• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.357-364
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• 2006

We study Hausdorff and packing dimensions of subsets of a general coding space with a generalized ultra metric from a multifractal spectrum induced by a self-similar measure on a self-similar Cantor set using a function satisfying a H${\ddot{o}}$older condition.

• 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.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.1-5
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• 2004

We study Hausdorff and packing dimensions of subsets of a coding space with an ultra metric from a multifractal spectrum induced by a self-similar measure on a Cantor set using a function satisfying a H$\ddot{o}$lder condition.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.527-532
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• 2008

We compare a coding space which has an ultra metric with the unit interval which has an associated generalized dyadic expansion. The two spaces are not homeomorphic but dimensionally equivalent in the sense that the Hausdorff and packing dimensions of the corresponding distribution sets in the two spaces coincide.

• 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.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.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.323-341
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• 2020

In this note, we investigate the multifractal analogues of the Hewitt-Stromberg measures and dimensions in a probability space.

• 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.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.547-552
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• 2007

The unit interval is not homeomorphic to a self-similar Cantor set in which we studied the dimensions of distribution subsets. However we show that similar results regarding dimensions of the distribution subsets also hold for the unit interval since the distribution subsets have similar structures with those in a self-similar Cantor set.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.157-171
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• 2014

We show that the recurrence rates of Laurent series about continued fractions almost surely coincide with their pointwise dimensions of the Haar measure. Moreover, let $E_{{\alpha},{\beta}}$ be the set of points with lower and upper recurrence rates ${\alpha},{\beta}$, ($0{\leq}{\alpha}{\leq}{\beta}{\leq}{\infty}$), we prove that all the sets $E_{{\alpha},{\beta}}$, are of full Hausdorff dimension. Then the recurrence sets $E_{{\alpha},{\beta}}$ have constant multifractal spectra.