论文标题
一维空间的指数随机压缩和146％
Exponential stochastic compression of one-dimensional space and 146 percent
论文作者
论文摘要
指数随机压缩是无限链的每个第二个细胞可能会增加其与左，右或两个相邻细胞随机合并的重量时的过程。假定总质量保护。之后，合并的单元格充满了空白空间，两次压缩链条。它们可能以两种不同的方式填充空空间：（i）仅使用移位，即保留订单； （ii）使用移位和随机排列。我们将初始同质链带有细胞重量$ 1 $多次，我们计算了最终密度$ρ_i$ρ_i$ wige $ i = 1,2,3，... $。主要结果是在有序情况（i）中$ρ_i/ρ_1= i $，而无序案例（ii）中的$ρ_i/ρ_1\ oft1.464910 ...（i-1/4）$。无序情况中的乘数具有分形性质。还讨论了最初不均匀链的压缩和重新定化的连续密度。
Exponential stochastic compression is the process when every second cell of an infinite chain may increase its weight merging randomly with left, right, or both neighboring cells. The total mass conservation is assumed. After that, merged cells fill the empty space, compressing the chain twice. They may fill empty spaces in two different ways: (I) using shifts only, i.e. preserving the order; (II) using shifts and random permutations. Compressing the initial homogeneous chain with cell weights $1$ many times, we compute final densities $ρ_i$ of cells with weight $i=1,2,3,...$. The main result is that $ρ_i/ρ_1=i$ in the ordered case (I), and $ρ_i/ρ_1\approx1.464910...(i-1/4)$ in the disordered case (II). The multiplier in the disordered case has a fractal nature. The compression of initially inhomogeneous chains and rescaled continuous densities are also discussed.
