The m-tuplings Morse sequence, as a fixed point of a constant length substitution, was discussed. An equivalent definition was given by the property of the m-adie development of the integers. Using the combinatorial p...The m-tuplings Morse sequence, as a fixed point of a constant length substitution, was discussed. An equivalent definition was given by the property of the m-adie development of the integers. Using the combinatorial properties of the m-tuplings Morse sequence, we mainly obtain this sequenee is an admissible sequence and the other two sequenees generated by it are also admissible sequences, which extends the conclusion that the Thue-Morse sequence is an admissible sequences.展开更多
In this paper,we consider sets of points with some restricts on the digits of theirα-Lroth expansions.More precisely,for any countable partitionα={An,n∈N}of the unit interval I,we completely determine the Hausdorf ...In this paper,we consider sets of points with some restricts on the digits of theirα-Lroth expansions.More precisely,for any countable partitionα={An,n∈N}of the unit interval I,we completely determine the Hausdorf dimensions of the sets F(α,φ)=x=[l1(x),l2(x),...]α∈I:ln(x)φ(n),n 1,whereφis an arbitrary positive function defined on N satisfyingφ(n)→∞as n→∞.展开更多
基金Supported by the Special Funds for Major StateBasic Research Projects (60472041)
文摘The m-tuplings Morse sequence, as a fixed point of a constant length substitution, was discussed. An equivalent definition was given by the property of the m-adie development of the integers. Using the combinatorial properties of the m-tuplings Morse sequence, we mainly obtain this sequenee is an admissible sequence and the other two sequenees generated by it are also admissible sequences, which extends the conclusion that the Thue-Morse sequence is an admissible sequences.
基金supported by National Natural Science Foundation of China (Grant No.11071090)
文摘In this paper,we consider sets of points with some restricts on the digits of theirα-Lroth expansions.More precisely,for any countable partitionα={An,n∈N}of the unit interval I,we completely determine the Hausdorf dimensions of the sets F(α,φ)=x=[l1(x),l2(x),...]α∈I:ln(x)φ(n),n 1,whereφis an arbitrary positive function defined on N satisfyingφ(n)→∞as n→∞.
