• 대한수학회보
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• 제47권1호
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• pp.187-193
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• 2010

In this paper, the moments of the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs(RNT) distribution over a general interval [a, b] $\subset$ [0, 1], are found through the moments of the RNT distribution over the unit interval, [0, 1]. This is done using some special features of the distribution and the fact that [0, 1] is a self-similar set in a dynamical system generated by the RNT distribution. The results are important for the study of the orthogonal polynomials with respect to the RNT distribution over a general interval.

• 대한수학회보
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• 제48권2호
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• pp.261-275
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• 2011

We give characterizations of the differentiability points and the non-differentiability points of the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) singulr function using the distribution sets in the unit interval. Using characterizations, we show that the Hausdorff dimension of the non-differentiability points of the RNT singular function is greater than 0 and the packing dimension of the infinite derivative points of the RNT singular function is less than 1. Further the RNT singular function is nowhere differentiable in the sense of topological magnitude, which leads to that the packing dimension of the non-differentiability points of the RNT singular function is 1. Finally we show that our characterizations generalize a recent result from the ($\tau$, $\tau$ - 1)-expansion associated with the RNT singular function adding a new result for a sufficient condition for the non-differentiability points.

• 대한수학회보
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• 제54권4호
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• pp.1173-1183
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• 2017

We give some sufficient conditions for the null and infinite derivatives of the $Riesz-N{\acute{a}}gy-Tak{\acute{a}}cs$ (RNT) singular function. Using these conditions, we show that the Hausdorff dimension of the set of the infinite derivative points of the RNT singular function coincides with its packing dimension which is positive and less than 1 while the Hausdorff dimension of the non-differentiability set of the RNT singular function does not coincide with its packing dimension 1.

• 호남수학학술지
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• 제30권4호
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• pp.671-676
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• 2008

We give the relation between the Riemann-Stieltjes integrals with respect to the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) distribution $H_{a,p}$ satisfying the equation a = $(1-a)^m$ and those with respect to the dual RNT distribution $H_{1-a,1-p}$, which leads to a generalization of recent results for a = $\frac{1}{2}$.

• 대한수학회논문집
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• 제30권1호
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• pp.7-21
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• 2015

We give the characterization of H$\ddot{o}$lder differentiability points and non-differentiability points of the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs (RNT) singular function ${\Psi}_{a,p}$ satisfying ${\Psi}_{a,p}(a)=p$. It generalizes recent multifractal and metric number theoretical results associated with the RNT function. Besides, we classify the singular functions using the singularity order deduced from the H$\ddot{o}$lder derivative giving the information that a strictly increasing smooth function having a positive derivative Lebesgue almost everywhere has the singularity order 1 and the RNT function ${\Psi}_{a,p}$ has the singularity order $g(a,p)=\frac{a{\log}p+(1-a){\log}(1-p)}{a{\log}a+(1-a){\log}(1-a)}{\geq}1$.

• 한국응용곤충학회지
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• 제41권1호
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• pp.27-32
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• 2002

애꽃노린재를 이용한 총채벌레의 방제효과를 구명하기 위하여 하우스 가지에서 천적방사구(NRT), 농약살포구(PAT)와 천적제거구(RNT)의 세처리를 하여 처리구별 총채벌레와 애꽃노린재의 밀도변동 및 가지 열매의 피해고 조사를 실시하였다. NRT에서 애꽃노린재의 약충은 최초방사후 21일부터 상위엽에서 조사되었으며. 총채벌레의 밀도는 정식 42일 후부터 낮아지기 시작하여 RNT보다 매우 낮은 밀도로 유지되었다. NRT, PAT와 RNT에서 가지 열매의 피해도 지수는 각각 1.35. 1.21과 2.90이었으며. 피해과율은 각각 70.3,78.6 99.0%로 NRT의 피해도 지수와 피해과율은 PAT보다는 높았으나, RNT에 비해서는 낮았다. 총채벌레와 애꽃노린재의 공간분포 양상은 Tailor의 b와 Iwao의 $\beta$값이 모두 1보다 커 집중분포를 하는 것으로 나타났다. 애꽃노린재의 공존지수는 총채벌레와 애꽃노린재의 밀도에 관계없이 매우 높았으며, 총채벌레의 도피지수는 애꽃노린재의 밀도에 따라 변동하였다. 본 연구 결과 하우스가지에서 총채벌레를 방제하는데 천적으로 애꽃노린재를 이용할 수 있을 것으로 판단된다.

• 충청수학회지
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• 제26권2호
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• pp.421-426
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• 2013

We give a series of discrete random variables which converges to a random variable whose distribution function is the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs (RNT) distribution. We show this using the correspondence theorem that if the moments coincide then their corresponding distribution functions also coincide.

• 호남수학학술지
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• 제30권2호
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• pp.227-231
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• 2008

We give some relation between the Riemann-Stieltjes integrals with respect to the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) distribution $H_{a,p}$ satisfying the equation 1 - a = $a^m$ over different intervals, which generalizes recent results([6]) for a = ${\frac{1}{2}}$.

• 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.