• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.13-18
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• 2004

We defined Cantor dimensions of a perturbed Cantor set, and investigated a relation between these dimensions and Hausdorff and packing dimensions of a perturbed Cantor set. In this paper, we introduce another expressions of the Cantor dimensions. Using these, we study some informations which can be derived from power equations induced from contraction ratios of a perturbed Cantor set to give its Hausdorff or packing dimension. This application to a deranged Cantor set gives us an estimation of its Hausdorff and packing dimensions, which is a generalization of the Cantor dimension theorem.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.241-246
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• 2007

We investigate the relation between Hausdorff(packing) measure and lower(packing) Cantor measure on a deranged Cantor set. If the infimum of some distortion of contraction ratios is positive, then Hausdorff(packing) measure and lower(packing) Cantor measure of a deranged Cantor set are equivalent except for some singular behavior for packing measure case. It is a generalization of already known result on the perturbed Cantor set.

• Journal of Haehwa Medicine
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• v.10 no.1
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• pp.115-120
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• 2001

We came to the conclusion after considering all of information from many kinds of books on the Bufobufo gargarizans Cantor. The result were as follows: 1. Bufobufo gargarizans Cantor is originated from the bufonidae of caudata of amphibia of chordata. 2. The form of Bufobufo gargarizans Cantor is obese, about 12 centimeter long and the color of Bufobufo gargarizans Cantor is dark brown, black. 3. The charateristics and the tastes of Bufobufo gargarizans Cantor is cold and spicy and the Guigyung of Bufobufo gargarizans Cantor is heart and stomach. 4. The significant gredient of Bufobufo gargarizans Cantor is Bufagin, Steroids, Cinobufotoxin, ${\beta}$-sitosterol, Bufothionine, Bufotenidine, Bufo tenine, Bufalin, Butotalidin Hellebrigenin, Bufochrome. 5. The efficacy of Bufobufo gargarizans Cantor is pajinggyunhyul(破懲堅血), salgamjok(殺疳積), taehuyol(退虛熱), etc. 6. In direction of Bufobufo gargarizans Cantor, one time dosage is 2-3 gram in internal medicine, in external medicine dosage depends on the width. 7. Bufobufo gargarizans Cantor should be cautious in use those who is pregnant, have heart disease, gastritis, gastric ulcer. 8. The side effect of Bufobufo gargarizans Cantor is nausea, vomiting, abdomen discomfort, diarrhea, palpitation, headache, lethargy, etc. 9. Bufobufo gargarizans Cantor could be use in hepatoma, esophgeal cancer, stomach cancer, skin cancer, breast cancer and leukemia.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.269-274
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• 2004

We investigate a deranged Cantor set (a generalized Cantor set) using the similar method to find the dimensions of cookie-cutter repeller. That is, we will use a Gibbs measure which is a weak limit of a subsequence of discrete Borel measures to find the dimensions. The deranged Cantor set that will be considered is a generalized form of a perturbed Cantor set (a variation of the symmetric Cantor set) and a cookie-cutter repeller.

• East Asian mathematical journal
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• v.19 no.2
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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 $(\frac{ln\;2}{ln\;3})^2$.

• 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.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.113-117
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• 2004

A deranged Cantor set (without the uniform bounded-ness condition away from zero of contraction ratios) whose weak local dimensions for all points coincide has its Hausdorff dimension of the same value of weak local dimension. We will show it using an energy theory instead of Frostman's density lemma which was used for the case of the deranged Cantor set with the uniform boundedness condition of contraction ratios. In the end, we will give an example of such a deranged 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.13 no.3
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• pp.595-601
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• 1998

In this paper we construct a homeomorphism on a Cantor set which is nearly periodic such that h(a) = b for given a, b $\in$ D$_{p}$. We also give an example which is not almost periodic and we discuss when a homeomorphism on a Cantor set is periodic.c.

• Journal for History of Mathematics
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• v.10 no.1
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• pp.33-38
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• 1997

본고는 수학적으로 취급된 Cantor의 무한을 소개하기보다는 그가 가졌던 무한에 대한 태도는 매우 종교적이었고 철학적으로는 실재론적인 입장에 있다는 것을 보이려고 한다. 이를 위해 먼저 Cantor의 초한수론과 무한의 역사를 약술하고 그의 무한관이 기독교 신앙과 중세 철학에 근거해 있음을 제시한다. 또한 Cantor의 초한수론은 당시의 세계관과 시대정신에 도전하고 있음을 밝히려 한다.