• Journal of the Chungcheong Mathematical Society
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• v.16 no.2
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• pp.1-10
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• 2003

We compare a self-similar measure on a self-similar Cantor set with a quasi-self-similar measure on a deranged Cantor set. Further we study some properties of a self-similar measure on a self-similar Cantor set.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.51-61
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• 2004

We find an easier formula to compute Hausdorff and packing dimensions of a subset composing a spectral class by local dimension of a self-similar measure on a self-similar Cantor set than that of Olsen. While we cannot apply this formula to computing the dimensions of a subset composing a spectral class by local dimension of a quasi-self-similar measure on a self-similar set on the way to a perturbed Cantor set, we have a set theoretical relationship between some distribution sets. Finally we compare the behaviour of a quasi-self-similar measure on a self-similar Cantor set with that on a self-similar set on the way to a perturbed Cantor set.

• The Pure and Applied Mathematics
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• v.14 no.1 s.35
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• pp.1-5
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• 2007

We study the topological magnitude of a special subset from the distribution subsets in a self-similar Cantor set. The special subset whose every element has no accumulation point of a frequency sequence as some number related to the similarity dimension of the self-similar Cantor set is of the first category in the self-similar Cantor set.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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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.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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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.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.497-503
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• 2007

We consider a non-empty subset having same local dimension of a self-similar measure on a most generalized Cantor set. We study trans-formed lower(upper) local dimensions of an element of the subset which are local dimensions of all the self-similar measures on the most generalized Cantor set. They give better information of Hausdorff(packing) dimension of the afore-mentioned subset than those only from local dimension of a given self-similar measure.

• Korean Journal of Mathematics
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• v.16 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.933-944
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• 2004

Packing dimension of a set is an upper bound for the packing dimensions of measures on the set. Recently the packing dimension of statistically self-similar Cantor set, which has uniform distributions for contraction ratios, was shown to be its Hausdorff dimension. We study the method to find an upper bound of packing dimensions and the upper Renyi dimensions of measures on a statistically quasi-self-similar Cantor set (its packing dimension is still unknown) which has non-uniform distributions of contraction ratios. As results, in some statistically quasi-self-similar Cantor set we show that every probability measure on it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely and it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely for almost all probability measure on it.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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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.