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Sierpinski锥及其Hausdorff维数与Hausdorff测度 总被引:1,自引:1,他引:0
首先给出了 Sierpinski锥的概念及构造过程 ,然后求出其计盒维数、Hausdorff维数和 Hausdorff测度 . 相似文献
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胡迪鹤 《数学物理学报(A辑)》1990,(4)
本文引进了向量维Hausdorff测度及其维向量的概念,研究了向量维Hausdorff测度的基本性质及其与经典Hausdorff测度(其维数为广义非负实数)的关系,引进两种类型的维向量,研究了它们之间的关系及其与经典Hausdorff维数的关系。 相似文献
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首先介绍广义Weierstrass型函数的Weyl-Marchaud分数阶导数,得到了带随机相位的广义Weierstrass型函数的Weyl-Marchaud分数阶导数图像的Hausdorff维数,证明了该分形函数图像的Hausdorff维数与Weyl-Marchaud分数阶导数的阶之间的线性关系. 相似文献
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设S_λ为压缩比为λ(λ≤1/3)的一类Sierpinski垫,s=-log_λ3为S_λ的Hausdorff维数,N为产生S_λ的所有基本三角形的集合.本文使用网测度方法,获得了S_λ的s-维Hausdorff测度的精确值H~s(S_λ)=1,同时证明了H~s(S_λ)可由S_λ关于网N的s-维Hausdorff测度H_N~s(S_λ)确定,获得了S_λ的非平凡的最佳覆盖. 相似文献
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作者进一步研究了在文章[1]中构造的广义统计自相似集的分形性质,得到了这类集合的Hausdorff维数和确切Hausdorff测度函数。文中的结果是[4]中结果的延拓。 相似文献
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给出了RN中某些分形子集的Hausdorff维数及其Hausdorff测度估计式. 相似文献
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§0.BasicConceptsThefolowingconceptsandtheirrelatedpropertieslistedinthissectioncanbefoundin[1,2,3].1.Anon-negativefunctionμ(E... 相似文献
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Richard Delaware 《Proceedings of the American Mathematical Society》2003,131(8):2537-2542
A set is -straight if has finite Hausdorff -measure equal to its Hausdorff -content, where is continuous and non-decreasing with . Here, if satisfies the standard doubling condition, then every set of finite Hausdorff -measure in is shown to be a countable union of -straight sets. This also settles a conjecture of Foran that when , every set of finite -measure is a countable union of -straight sets.
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Inci Albayrak 《Journal of Mathematical Analysis and Applications》2007,328(1):414-428
In the present paper we investigate when Hausdorff matrices and generalized Hausdorff matrices, with the same mass function, are equivalent, as bounded operators on c and ?p. 相似文献
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This paper gives a formula of integral for the rectifiable curves in the plane by the Hausdorff fractional derivation and
integral.
Received August 10, 1999, Revised December 27, 1999, Accepted January 14, 2000 相似文献
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In this paper we study a class of subsets of the general Sierpinski carpets for which the allowed two digits in the expansions occur with proportional frequency. We calculate the Hausdorff and box dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive finite. 相似文献
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On the Lower Bound of the Hausdorff
Measure of the Koch Curve 总被引:1,自引:0,他引:1
ZhiWeiZHU ZuoLingZHOU BaoGuoJIA 《数学学报(英文版)》2003,19(4):715-728
This paper gives a lower bound of the Hausdorff measure of the Koch curve by means of the mass distribution principle. 相似文献
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LetE be a Moran fractal andH
s
(E) denote thes-dimensional Hausdorff measure ofE. In this paper, we define a orthonormal and complete system of functions in the Hilbert spaceL
2(E,H
s
) and prove that partial sums of the Fourier series, with respect to , of each functionf(x)L
1(E,H
s
) converge tof(x) atH
s
-a.e.xE. Moreover, the Fourier series off, forfL
p
(E,H
s
),p1, converges off inL
p
-norm. When Moran fractals degenerate into self-similar fractals, our results well agree with M. Reyes's results.This work is supported in part by the National Natural Science Foundation of China. 相似文献
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P. Frosini 《Applied Mathematics Letters》2002,15(8):931-935
Consider the set K of all nonempty compact subsets of a compact metric space (M, d), endowed with the Hausdorff metric. In this paper, we prove that K is isometric to a subset of l∞(
). An approximation result is also proved. 相似文献
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In this article,the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions.Several examples are given at the end. 相似文献