For a family of homogeneous Moran sets, where at each level, subintervals are arranged with in-creasing spaces between neighboring subintervals from left to right, we obtained a formula of the Hausdorff dimensions.
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
Let M({nk}k≥1,{ck}k≥1) be the collection of homogeneous Moran sets determined by {nk}k≥1and {ck}k≥1, where {nk}k≥1 is a sequence of positive integers and {ck}k≥1 a sequence of positive numbers. Then the maximal ...Let M({nk}k≥1,{ck}k≥1) be the collection of homogeneous Moran sets determined by {nk}k≥1and {ck}k≥1, where {nk}k≥1 is a sequence of positive integers and {ck}k≥1 a sequence of positive numbers. Then the maximal and minimal values of Hausdorff dimensions for elements in M are determined. The result is proved that for any value s between the maximal and minimal values, there exists an element in M{nk}k≥1, {ck}k≥1) such that its Hausdorff dimension is equal to s. The same results hold for packing dimension. In the meantime, some other properties of homogeneous Moran sets are discussed.展开更多
文摘For a family of homogeneous Moran sets, where at each level, subintervals are arranged with in-creasing spaces between neighboring subintervals from left to right, we obtained a formula of the Hausdorff dimensions.
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Project supported by the National Climbing Project"Nonlinear Science"and the Scientific Foundation of the State Education Commission of China.
文摘Let M({nk}k≥1,{ck}k≥1) be the collection of homogeneous Moran sets determined by {nk}k≥1and {ck}k≥1, where {nk}k≥1 is a sequence of positive integers and {ck}k≥1 a sequence of positive numbers. Then the maximal and minimal values of Hausdorff dimensions for elements in M are determined. The result is proved that for any value s between the maximal and minimal values, there exists an element in M{nk}k≥1, {ck}k≥1) such that its Hausdorff dimension is equal to s. The same results hold for packing dimension. In the meantime, some other properties of homogeneous Moran sets are discussed.
