• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.447-454
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• 2004

We study the Hausdorff and packing dimensions of subsets composing multifractal spectrum generated by a quasi-self-similar probability measure on a perturbed Cantor set.

• 대한수학회논문집
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• 제20권4호
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• pp.695-702
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• 2005

We study the transformed measures with respect to the real parameters of a self-similar measure on a self-similar Can­tor set to give a simple proof for some result of its multifractal spectrum. A transformed measure with respect to a real parameter of a self-similar measure on a self-similar Cantor set is also a self­similar measure on the self-similar Cantor set and it gives a better information for multifractals than the original self-similar measure. A transformed measure with respect to an optimal parameter deter­mines Hausdorff and packing dimensions of a set of the points which has same local dimension for a self-similar measure. We compute the values of the transformed measures with respect to the real parameters for a set of the points which has same local dimension for a self-similar measure. Finally we investigate the magnitude of the local dimensions of a self-similar measure and give some correlation between the local dimensions.

• 충청수학회지
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• 제21권2호
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• pp.157-163
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• 2008

We study essentially disjoint one dimensionally indexed classes whose members are distribution sets of a self-similar Cantor set. The Hausdorff dimension of the union of distribution sets in a same class does not increases the Hausdorff dimension of the characteristic distribution set in the class. Further we study the Hausdorff dimension of some uncountable union of distribution sets.

• East Asian mathematical journal
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• 제19권2호
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• pp.213-219
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• 2003

We study the properties of non-diffenrentiable points of a self-similar Cantor function from which we conjecture a generalization of Darst's result that the Hausdorff dimension of the non-diffenrentiable points of the Cantor function is $(\frac{ln\;2}{ln\;3})^2$.

• 대한수학회논문집
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• 제16권1호
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• pp.95-102
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• 2001

We consider a Cantor set with overlaps Λ in R$^1$. We calculate its correlation dimension with respect to the push-down measure on Λ comparing with its similarity dimension.

• 대한수학회논문집
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• 제18권2호
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• pp.281-288
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• 2003

In this paper, we calculate the lower and upper bound of the correlation dimension([4], [6]) for a Cantor-like set([5])

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.733-738
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• 2008

Using an information of dimensions of divergence points, we give full information of dimensions of the completely decomposed class of the lower(upper) distribution sets of a self-similar Cantor set. Further using a relationship between the distribution sets and the subsets generated by the lower(upper) local dimensions of a self-similar measure, we give full information of dimensions of the subsets by the local dimensions.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.157-163
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• 2008

Using informations of subsets of divergence points and the relation between members of spectral classes, we give another complete decomposition of spectral classes generated by lower(upper) local dimensions of a self-similar measure on a self-similar Cantor set with full information of their dimensions. We note that it is a complete refinement of the earlier complete decomposition of the spectral classes. Further we study the packing dimension of some uncountable union of distribution sets.

• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.503-510
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• 2005

Let $\left{K_{\alpha}\right}_{{\alpha}{\in}{\mathbb{R}}}$ be the multifractal spectrums of a perturbed Cantor set K. We find the set of values ${\alpha}$ of nonempty set $K_{\alpha}$ by using the Birkhoff ergodic theorem. And we also show that such $K_{\alpha}$ is a fractal set in the sense of Taylor [12].

• 대한수학회논문집
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• 제19권4호
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• pp.683-689
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• 2004

In this paper we define a Cantor-like set K with overlaps in R$^1$. We find the correlation dimension of the set K without two conditions: the control of placements of basic sets constructing K and the thickness of K being greater than 1.