The obiect of this note is to establish two propositions on de-termining the Hausdorff dimension dim and the packing dimension Dim inR￣d(Theorem 1 and Theorem 2),and further seek the conditions that the Hausdorffdimension dim is equal to the pachng dimension Dim in R￣d(Theorem 3);
In this paper,we relate our the definition of packing dimension in(Ω,μ)to the classical definition on the real line, and prove that in the Lebesgue case,for all A ∈,the index Dim_μ(A)is identical with the index Dim(A)defined by Tay-lor and Tricot.
The cookie cutter set of real line is an invariant set of a expanding dynamical system and a fractal set. In this paper, we get packing dimensions of multifractal decomposition of Cookie cutter and show that they are all fractal set in the sense of Taylor.
It explains, as appearing from stochastic processes(e.g.Levy proceses,Gaussian fields)(1)the Harsdorff as well as the packing dimensions and measure functions of various randomfractal sets(e.g.image set,level set);
Fractal properties of sample path of d dimension stationary Gaussian process. The Hausdorff and Packing dimensions of graph set and level set for d dimension stationary Gaussian process are obtained.
The Hausdorff and packing dimensions of the range BH ([0, 1]N), the
The Hausdorff and packing dimensions for a class of Moran sets are obtained.
The relevance of instrumental parameters and of column and packing dimensions, upon the potential for improved performance is discussed.
Under certain conditions, we investigate the fractal dimensions of the graphs of these functions, compute the precise values of Box and Packing dimensions, and evaluate the Hausdorff dimension.
We also compute several fractal dimensions of Lévy trees, including Hausdorff and packing dimensions, in terms of lower and upper indices for the branching mechanism function ψ which characterizes the distribution of the tree.
Consider the functions f(x) where 0<α<1, is an arbitrary number. Under some hypotheses we give lower bounds on the Hausdorff dimension of graphs of /, and obtain the Box dimension and Packing dimension of graphs of ω as well.
考虑函数f(x)=sum from i=1 to ∞(?)~(-1)φ((?)+θ_n)和w(x)=sum from n=1 to ∞(?)φ_(?)((?)x+θ_(?)),式中0<α<(?)是任意实数,在一定条件下,估计了函数f图象的Hausdorff维数的下界,并求得了w函数图象的Box维数和Packing维数。
In this paper,we have discussed some continuous but nowhere differentiable complex valued functions,and obtained the box and the packing dimensions expressions for graphs of the functions.
We introduce the multi - layer constructions for Cookie - Cutter sets. For each such construction, we calculate the Hausdorff measures and Packing measures and the Hausdorff dimensions and Packing dimensions are obtained.