The authora develop an algorithm to show that a class of self-affine sets with overlaps can be viewed as sofic affine-invariant sets without overlaps,thus by using the results of [11] and [10],the hausdorff and minkow...The authora develop an algorithm to show that a class of self-affine sets with overlaps can be viewed as sofic affine-invariant sets without overlaps,thus by using the results of [11] and [10],the hausdorff and minkowski dimensions are detemined展开更多
Let Ω belong to R be a non-empty open subset with finite Lebesgue measure ｜Ω｜1 and boundary Г= δΩ2. We can write f2 as the union of its connected components, i.e.,
LetΩ,with finite Lebesgue measure|Ω|,be a non-empty open subset of R,andΩ=∪∞j-1Ωj,where the open setsΩj are pairwise disjoint and the boundaryГ=■Ωhas Minkowski dimension D∈(0,1).In this paper we study the D...LetΩ,with finite Lebesgue measure|Ω|,be a non-empty open subset of R,andΩ=∪∞j-1Ωj,where the open setsΩj are pairwise disjoint and the boundaryГ=■Ωhas Minkowski dimension D∈(0,1).In this paper we study the Dirichlet eigenvalues problem on the domainΩand give the exact second asymptotic term for the eigenvalues,which is related to the Minkowski dimension D.Meanwhile,we give sharp lower bound estimates for Dirichlet eigenvalues for such one-dimensional fractal domains.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘The authora develop an algorithm to show that a class of self-affine sets with overlaps can be viewed as sofic affine-invariant sets without overlaps,thus by using the results of [11] and [10],the hausdorff and minkowski dimensions are detemined
基金the NNSP (10025107) of China and the 973 Projects.
文摘Let Ω belong to R be a non-empty open subset with finite Lebesgue measure ｜Ω｜1 and boundary Г= δΩ2. We can write f2 as the union of its connected components, i.e.,
基金The research has been supported by the grants from National Natural Science Foundation of China(Grants No.11631011).
文摘LetΩ,with finite Lebesgue measure|Ω|,be a non-empty open subset of R,andΩ=∪∞j-1Ωj,where the open setsΩj are pairwise disjoint and the boundaryГ=■Ωhas Minkowski dimension D∈(0,1).In this paper we study the Dirichlet eigenvalues problem on the domainΩand give the exact second asymptotic term for the eigenvalues,which is related to the Minkowski dimension D.Meanwhile,we give sharp lower bound estimates for Dirichlet eigenvalues for such one-dimensional fractal domains.
