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
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
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
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.
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.
