• 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 $(\frac{ln\;2}{ln\;3})^2$.

• 충청수학회지
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• 제23권2호
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• pp.231-236
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• 2010

Using the properties of the concave function, we show that the Hausdorff dimension of the product $C_{\frac{a+b}{2},\frac{a+b}{2}}{\times}C_{\frac{a+b}{2},\frac{a+b}{2}}$ of the same symmetric Cantor sets is greater than that of the product $C_{a,b}{\times}C_{a,b}$ of the same anti-symmetric Cantor sets. Further, for $1/e^2$ < a, b < 1/2, we also show that the dimension of the product $C_{a,a}{\times}C_{b,b}$ of the different symmetric Cantor sets is greater than that of the product $C_{\frac{a+b}{2},\frac{a+b}{2}}{\times}C_{\frac{a+b}{2},\frac{a+b}{2}}$ of the same symmetric Cantor sets using the concavity. Finally we give a concrete example showing that the latter argument does not hold for all 0 < a, b < 1/2.

• 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.

• 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].

• 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.

• 한국데이타베이스학회:학술대회논문집
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• 한국데이타베이스학회 2000년도 추계학술대회 E-Business와 정보보안
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• pp.116-118
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• 2000

본 논문은 만델브로트 집합의 쌍곡성분과 0＜λ＜1/e에서 초월 정함수 $E_{λ}$(z)의 Julia집합의 성질에 대한 연구이다. 만델브로트 집합의 쌍곡성분은 $P_{c}$ $^{n}$ (0)의 영점을 항상 포함하고 있고 역으로 $P_{c}$ $^{n}$ (0)의 각각의 영점은 만델브로트 집합의 한 쌍곡성분에 포함된다. 그리고 $E_{λ}$(z)의 Julia 집합이 Cantor bouquet를 포함하고 있다는 사실을 Devaney 와 Tangerman의 결과를 이용하여 설명하였다.여 설명하였다.하였다.

• 충청수학회지
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• 제19권4호
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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.

• Hip & pelvis
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• 제35권1호
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• pp.6-14
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• 2023

Purpose: The aim of this study was to determine correlation between the spinopelvic parameters in sitting and standing positions (sacral slope [SS], lumbar lordosis [LL], spinopelvic tilt [SPT], pelvic incidence [PI], and pelvic femoral angle [PFA]), with hip function assessed using the modified Harris hip scores (mHHs) in patients with symptomatic femoroacetabular impingement (FAI) at diagnosis. Materials and Methods: A retrospective study of 52 patients diagnosed with symptomatic FAI was conducted. Evaluation of the spinopelvic complex in terms of SS, LL, SPT, PI and PFA was performed using lateral radiographs of the pelvis and lumbosacral spine in standing and sitting positions. Assessment of hip function at diagnosis was performed using the mHHs. Calculation of spinopelvic mobility was based on the difference (Δ) between measurements performed in standing and sitting position. Results: The median time of pain evolution was 11 months (interquartile range [IQR], 5-24 months) with a median mHHs of 66.0 points (IQR, 46.0-73.0) at diagnosis. The mean change of LL, SS, SPT, and PFA was 20.9±11.2°, 14.2±8.6°, 15.5±9.0°, and 70.7±9.5°, respectively. No statistically significant correlation was observed between spinopelvic parameters and the mHHs (P>0.05). Conclusion: Radiological parameters of the spinopelvic complex did not show correlation with hip function at the time of diagnosis in patients with symptomatic FAI. Conduct of further studies will be required in the effort to understand the effect of the spinopelvic complex and its compensatory mechanics, primarily between the hip and spine, in patients with FAI before and after hip arthroscopy.

• 한국수학사학회지
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• 제23권3호
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• pp.57-73
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• 2010

초월수의 연구는 2000년 이상 수학자들을 괴롭혀 왔던 고대 그리스의 기하학 문제의 하나인 원적문제가 불가능하다는 것을 보여줌으로써 수학사의 중요한 분야임을 입증하였다. Liouville은 1844년에 처음으로 구체적인 초월수의 예를 제시하였고, 칸토어는 1874년에 초월수의 존재성을 증명하였다. Louville 정리는 많은 초월수를 만들어 낼 뿐 아니라 초월수의 존재성을 증명하는데 이용할 수 있다. 1873년에 Hermite가 자연로그의 밑수 e가 초월수임을 보이고, 1882년에 Lindemann이 원주율 $\pi$가 초월수임 증명하였다. 1934년에 Gelfond와 Schneider는 각각 힐버트의 7번째 문제에 대한 서로 다른 완전한 해를 찾았다. 1966년에 Baker는 Gelfond-Schneider 정리의 일반화된 결과를 증명하였다. 이 연구의 목적은 초월수의 개념과 발달과정을 살피고, 미해결 문제를 제시하여 초월수의 연구가 촉진되도록 후학들에게 연구 동기를 부여하고자 한다.