• 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.

• 대한수학회지
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• 제31권4호
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• pp.539-544
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• 1994

We [1] investigated the Hausdorff dimension and the packing dimension of a certain perturbed Cantor set whose ratios are unformly bounded. In this paper, we consider a specific Cantor set whose ratios are not necessarily uniformly bounded but satisfy some other conditions. In fact, in the hypothesis, only the condition of the unform boundedness of ratios on the set is substituted by a "*-condition". We use energy theory related to Hausdorff dimension in this study while we [1] used Hausdorff density theorem to find the Hausdorff dimension of some perturbed Cantor set. In the end, we given an example which explains aformentioned facts.ned facts.

• 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.

• 대한수학회보
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• 제52권5호
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• pp.1737-1751
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• 2015

For every doubling gauge g, we prove that there is a Cantor set of positive finite $H^g$-measure, $P^g$-measure, and $P^g_0$-premeasure. Also, we show that every compact metric space of infinite $P^g_0$-premeasure has a compact countable subset of infinite $P^g_0$-premeasure. In addition, we obtain a class of uniform Cantor sets and prove that, for every set E in this class, there exists a countable set F, with $\bar{F}=E{\cup}F$, and a doubling gauge g such that $E{\cup}F$ has different positive finite $P^g$-measure and $P^g_0$-premeasure.

• Korean Journal of Mathematics
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• 제12권1호
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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 applied mathematics & informatics
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• 제14권1_2호
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• pp.397-403
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• 2004

Cutler showed some duality results about Hausdorff and packing dimensions of a measure on a compact set in Euclidean space if its s-dimensional Hausdorff measure or packing measure is positive. We show that the similar results in a perturbed Cantor set hold according to its quasi s-dimensional Hausdorff measure or packing measure and we find concrete measures in this case while Cutler showed the existence of such measures. Finally under some strong condition, we give a concrete measure whose Hausdorff and packing dimensions are the same as those of the perturbed Cantor set without the condition that it has positive s-dimensional Hausdorff or packing measures.

• 한국동물학회지
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• 제6권2호
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• pp.6-10
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• 1963

가물치( Ophicephalus argus CANTOR) 2 년생(168$\pm$4g)107마리를 대조군과 실험적으로 나누고 실험군에는 일시에 2.9mg/kg 체동의 potassium cyanide을 배근에 직접 주사하였다. 약물 처리후 시간의 경과에 따라 나타나는 Albumin/Blbulin(A/G)비, 총혈청단백질량, hematocrit 비 및 간장 및 신장의 중량변화를 측정하였다. 약물 처리 직후는 A/G 비 , 총혈청단백질량 및 hematocrit 비는 각각 현저하게 감소되었으나 많은 시간이 경과함에 따라 점차 증가되어 228시간이후는 거의 대조군과 그것과 가까운 결과를 얻었다. 그러나 간장과 신장의 중량은 약물 처리 직후는 오히려 약간 증가되는 상태였으나 , 48시간이후 급히 감소되었다가 점차 역시 대조군과 가까운 결과를 나타냈다. 이상의 결과로서 KCN가 어류의 호흡 억제작용뿐만 아니라 단백질대사에도 영향을 미치는 것으로 생각된다.

• East Asian mathematical journal
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• 제25권3호
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• pp.229-245
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• 2009

G. Cantor gave a deep influence to the society of mathematics in many ways, especially in the set theory. It is important for gifted and talented high school students in mathematics to understand the Euler constant and the fractal dimension of the Cantor set in a heuristic sense. On the historic basis of mathematics and the standard of high school students, we give the teaching method for the talented high school student to understand them better. Further we introduce the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs distribution and its first moment. We hope that from these topics, the gifted and talented students in mathematics will have insight in the analysis of mathematics.

• 충청수학회지
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• 제12권1호
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• pp.1-13
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• 1999

The purpose of this paper is to show that if the Fatou set F(f) of a CF-meromorphic function f has two completely invariant components, then they are the only components of F(f) and that the Julia set of the entire transcendental function $E_{\lambda}(z)={\lambda}e^z$ for 0 < ${\lambda}$ < $\frac{1}{e}$ contains a Cantor bouquet by employing the Devaney and Tangerman's theorem[10].

• 대한수학회지
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• 제33권1호
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• pp.47-55
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• 1996

Let $0 < \alpha < 2$ and let $T_\alpha (\theta) = \alpha tan(\theta/2)$. $T_\alpha$ has an attractive fixed point at $\theta = 0$. We denote by $C(\alpha)$ the set of points in $I = [-\pi, \pi]$ which are not attracted to $\theta = 0$ by the succesive iterations of $T_\alpha$. That is, $C(\alpha)$ is the set of points in I where the dynamics of $T_\alpha$ is chaotic.