)在pc点是不连续的,同时得到当p<pc时,三维Mandelbrot渗流A的最大连通分支是点,即A是"尘状"的. The paper considers the lower state of Mandelbrot's process. It is proved that the percolation function θ(p) is discontinuous at pc,shows that the set A contains no connected components larger than one point(a, e. ) for p〈pc,o, e. ,the set A is dust--like.
作者 马先南
出处 《数学理论与应用》 2007年第3期30-33,共4页 Mathematical Theory and Applications
关键词 n-水平立方体 渗流函数 临界概率 n-level Cube Percolation Function Critical Probability
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参考文献3

  • 1陈超,邹捷中.三维随机SIERPINSKI地毯的相位和临界概率[J].数学理论与应用,1999,19(2):86-89. 被引量:1
  • 2F. M. Dekking,R. W. J. Meester. On the structure of Mandelbrot’s percolation process and other random cantor sets[J] 1990,Journal of Statistical Physics(5-6):1109~1126
  • 3J. T. Chayes,L. Chayes,R. Durrett. Connectivity properties of Mandelbrot’s percolation process[J] 1988,Probability Theory and Related Fields(3):307~324

二级参考文献2

  • 1F. M. Dekking,R. W. J. Meester. On the structure of Mandelbrot’s percolation process and other random cantor sets[J] 1990,Journal of Statistical Physics(5-6):1109~1126
  • 2J. T. Chayes,L. Chayes,R. Durrett. Connectivity properties of Mandelbrot’s percolation process[J] 1988,Probability Theory and Related Fields(3):307~324

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