M（J, {ms ＊ ns}, {Cs}） be the collection of Cartesian products of two homogenous Moran sets with the same ratios {cs} Where J = [0, 1] × [0, 1]. Then the maximal and minimal values of the Hausdorff dimensions f...M（J, {ms ＊ ns}, {Cs}） be the collection of Cartesian products of two homogenous Moran sets with the same ratios {cs} Where J = [0, 1] × [0, 1]. Then the maximal and minimal values of the Hausdorff dimensions for the elements in M are obtained without any restriction on {msns} or {cs}.展开更多
This paper studies the quasisymmetric mappings on Moran sets. We introduce a gener- alized form of weak quasisymmetry and prove that, on Moran set satisfying the small gap condition, a generalized weakly quasisymmetri...This paper studies the quasisymmetric mappings on Moran sets. We introduce a gener- alized form of weak quasisymmetry and prove that, on Moran set satisfying the small gap condition, a generalized weakly quasisymmetric mapping is quasisymmetric. We further give a criterion for the quasisymmetry of mappings between Moran sets with some regular structure.展开更多
We obtain the Assouad dimensions of Moran sets under suitable condition. Using the homogeneous set introduced in [J. Math. Anal. Appl., 2015, 432：888 917], we also study the Assouad dimensions of Cantor-like sets.
In this paper, the dimensional results of Moran-Sierpinski gasket are considered. Moran-Sierpinski gasket has the Moran structure, which is an extension of the Sierpinski gasket by the method of Moran set. By the tech...In this paper, the dimensional results of Moran-Sierpinski gasket are considered. Moran-Sierpinski gasket has the Moran structure, which is an extension of the Sierpinski gasket by the method of Moran set. By the technique of Moran set, the Hausdorff, packing, and upper box dimensions of the Moran-Sierpinski gasket are given. The dimensional results of the Sierpinski gasket can be seen as a special case of this paper.展开更多
基金Supported by the National Natural Science Foundation of China (No.10771082 and 10871180)
文摘M（J, {ms ＊ ns}, {Cs}） be the collection of Cartesian products of two homogenous Moran sets with the same ratios {cs} Where J = [0, 1] × [0, 1]. Then the maximal and minimal values of the Hausdorff dimensions for the elements in M are obtained without any restriction on {msns} or {cs}.
基金Supported by NSFC(Grant Nos.11071224,11201155)Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications
文摘This paper studies the quasisymmetric mappings on Moran sets. We introduce a gener- alized form of weak quasisymmetry and prove that, on Moran set satisfying the small gap condition, a generalized weakly quasisymmetric mapping is quasisymmetric. We further give a criterion for the quasisymmetry of mappings between Moran sets with some regular structure.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11371329, 11471124, 11271137, 11201152）, K. C. Wong Magna Fund in Ningbo University, the Fund for the Doctoral Program of Higher Education of China （No. 20120076120001）, the Natural Science Foundation Zhejiang Province （No. LR13A010001）, and Natural Science Foundation of Shanghai （No. 11ZR1410300）.
文摘We obtain the Assouad dimensions of Moran sets under suitable condition. Using the homogeneous set introduced in [J. Math. Anal. Appl., 2015, 432：888 917], we also study the Assouad dimensions of Cantor-like sets.
基金Supported by the National Natural Science Foundation of China(10771082 and 10871180)
文摘In this paper, the dimensional results of Moran-Sierpinski gasket are considered. Moran-Sierpinski gasket has the Moran structure, which is an extension of the Sierpinski gasket by the method of Moran set. By the technique of Moran set, the Hausdorff, packing, and upper box dimensions of the Moran-Sierpinski gasket are given. The dimensional results of the Sierpinski gasket can be seen as a special case of this paper.
