In this paper, authors study the properties of multifractal Hausdorff and packing measures for a class of self-affine sets and use them to study the multifractal properties of general Sierpinski carpet E, and they get...In this paper, authors study the properties of multifractal Hausdorff and packing measures for a class of self-affine sets and use them to study the multifractal properties of general Sierpinski carpet E, and they get that the multifractal Hausdorff and packing measure are mutual singular, when they are restricted on some subsets of E.展开更多
In this paper, a lemma as a new method to calculate the Hausdorff measure of fractal is given. And then the exact values of Hausdorff measure of a class of Sierpinski sets which satisfy balance distribution and dimens...In this paper, a lemma as a new method to calculate the Hausdorff measure of fractal is given. And then the exact values of Hausdorff measure of a class of Sierpinski sets which satisfy balance distribution and dimension ≤ 1 are obtained.展开更多
Suppose F0 is an arbitrary triangle and F is a kind of Sierpinski carpet generated by F0.We construct a projection mapping to obtain the lower bound of the Hausdorff measure of F ;meanwhile the upper bound of the Haus...Suppose F0 is an arbitrary triangle and F is a kind of Sierpinski carpet generated by F0.We construct a projection mapping to obtain the lower bound of the Hausdorff measure of F ;meanwhile the upper bound of the Hausdorff measure of F is calculated by the general covering.展开更多
By means of the idea of [2]（Jia Baoguo,J.Math.Anal.Appl.In press） and the self.similarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach ...By means of the idea of [2]（Jia Baoguo,J.Math.Anal.Appl.In press） and the self.similarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach the Hausdorff Measure of Sierpinski carpet infinitely.展开更多
In this paper, we address the problem of exact computation of the Hausdorff measure of a class of Sierpinski carpets E- the self-similar sets generating in a unit regular pentagon on the plane. Under some conditions, ...In this paper, we address the problem of exact computation of the Hausdorff measure of a class of Sierpinski carpets E- the self-similar sets generating in a unit regular pentagon on the plane. Under some conditions, we show the natural covering is the best one, and the Hausdorff measures of those sets are euqal to ｜E｜^S, where s = dimHE.展开更多
In this paper we study a class of subsets of the general Sierpinski carpets for which two groups of allowed digits occur in the expansions with proportional frequency. We calculate the Hausdorff and Box dimensions of ...In this paper we study a class of subsets of the general Sierpinski carpets for which two groups of allowed digits occur in the expansions 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 and finite.展开更多
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 ...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.展开更多
基金the National Natural Sciences Foundation of China Special Funds of State Education Committee for Doctorate Scientific Resear
文摘In this paper, authors study the properties of multifractal Hausdorff and packing measures for a class of self-affine sets and use them to study the multifractal properties of general Sierpinski carpet E, and they get that the multifractal Hausdorff and packing measure are mutual singular, when they are restricted on some subsets of E.
文摘In this paper, a lemma as a new method to calculate the Hausdorff measure of fractal is given. And then the exact values of Hausdorff measure of a class of Sierpinski sets which satisfy balance distribution and dimension ≤ 1 are obtained.
文摘Suppose F0 is an arbitrary triangle and F is a kind of Sierpinski carpet generated by F0.We construct a projection mapping to obtain the lower bound of the Hausdorff measure of F ;meanwhile the upper bound of the Hausdorff measure of F is calculated by the general covering.
文摘By means of the idea of [2]（Jia Baoguo,J.Math.Anal.Appl.In press） and the self.similarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach the Hausdorff Measure of Sierpinski carpet infinitely.
基金Partially supported by National Natural Science Foundation of China (No.10961003)
文摘In this paper, we address the problem of exact computation of the Hausdorff measure of a class of Sierpinski carpets E- the self-similar sets generating in a unit regular pentagon on the plane. Under some conditions, we show the natural covering is the best one, and the Hausdorff measures of those sets are euqal to ｜E｜^S, where s = dimHE.
基金Supported by the Educational Office of Hubei Province #Q20082802 the Science and Technology Commission of Shanghai Municipality #06ZR14029
文摘In this paper we study a class of subsets of the general Sierpinski carpets for which two groups of allowed digits occur in the expansions 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 and finite.
基金supported by the Educational Office of Hubei Province #Q20082802supported by National Natural Science Foundation of China (Grant No. 10571058)Shanghai Leading Academic Discipline Project #B407
文摘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.
